P C A A D 7.0
Personal
Computer
Aided
Antenna
DesignVersion 7.0
Antenna Design Associates, Inc.
Leverett, MA 01054
USAOn the cover: A 3-D pattern plot of a 3 x 4 rectangular array of horizontal dipoles
λ/4 above a ground plane, with 0.4λ spacing.

Copyright  2014
David M. Pozar
Antenna Design Associates, Inc.
55 Teawaddle Hill Road
Leverett, MA 01054
USA
All rights reserved. Printed and bound in the United States of America. No part ofthis book may be reproduced or utilized in any form or by any means, electronic ormechanical, including photocopying, recording, or by any information storage andretrieval system, without permission in writing from the author.

Contents
I. Introduction to PCAAD 7.0

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A. What's New in PCAAD 7.0
B. Disclaimer

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II. Getting Started With PCAAD 7.0

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A. System Requirements
B. Installing PCAAD 7.0
C. Folders Used By PCAAD 7.0
D. The PCAAD7.INI file

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III. Using PCAAD 7.0 - General Instructions

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A. Organization of PCAAD 7.0
B. Entering Data and Running the Routines
C. Pattern Calculation and Plotting
D. Saving Pattern Data
E. Impedance Calculation and Plotting
F. Help

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IV. Using PCAAD 7.0 – Instructions and Examples

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A. The Plot Menu
1. Polar Pattern Plot
2. Rectangular Pattern Plot
3. 3-D Pattern Plot
4. Smith Chart Plot
5. VSWR/Return Loss Plot
6. Default Plot Types
7. Default Plot Colors
8. Default Directory Path
9. Exit

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B. The Edit Menu
1. Copy Window
2. Copy Graph
3. Copy Text
4. Paste Text
5. Edit File
6. Print Window

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C. The Wire Antennas Menu
1. Dipole Antenna
2. Dipole Radar Cross Section
3. Horizontal Dipole Over Ground Plane

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4. Vertical Dipole Over Ground Plane
5. V-Dipole Antenna
6. Loop Antenna
7. Yagi Antenna
8. Dipole Array
9. Log Periodic Dipole Array Design
10. Log Periodic Dipole Array Analysis
11. General Wire Antenna

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D. The Array Antennas Menu
1. Uniform Linear Array
2. Linear Subarray
3. Uniform Rectangular Array
4. Uniform Circular Array
5. Arbitrary Planar Array
6. Infinite Printed Dipole Array
7. Linear Array Pattern Synthesis
8. Grating Lobe Diagram
9. Effect of Random Array Errors

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E. The Aperture Antennas Menu
1. Line Source
2. Rectangular Aperture
3. Circular Aperture
4. E-Plane Sectoral Horn
5. H-Plane Sectoral Horn
6. Pyramidal Horn
7. Diagonal Horn
8. Corrugated Pyramidal Horn
9. Conical Horn
10. Corrugated Conical Horn
11. Parabolic Reflector (approximate model)
12. Symmetric Parabolic Reflector Analysis
13. Offset Parabolic Reflector Analysis
14. Spherical Reflector Analysis
15. Beam Efficiency

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F. The Microstrip Antennas Menu
1. Rectangular Probe-Fed (Carver model)
2. Rectangular Probe-Fed (cavity model)
3. Rectangular Line-Fed (t-line model)
4. Rectangular Proximity-Fed (t-line model)
5. Rectangular Aperture-Fed (cavity model)
6. Circular Probe-Fed (cavity model)

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G. The Transmission Lines and Waveguides Menu

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1. Coaxial Line
2. Rectangular Waveguide
3. Rectangular Waveguide Data
4. Circular Waveguide
5. Microstrip Line (quasi-static)
6. Stripline (quasi-static)
7. Multilayer Microstrip Line (full-wave)
8. Multilayer Stripline (full-wave)
9. Coupled Microstrip Lines (full-wave)
10. Coupled Striplines (full-wave)
11. Single Layer Surface Wave Modes (full-wave)
12. Multilayer Surface Wave Mode (full-wave)

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H. The Miscellaneous Menu
1. Link Loss
2. Polarization Mismatch
3. Atmospheric Attenuation
4. Axial Ratio vs. Errors
5. Antenna Temperature
6. Calculator

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I. The Help Menu
1. Help Table of Contents
2. Help Index
3. Context Help (F1)
4. Short Course and Tutorials
5. About PCAAD

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V. References

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I. Introduction to PCAAD 7.0
PCAAD 7.0 (Personal Computer
Aided Antenna Design, version 7) is a
Windows-compatible
softwarepackage that contains over 55 separate
routines for the analysis and design ofwire antennas, array antennas, apertureantennas,
microstrip
antennas,transmission lines and waveguides,
and additional utilities. These routines
are integrated into a menu-driven,user-friendly software package thatallows you to quickly evaluate thecharacteristics of a large variety ofantennas. Some of the key features of
PCAAD 7.0 include the following:
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An improved user-friendly Windows interface
Very simple and intuitive operation
Fast results for first-cut designs
Graphic illustrations of each antenna geometry
Polar, rectangular, and 3-D pattern plots
Smith chart, VSWR, and return loss plots for input impedanceData file output for patterns and impedance matrices
On-line help and a hard-copy manual
Validation examples for each analysis routine

A. What's New in PCAAD 7.0
PCAAD 7.0 for Windows features a complete rewrite of the software with up-todate user interface elements, new analysis routines, and improved features. Some of
the most significant improvements in this version of PCAAD include:
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analysis of symmetric and offset parabolic reflector antennas
analysis of spherical reflector antennas
viewing of amplitude and phase distributions for reflectors
modeling of horizontal and vertical dipoles over a ground planefull-wave analysis of multilayer striplinefull-wave analysis of multilayer microstrip line
full-wave analysis of surface waves on a multilayer substrate
analysis of coupled striplines and coupled microstrip lines
calculation of antenna beam efficiency
polar and rectangular pattern plots with up to five patterns
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Smith chart plots with up to five plots
3-D pattern plots have an optional cross-section view
optional setting of a default data file directory pathtutorials on transmission lines, the Smith chart, and small antennas
improved user interface
faster graphics

PCAAD 7.0 is intended for use by systems and design engineers, researchers, andstudents who need quick solutions to canonical antenna design or analysis
problems. The routines implemented in PCAAD 7.0 are based on proven antenna
theory and analysis as described in numerous textbooks, handbooks, and otherliterature [1]-[8].

B. Disclaimer
This software package has been written and tested with care. Nevertheless, thissoftware and its associated user's manual are provided as is, without warranty of
any kind. Neither the author nor Antenna Design Associates, Inc., make any
warranties, expressed or implied, that the software or the manual are free of error,
or will meet specific requirements of any particular application. The software
should not be relied upon for the generation of data where such data, if incorrect orinapplicable, could result in loss of property or personal injury. Any use of thesoftware or the manual in such a manner is at the user's own risk. The author andAntenna Design Associates, Inc., disclaim all liability for direct, incidental, or
consequential damages resulting from any use of the software or manual.

5II. Getting Started With PCAAD 7.0
A. System Requirements
PCAAD 7.0 will operate on computers running Windows XP, Windows Vista,
Windows 7, or Windows 8. The software is distributed on a CD-ROM, andinstallation requires a CD-ROM drive. PCAAD 7.0 occupies less than 5 MB of disk
space.
Since PCAAD 7.0 runs under Microsoft Windows operating systems, the user
should be familiar with basic Windows usage, such as how to run programs from
Windows; how to create and rearrange program shortcuts on the desktop; how tocreate, copy, and delete files and directories; how to use Windows menus, text
boxes, and control buttons; and how to open, close, move, and resize windows.

B. Installing PCAAD 7.0
Installing PCAAD 7.0 on your system is easy. Insert the distribution CD into yourCD drive, and execute the Setup.exe file that is located on the CD. Installation
may require Administrator access, depending on your operating system and yourUser settings. The setup program will decompress and install all necessary files,
and create the necessary directories. A PCAAD 7.0 entry will be created on yourStart Menu, and a PCAAD 7.0 icon should be installed on your desktop.
To uninstall PCAAD 7.0, use the Uninstall facility from the Windows Control
Panel. This will properly remove the PCAAD 7.0 systems files from yourcomputer and entries from the registry. Any data files that you created when using
PCAAD 7.0 can be deleted separately, from your user directory, if desired.

C. Folders Used By PCAAD 7.0
The PCAAD 7.0 installer program will create two new folders. A folder called
PCAAD 7.0, in the Program Files folder (or the Programx86 Files folder), isused for the system operating files for PCAAD 7.0. A separate folder will becreated for your PCAAD user data files. This folder typically has a path name suchas C:\USERS\username\AppData\Roaming\PCAAD7, but this may bedifferent for different operating systems. Note that you can save your user data files
in other directories, but preferably not in the PCAAD 7.0 Program Files directory(which is reserved for system files). You can easily view the locations of thevarious directories being used by PCAAD 7.0 from About PCAAD, via the
PCAAD Help menu. You can set a default file directory using the Default
Directory Path option from the Plot menu.
The setup procedure also installs PDF files for the introductory short course on
basic antenna theory, and tutorials on transmission lines, the Smith chart, andelectrically small antenna design. The antenna short course is arranged by Chapters
0 through 7, where Chapter 0 lists the contents and syllabus for the course. Chapters6

1 through 7 provide a basic introduction to antenna theory and design, and include
examples, review questions, and problems. The short course concludes with the
Antenna IQ test. Answers to the test and all problems are given in theAnswers.pdf file. There is also a short Glossary on commonly used terms
related to antenna technology. All of these files may be accessed from the PCAAD
7.0 Help menu, or directly from the PCAAD user data file directory. The Acrobat
PDF reader is required to view the short course and tutorial files.

D. The PCAAD7.INI file
PCAAD 7.0 uses an initialization file, called PCAAD7.INI, located in yourPCAAD 7.0 user directory, to set various options and directory locations that are
required for proper operation of PCAAD. Generally, you will not have to modify
this file, and, like most .INI files, improper entries can cause errors when running
PCAAD. Here we describe the entries in the PCAAD7.INI file, with their default
values:[PCAAD7]
Bitmaps=1

PCAAD bitmap option(0-off; 1-on)
SavePhaseData=0phase data save option(0-don’t save; 1-save phase data)
PatternPlotType=1
default pattern plot type(1-polar; 2-rectangular, 3 -3D)
ImpedancePlotType=0
default impedance plot type(0-Smith chart; 1-VSWR/RL)
PatternAzimuthAngle=0.0
azimuth angle for pattern plots
PatternStepSize=0.5
step size for pattern plots
3DAzimuthStep=5.0
azimuth step size for 3-D plots
3DElevationStep=2.0
elevation step size for 3-D plots
UpperHemisphereOnly=0
3-D plot type(0-both hemispheres; 1-upper only)
PlanarPlotData#1Color=255
color for data set #1 (pattern plots)
PlanarPlotData#2Color=16711680
color for data set #2 (pattern plots)
PlanarPlotData#3Color=32768
color for data set #3 (pattern plots)
PlanarPlotData#4Color=16744700
color for data set #4 (pattern plots)
PlanarPlotData#5Color=4194304
color for data set #5 (pattern plots)
AngleCursor=65535
color for angle cursor
PlotBackgroundColor=12632256
color for plot background
RL/VSWRPlotData#1Color=255
color for data set #1 (RL/VSWR)
RL/VSWRPlotData#2Color=16711680
color for data set #1 (RL/VSWR)
RectangularPatternPlotLabel=Pattern (dB) vertical label on rectangular
PatternPlaneType=1
type of pattern cut
SmithPlotData#1Color=255
color for data set #1 (Smith plot)
SmithPlotData#2Color=16711680
color for data set #2 (Smith plot)
SmithPlotData#3Color=32768
color for data set #3 (Smith plot)
SmithPlotData#4Color=16744700
color for data set #4 (Smith plot)7

color for data set #5 (Smith plot)
default path for data files

SmithPlotData#5Color=4194304
FileDir=C:\Users\user\..

The above values are typical entries that are set upon installation, but most of thesevalues will change according to the plotting and color options that are set and saved
when using the Plot Default Types and Plot Default Colors options from the Plotmenu. It is recommended that the user not directly modify the PCAAD7.INI file,
except perhaps to set the vertical axis label for the rectangular pattern plot routine.

8III. Using PCAAD 7.0 – General Instructions
A. Organization of PCAAD 7.0
The main window is displayed when PCAAD 7.0 starts, and forms the
background for all modules and routines. The menu bar at the top of the window
categorizes the antenna modules into several groups, along with plotting
routines and other utilities. The individual menus and routines are listed andsummarized below:
Plot
Polar Pattern Plot
Rectangular Pattern Plot
3-D Pattern Plot
Smith Chart Plot
VSWR/Return Loss Plot
Plot Default Types . . .
Plot Default Colors . . .
Default Directory Path
Exit

-plot antenna patterns in polar form
-plot antenna patterns in rectangular form
-plot antenna patterns in 3-D form
-plot and tune impedance on a Smith chart-plot VSWR or Return Loss-set default types of pattern and impedance plots-set color preferences for plots-set the default directory path for data files-exit PCAAD 7.0

Edit
Copy Window
Copy Graph
Copy Text
Paste Text
Edit File
Print Window-copy current Window to Windows clipboard-copy current plot to Windows clipboard-copy selected text to Windows clipboard-paste text from Windows clipboard-invoke system text editor (Notepad)-print current PCAAD window and its contents

Wire
Dipole Antenna
Dipole RCS
Dipole (H) Over Ground Plane
Dipole (V) Over Ground Plane
V-dipole Antenna
Loop Antenna
Yagi Antenna
Dipole ArrayLPDA Design
LPDA Analysis
General Wire Antenna-analyze wire dipole antenna-compute radar cross section of wire dipole-analyze horizontal dipole over ground plane-analyze vertical dipole over ground plane-analyze V-dipole wire antenna-analyze wire loop antenna-analyze wire dipole Yagi array-analyze finite planar dipole array-design log periodic dipole array-analyze log periodic dipole array-analyze arbitrary wire antenna geometry

Arrays
Uniform Linear Array
Linear Subarray
Uniform Rectangular Array
Uniform Circular Array
Arbitrary Planar Array
Infinite Printed Dipole Array
Linear Array Pattern Synthesis
Grating Lobe Diagram
Effect of Random Array Errors-patterns and directivity of a uniform linear array-patterns of a linear array of subarrays-patterns and directivity of a rectangular array-patterns and directivity of a circular planar array-patterns and directivity of an arbitrary planar array-active impedance of infinite printed dipole array-Woodward-Lawson array synthesis-grating lobe diagram for a planar array-effect of random array excitation errors

9Apertures
Line Source-patterns of an arbitrary line source
Rectangular Aperture-patterns of a rectangular aperture antenna
Circular Aperture-patterns of a circular aperture antenna
E-plane Sectoral Horn-analyze an E-plane sectoral horn
H-plane Sectoral Horn-analyze an H-plane sectoral horn
Pyramidal Horn-analyze a pyramidal horn
Diagonal Horn-analyze a diagonal horn antenna
Corrugated Pyramidal Horn-analyze a corrugated pyramidal horn
Conical Horn-analyze a conical horn
Corrugated Conical Horn-analyze a corrugated conical horn
Parabolic Reflector (approximate)-approximate analysis of prime-focus reflector
Symmetric Parabolic Reflector Analysis -analyze a symmetric parabolic reflector
Offset Parabolic Reflector Analysis-analyze an offset parabolic reflector
Spherical Reflector Analysis-analyze a spherical reflector
Beam Efficiency-beam efficiency of an aperture antenna

Microstrip
Rectangular Probe-fed (Carver)
Rectangular Probe-fed (cavity)
Rectangular Line-fed (t-line)
Rectangular Proximity-fed (t-line)
Rectangular Aperture-fed (cavity)
Circular Probe-fed (cavity)-probe-fed patch analysis (Carver's model)-probe-fed patch analysis (cavity model)-line-fed patch analysis (t-line model)-proximity-fed patch analysis (t-line model)-aperture coupled patch analysis (cavity model)-probe-fed patch analysis (cavity model)

Transmission Lines
Coaxial Line
Rectangular Waveguide
Rectangular Waveguide Data
Circular WaveguideMicrostrip Line (quasi-static)
Stripline (quasi-static)
Multilayer Microstrip (full-wave)
Multilayer Stripline (full-wave)
Coupled Microstrip Lines (full-wave)
Coupled Striplines (full-wave)
Single Layer Surface Wave Modes
Multilayer Surface Wave Mode-analyze a coaxial line
-analyze a rectangular waveguide-standard rectangular waveguide data
-analyze a circular waveguide-quasi-static analysis and design of microstrip line
-quasi-static analysis and design of stripline-full-wave analysis of multilayer microstrip line
-full-wave analysis of multilayer stripline-full-wave analysis of coupled microstrip lines-full-wave analysis of coupled striplines-surface wave modes of a dielectric layer-surface wave mode of multilayer dielectric

Miscellaneous
Link Loss
Polarization Mismatch
Atmospheric Attenuation
Axial Ratio vs. Errors
Antenna Temperature
Calculator-Friis formula for radio links-polarization mismatch between two antennas-propagation loss due to atmosphere or rain
-axial ratio vs. amplitude and phase errors-antenna sky noise temperature-useful antenna and microwave calculations

Help
Help Table of Contents
Help Index
Context Help (F1)
Short Course and Tutorials
About PCAAD-contents of Help
-index for Help-context help for current routine (also F1 key)-antenna short course and related tutorials-information about PCAAD 7.0 and directories

10After selecting a particular antenna or transmission line topic from the main
PCAAD menu, a window will open for that routine. The windows for all
routines have the same format: a small graphic image of the antenna ortransmission line geometry is shown at the top left of the window, with data
entry at the top right, and output data listed below. Most routines have a
Compute button that is used to initiate computations after all data has beenentered. Results are displayed after the computation is finished, and mostroutines then show a Results tree that allow the option of plotting data, saving
data in a file, or showing related output data. Input data values are retained until
the window is closed, making it easy to change one parameter and run a new
solution. Most routines have error checking of input data, but the software is notcompletely foolproof.

B. Entering Data and Running the Routines
Numerical values are entered in PCAAD 7.0 using text boxes. When a routine
starts, a flashing cursor bar will appear in the text box for the first data entry
item. Type in a numerical value, and press Enter on the keyboard to move to thenext entry. You can also use the Tab key, or the mouse, to move to the next data
entry. Error checking is performed for most data entries, generally after theCompute button is pressed. If a value is found to be in error, a small error
message box is displayed. Click the OK button on this box, and focus will returnto the data item that was found to be in error. After you have computed asolution, you can change one or more problem parameters by simply entering
new values for those items, without having to re-enter all other parameters.

C. Pattern Calculation and Plotting
Many routines involve the calculation of far-field radiation patterns. These may
be plotted as planar pattern cuts on a polar or rectangular plot, or as a 3-Dvolumetric plot. The type of plot desired for a particular routine is specified byclicking the Pattern Type select button. Elevation plane patterns can be plotted at a
specified azimuthal angle for E-theta / E-phi or Co-pol / X-pol patterns (using
Ludwig’s third definition), or E-plane / H-plane patterns can be selected. Plotting
parameters, such as azimuth angle and step sizes, are also specified with thiswindow. Default values can be set with the Plot Default Types option from the
Plot menu. Pattern plots can be invoked directly from a PCAAD antenna analysis
routine (from the Results tree), or patterns can be plotted from data files throughthe Plot menu. Up to five separate patterns can be plotted on the polar orrectangular plots, but only one pattern can be plotted as a 3-D plot. Plots may be
printed (click the Print Plot button in the plotting window), or copied to the
Windows clipboard for use in other applications (click the Copy to Clipboard
button on the plotting window, or use the Copy Graph option from the Editmenu).

D. Saving Pattern Data
Routines that provide far-field radiation patterns also allow the option of saving
pattern data (planar or 3-D patterns) to a file with the Save Patterns entry on the11Results tree. PCAAD 7.0 now allows saving of far-field phase data, in addition
to the pattern amplitude (for planar patterns). Phase data can be useful whenusing PCAAD results with other programs, such as characterizing a feed forreflector antenna analysis. Planar pattern data is saved as an ASCII text file,with one row for each angle. The format is: pattern angle in degrees, patternamplitude in dB, and pattern phase in degrees. These values are delimited with
one or more spaces. The PCAAD polar and rectangular pattern plotting routines
can read these files, with or without the phase column. You can control whether
the phase information is saved by using the check box on the Default Plot
Types menu. For 3-D volumetric patterns the following data file format is used:
the first line has three values: the elevation angle step size (degrees), the azimuth
angle step size (degrees), and the maximum elevation angle range (90º for upper
hemisphere only, or 180º for both hemispheres). This is followed by N = 1 +360 / (azimuth step size) lines, one for each azimuth angle. Each line contains 1+ 90/(elevation angle step size) pattern values, normalized from 0 to 1.

E. Impedance Calculation and Plotting
Several routines, such as the wire antenna and microstrip antenna routines,
perform calculations of input impedance over a swept frequency range. The
parameters of this sweep are specified as the center frequency, the frequency
step size, and the number of frequency points. You can enter specific values forthese parameters in the appropriate boxes, or allow PCAAD to provide estimatesby clicking the Compute button. Note that the center frequency parameter refers
to the middle of the frequency sweep range, which may be different from theoperating frequency of the antenna. Impedance versus frequency can be plottedon a Smith Chart plot or on a VSWR/Return Loss plot; the default type of
impedance plot can be set from the Plot Default Types option from the Plotmenu. The Smith chart window also contains a powerful impedance matchingutility.

F. Help
PCAAD 7.0 contains a comprehensive help file in standard Windows format,
with convenient cross-references and search options. The help file is contextsensitive, meaning that you can simply press the F1 key while using any
analysis routine to get help on that particular routine. Pressing the F1 key whileon the main window will bring up the help contents for PCAAD 7.0. Help canalso be accessed by clicking Help - Context Help from the main menu bar. The
Help Table of Contents and Help Index are also available from the Helpmenu.
You can also access the antenna short course and tutorials from the Help menu.
The short course is grouped by chapters into individual PDF files, along with a
Glossary, and a quiz on antennas. Select Short Course and Tutorials from theHelp menu, and the desired file from the directory listing. The file should openwith the Acrobat Reader. You need to have the Acrobat Reader installed on yourcomputer.
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IV. Using PCAAD 7.0 – Instructions and Examples
This chapter will describe in detail the operation of each antenna, transmission line,
and utility routine in PCAAD 7.0 in terms of the input and output data, and a brief
discussion of the theory of the solution. Validation examples are also included forthe analysis routines.

A. The Plot Menu
The first five of the entries on the Plot menu allow you to plot data from files using
PCAAD’s plotting routines. Antenna patterns can be plotted in planar polar orrectangular form, or in 3-D volumetric form. Impedance data can be plotted on aSmith chart, or on a VSWR / Return Loss plot. The Default Plot Types option isused to control the default plot type when patterns or impedances are plotted
directly from PCAAD’s antenna routines. Default Plot Colors is used to set thepreferred colors used in the pattern and impedance plots. Exit is used to exit the
program.

A.1. Polar Pattern PlotThis routine is used to plot up to five planar antenna patterns in polar form. It
can be invoked directly from most of the PCAAD antenna routines to plot
patterns, or used independently from the Plot menu to plot patterns from data
files. The routine also computes the main beam pointing angle, the 3 dB
beamwidth of the main beam, and provides a movable angle cursor to readpattern values at any angle. The Plot Options window allows control of various
plot parameters such as the number of divisions, scales, plotting ranges, offsets,line styles, and colors. The resulting plot can be printed on your printer, or
exported to another application using the Windows clipboard and the Copy to
Clipboard button, or the Copy Graph option from the Edit menu.
To read pattern data from a data file, click the Read Data File button, and use
the file dialog box to specify a filename. The data file should be in ASCII form,
with each line consisting of an angle (in degrees) and the pattern (in dB) at thatangle (a phase entry is optional, and not used for plotting). The data must be
sequential, in order of increasing angle. The pattern files written by PCAAD 7.0
are in this format, and can be read by either the polar or the rectangular plotting
routine. Up to five separate patterns can be plotted simultaneously, either fromdata files or PCAAD antenna routines. Each data set may be offset by a fixedamount (through the Plot Options window), allowing patterns to be plotted interms of absolute gain, or to facilitate comparison of patterns normalized todifferent values. The default file extension for planar pattern data files is .DAT.
Pattern parameters for a selected pattern are shown at the top left of the polar
plotting window. Select the desired pattern by using the pull-down box. The
displayed parameters include the name of the file (or the name of the data set, as

13

set in the Plot Options window), the main beam pointing angle, the 3 dB
beamwidth, the pattern value at the moveable angle cursor, and the offset of thedata (as set in the Plot Options window). If the pattern does not have a welldefined main beam, or has more than one main beam (e.g., grating lobes), thebeam position and beamwidth may not be meaningful, and may not be shown.
The angle cursor is drawn as a dashed radial line, and can be moved by clicking
or dragging with the mouse. Notice that the mouse cursor changes from anarrow to a cross-hair when moved inside the polar plotting region. Clicking themouse inside the polar plot will snap the angle cursor to that angular position on
the graph. Alternatively, the angle cursor can be moved by clicking the mouseon the angle cursor (note that the mouse cursor changes to a directional icon
when over the angle cursor), and dragging to the desired position. The patternvalue display is updated instantly. This feature is useful for reading sidelobe or
cross-pol levels. In addition, moving the mouse over the pattern will provide an
immediate display of the angle and pattern value at the mouse cursor point (themouse cursor must be near a data point of the pattern for this to occur).
Each pattern can be identified with a movable text label. The text is set from
Plot Options, and the labels can be turned on or off using the check box forShow Pattern Labels. Use the mouse to drag the label to the desired position on
the plot.

A.2. Rectangular Pattern PlotThis routine is used to plot up to five planar antenna radiation patterns inrectangular form. It can be invoked directly from most of the PCAAD antennaroutines to plot patterns, or used independently from the Plot menu to plot
patterns from a data file. The routine also computes the main beam pointing
angle, the 3 dB beamwidth of the main beam, and provides a movable angle
cursor to read pattern values at any angle. The Plot Options window allows
control of various plot parameters such as the number of divisions, scales,plotting ranges, offsets, line styles, and colors. The resulting plot can be printed
on your printer, or exported to another application using the Windows clipboard
and the Copy to Clipboard button, or the Copy Graph option from the Editmenu.
To read pattern data from a data file, click the Read Data File button, and use
the file dialog box to specify a filename. The data file should be in ASCII form,
with each line consisting of an angle (in degrees) and the pattern (in dB) at thatangle (a phase entry is optional, and not used for plotting). The data must be
sequential, in order of increasing angle. The pattern files written by PCAAD 7.0
are in this format, and can be read by either the polar or the rectangular plotting
routine. Up to five separate patterns can be plotted simultaneously, either fromdata files or PCAAD antenna routines. Each data set may be offset by a fixedamount (through the Plot Options window), allowing patterns to be plotted interms of absolute gain, or to facilitate comparison of patterns normalized todifferent values. The default file extension for planar pattern data files is .DAT.
14

Pattern parameters for a selected pattern are shown at the top left of the polar
plotting window. Select the desired pattern by using the pull-down box. The
displayed parameters include the name of the file (or the name of the data set, as
set in the Plot Options window), the main beam pointing angle, the 3 dB
beamwidth, the pattern value at the moveable angle cursor, and the offset of thedata (as set in the Plot Options window). If the pattern does not have a welldefined main beam, or has more than one main beam (e.g., grating lobes), thebeam position and beamwidth may not be meaningful, and may not be shown.
The angle cursor is drawn as a dashed vertical line, and can be moved by either
clicking or dragging with the mouse. When using the mouse, notice that themouse cursor changes from an arrow to a cross-hair when moved inside therectangular plotting region. Clicking the mouse inside the rectangular plot will
snap the angle cursor to that angular position on the graph. Alternatively, theangle cursor can be moved by clicking the mouse on the angle cursor (note thatthe mouse cursor changes to a directional icon when over the angle cursor), anddragging to the desired position. The pattern value display is updated instantly.
This feature is useful for reading sidelobe or cross-pol levels. In addition,
moving the mouse over the pattern will provide an immediate display of theangle and pattern value at the mouse cursor point (the mouse cursor must benear a data point of the pattern for this to occur).
Each pattern can be identified with a movable text label. The label is set from
Plot Options, and the labels can be turned on or off using the check box forShow Pattern Labels. Use the mouse to drag the label to the desired position on
the plot. The vertical axis is normally labeled as Pattern (dB), but this label canbe changed by modifying the PCAAD7.INI file - this can be useful whenplotting directivity or gain.

A.3. 3-D Pattern PlotThis routine plots an antenna radiation pattern in a 3-D volumetric form. It canbe invoked directly from most of the PCAAD antenna routines to plot patterns,
or used independently from the PLOT menu to plot patterns from a data file.
Data files of this type can be generated from most of the PCAAD routines, andare given the default file extension .3DP, to distinguish them from planar patterndata files. The 3-D pattern plot can be printed on your printer, or exported toanother application using the Windows clipboard and the Copy to Clipboard
button, or the Copy Graph option from the Edit menu.
For 3-D volumetric patterns, the following data file format is used. The first line
has three values: the elevation angle step size (degrees), the azimuth angle step
size (degrees), and the maximum elevation angle range (90º for upper
hemisphere only, or 180º for both hemispheres). This is followed by N = 1 +360 / (azimuth step size) lines, one for each azimuth angle. Each of these lines
contains 1 + 90/(elevation angle step size) pattern values, normalized from 0 to
1. (The data is generated by normalizing the pattern to 0 dB, limiting the lowest
15

pattern value to -30 dB, then scaling to the range of 0 to 1 for plotting.)
The routine has three slider controls to allow adjustment of the plot size, theelevation view angle, and the azimuth view angle. The plot is redrawn after eachadjustment of these controls. A color bar near the bottom of the window shows
the scale, with red corresponding to 0 dB, and blue to -30 dB. There arecheckbox options for showing the gridlines on the plot, for displaying thecoordinate axes, and for showing the reference scale. There is also an option todisplay a cross-sectional view of the 3-D plot over a 90º sector.

A.4. Smith Chart Plot
The Smith Chart plotting routine is a very versatile tool, capable of plotting up
to five sets of impedance data, and incorporating an easy-to-use impedance
matching capability. It can be invoked directly from routines that calculate
impedance, such as the wire antenna and microstrip element routines, or it canbe used independently from the Plot menu to plot impedance data from ASCII
data files. The Smith chart plot can be printed on your printer, or exported toanother application using the Windows clipboard and the Copy to Clipboard
button, or the Copy Graph option from the Edit menu.
When used with data files, the file should be in ASCII form with one line foreach data point. The real part, the imaginary part, and an optional data pointlabel (up to five characters long) should be delimited with commas or spaces.
The data point labels are commonly used as frequency markers, but otherparameters can be used as well (such as scan angle). The impedance data is
assumed to be in absolute (ohms, not normalized) form. Click the Read Data
File button to select a data file. Up to five data sets can be displayed, except
when the impedance matching solution is used. The impedance matching
response must always be the last data set, so further data is prevented from being
read when the impedance matching response is on.
From the Smith chart window, you can use the mouse to click on any data point,
and read the exact value of its impedance in the data box at the top left of thewindow. This display also gives the corresponding normalized impedance, andthe reflection coefficient for that impedance. The chart also shows a constant
VSWR circle (dashed circle), which may be adjusted by either dragging with themouse cursor, or by entering a new value in the SWR data entry box at the left
side of the chart. Similarly, the chart also shows a dashed radial line indicating
wavelengths toward the load (WTL), and wavelengths toward the generator(WTG). This line may be set by dragging with the mouse, or by entering a valueof WTL or WTG in the appropriate data box. In addition, the VSWR and
WTL/WTG cursors may be set to a particular data point by double clicking onthat point. Smith chart options such as interpolation, characteristic impedance, arotated 1+jx circle, colors, and other display options can be set by clicking the
Plot Options button. Colors can be set from the Default Plot Colors window
available under Plot on the main menu bar - this window also allows saving of16

your color selections as defaults. Each impedance data set can be identified witha movable text label. The label is initially set as the filename for that data set (ifthe data was read from a file), or the name of the calling routine (if the data was
obtained from another PCAAD routine). You can also set the labels from the
Plot Options window, and the labels can be turned on or off using the checkbox for Show Data Point and Set Labels (enter blanks for the data set label if
you want data point labels but not a data set label). Use the mouse to drag thelabel to the desired position on the Smith chart.
PCAAD also features a general purpose impedance matching routine coupled to
the Smith chart. With one or more (but less than five) data sets displayed, first
select a data set and a matching frequency by clicking on the desired data point(if you do not select a data point, the program will use the midpoint of the firstdata set). Then turn on the impedance matching feature by clicking the On
button in the Impedance Matching frame. The response of the matched
impedance data will be displayed. You may change the matching frequency
using the scroll box (the impedance data set must have frequency labels for eachdata point). You may choose the type of matching circuit from the list box – aquarter-wave transformer, LC networks, open- and short-circuit shunt stubs, andopen- and short-circuit series stubs are available (see [9] for a discussion ofimpedance matching techniques). Except for the quarter-wave transformer, eachof these circuits yields two different matching solutions, which can be selectedwith the buttons marked Solution #1 and Solution #2. Each matching solution
has two parameters (transformer impedance and length; series and shuntcomponent values; or stub length and position). These values are listed for theselected matching network and solution. (For the stub tuners, the characteristic
impedance of the transmission line and stub are assumed to be the same as thecharacteristic impedance of the Smith chart.) Only a single impedance data set
can be matched at one time; to change the data set to be matched, turn off the
impedance matching feature, select a data point on the new data set, and turn
impedance matching back on. Once the matching parameters have been selected,
the routine calculates the input impedance seen looking into the matching
network at each frequency, and plots this as a new impedance locus on the chart.
The user can study the effect of changing matching circuits, the match
frequency, and different matching solutions very easily with this routine. The
effect of changes in component values can be studied simply be entering newvalues in the component value boxes. Note that, for data sets having a wide
frequency range between data points, it is possible that the plotted impedanceloci for the original or matched data sets may run off the edge of the chart – thisis because the accuracy of interpolation may not be sufficient. If this is aproblem, interpolation may be turned off in the Plot Options window. When the
impedance matching feature is in use, no further data sets may be read.

A.5. VSWR / Return Loss PlotThis routine plots up to two sets of impedance data as either VSWR or returnloss (in dB) versus frequency. It can be invoked directly from PCAAD routines17

that calculate impedance, such as the wire antenna and microstrip element
routines, or it can be used independently from the Plot menu to plot impedance
data from a file. The resulting plot can be printed on your printer, or exported toanother application using the Windows clipboard and the Copy to Clipboard
button, or the Copy Graph option from the Edit menu.
Select either a VSWR or Return Loss plot by clicking the appropriate option
button to the left of the plot. Plot options, such as interpolation and color ofplotted data, characteristic impedance, and the range and number of divisions forthe vertical and frequency scales, can be set by clicking the Plot Options button.
When used with a data file, the file should be in ASCII form with one line foreach data point. The real part, the imaginary part, and the frequency (up to fivecharacters) should be delimited with commas or spaces. The impedance data is
assumed to be in absolute (ohms, not normalized) form. This is the same format
used by the Smith chart routine, and the format that PCAAD uses when saving
impedance data to a file.

A.6. Default Plot Types
The default type of antenna pattern plots (polar, rectangular or 3-D), andimpedance plots (Smith chart or VSWR/Return Loss) are selected with thiswindow. You can select planar pattern cuts in polar or rectangular form, or athree dimensional volumetric pattern plot. Your selections on this window canbe saved as default values by clicking the Save Defaults button.
For planar patterns, you have the choice of viewing either E-theta / E-phi, Copol / X-pol (Ludwig’s third definition) or E-plane / H-plane patterns, at aparticular azimuth angle. (E-plane / H-plane patterns are not available in some
PCAAD routines.) The elevation angle step size can also be specified. You canalso control whether or not phase data is saved with the planar pattern data to a
file by using the check box.
For 3-D volumetric patterns, the elevation and azimuth step sizes can be specified these values should generally be between 2º to 10º for best results. Volumetricpatterns may be plotted over either the upper hemisphere, or both upper and lower
hemispheres, depending on the type of antenna. You can choose to display only theupper hemisphere of a 3-D pattern plot by using the check box. Note that manyantennas in PCAAD (microstrip antennas, horn antennas, and antennas over a
ground plane) have volumetric patterns that extend only over the upper hemisphere.

A.7. Default Plot Colors
This window is used to set the default colors used in the pattern (polar andrectangular) and impedance (Smith chart and VSWR/Return Loss) plotting
routines. Line colors for data sets can be set, as well as the cursor color andbackground color. Color selections can be saved as defaults for later use.
18

A.8 Default Directory Path
Windows usually defines a preferred directory for user applications. For example,
Windows 7 may use C:\Users\user\AppData\Roaming\PCAAD7 as the
directory path for your data files. The Default Directory Path menu option allows
you to choose alternate directories where PCAAD data files are stored. The
window displays the current default directory that PCAAD is using for data files,
and the Windows user directory path for the PCAAD application. You can change
the default directory to the Windows User directory, or to another directory of yourchoosing. You may also save your choice of default directory to the PCAAD.INI
file. Directories can also be chosen when using a File Dialog to read or save aparticular data file in PCAAD.

A.9. Exit
Click this option to exit PCAAD, or close the main PCAAD window.

19

B. The Edit Menu
Being a Windows application, PCAAD 7.0 allows use of the standard Windows
methods of cutting, copying, and pasting data and graphics from PCAAD routines
to or from the Windows clipboard. PCAAD has some useful additional commands
available from the Edit menu to facilitate copying, editing, and printing, as
described below.

B.1. Copy Window
Copy Window allows you to copy the currently active window to the Windows
clipboard. This image may then be pasted into another Windows application, suchas PowerPoint or Word. This action is similar to pressing Alt-PrintScreen, which
also copies the active window to the clipboard. Note that the entire screen image
can be copied to the clipboard by pressing PrintScreen (these are standard
Windows commands).

B.2. Copy Graph
Copy Graph allows you to copy the current graph or plot to the Windows
clipboard. The graph or plot may then be pasted into another Windows application,such as PowerPoint or Word. Note that this command only copies the graph or plot,
not the complete window.

B.3. Copy Text
To copy a value from a data box to the Windows clipboard, first select the datausing the mouse. Then click Copy Text from the Edit menu. This function can also
be accomplished by pressing Ctrl-C after selecting the desired data, or by rightclicking the mouse and selecting Copy.

B.4. Paste Text
To copy a value from the Windows clipboard to a data box in PCAAD, click on thedesired data box, then click Paste Text from the Edit menu. This function can also
be accomplished by pressing Ctrl-V, or by right-clicking the mouse and selecting
Paste.

B.5. Edit FileClick the Edit File option from the Edit menu to invoke the Windows system text
editor (typically Notepad). This allows you to easily view or edit data files whenusing PCAAD 7.0.

B.6. Print Window
This option is used to print the current active analysis or plotting routine window.
This feature is useful for obtaining a hard copy of the complete set of input andoutput data associated with a PCAAD 7.0 routine. Input data, output data, andgraphics are printed.

20

C. The Wire Antennas Menu
These nine routines involve the analysis and design of various wire antennas. Wire
dipoles, loops, Yagi-Uda arrays, planar dipole arrays, log periodic dipole arrays,
and more general wire antenna geometries are modeled using a standard thin-wireGalerkin moment method solution with piecewise sinusoidal modes, as described inreferences [2], [10].

C.1. Dipole AntennaThis routine computes the input impedance,broadside gain, and radiation pattern of adipole antenna. The feed point can be placedat the center of any expansion mode. The
solution uses the piecewise sinusoidal
expansion (PWS) Galerkin method, with theexact exponential integral expressions used forthe impedance matrix elements, as detailed inreferences [10], [11]. This method has provento be an accurate and efficient technique forsolving thin wire antenna and scattering
problems.
Begin by entering the dipole length, the dipole radius, the number of PWS
expansion modes, and the position of the feed generator. The generator feed
point must be located at the center of a PWS expansion mode. If the dipole iscenter-fed, the number of expansion modes should be odd, and the mode numberof the generator should be the middle mode (this mode number is automaticallyselected as the default mode number for the generator). Pattern plots can bemade in the E- and H-planes of the dipole, or E-theta / E-phi or Co-pol / X-pol
patterns can be made at an arbitrary azimuth angle. Patterns can be plotted inpolar, rectangular, or volumetric (3-D) form, and patterns can be saved as data
files. Select the pattern type and parameters with the Pattern Type selectbutton. The resonant frequency of the dipole, the frequency step size, and thedefault number (7) of frequency points are displayed to the right of theCompute button. These values can be estimated by the routine by clicking theCompute button, or you can enter your own values for center frequency,
frequency step size, and the number of frequency points.
Upon clicking the Compute button, the routine will calculate the moment
method solution for the dipole, and list the input impedance versus frequency inthe list box. The scroll bar can be used to scroll through the data. The gain of thedipole at its beam maximum is computed at the center frequency of thefrequency sweep. At this point, from the Results tree, you can plot the
impedance characteristics versus frequency on a Smith chart plot or a
VSWR/Return Loss plot, and can save the impedance data in a data file. The
21

specified patterns are calculated at the center frequency, and may be plotted byclicking the appropriate option in the Results tree, or saved to data files. The
geometry of the dipole may be viewed in three dimensions by clicking the Show
Geometry item in the Results tree. After each computation, data is
automatically written to a log file called WIRE.LOG, located in your PCAAD
user directory. This data includes the frequency, wire radius, coordinates of all
points on the wire structure, the definition of the PWS expansion modes, themoment method impedance matrix, and the voltage and current vectors.
Validation
Consider a half-wave dipole with a radius of 0.001. Calculated input impedance
results from PCAAD 7.0 are compared with those from [1] and [10], versus N, thenumber of expansion modes:

N

Reference [1]PCAAD 7.0

1
3
5

73.1 + j 42.3 Ω

73.1 + j 42.2 Ω

81.2 + j 41.3 
82.8 + j 42.0 
83.6 + j 42.7 

81.2 + j 41.3 
82.8 + j 42.0 
83.6 + j 42.7 

7The gain of a half-wave dipole is 2.15 dB; PCAAD 7.0 gives 2.2 dB.

22

C.2. Dipole Radar Cross-Section
This routine is very similar to the dipole
antenna routine, except that it computes thebistatic radar cross section (RCS) for a loaded
wire dipole. The solution uses the piecewisesinusoidal expansion (PWS) Galerkin method,with the exact exponential integral expressions
used for the impedance matrix elements, asdetailed in references [10], [11]. This method
has proven to be an accurate and efficienttechnique for solving thin wire antenna andscattering problems.
Begin by entering the dipole length, the dipole radius, and the incidence andscattering angles. These angles are measured from the axis of the dipole, andhave default values of 90º (broadside). Next enter the number of PWS expansion
modes, and the mode number of the lumped-element load impedance. The
default number of expansion modes is 3, and the default position of the lumped
load is at the terminals of the middle expansion mode. Then enter the real andimaginary parts of the load impedance; the default values are zero. The resonant
frequency of the dipole, the frequency step size, and the default number (7) of
frequency points are displayed to the right of the Compute button. These values
can be estimated by the routine by clicking the Compute button, or you canenter your own values for center frequency, frequency step size, and the numberof frequency points. The geometry of the dipole may be viewed in three
dimensions by clicking the Show Geometry button.
Upon clicking the Compute button, the routine will calculate the moment
method solution for the dipole, compute the RCS of the dipole over the specified
frequency sweep, and list the results in dB per square meter, and in dB per
square wavelength, in a list box. The scroll bar can be used to scroll through thedata. After each computation, data is automatically written to a log file called
WIRE.LOG, located in your PCAAD user directory. This data includes thefrequency, wire radius, coordinates of all points on the wire structure, thedefinition of the PWS expansion modes, the moment method impedance matrix,
and the voltage and current vectors. The RCS data (in dBsm) can be written to adata file by clicking Save Data.
Validation
Consider a dipole 6.0 cm long with a radius of 0.002 cm. At 3 GHz, using three
PWS expansion modes, the RCS was computed at broadside and compared withresults from [10] for two values of load impedance:

23

ZL

Reference [10]PCAAD 7.00
70 

-22.0 dBsm
-26.5 dBsm

-21.9 dBsm
-26.7 dBsm

Results were also compared with RCS data from [3]. The angle dependence of theroutine was checked by verifying that the RCS of a short dipole dropped off by 6
dB when both the incidence and scattering angles were changed to 45.

24

C.3. Horizontal Dipole Over Ground Plane
This routine computes the input impedance,broadside gain, and radiation pattern of ahorizontal dipole antenna over an infinite
perfectly conducting ground plane. The feed
point can be placed at the center of any
expansion mode. The solution uses thepiecewise sinusoidal expansion (PWS)
Galerkin method, with the exact exponential
integral expressions used for the impedance
matrix elements, as detailed in references [10],[11]. This method has proven to be an accurate
and efficient technique for solving thin wire
antenna and scattering problems.
Begin by entering the dipole length, the dipole radius, the height above theground plane, the number of PWS expansion modes, and the position of the feed
generator. The dipole must be above the ground plane. The generator feed point
must be located at the center of a PWS expansion mode. If the dipole is centerfed, the number of expansion modes should be odd, and the mode number of thegenerator should be the middle mode (this mode number is automaticallyselected as the default mode number for the generator). Pattern plots can bemade in the E- and H-planes of the dipole, or E-theta / E-phi or Co-pol / X-pol
patterns can be made at an arbitrary azimuth angle. Patterns can be plotted inpolar, rectangular, or volumetric (3-D) form, and patterns can be saved as data
files. Select the pattern type and parameters with the Pattern Type selectbutton. The resonant frequency of the dipole, the frequency step size, and thedefault number (7) of frequency points are displayed to the right of theCompute button. These values can be estimated by the routine by clicking theCompute button, or you can enter your own values for center frequency,
frequency step size, and the number of frequency points.
Upon clicking the Compute button, the routine will calculate the moment
method solution for the dipole, and list the input impedance versus frequency inthe list box. The scroll bar can be used to scroll through the data. The gain of thedipole at its beam maximum is computed at the center frequency of thefrequency sweep. At this point, from the Results tree, you can plot the
impedance characteristics versus frequency on a Smith Chart plot or a
VSWR/Return Loss plot, and can save the impedance data in a data file. The
specified patterns are calculated at the center frequency, and may be plotted byclicking the appropriate option in the Results tree, or saved to data files. The
geometry of the dipole may be viewed in three dimensions by clicking the Show
Geometry item in the Results tree. After each computation, data is
automatically written to a log file called WIRE.LOG, located in your PCAAD
user directory. This data includes the frequency, wire radius, coordinates of all25

points on the wire structure, the definition of the PWS expansion modes, themoment method impedance matrix, and the voltage and current vectors.
Validation
Consider a horizontal center-fed dipole with length λ/2 and radius 0.001λ, withthree expansion modes. PCAAD gives the following results for input impedanceand directivity, for three values of ground plane spacing:d/λInput ImpedanceDirectivity

0.10
0.25
0.55

24.9 + j 66.9 Ω
99.7 + j 73.1 Ω
66.4 + j 30.5 Ω

8.8 dB
7.5 dB
9.0 dB

These values are in close agreement with the results from the finite dipole arrayroutine, after applying image theory to remove the ground plane, and replacing thehorizontal dipole with an array of two parallel dipoles having excitations of unit
amplitude and a 180º phase shift. Three dB is added to the directivity of the array to
account for the ground plane.

26C.4. Vertical Dipole Over Ground Plane
This routine computes the input impedance,broadside gain, and radiation pattern of avertical dipole antenna over an infinite
perfectly conducting ground plane. The feed
point can be placed at the center of any
expansion mode. The solution uses thepiecewise sinusoidal expansion (PWS)
Galerkin method, with the exact exponential
integral expressions used for the impedance
matrix elements, as detailed in references [10],[11]. This method has proven to be an
accurate and efficient technique for solving
thin wire antenna and scattering problems.
Begin by entering the dipole length, the dipole radius, the height (of the centerof the dipole) above the ground plane, the number of PWS expansion modes,
and the position of the feed generator. The entire dipole must be above theground plane. The generator feed point must be located at the center of a PWS
expansion mode. If the dipole is center-fed, the number of expansion modes
should be odd, and the mode number of the generator should be the middle
mode (this mode number is automatically selected as the default mode number
for the generator). Pattern plots can be made in the E- and H-planes of thedipole, or E-theta / E-phi or Co-pol / X-pol patterns can be made at an arbitrary
azimuth angle. Patterns can be plotted in polar, rectangular, or volumetric (3-D)
form, and patterns can be saved as data files. Select the pattern type andparameters with the Pattern Type select button. The resonant frequency of thedipole, the frequency step size, and the default number (7) of frequency points
are displayed to the right of the Compute button. These values can be estimatedby the routine by clicking the Compute button, or you can enter your own
values for center frequency, frequency step size, and the number of frequency
points.
Upon clicking the Compute button, the routine will calculate the moment
method solution for the dipole, and list the input impedance versus frequency inthe list box. The scroll bar can be used to scroll through the data. The gain of thedipole at its beam maximum is computed at the center frequency of thefrequency sweep. At this point, from the Results tree, you can plot the
impedance characteristics versus frequency on a Smith chart plot or a
VSWR/Return Loss plot, and can save the impedance data in a data file. The
specified patterns are calculated at the center frequency, and may be plotted byclicking the appropriate option in the Results tree, or saved to data files. The
geometry of the dipole may be viewed in three dimensions by clicking the Show
Geometry item in the Results tree. After each computation, data is
automatically written to a log file called WIRE.LOG, located in your PCAAD
27

user directory. This data includes the frequency, wire radius, coordinates of all
points on the wire structure, the definition of the PWS expansion modes, themoment method impedance matrix, and the voltage and current vectors.
Validation
Consider a vertical center-fed dipole with length λ/2 and radius 0.001λ, with three
expansion modes. PCAAD gives the following results for input impedance anddirectivity, for three values of ground plane spacing:d/λInput ImpedanceDirectivity

0.25001
0.45
0.55

118.2 + j 62.1 Ω
76.8 + j 37.4 Ω
78.0 + j 43.3 Ω

6.8 dB
8.4 dB
8.4 dB

These values are in agreement with the results from the finite dipole array routine,
after applying image theory to remove the ground plane, replacing the vertical
dipole with an array of two collinear dipoles having the same excitation. Three dBis added to the directivity of the array to account for the ground plane.

28C.5. V-Dipole AntennaThis routine computes the input impedance,
gain, and radiation pattern of a V-dipole
antenna. The internal angle of the V-dipole isvariable (an angle of 180º corresponds to astraight dipole). The feed point is at the apexof the wire arms. The solution uses thepiecewise sinusoidal expansion (PWS)
Galerkin method, with the exact exponential
integral expressions used for the impedance
matrix elements, as detailed in references [10],[11]. This method has proven to be an
accurate and efficient technique for solving
thin wire antenna and scattering problems.
Begin by entering the dipole arm length, the dipole radius, the number of PWS
expansion modes, and the internal angle of the dipole (between 2º and 180º).
Because of symmetry, the number of PWS expansion modes must be odd.
Pattern plots can be made in the E- and H-planes of the dipole, or E-theta / E-phi
or Co-pol / X-pol patterns can be made at an arbitrary azimuth angle. Patterns
can be plotted in polar, rectangular, or volumetric (3-D) form, and patterns canbe saved as data files. Select the pattern type and parameters with the Pattern
Type select button. The resonant frequency of the V-dipole, the frequency stepsize, and the default number (7) of frequency points are displayed to the right of
the Compute button. These values can be estimated by the routine by clicking
the Compute button, or you can enter your own values for center frequency,
frequency step size, and the number of frequency points.
Upon clicking the Compute button, the routine will calculate the moment
method solution for the V-dipole, and list the input impedance versus frequency
in the list box. The scroll bar can be used to scroll through the data. The gain of
the dipole at its beam maximum is computed at the center frequency of thefrequency sweep. At this point, from the Results tree, you can plot the
impedance characteristics versus frequency on a Smith chart plot or a
VSWR/Return Loss plot, and can save the impedance data in a data file. The
specified patterns are calculated at the center frequency, and may be plotted byclicking the appropriate option in the Results tree, or saved to data files. The
geometry of the V-dipole antenna may be viewed in three dimensions byclicking the Show Geometry item in the Results tree. After each computation,
data is automatically written to a log file called WIRE.LOG, located in yourPCAAD user directory. This data includes the frequency, wire radius,
coordinates of all points on the wire structure, the definition of the PWS
expansion modes, the moment method impedance matrix, and the voltage andcurrent vectors.

29

Validation #1
Consider a V-dipole antenna with arm lengths of 0.25, radius of 0.001, andvariable angle. Calculated input impedance results from PCAAD are comparedwith data from [10], using one PWS expansion mode:

Angle

Reference [10]PCAAD 7.0

90
150
180

40.9 + j 9.0 
69.3 + j 39. 
73.1 + j 42. 

40.1 + j 8.9 
69.1 + j 38.9 
73.1 + j 42.2 

Validation #2
Consider a V-dipole with arm lengths of 1.5, and radius 0.001. From [2], theinternal angle that results in maximum directivity is 82.5. The resulting directivity
from [2] is approximately 7.5 dB. Using 11 expansion modes, PCAAD gives avalue of 7.8 dB.

30

C.6. Loop AntennaThis routine computes the input impedance,
gain, and radiation pattern of a wire loop
antenna. The solution uses the piecewisesinusoidal expansion (PWS) Galerkin method,with the exact exponential integral expressions
used for the impedance matrix elements, asdetailed in references [10], [11]. This method
has proven to be an accurate and efficienttechnique for solving thin wire antenna andscattering problems.
Begin by entering the radius of the loop, thewire radius, and the number of PWS expansion modes. Pattern plots can bemade in the E- and H-planes of the loop, or E-theta / E-phi or Co-pol / X-pol
patterns can be made at an arbitrary azimuth angle. Note that electrically smallloops have an E-phi polarization, but larger loops may have E-theta polarization(the Co- and X-pol fields are assumed to be E-phi and E-theta for this routine).
Patterns can be plotted in polar, rectangular, or volumetric (3-D) form, andpatterns can be saved as data files. Select the pattern type and parameters with
the Pattern Type select button. The resonant frequency of the loop, thefrequency step size, and the default number (7) of frequency points are
displayed to the right of the Compute button. These values can be estimated by
the routine by clicking the Compute button, or you can enter your own values
for center frequency, frequency step size, and the number of frequency points.
Upon clicking the Compute button, the routine will calculate the moment
method solution for the loop antenna, and list the input impedance versus
frequency in the list box. The scroll bar can be used to scroll through the data.
The gain of the loop at its beam maximum is computed at the center frequencyof the frequency sweep (note that electrically small loops have a pattern null on
axis, while larger loops have a beam maximum on the axis of the loop). At thispoint, from the Results tree, you can plot the impedance characteristics versus
frequency on a Smith chart plot or a VSWR/Return Loss plot, and can save theimpedance data in a data file. The specified patterns are calculated at the center
frequency, and may be plotted by clicking the appropriate option in the Results
tree, or saved to data files. The geometry of the loop may be viewed in three
dimensions by clicking the Show Geometry item in the Results tree. After eachcomputation, data is automatically written to a log file called WIRE.LOG,
located in your PCAAD user directory. This data includes the frequency, wireradius, coordinates of all points on the wire structure, the definition of the PWS
expansion modes, the moment method impedance matrix, and the voltage andcurrent vectors.

31

Validation
Consider a wire loop antenna with a wire radius of 0.001. The calculated input
impedance from [10] is compared with results from PCAAD 7.0 for various
loop radii and expansion modes. Note that using four expansion modes
corresponds to a square loop, while eight modes corresponds to an octagonalloop, etc.
Loop
Radius
0.0707 
0.1592 
0.1592 
0.1592 
0.1592 

PWS
Modes
4
4
8
16
64

Zin
Reference [10]44.8 + j 1589. 
92.4 – j 300.9 
109.7 – j 149.3 
116.0 – j 109.1 
117.5 – j 95. Zin
PCAAD 7.0
44.8 + j 1589. 
92.4 –j 300.9 
109.7 – j 149.3 
116.0 – j 109.1 
117.5 – j 95.4 

The directivity of a loop having a circumference of 1  (radius = 0.1592 ) is about
3.4 dB [2]. PCAAD 7.0 gives a value of 3.3 – 3.5 dB, depending on the number of
expansion modes used.

32

C.7. Yagi AntennaThis routine analyzes a Yagi-Uda dipole arrayusing a moment method solution that includes
all mutual coupling terms. Dipole currents are
expanded using piecewise sinusoidal (PWS)
modes, as described in references [10], [11].
The routine computes input impedance, gain,
front-to-back ratio, and patterns for the array.
The array is assumed to have one dipole
reflector element, one driven dipole element,
and an arbitrary number of dipole director
elements. The length and spacing for eachelement is variable, but the radius is assumed
to be the same for all elements.
Begin by entering the frequency, the dipole radius, the number of PWS modeson each dipole, and the number of director elements. Next, specify the lengths
and spacings of the elements using the scroll bar and boxes. The name of eachelement is listed in the box to the right of the scroll bar, followed by boxes for
its length and spacing from the previous element. Thus, the spacing of the firstelement (the reflector) is not used, and is set to zero. Use the scroll bar to scroll
through the elements to set or change lengths and spacings. Pattern plots can bemade in the E- and H-planes of the array, or E-theta / E-phi or Co-pol / X-pol
patterns can be made at an arbitrary azimuth angle. Patterns can be plotted inpolar, rectangular, or volumetric (3-D) form, and patterns can be saved as data
files. Select the pattern type and parameters with the Pattern Type selectbutton.
When all data is entered, click the Compute button to calculate the moment
method solution for the Yagi antenna. The input impedance, gain, and front-toback ratio will be listed. The specified patterns may be plotted by clicking theappropriate option in the Results tree, or saved to data files. The geometry of theYagi may be viewed in three dimensions by clicking the Show Geometry itemin the Results tree. After each computation, data is automatically written to alog file called WIRE.LOG, located in your PCAAD user directory. This data
includes the frequency, wire radius, coordinates of all points on the wire
structure, the definition of the PWS expansion modes, the moment method
impedance matrix, and the voltage and current vectors.

33

Validation
Consider a Yagi array with the following specifications:
Reflector length
Fed element length
Director length (1)Spacing between reflector and feedSpacing between feed and director
Dipole radiusFrequency

47.9 cm
45.3 cm
45.1 cm
25.0 cm
25.0 cm
0.25 cm
0.30 GHz

This geometry is analyzed in [3], although the number of expansion modes is notstated. Running PCAAD 7.0 with 9 PWS modes per element (27 modes total) gives
the following results:
Quantity

Reference [3]PCAAD 7.0

Input impedance
Gain
Front-to-back ratio

22 + j 15 
9.4 dB
5.6 dB

22 + j 14 
9.5 dB
5.7 dBThe principal plane patterns of the Yagi array are shown below.

Figure 1. E-plane and H-plane patterns of the Yagi array example.
34

C.8. Dipole Array
This routine analyzes a finite planar wire
dipole array using a moment method solutionthat includes all mutual coupling terms.
Dipole currents are expanded using piecewisesinusoidal (PWS) modes, as described inreferences [10], [11]. The routine computes
input impedance at each dipole, the array gain,
and patterns for the array. The number andspacing of dipoles in each plane of the array isvariable, but all dipoles are assumed to havethe same length and radius. Each dipole iscenter-fed with an arbitrary voltage generator,
with a series generator impedance. As shown in the graphic, the dipoles are allparallel to the x-axis, and are numbered by rows along the x-axis.
Begin by entering the frequency, the number of dipoles in the x and y-directions,and the spacings (center-to-center) of the dipoles in the x and y-directions. Also
enter the dipole length, the dipole radius, the number of PWS modes on each
dipole, and the series generator resistance. The generator resistance is the samefor all dipoles. Next, specify the generator voltage at each dipole using the scroll
bar and boxes. The dipole index (numbered along the x axis, by rows, starting at
the bottom) is listed in the box to the right of the scroll bar, followed by boxes
for the generator voltage magnitude and phase (in degrees). Use the scroll bar toscroll through the elements to set or change generator voltages. Pattern plots canbe made in the E- and H-planes of the array, or E-theta / E-phi or Co-pol / X-pol
patterns can be made at an arbitrary azimuth angle. Patterns can be plotted inpolar, rectangular, or volumetric (3-D) form, and patterns can be saved as data
files. Select the pattern type and parameters with the Pattern Type selectbutton.
When all data is entered, click the Compute button to calculate the moment
method solution. The input impedance for each dipole will be listed in the box
below the Compute button; use the scroll bar to scroll through the data. The
input impedance is that seen looking into the dipole terminals, in contrast to theimpedance seen from the generator (which would include the generator series
resistance). The routine computes the gain of the array at the main beam
position, assuming the main beam occurs in the plane where the patterns havebeen specified. The gain is computed in terms of the input power to the dipoles,
and does not include power dissipated in the generator impedance. The logic
here is that a realistic source will consist of a voltage generator and a series
generator impedance, and the power dissipated in the source impedance should
not be considered as a loss in the antenna itself.
The specified patterns may be plotted by clicking the appropriate option in the35Results tree, or saved to data files. The geometry of the dipole array may beviewed in three dimensions by clicking the Show Geometry item in the Results
tree. After each computation, data is automatically written to a log file called
WIRE.LOG, located in your PCAAD user directory. This data includes thefrequency, wire radius, coordinates of all points on the wire structure, thedefinition of the PWS expansion modes, the moment method impedance matrix,
and the voltage and current vectors. The modes are counted from left to right foreach element, and along the E-plane rows of the array.
Validation
Consider a 12-element linear H-plane dipole array. The dipole length is 5 cm, theradius is 0.001 cm, the spacing between the elements is 5 cm, and the frequency is
3 GHz. The generator impedance is 0 , and the voltage sources are phased to scan
the beam to -45 in the H-plane. Five PWS modes are used on each dipole. Thisgeometry is the same as that treated in reference [2]. Input impedance magnitudes
from [2] are compared below with data computed from PCAAD 7.0:

DipoleGenerator
Voltage

Zin
PCAAD 7.0

|Zin|
PCAAD 7.0

|Zin|
Ref [2]12
3
4
5

1.0/0
1.0/127
1.0/254
1.0/381
1.0/508

107.1 + j 9.6 
97.8 + j 42.0 
91.0 + j 46.0 
87.8 + j 45.3 
86.4 + j 43.9 

107.5 106.4 102.0 98.8 
96.9 

107.1 105.9 101.5 98.2 
96.3 

6
7
8
9
10
11

1.0/635
1.0/762
1.0/889
1.0/1016
1.0/1143
1.0/1270
1.0/1397

85.9 + j 42.5 
86.1 + j 41.0 
87.5 + j 39.3 
90.7 + j 38.9 
95.0 + j 42.6 
92.8 + j 55.2 
57.4 + j 47.8 

95.8 
95.3 
95.9 
98.7 
104.2 108.0 74.7 

95.2 
94.7 
95.4 
98.2 
103.7 107.3 74.0 

12

The H-plane pattern for this case is shown in Figure 2 below, and is in good
agreement with the pattern in [2] (the pattern in [2] is scanned to 45, while the
PCAAD results are for an array scanned to -45; the difference can be attributed toa difference in numbering the dipoles).

36Figure 2. H-plane pattern of the dipole array example.

37

C.9. Log Periodic Dipole Array Design
This routine gives an approximate design for alog-periodic dipole array, for a specified
bandwidth and gain, based on the formulas
given in reference [1], with corrections fromreference [7]. The routine computes thenecessary number of dipoles in the array, andthe spacings, lengths, and radii for each element.
First enter the lower and upper frequencies ofthe desired operating band. Then enter thedesired gain (between 7 and 11 dB), and theradius of the largest dipole. The routine prints
out the log-periodic array scale factors,  and , followed by a list of the spacing,length, and radius for each element in the array. The scroll bar in the list box can beused to scroll through the elements. Spacings are measured from the largest dipole;
the last spacing is not used.
Validation
Consider an LPDA design with a lower frequency of 54 MHz, an upper frequencyof 216 MHz, a directivity of 7.5 dB, and a largest dipole radius of 1 cm. This case isgiven in [1], with the following results:

Quantity

Reference [1]PCAAD 7.0



0.147

0.147


First dipole length
Spacing to second dipole
Third dipole radius
Last dipole length

0.822
264.8 cm
77.8 cm
0.64 cm
55.2 cm

0.822
264.8 cm
77.8 cm
0.64 cm
55.2 cm

38

C.10. Log Periodic Dipole Array Analysis
This routine performs a complete analysis of alog-periodic dipole array using a moment
method solution that includes all mutual
coupling terms. Dipole currents are expanded
using piecewise sinusoidal (PWS) modes, as
described in references [10], [11]. The array is
fed with a transmission line having alternating
terminals, and analyzed using port admittancematrices as described in reference [2]. The
routine computes the input impedance at thefeed port, the array directivity and gain, andthe patterns for the array. As shown in thegraphic, the dipoles are all parallel to the x-axis, with the main beam in the z
direction. The feed is assumed to be at the terminals of the smallest dipole, and amatched load is assumed to be located at the terminals of the largest dipole. The
dimensions and spacings can be manually entered for each dipole, or you canenter the σ and τ parameters for the array and let the routine calculate allnecessary dimensions.
Begin by entering the frequency, the feed line characteristic impedance, thenumber of dipoles in the array, and the number of expansion modes to be usedon each dipole (this value may need to be increased for frequencies at the highend of the operating range). At this point you can click the Get Data button toenter the σ and τ parameters of the LPDA array, along with the length and radiusof the first (longest) dipole in the array. The routine will then compute allnecessary dimensions and spacings for the array, and automatically enter thesevalues (upon clicking the OK button) into the scroll boxes. Alternatively, you
can manually enter the length, spacing, and radius for each dipole in the array.
The dipoles are numbered starting from the largest element; the last spacing
value is not used. Pattern plots can be made in the E- and H-planes of the array,or E-theta / E-phi or Co-pol / X-pol patterns can be made at an arbitrary azimuth
angle. Patterns can be plotted in polar, rectangular, or volumetric (3-D) form,
and patterns can be saved as data files. Select the pattern type and parameterswith the Pattern Type select button.
When all data is entered, click the Compute button to calculate the moment
method solution. The input impedance, directivity, and gain (accounting for
power lost in the termination resistor), and the front-to-back ratio are listed,along with the magnitude and phase of the terminal currents at each dipole(these values include the 180º phase reversal introduced by the feed line). Thisdata can be used to observe how the "active region" moves along the array as
frequency changes. From the Results tree, you can plot the patterns of the
LPDA by clicking the appropriate option in the Results tree, or save the patterns
to data files. The geometry of the LPDA may be viewed in three dimensions by39

clicking the Show Geometry item in the Results tree. After each computation,
data is automatically written to a log file called WIRE.LOG, located in yourPCAAD user directory. This data includes the frequency, wire radius,
coordinates of all points on the wire structure, the definition of the PWS
expansion modes, the moment method impedance matrix, and the voltage andcurrent vectors.
Validation
Consider a log periodic dipole array having 18 elements and   0.169 ,  0.917 , with the largest dipole having a length of 75 cm and radius of 0.3 cm.
The characteristic impedance is 83 . The table below compares the calculated
input impedance and gain with values from [2]. Five expansion modes per dipole
were used in the PCAAD solution.

Reference [2]PCAAD 7.0

Frequency(MHz)

Zin ()Gain (dB)Zin ()Gain (dB)

200
300
450
600

69 – j 7
72 – j 4
76 – j 6
78 – j 11

8.8
9.4
9.5
9.4

71 – j 6
72 – j 3
75 – j 8
80 – j 12

9.0
9.5
9.6
9.3

The figure below show the principal plane patterns for the array at 300 MHz.

40

Figure 3. E-plane and H-plane patterns of the LPDA array example.

41

C.11. General Wire AntennaThis routine analyzes a general wire antenna
geometry using a moment method solutionthat includes all mutual coupling terms. An
arbitrary number of bent wire segments can be
specified, with arbitrary positions, and voltage
generators and lumped loads can be specified
at the terminals of any expansion mode. The
main limitation is that junctions between morethan two wires are not allowed. All wires mustalso have the same radius. Wire currents are
expanded using piecewise sinusoidal (PWS)
modes, as described in references [10], [11].
The wire geometry is specified by defining a set of x, y, z coordinates to define
the terminals of each PWS expansion mode on the wire structure. The geometryis specified in an ASCII data file (extension .ANT), with the following format:
FREQ, ANP
X, Y, ZNM
I1, I2, I3
NPORTSPMODE, VGR, VGI, ZLR, ZLI

frequency (GHz), wire radius (cm)number of points on the wire structure
coordinates (in cm) of each point on thewire geometry (one row for each point)
number of PWS expansion modes
indices of the three coordinates that define
each PWS mode
number of generator and/or load ports
mode number of port, real and imaginary
generator voltage, real and imaginary load
impedance (one line for each port)

This data file can be created using a standard text editor; (see the
DIPOLE.ANT, ARRAY.ANT, and YAGI.ANT files in the PCAAD user
directory for examples of how the geometry files can be written). PWS
expansion modes are laid out along the wires starting from the first endpoint at
point I1, to the terminals at point I2, and to the second endpoint at point I3. Notethat each arm of a PWS expansion mode must be less than a quarter-wavelength
long at the operating frequency. The routine computes the currents on the wires,the input impedance at each port, the directivity and gain of the antenna, theradiation efficiency, and the radiation patterns for the antenna.
The routine begins with a dialog box to enter a filename for the wire antenna
geometry. The routine then lists some of the parameters of the wire geometry(number of points, number of expansion modes, and the number of feed ports) inthree text boxes - these can only be changed by changing the geometry data file.
The routine also reads the operating frequency from the data file, but you may

42enter a different operating frequency, if desired. Because the polarization of anarbitrary wire antenna is not known, E-plane / H-plane patterns and Co-pol / Xpol patterns are not available for this routine, but E-theta and E-phi patterns canbe made at an arbitrary azimuth angle. Patterns can be plotted in polar,
rectangular, or volumetric (3-D) form, and patterns can be saved as data files.
Select the pattern type and parameters with the Pattern Type select button.
Click the Compute button to begin computation of the moment method
solution. When this calculation is complete, the gain, directivity, radiation
efficiency, port impedances, and mode currents will be listed. At this point, fromthe Results tree, you can plot the specified patterns by clicking the appropriate
option in the Results tree, or save the patterns to data files. The geometry of thewire antenna may be viewed in three dimensions by clicking the Show
Geometry item in the Results tree. The perspective view may be rotated inelevation and azimuth using the scroll bars at the sides of the graph, and can be
adjusted in size by using the zoom scroll bar. After each computation, data is
automatically written to a log file called WIRE.LOG, located in your PCAAD
user directory. This data includes the frequency, wire radius, coordinates of all
points on the wire structure, the definition of the PWS expansion modes, themoment method impedance matrix, and the voltage and current vectors.
As in the case of the planar dipole array, this routine computes the input
impedance at each port as seen looking into the wire terminals, and does notdirectly include the series load impedance, if present. Similarly, the power
dissipated in the antenna does not include power lost in the series generator
impedances. If a port has a load impedance without a generator, however, thepower lost in that load is included in the antenna loss. The logic here is that arealistic source will consist of a voltage generator and a series generator
impedance, and the power dissipated in the source impedance should not be
considered as a loss in the antenna itself. Lumped loads apart from thegenerators will, however, contribute to antenna loss. Thus an antenna withmatched generators, but without separate lumped loads, will have an efficiencyof 100%. An antenna having resistive lumped loads (e.g., a loaded dipole) will
have an efficiency less than 100%.
Validation
The Yagi-Uda array example described in Section C.7. is used as a validation
example for this routine, but with one expansion mode per element. The data filefor this antenna is shown below (this file, YAGI.ANT, is supplied with PCAAD
7.0):
0.3,.259-23.95,0,00,0,023.95,0,043

-22.65,0,25.
0.,0.,25.
22.65,0,25.
-22.55,0.,50.
0.,0.,50.
22.55,0.,50.
3
1,2,3
4,5,6
7,8,9
1
2,1.,0.,0.,0.
PCAAD 7.0 produced the following results:
18.6 - j 3.0 
9.5 dB
6.6 dB

Input impedance
Gain
Front-to-back ratio

These results agree with those obtained from the Yagi array example in Section C.7
with one expansion mode per element.

44

D. The Array Antennas Menu
This set of routines can be used to plot patterns for linear, rectangular planar, andcircular planar arrays, to compute the input impedance of an infinite array ofprinted dipoles, and to plot a grating lobe diagram for planar arrays. Arrays ofsubarrays or elements with arbitrary patterns, and planar arrays with elements
having arbitrary positions, can also be treated, and pattern synthesis can be
performed for linear arrays using the Woodward-Lawson method. The array patternroutines are very flexible, allowing you to specify amplitude and phase variations,amplitude and phase errors, and the type of radiating element.

D.1. Uniform Linear Array
This routine is used to plot patterns andcompute directivity of a linear array antenna
having uniform spacing. You can specify arraysize, amplitude taper, phase distribution, andelement type. Co-pol and cross-pol patterns canbe calculated in an arbitrary elevation plane, andcan be plotted either separately or together on apolar or rectangular pattern plot, or saved todata files. The routine can also be used tocompute the directivity of the array. As
indicated in the picture at the top left of theform, the array is assumed to lie along the xaxis; if a ground plane is present (depending on the element type), it is positioned
below the array parallel to the x-y plane. The pattern is computed using the arrayfactor of the array multiplied by the element factor. Mutual coupling effects are notincluded in this routine. Directivity is computed by numerical integration of thepattern, which can be time consuming for large arrays. The maximum size of thearray is limited to 200 elements. This routine uses three additional windows to
select the array amplitude distribution, the array phase distribution, and the arrayelement type. These windows are accessed by clicking the small Select button to
the right of the appropriate text box for amplitude, phase, and element type.
Pattern plots can be made in the E- and H-planes of the array, or E-theta / E-phi or
Co-pol / X-pol patterns can be made at an arbitrary azimuth angle. Note that Eplane / H-plane patterns are not available when the array elements are verticalmonopoles. Patterns can be plotted in polar, rectangular, or volumetric (3-D) form,
and patterns can be saved as data files. Select the pattern type and parameters with
the Pattern Type select button.
The Array Amplitude Distribution window allows you to choose from fourcommonly-used amplitude distributions, or to read amplitude data from a data file:

45




Uniform
Chebyshev

Taylor

Cosine on a pedestalData Fileuniform amplitude distribution
Chebyshev amplitude taper for a specified
sidelobe level
Taylor amplitude taper for a specified
sidelobe level and n-bar parametercosine on a pedestal distribution of the formC  1  C  cos   x / L amplitude data is read from a specified data
file

Select one of the five amplitude distribution options by clicking the appropriate
button. For the Chebyshev distribution the desired sidelobe level must also beentered as a positive value in dB. The Chebyshev coefficients are computed using
the highly accurate and efficient algorithm discussed in reference [18]. The Taylor
distribution option requires sidelobe level as well as the n-bar parameter to beentered; the n-bar parameter must be in the range from 2 to 6. The Taylor
coefficients are computed using the algorithm of reference [19], which is much
more accurate and efficient for large arrays than the null-matching or aperturesampling techniques. The cosine-on-a-pedestal distribution requires entry of thepedestal height, C, in negative dB. Data read from an ASCII data file should be inabsolute (not dB) voltage or current form (not power), with one line for eachelement in the array. If the size of the array is larger than the number of elements inthe specified data file, the unspecified element amplitudes will be set to zero. The
elements are counted by rows along the x-dimension, from left to right. You also
have the option of adding gaussian distributed zero-mean random errors to any
amplitude distribution. This is done by specifying the rms value (or standard
deviation) of the errors in dB; specifying a value of zero rms error implies noamplitude error. Entering a new value for the rms error will cause the amplitude
excitation to be re-computed, and updated in the list box. The excitation amplitudes
for the array elements are shown in the list box in the amplitude distribution
window, in absolute form (voltage or current amplitudes), and in dB. The scroll bar
can be used to scroll through the list of excitations. You also have the option ofsaving the amplitude distribution to a data file, by clicking the Save Data button.
The Array Phase Distribution window allows you to choose the phase variation
across the array from one of three options, or to read phase data from a data file.


Broadside BeamSpecify Scan AngleSpecify Phase Shift
Data Filephase set to zero on each element
progressive phase shift to steer beam to a
specified scan angle
progressive phase shift applied
phase data is read from a specified data file46

The Specify Scan Angle and Specify Phase Shift options require entry of the main
beam scan angle, or the interelement phase shift, respectively. Specifying the scanangle for a linear array requires only the elevation angle, while the scan angle for aplanar array requires both the elevation angle and the azimuth angle. Once a phase
distribution has been selected, the routine will calculate the new set of excitation
phases for the array elements, and display them in the list box. The scroll bar can beused to scroll through the list of excitation phases. These quantities will change
when the frequency or element spacing is changed from the linear array window.
Gaussian distributed zero-mean errors can also be added to the phase distribution
by entering a non-zero value for the rms error (standard deviation). Entering a nonzero value causes the phase excitation to be modified, and updated in the list box.
The phase excitation data can also be saved in an ASCII data file by clicking theSave Data button.
The Array Element Selection window allows you to select from one of six
different element types, and to select the polarization of the element when possible:

Isotropic
Wire Dipole

Rectangular WaveguideCircular Waveguide

Rectangular Microstrip PatchCircular Microstrip Patch

ideal isotropic point source elements
thin wire dipole with or without aground plane
rectangular waveguide aperture in aground planecircular waveguide aperture in aground plane
rectangular microstrip patch
elements
circular microstrip patch elements

Select the array element type by clicking the appropriate button. All but theisotropic element option requires entry of the element dimensions and polarization.
The waveguide elements and the microstrip patch elements may be polarized ineither the x direction (the plane of the array), or in the y direction (orthogonal to theplane of the array). The wire dipole may be polarized in the x, y, or z (vertical)
direction, and may include a ground plane spaced a specified distance below theelement. Specify no ground plane by setting the ground plane spacing to zero. The
rectangular waveguide is assumed to have a TE10 mode distribution, while thecircular waveguide is assumed to have a TE11 mode distribution. The patch
elements are assumed to be operating in the dominant resonant mode.
Validation #1
We first consider the directivity of a single element computed from PCAAD andcompared with data from the literature, for each of the possible element types:

47

Element type

Literature

PCAAD 7.0

Isotropic

0.00 dB [1]0.00 dB

Dipole(L = /2)

2.15 dB [1]2.2 dB

Dipole, horizontal(L = /20, /4 above GP)

7.17 dB [1]7.2 dB

Dipole, vertical(L = /20, /4 above GP)

6.63 dB [1]6.6 dB

Rectangular aperture(L = W = 10)

30.1 dB [1]30.0 dB

Circular aperture(radius = 5)29.2 dB [1]29.1 dB

Rectangular patch(L = 0.328, W = 0.219)

7.0 dB [8]7.1 dB

Circular patch(radius = 0.185)

7.1 dB [8]7.1 dB

Validation #2
Consider a five element array of isotropic elements, with 0.4 spacing, uniform
amplitude, and phased to scan at 60. Reference [1] gives the directivity as 7.0 dB;
PCAAD 7.0 gives 7.1 dB.
Validation #3
Consider a 10 element broadside array of isotropic elements with a spacing of /2
and a 26 dB Chebyshev amplitude distribution. Element excitations from [1] arecompared with results from PCAAD:

Element #Reference [1]PCAAD 7.0

1

0.357

0.361

2
3
4
5

0.485
0.706
0.890
1.000

0.489
0.711
0.895
1.000

48

The excitations for elements 6 through 10 are symmetric with these. The
differences in the third decimal place in the above results can be attributed to roundoff error in the calculations in [1], as carrying through those calculations with five
digit accuracy gives exact agreement with the results from PCAAD. The directivity
from PCAAD is 9.5 dB, while in [1] an approximate result of 9.6 dB is given.
Validation #4
Consider a 10 element broadside array of isotropic elements with a spacing of 0.5and a 25 dB Taylor amplitude weighting with n-bar = 2. Element excitations from[19] are compared with results from PCAAD below. Excitations for elements 6
through 10 are symmetric with these.

Element #Reference [19]PCAAD 7.0

1

0.417

0.417

2
3
4
5

0.528
0.709
0.889
1.000

0.528
0.709
0.889
1.000

Validation #5
Consider a 20 element broadside array of isotropic elements with a spacing of /2.
If the elements are uniformly excited the directivity of this array is D0 = N = 20 =13 dB. If phase or amplitude errors are added to the excitations, the directivity will
be reduced according to the formula, D = D0 / (1 + 2 ), where  is the rms error.
Running PCAAD for a rms phase error of 30, or a rms amplitude error of 3 dB,
and averaging over ten trials gives the following results:

no errors(rms error)0D(formula)
13.0 dBD
PCAAD 7.0
13.0 dBphase errors
amplitude errors

30
3 dB

11.9 dB
12.3 dB

11.7 dB
12.4 dBCase

49

D.2. Linear Subarray
This routine is used to plot patterns of a linear
array antenna composed of elements having an
arbitrary element pattern defined by a data file.
This is useful for analyzing arrays of subarrays,or arrays of elements that are not available
through the element menu of the linear arrayroutine. For example, this routine can be used tofind patterns of an array of elements having ameasured element pattern, an array of hornantennas, or an array of subarrays. You canspecify array size (number of elements or
subarrays), the amplitude taper, and the phase
distribution. The element spacing is measured between the centers of adjacentelements (or subarrays). The element pattern is specified only in the plane of thearray, and assumed to be constant in the plane orthogonal to the array. For thisreason the directivity may not be meaningful, and is not calculated. Without loss ofgenerality, the polarization of the elements or subarrays is assumed to be along thex-axis. Pattern plots can be made in the E- and H-planes of the array, or E-theta / Ephi or Co-pol / X-pol patterns can be made at an arbitrary azimuth angle. Patterns
can be plotted in polar, rectangular, or volumetric (3-D) form, and patterns can besaved as data files. Select the pattern type and parameters with the Pattern Typeselect button. As indicated in the picture at the top left of the form, the array is
assumed to lie along the x-axis; if a ground plane is present (depending on theelement type), it is positioned below the array parallel to the x-y plane. The patternis computed using the array factor of the array multiplied by the subarray pattern.
Mutual coupling effects are not included in this routine. The maximum size of thearray is limited to 200 elements.
This routine uses two additional windows to select the array amplitude distribution,and the array phase distribution. The available amplitude and phase options are thesame as those for the linear array module described in Section D.1., and areaccessed by clicking the small Select button to the right of the appropriate text box
for amplitude and phase. The selected amplitude and phase distributions can eachbe modified with gaussian distributed random errors, and can be saved as data files.
The element pattern file is selected with a file dialog box. The element pattern data
is assumed to be in the format of (angle in degrees, pattern in dB), with an angle
range from -90º to 90. The step size of the element data file is arbitrary –numerical interpolation is used when necessary. Pattern files generated by other
PCAAD routines follow this format, allowing other PCAAD routines to be used togenerate element patterns for direct use in this routine. For example, a horn antenna
module can be used to generate a pattern file, which can then be used in this routine
to find the pattern of an array of horns.

50

Validation
Consider an H-plane broadside array of 8 half-wave dipoles in free-space having a
spacing of 0.6, and a uniform amplitude distribution. The pattern can be calculatedusing the linear array analysis routine, which gives a 3 dB beamwidth of 10.6.
This same array can also be considered as a 4 element array, where each element
now consists of a two-element H-plane subarray of two dipoles with a spacing of
0.6. The subarray pattern can be calculated using the linear array routine, andsaved as a data file. This data file can then be used in the linear subarray routine,with N = 4 subarrays, and a spacing of 1.2 between subarrays. The computed
pattern and beamwidth agrees with the pattern obtained from the linear arrayroutine. The pattern is shown below.

Figure 4. Pattern of an array consisting of four two-element H-plane dipole
subarrays.

51

D.3. Uniform Rectangular Array
This routine is used to plot patterns andcompute the directivity of a rectangular planar
array antenna having uniform spacing. You canspecify array size, amplitude taper, phase
distribution, and element type. The number of
elements and the element spacing (center-tocenter) in each plane can be specified
separately. Pattern plots can be made in the Eand H-planes of the array, or E-theta / E-phi or
Co-pol / X-pol patterns can be made at anarbitrary azimuth angle. Note that E-plane / Hplane patterns are not available when the arrayelements are vertical monopoles. Patterns can be plotted in polar, rectangular, orvolumetric (3-D) form, and patterns can be saved as data files. Select the pattern
type and parameters with the Pattern Type select button. The directivity of thearray can also be calculated. As indicated in the picture at the top left of the form,
the array is assumed to lie in the x-y plane; if a ground plane is present (dependingon the element type), it is positioned below the array parallel to the x-y plane. The
pattern is computed using the array factor of the array multiplied by the element
factor. Mutual coupling effects are not included in this routine. Directivity iscomputed by numerical integration of the pattern, which can be very time
consuming for large arrays. The maximum size of the array is limited to 200
elements in each dimension.
As indicated in the picture at the top left of the form, the array is assumed to lie inthe x-y plane; if a ground plane is present (depending on the element type), it ispositioned below the array parallel to the x-y plane. The angle of the grid can be
adjusted to treat arrays having either a rectangular or a triangular grid. The grid
angle is 90 for a rectangular grid; for an equilateral triangular grid the grid angle is60, and the relation between the element spacings in the x and y directions is

d y  d x sin  

3
2

dx .

Like the linear array routine, this routine uses three additional windows to select theArray Amplitude Distribution, the Array Phase Distribution, and the Array
Element Selection. These three windows are described in Section D.1.

52

Validation #1
Consider a 22 broadside array of isotropic elements, with /2 spacings anduniform amplitude excitation. An exact expression for the directivity of broadsideplanar arrays of isotropic sources is given in [5]. This expression gives a directivityof 7.08 dB for this array; PCAAD gives 7.1 dB.
This routine was also validated by checking several special cases of single elements
and linear arrays with the linear array routine. Planar array patterns were also
checked for the correct scan angles and sidelobes.
Validation #2
Consider a 44 planar array of x-polarized rectangular microstrip patches, with atriangular grid of 60, a spacing in the x-direction of 0.5774, and a spacing in they-direction of 0.5. The patch length and width are 0.3. PCAAD 7.0 gives thefollowing results:

Quantity

PCAAD 7.0

3 dB beamwidth in =0 plane

21.7

3 dB beamwidth in =45 plane
3 dB beamwidth in =90 plane
Directivity

22.7
25.1
18.0 dB

These results should be similar to those obtained with an array using a rectangulargrid and filling the same aperture area. For example, a patch array with arectangular grid having 8 elements in the x-direction with a spacing of 0.289 (= 4
 0.5774 / 8), and 4 elements in the y-direction with a spacing of 0.5, yields a
directivity of 18.1 dB.

53

D.4. Uniform Circular Array
This routine is used to plot patterns andcompute the directivity of a circular planar
array. You can specify the radius of the array,element spacing (center-to-center), a radial
amplitude taper, and the element type. The grid
spacing of the elements is rectangular, and theroutine calculates the number of elements thatwill approximately fit within a circular area ofthe specified radius. The amplitude taper isapplied linearly (in dB) in the radial direction,
assuming 0 dB at the center of the array, and anedge taper as specified. The element type isselected by clicking the small Select button to the right of the text box for element
type. Pattern plots can be made in the E- and H-planes of the array, or E-theta / Ephi or Co-pol / X-pol patterns can be made at an arbitrary azimuth angle. Note thatE-plane / H-plane patterns are not available when the array elements are verticalmonopoles. Patterns can be plotted in polar, rectangular, or volumetric (3-D) form,
and patterns can be saved as data files. Select the pattern type and parameters with
the Pattern Type select button. The directivity of the array can also be calculated.
As indicated in the picture at the top left of the form, the array is assumed to lie inthe x-y plane; if a ground plane is present (depending on the element type), it ispositioned below the array parallel to the x-y plane. The pattern is computed using
the array factor of the array multiplied by the element factor. Mutual coupling
effects are not included in this routine. Directivity is computed by numericalintegration of the pattern, which can be very time consuming for large arrays. Thereis no limit to the maximum size of the array, but the directivity calculation will be
unacceptably time consuming for more than about 100 elements.
Validation #1
First consider a circular planar array with an outer radius of 1 and an element
spacing of 0.6, with isotropic elements. This results in a uniform rectangular gridof 33 elements, for which the circular array routine gives a directivity of 11.6 dB,
and a half-power beamwidth of 30.6. The rectangular planar array routine can beused for the same geometry, and gives identical results.
Validation #2
Next consider a circular planar array with an outer radius of 5 and an element
spacing of 0.5, with rectangular microstrip patches of size 0.3  0.3. This
results in an array of 317 elements. For a uniform amplitude distribution, PCAAD
7.0 gives a directivity of 30.1 dB for this array. Using the formula D  4 R / 
gives a value of 29.9 dB.
2

54

2

2

D.5. Arbitrary Planar Array
This routine is used to plot patterns andcompute directivity of a planar array ofelements having arbitrary locations in the x-yplane, and arbitrary excitations. This can be
useful for treating arrays that do not conform to
the linear or planar apertures of the other arrayroutines in PCAAD. A data file is used to
specify element coordinates, excitation
amplitude, and excitation phase. You canspecify the element type from the same
selection of elements available in the other arrayroutines. Pattern plots can be made in the E- andH-planes of the array, or E-theta / E-phi or Co-pol / X-pol patterns can be made at
an arbitrary azimuth angle. Note that E-plane / H-plane patterns are not available
when the array elements are vertical monopoles. Patterns can be plotted in polar,
rectangular, or volumetric (3-D) form, and patterns can be saved as data files.
Select the pattern type and parameters with the Pattern Type select button. The
directivity of the array can also be calculated. As indicated in the picture at the top
left of the form, the array is assumed to lie in the x-y plane; if a ground plane ispresent (depending on the element type), it is positioned below the array parallel tothe x-y plane. The pattern is computed using the array factor of the array multipliedby the element factor. Mutual coupling effects are not included in this routine.
Directivity is computed by numerical integration of the pattern, which can be verytime consuming for large arrays. The maximum size of the array is limited to 200
elements in each dimension.
The element data file is selected with a file dialog box. The data file should havethe format of (x-coord in cm, y-coord in cm, amplitude, phase in degrees), with one
line for each element. The amplitude data is in absolute voltage or current form (notin dB). The routine uses an additional window to select the array element type,accessed by clicking the Select button to the right of the text box.
Validation
The 44 patch array with a triangular grid that was treated in Validation #2 of
Section D.3 was used here as well. The data file listing the element coordinates andexcitations for this array is listed below (this file, ARRAY4X4.DAT, is suppliedwith PCAAD 7.0):0.
0.57741.154
1.732
0.28870.8661

0.0
0.0
0.0
0.0
0.5
0.5

1.0
1.0
1.0
1.0
1.0
1.0

0.0
0.0
0.0
0.0
0.0
0.0
55

1.4442.02090.
0.57741.154
1.732
0.28870.86611.444
2.0209

0.5
0.5
1.0
1.0
1.0
1.0
1.5
1.5
1.5
1.5

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

Results from this routine are in agreement with those obtained in Section D.3.

56

D.6. Infinite Printed Dipole Array
This routine computes the input impedance ofan infinite array of dipole antennas printed on a
grounded dielectric substrate using the fullwave solution described in reference [12]. It
uses the exact Green’s function for the dielectric
substrate, and includes all mutual coupling
effects. It can be used to treat dipoles in freespace above a ground plane by using a substratedielectric constant of 1.0 The number ofpiecewise sinusoidal expansion modes on each
dipole can also be chosen; this should be an odd
number since the dipoles are assumed to becenter-fed. One to three modes is usually sufficient for accurate results.
The required array parameters include the element spacings in the E and H planes,
the dipole length and width, and the substrate thickness and dielectric constant.
Input impedance data will be calculated for a fixed azimuth scan angle, and forelevation angles from zero to 90. You must enter both the azimuth angle and theelevation step size. Since this is a full-wave calculation, it can be time consuming
on slow computers, so it is helpful to not specify too small of a step size, to avoid
unreasonably long run times. The input impedance at each elevation angle is listed
in the list box as it is computed. Scroll through the list using the scroll bar. You
also have the option, from the Results tree, of plotting the impedance data on aSmith chart plot or a VSWR/Return Loss plot, or saving the data to a file.
Validation
Consider an infinite array with an E- and H-plane spacing of 5 cm, a dipole lengthof 3.9 cm, a dipole width of 0.02 cm, a substrate with a thickness of 1.9 cm and adielectric constant of 2.55, and a frequency of 3 GHz. This example corresponds tothe first case considered in [12]. For  = 0, with three expansion modes per dipole,
we obtain the following results:

Theta

Zin - Reference [12]Zin - PCAAD 7.0

0
30
60
90

74.8 + j 2.7 
73.3 + j 37.3 
40.7 + j 1.9 
0.10 + j 55.7 

74.8 + j 2.8 
73.4 + j 37.3 
40.7 + j 2.0 
0.10 + j 55.7 

57

D.7 Linear Array Pattern Synthesis
This routine is used to synthesize the pattern ofa uniform linear array using the WoodwardLawson method [1], [2]. You can specify arraysize, element spacing, and frequency. The
pattern values to be synthesized are specified at
discrete pattern angles according to the
Woodward-Lawson algorithm. The amplitude
and phase excitation for each element arecomputed. Planar patterns may be plotted forthe array plane, or a volumetric (3-D) pattern
may be plotted. The array elements are assumed
to be isotropic sources. The pattern is computed
using the array factor of the array; mutual coupling effects are not included. A
property of the Woodward-Lawson synthesis method is that it will provide a patternthat exactly matches the desired pattern at the sample angles. The maximum size ofthe array is limited to 200 elements.
Begin by entering the operating frequency, the number of elements in the array, andthe element spacing. The routine will calculate discrete angles where the pattern
will be sampled, and list these in the scroll box. The desired pattern value (in dB)
can then be filled in the text box for each angle. Use the scroll bar to scroll throughthe set of samples. Select the pattern type and parameters with the Pattern Typeselect button. The routine will then compute the required amplitude and phase
necessary to reproduce the desired pattern at the sample values, list these values in a
scroll box, and compute the resulting synthesized pattern. From the Results tree
you can plot the patterns of the array by clicking the appropriate option, or savethe patterns to data files. The calculated pattern is not normalized (other PCAAD
routines normalize the maximum pattern value to 0 dB), in order to compare thesynthesized pattern with the specified pattern values. For this reason, it may benecessary to adjust the maximum value of the pattern plot to view the entire pattern.
When plotting the pattern of sample points, it may be helpful to set the Line Style
to Data Points Only, via the Plot Options routine.
Validation
Consider the synthesis of a sector pattern with an 11 element array having 0.5
spacing. The sector pattern is defined as 0 dB between the angles of -45 and 45,and -60 dB elsewhere. The following pattern values are entered at the sample points
in the routine:
65.4
46.7
33.1
21.3

-60 dB-60 dB
0 dB
0 dB

58

10.5
0.0

0 dB
0 dB

The resulting synthesized pattern is plotted below. Note that the pattern values
match those listed above.

Figure 5. Synthesized sector pattern for an 11 element array. The specified
pattern samples are shown as blue circles.

59D.8. Grating Lobe Diagram
This routine plots a grating lobe diagram for aperiodic planar array antenna, including theoptional plotting of surface wave circles. A
grating lobe diagram can be very helpful for
determining the presence and location of grating
lobes, and the movement of grating lobes withscan angle. In conjunction with surface wave
circles, the grating lobe diagram can be used to
predict the location of scan blindness angles inprinted array antennas, as discussed in reference[12], or other arrays having a structure that
supports guided waves. This routine provides azoom control to adjust the size of u  v space that is plotted, and a convenient
readout in u  v and    coordinates of the mouse cursor when it is positioned
in the visible space region of the grating lobe diagram.
Begin by entering the array operating frequency, and the element spacings(center-to-center) in the horizontal and vertical directions. Next, enter the arraygrid angle. A grid angle of 90º corresponds to a rectangular array, while a grid
angle of 60º corresponds to an array with a hexagonal grid. (For a hexagonal
grid, the maximum element spacings with no grating lobes in visible space are
0.5774λ (horizontal), 0.5λ (vertical)). If you want to plot surface wave circles,
enter a non-zero value for the normalized surface wave propagation constant;this can be computed using the Surface Waves routine under the Transmission
Lines menu. Click the Plot Circles button to draw the grating lobe circles; theplot will automatically be updated if new data is entered, or if the zoom scroll
bar is used. By default, the routine plots a segment of the u  sin  cos  ,v  sin  sin  plane from 3  u  3 and 3  v  3 . The zoom scroll bar
near the top of the window can be used to adjust this range. The visible space
region of the grating lobe diagram occurs for u  v  1 , and is colored inlight gray on the plot. The grating lobe circles are drawn in blue, and the surface
wave circles are drawn as red circles. Moving the mouse cursor through thevisible space region of the diagram will cause the readout box near the middle of
the window to give a display of the cursor position in u-v space, as well as thecorresponding    scan angle. In this way, you can easily determine the scanangle at which a grating lobe enters visible space, or the angle at which a scan
blindness will occur. More accuracy can be obtained by zooming in on thevisible space region by using the zoom scroll bar.
2

60

2

Validation
Consider an example from [12], for an array of printed dipoles with E- and H-planespacings of /2, on a dielectric substrate with  r  12.8 and a thickness of 0.06.
The array grid is rectangular. The PCAAD 7.0 Surface Waves routine gives anormalized surface wave propagation constant of 1.285816. Plotting the grating
lobe diagram shows that no grating lobes will be present in visible space. Using the
cursor to move to the intersection of a surface wave circle and the E-plane scanplane (v = 0) indicates a scan blindness will occur at 45, in close agreement withthe result of 46 from the full-wave solution in [12].

61D.9. Effect of Random Array Errors
The effect of random amplitude and phaseerrors on the pattern of an array is to raise thesidelobe level and decrease the gain. Thisroutine computes the average sidelobe level andaverage loss in gain for an array having random
amplitude and phase errors. The routine also
includes the effect of failed elements in anarray, and the quantization phase error andquantization lobe level due to phase shifter
quantization. This routine is based on resultsfrom [25].
Begin by entering the rms amplitude error, in +dB, followed by the rms phase error,
in degrees. Each of these errors is assumed to have a normal distribution with zeromean. The phase error may be positive or negative. If desired, also enter thepercentage of elements in the array considered to have failed (this value should beless than 100%). Click the Compute button to calculate the resulting average
sidelobe level, and loss in gain, due to the entered errors and failed elements.
Note that the average sidelobe level is given relative to isotropic. The arraydirectivity must be known to convert this value to a sidelobe level relative to themain beam of the array. For example, if the average sidelobe level due to errors is 5
dBi, and the error-free directivity of the array is 23 dB, then the sidelobe level
relative to the main beam would be 5 – 23 = -18 dB. Note that this is a residual
sidelobe level caused by errors, in contrast to the design sidelobe level that isdetermined by the amplitude taper. The resulting sidelobe level will be the larger ofthese two levels. Thus, for the example above, if the array were designed for -13 dB
sidelobes, the average error sidelobe level of -18 dB would probably not be
noticeable. If, however, the array were designed for -25 dB sidelobes, the actual
sidelobe level in the presence of errors would be in the range of -18 dB.
A separate frame is provide for phase shifter quantization effects. Use the list box toenter the number of bits for the phase shifters. Once a value is selected, the peakphase error (+/- degrees) will be displayed, along with the rms phase error (+/degrees). The rms phase error value is also transferred to the phase error box in the
excitation errors frame, for convenience. The level of the quantization lobe is also
displayed – note that this value is given relative to the main beam of the array. The
quantization lobe is due to the periodic phase error that is introduced when digitalphase shifters are used in an array. This lobe is often higher than nearby sidelobes,
especially when a small number of phase shifter bits are used. See [25] fortechniques to reduce the effects of quantization lobes. Setting the phase shifter bits
to Off turns off the phase shifter calculation functions.

62

Validation
The average sidelobe level due to amplitude and phase errors, relative to isotropic,
is given by,

SLLi   2   2 ,
  dB  / 20

where    10 

 1 is the rms amplitude error, and   is the rms phaseerror (in radians). Direct calculations shows that a 10 rms phase error leads to an
average isotropic sidelobe level of -15.2 dB, and a 1.5 dB rms amplitude error leads
to an average isotropic sidelobe level of -14.5 dB. PCAAD gives -15.2 dB, and 14.5 dB, respectively, for these two cases. If 50% of the array elements have failed,the gain is seen to be reduced by 3 dB, as expected.

63

E. The Aperture Antennas Menu
These routines are used for the analysis of various aperture antennas. Patterns anddirectivity can be calculated for line sources, rectangular and circular apertures, E
and H-plane sectoral horns, pyramidal horns, corrugated pyramidal horns, conicalhorns, and corrugated conical horns. New in PCAAD 7.0 are fast and accurate
analysis routines for parabolic reflectors, offset parabolic reflectors, and sphericalreflectors, based on the Jacobi-Bessell expansion technique described in reference[29]. These routines calculate patterns, directivity, and aperture efficiencies, andallow feed displacements for limited beam scanning. Prime focus parabolicreflectors can also treated using an idealized feed pattern of the cos  form,
providing aperture efficiency and directivity [1]. Also new is a routine to calculate
the beam efficiency of a variety of aperture antennas.
nWaveguide horns are analyzed by the usual assumption of a waveguide field
distribution in the aperture plane multiplied by a quadratic phase factor. For
sectoral and pyramidal horns this results in closed-form expressions for patterns
and directivity in terms of Fresnel integrals [1], [2]. No such results are available
for the conical or corrugated conical horns, so these cases are treated using a fairly
efficient numerical integration technique.
The phase center is calculated for sectoral, pyramidal, corrugated pyramidal,
diagonal, conical, and corrugated conical horn antennas using the derivative
method with numerical integration, described in reference [28]. The phase center ofan antenna is defined as the apparent center (along the axis of the main beam) of thecircular far-zone phase fronts. For an ideal point source, the phase center is locatedat the point source. For small apertures with uniform phase, the phase center islocated at the center of the aperture. For antennas with non-uniform phase,
however, the phase center may be behind or in front of the aperture, and isgenerally different for different azimuthal planes. In many cases a unique phasecenter cannot be defined. The phase center location calculated in PCAAD may not
be accurate for horns with very wide angles or very large phase errors

64E.1. Line SourceThis routine calculates the pattern anddirectivity for a traveling wave electric line
source antenna on the z-axis. Examples ofsuch antennas include long wire antennas,
dielectric rod antennas, electrically long slot
antennas, and leaky wave antennas. The phase
constant and attenuation constant can be
specified, and the antenna can be fed at either
the end or at the center of the line. A sin element pattern factor can also be included, if
desired. Patterns are computed using theclosed-form expressions found in reference [1]. Directivity is also calculatedusing closed-form expressions.
Begin by entering the frequency, line source length, and phase and attenuation
constants. Select the pattern type and parameters with the Pattern Type selectbutton. Click the Compute button to calculate the patterns and directivity. The
specified patterns may be plotted by clicking the appropriate option in the
Results tree, or saved to data files.
Validation
Consider a traveling wave end-fed wire antenna with a length of 5. The phase
constant will be close to 360/, and the attenuation may be neglected. Since
this is a wire antenna, a sin  factor should be used. Reference [1] gives a beammaximum angle of 22.0 from the axis of the wire, in agreement with the patterncalculated by PCAAD. The free-space directivity from [1] is 10.7 dB, also inagreement with PCAAD.

65

E.2. Rectangular ApertureThis routine computes the patterns anddirectivity of a rectangular aperture antenna
having a uniform phase distribution and either
uniform or cosine tapered amplitude
distributions in the E- and H-planes. The
patterns are computed using closed-form
expressions from references [1], [2]. For
accuracy for small apertures, the directivity is
calculated by numerical integration when theaperture is smaller than 10λ on a side. For
electrically large apertures the usual directivity
approximation of 4 A / (with theappropriate aperture efficiency) is used. The aperture is assumed to be located in an
infinite ground plane, polarized in the y-direction, and the radiation is assumed to
be one-sided. This analysis assumes an equivalent magnetic current only, and sodoes not include a 1  cos   obliquity factor, in contrast to the horn antenna
2

analyses.
Begin by entering the frequency, and the E-plane and H-plane aperture dimensions.
Then select the amplitude taper using the pull-down menu. You may choose tohave either a uniform or a cosine taper in either of the two dimensions of theaperture (a TE10 waveguide mode corresponds to uniform in y, cosine in x). Selectthe pattern type and parameters with the Pattern Type select button. Click theCompute button to compute the patterns and directivity. The specified patterns
may be plotted by clicking the appropriate option in the Results tree, or saved todata files.
Validation #1
An open-ended X-band waveguide has an E-plane aperture dimension of 1.016
cm, and an H-plane aperture dimension of 2.286 cm. At 10 GHz, the linear arrayroutine of PCAAD, with one waveguide element in the array, gives a directivityof 6.3 dB. The rectangular aperture routine, with a uniform amplitude taper inthe E-plane and a cosine taper in the H-plane, gives a directivity of 6.3 dB.
Validation #2
A rectangular array of 24 x 24 microstrip patches, with lengths and widths of
0.3λ, element spacings of 0.5λ, and uniform amplitude and phase distributions,yields a directivity of 32.6 dB (using the PCAAD planar array routine). The
rectangular aperture routine, for an aperture of 12λ x 12λ with uniform
amplitude tapers in both directions, gives a directivity of 32.6 dB.

66

E.3. Circular ApertureThis routine computes the patterns anddirectivity of a circular aperture antenna having
a uniform phase distribution and either uniform
or a parabolic tapered amplitude distributions in
the radial plane. The patterns are computed
using closed-form expressions from references[1], [2]. For accuracy for small apertures, thedirectivity is calculated by numerical integration
when the aperture is smaller than 10λ in
diameter. For electrically large apertures theusual directivity approximation of 4 A / (with the appropriate aperture efficiency) is used. The aperture is assumed to belocated in an infinite ground plane, polarized in the y-direction, and the radiation isassumed to be one-sided. This analysis assumes an equivalent magnetic current
only, and so does not include a 1  cos   obliquity factor, in contrast to the horn2antenna analyses.
Begin by entering the frequency, and the aperture diameter. Then select theamplitude taper using the pull-down menu. You may choose to have either auniform or a parabolic taper in the radial direction (the parabolic taper has amaximum at the center of the aperture, and is zero at the edge). Select the pattern
type and parameters with the Pattern Type select button. Click the Computebutton to calculate the patterns and directivity. The specified patterns may beplotted by clicking the appropriate option in the Results tree, or saved to data
files.
Validation
A circular planar array of diameter 10λ, with microstrip patches having lengths
and widths of 0.3λ, element spacings of 0.5λ, and uniform amplitude and phase
distributions, yields a directivity of 30.1 dB (using the PCAAD circular planar
array routine). The circular aperture routine, for an aperture of 10λ diameter anda uniform amplitude taper, gives a directivity of 30.0 dB.

67

E.4. E-plane Sectoral Horn
This routine computes the patterns anddirectivity of an E-plane sectoral hornantenna, using closed-form expressions fromreference [1]. The directivity expression has
been corrected according to reference [17].
The phase center, for both principal planes, isalso computed. The phase center is measured
back from the aperture, toward the apex of thehorn.
Begin by entering the frequency, the E-plane
aperture dimension, the H-plane aperture
dimension, and the axial length of the horn. This length is the distance from theimaginary apex of the horn to the mouth of the horn (not the slant length). Selectthe pattern type and parameters with the Pattern Type select button. Click theCompute button to calculate the patterns and related antenna parameters. The
routine prints out the maximum phase error at the edge of the aperture (relative
to the center of the aperture), the optimum E-plane aperture dimension, thedirectivity of the horn, and the E- and H-plane phase centers. The optimum
aperture dimension is the dimension that will result in maximum directivity for ahorn of the same length. The specified patterns may be plotted by clicking theappropriate option in the Results tree, or saved to data files.
Validation
Consider an E-plane sectoral horn at 3 GHz with an E-plane aperture dimension of
27.5 cm, an H-plane aperture dimension of 5 cm, and an axial length of 60 cm.
Results for this example can be found in [1], and are compared with results fromPCAAD below:

Quantity

Reference [1]PCAAD 7.0

Max. phase error
Directivity

56.7
11.1 dB-5 dB (approx)

56.7
11.1 dB-4.1 dB

H-plane pattern at 60

68

E.5. H-plane Sectoral Horn
This routine computes the patterns anddirectivity of an H-plane sectoral horn antenna,using closed-form expressions from reference[1]. The phase center, for both principal
planes, is also computed. The phase center ismeasured back from the aperture, toward theapex of the horn.
Begin by entering the frequency, the E-plane
aperture dimension, the H-plane aperture
dimension, and the axial length of the horn.
This length is the distance from the imaginary
apex of the horn to the mouth of the horn (not the slant length). Select thepattern type and parameters with the Pattern Type select button. Click theCompute button to calculate the patterns and related antenna parameters. The
routine prints out the maximum phase error at the edge of the aperture (relative
to the center of the aperture), the optimum E-plane aperture dimension, thedirectivity of the horn, and the E- and H-plane phase centers. The optimum
aperture dimension is the dimension that will result in maximum directivity for ahorn of the same length. The specified patterns may be plotted by clicking theappropriate option in the Results tree, or saved to data files.
Validation
Consider an H-plane sectoral horn at 3 GHz with an E-plane aperture dimension of
2.5 cm, an H-plane aperture dimension of 55 cm, and an axial length of 60 cm.
Results for this example can be found in [1], and are compared with results fromPCAAD below:

Quantity

Reference [2]PCAAD 7.0

Max. phase error
Directivity
E-plane pattern at 60

226.9
8.76 dB-3.5 dB (approx)

226.9
8.8 dB-3.2 dB

H-plane pattern at 30

-15 dB (approx)-15.7 dB69

E.6. Pyramidal Horn
This routine computes the patterns anddirectivity of a pyramidal horn antenna, using
closed-form expressions from reference [1].
For horns with small apertures, accuracy isimproved by computing the directivity bynumerical integration of the pattern. The phasecenter, for both principal planes, is also
computed.
Begin by entering the frequency, the E and Hplane aperture dimensions, and the axial lengthsof the horn in the E and H planes. The axial
lengths are the distances from the imaginary apex of the horn in the E and H planes
to the mouth of the horn (not the slant lengths). Select the pattern type andparameters with the Pattern Type select button. Click the Compute button tocompute the patterns and related antenna parameters. The routine prints out the
maximum phase errors at the edges of the aperture (relative to the center of theaperture), the optimum aperture dimensions, the directivity of the horn, and the Eand H-plane phase centers. The specified patterns may be plotted by clicking theappropriate option in the Results tree, or saved to data files.
Validation #1
Consider a pyramidal horn at 3 GHz with an E-plane aperture dimension of 27.5
cm, an H-plane aperture dimension of 55 cm, and an axial length of 60 cm. Results
for this example can be found in [1], and are compared with results from PCAAD
below:

Quantity

Reference [1]PCAAD 7.0

Max. phase error (E-plane)
Max. phase error (H-plane)
Directivity

56.7
226.9
18.8 dB

56.7
226.9
18.8 dB

Validation #2
Consider a pyramidal horn at 3.333 GHz with an E-plane aperture dimension 24cm, an H-plane aperture dimension of 32.41 cm, an E-plane axial length of 40.41
cm, and an H-plane axial length of 44.59 cm. Reference [17] gives a directivity of
18.6 dB for this example; PCAAD gives 18.5 dB.

70

Validation #3
A standard gain horn has an E-plane aperture dimension of 8.3 cm, an H-plane
aperture dimension of 10.2 cm, an E-plane axial length of 22.7 cm, and an H-plane
axial length of 24.1 cm. At 24 GHz, the measured gain is 24.7 dB; PCAAD gives a
directivity of 24.7 dB. Comparisons with measurements of other standard gainhorns typically are in agreement to within about 0.1 dB.

71

E.7. Diagonal Horn
The diagonal horn antenna has a square
aperture with the exciting electric fieldoriented along a diagonal axis. The main beamof the diagonal horn has circular symmetry,
and the principal plane patterns have low
sidelobes, with no cross-polarization. Further
discussion of the diagonal horn antenna can befound in [27].
Begin by entering the frequency, the (square)
aperture dimension, and the axial length of thehorn. Select the pattern type and parameterswith the Pattern Type select button. Click the Compute button to compute thepatterns and related antenna parameters. The routine prints out the maximum phaseerror at the edges of the aperture (relative to the center of the aperture), thedirectivity of the horn, and the E- and H-plane phase centers (which are always
identical). The phase center is measured back from the aperture, toward the apexof the horn. The specified patterns may be plotted by clicking the appropriate
option in the Results tree, or saved to data files.
Validation
A square diagonal horn with a width of 12.7 cm, and a very long length, isdescribed in [27]. At 16.5 GHz the 3 dB beamwidth is given as 8.5 in bothprincipal planes and the diagonal planes. PCAAD gives a 3 dB beamwidth of 8.3.
Reference [27] lists the aperture efficiency of the diagonal horn as 81% which,given the aperture area, yields a directivity of 27.0 dB. PCAAD gives 27.0 dB. The
patterns show relatively high cross-polarization lobes of -15 dB in the diagonalplanes.

72

E.8. Corrugated Pyramidal Horn
This routine computes the patterns anddirectivity of a corrugated pyramidal hornantenna, using closed-form expressions fromreference [1]. For horns with small apertures,
accuracy is improved by computing thedirectivity by numerical integration of thepattern. The phase center, for both principal
planes, is also computed.
Begin by entering the frequency, the E and Hplane aperture dimensions, and the axial lengthsof the horn in the E and H planes. The axial
lengths are the distances from the imaginary apex of the horn in the E and H planes
to the mouth of the horn (not the slant lengths). Select the pattern type andparameters with the Pattern Type select button. Click the Compute button tocompute the patterns and related antenna parameters. The routine prints out the
maximum phase errors at the edges of the aperture (relative to the center of theaperture), the optimum aperture dimensions, the directivity of the horn, and the Eand H-plane phase centers. The phase center is measured back from the aperture,
toward the apex of the horn. The specified patterns may be plotted by clicking
the appropriate option in the Results tree, or saved to data files.
Validation
A corrugated pyramidal horn has E- and H-plane aperture dimensions of 24.2 cm,
and E- and H-plane axial lengths of 57.6 cm. Reference [21] provides measured 3
dB beamwidths versus frequency, along with independent calculations. This data iscompared with results from PCAAD below:

Frequency(GHz)

Measured
Beamwidth [21]Calculated
Beamwidth [21]PCAAD
Beamwidth

4.5
6.0
7.2

18
15
13

19.3
14.9
12.8

19.2
14.8
12.7

73

E.9. Conical Horn
This routine computes the patterns anddirectivity of a conical (TE11 mode) hornantenna. The principle plane patterns arecomputed using an efficient numericalintegration algorithm that includes the quadraticphase error term. The phase center, for bothprincipal planes, is also computed.
Begin by entering the frequency, the aperture
radius, and the axial length of the horn. This
length is the distance from the imaginary apexof the horn to the mouth of the horn (not theslant length). Select the pattern type and parameters with the Pattern Type selectbutton. Click the Compute button to compute the patterns and related antenna
parameters. The routine prints out the maximum phase error at the edge of theaperture (relative to the center of the aperture), the directivity of the horn, and theE- and H-plane phase centers. The phase center is measured back from theaperture, toward the apex of the horn. The specified patterns may be plotted byclicking the appropriate option in the Results tree, or saved to data files.
Validation
Consider a conical horn at 5 GHz with an aperture radius of 12 cm and an axial
length of 48.6 cm. Results from reference [4] are compared with PCAAD:

Quantity

Reference [4]PCAAD 7.0

Max. phase error
Directivity

86.4
20.4 dB-13.4 dB
-15.0 dB

88.920.3 dB-12.9 dB
-14.8 dB

E-plane pattern at 20
H-plane pattern at 20

74

E.10. Corrugated Conical Horn
This routine computes the patterns anddirectivity of a corrugated conical (HE11 mode)
horn antenna. The principle plane patterns arecomputed using an efficient numericalintegration algorithm that includes the quadraticphase error term. The phase center, for bothprincipal planes, is also computed.
Begin by entering the frequency, the aperture
radius, and the axial length of the horn. This
length is the distance from the imaginary apexof the horn to the mouth of the horn (not theslant length). Select the pattern type and parameters with the Pattern Type selectbutton. Click the Compute button to compute the patterns and related antenna
parameters. The routine prints out the maximum phase error at the edge of theaperture (relative to the center of the aperture), the directivity of the horn, and theE- and H-plane phase centers (which are always identical). The phase center ismeasured back from the aperture, toward the apex of the horn. The specified
patterns may be plotted by clicking the appropriate option in the Results tree, or
saved to data files.
Validation
Consider a corrugated conical horn at 5 GHz with an aperture radius of 12 cm andan axial length of 48.6 cm. Results from reference [4] are compared with PCAAD:

Quantity

Reference [4]PCAAD 7.0

Max. phase error
Directivity

86.4
19.9 dB-10 dB-10 dB

88.9
19.4 dB-9.9 dB-10.3 dB

E-plane pattern at 17.5
H-plane pattern at 17.5

75

E.11. Parabolic Reflector (Approximate Model)This routine analyzes the performance of aprime-focus parabolic reflector antenna, under
the assumption that the feed antenna has arotationally symmetric power pattern that can beapproximated as cos  . In this case, simple(but exact) expressions can be obtained for the
spillover and taper efficiencies, as discussed inreference [1]. The effect of surface roughness
can also be included.
nBegin by entering the frequency, the f / D ratio,
the dish diameter, and the rms surface roughness. The surface roughness dimension
has a default value of zero. Next, specify the feed pattern in one of three forms:
enter either the 3 dB beamwidth, the 10 dB beamwidth, or the actual value of n = 2,
4, 6, or 8 for a power pattern of the form cos  . If you specify a beamwidth, theroutine will calculate the closest value of n that approximates this beamwidth, andwill display the value of n that it will use. The routine computes the spillover, taper,roughness, and total aperture efficiencies, then computes the directivity of theantenna. The 3 dB beamwidth is calculated from the directivity.
n

Validation
A parabolic reflector has a diameter of 1000 cm, an f / D ratio of 0.5, a feed patternwith n = 2, and no surface roughness. The operating frequency is 3 GHz. This
example is considered in [1], and compared with PCAAD below:

Quantity

Reference [1]PCAAD 7.0

Spillover efficiency
Taper efficiency
Aperture efficiency
Directivity

0.784
0.957
0.750
48.7 dB

0.784
0.957
0.751
48.7 dB76

E.12. Symmetric Parabolic Reflector Analysis
This routine computes the patterns of asymmetric parabolic reflector antenna using
the Jacobi-Bessel series method described in[29]. This method is rigorous, but does not
require integration of the aperture for eachpattern angle, and therefore is extremely fastcomputationally. It provides accurate patterns
at wide angles, for a variety of feeds,
including displaced feeds. In addition tocomputing co- and cross-pol patterns, thisroutine can also provide plots of the aperture
amplitude distribution, the aperture phase
distribution, the reflector geometry, the antenna gain, and the losses associatedwith spillover, amplitude taper, polarization loss, surface roughness, and feed
blockage. The user can choose from a set of built-in feed antennas, including an
ideal cos  pattern, a dipole, a pyramidal horn, or circular horns. The feedpattern may also be specified using data files for the E- and H-plane patterns.
qBegin by entering the frequency, the f / D ratio, the dish diameter, and thesurface roughness for the reflector (the surface roughness dimension has adefault value of zero). Next, select the feed antenna from one of the five choices
using the pull-down list, or select Feed From Data Files to use external feedpattern data. Depending on the choice of feed, additional parameters will be
specified for the feed dipole or horn dimensions. For the ideal cos  (field)
feed, specify either the exponent, q>0, or specify the -10 dB angle of the feed(the half-angle, in degrees). When specifying the feed pattern from data files, thefeed pattern data must be in the format of (angle in degrees, pattern amplitude indB), with delimiters of either commas, spaces, or tabs, with an angle range that
extends at least from -90º to 90º. Optionally, feed pattern phase can be included
as (angle in degrees, pattern amplitude in dB, pattern phase in degrees). The step
size of the feed pattern data file is arbitrary - numerical interpolation is used
when necessary. Pattern files generated by other PCAAD routines follow thisformat, allowing other PCAAD routines to be used to generate feed patterns for
direct use in this routine. For example, the array antenna module can be used togenerate E- and H-plane feed pattern files, which can then be used in this routine
to find the secondary patterns of the reflector.
q

Next, specify the displacement of the feed from the focal point of the reflector.
The feed may be displaced laterally (the x or y directions), or axially (the z
direction). The displacement is limited to less than 2λ in the lateral directions to
avoid long computation times (and because large displacements are generally
not used in practice due to large drops in gain). A lateral displacement will resultin a shift of the main beam in the opposite direction, while a axial displacement
77

will result in de-focusing of the main beam. Note that the coordinate reference
point for the feed is at the center of the dipole, or at the center of the aperture forhorns. This point may not coincide with the true phase center of the feed
antenna. Aperture blockage by the feed can also be specified, if desired. Feedblockage is computed by eliminating a central disk of the aperture excitation
during numerical integration. The feed polarization can be chosen to be either
vertical (y direction), or horizontal (x direction).
Select the pattern type and parameters with the Pattern Type select button.
Pattern plots can be made in the E- and H-planes of the reflector, or E-theta / Ephi or Co-pol / X-pol patterns can be made at an arbitrary azimuth angle. 3-Dvolumetric patterns are not available because the beamwidth of most reflectors
is too narrow to be plotted in volumetric form. Since most reflector antennas
have narrow beamwidths, the elevation step size should be small, typicallybetween 0.01º and 0.1º. Also specify the maximum angular range of theelevation pattern plot. Because of the narrow beamwidth of most reflector
antennas, the maximum angular range of the pattern calculation usually does notneed to exceed a few degrees. Unlike other methods of reflector antenna
analysis, the Jacobi-Bessel method does not use appreciably more computer
time as the pattern step size, or pattern angle range, is increased.
After clicking the Compute button, the patterns will be calculated and various
results will be presented. On the right side of the window a loss budget for thereflector will be given, starting with the maximum directivity that is available
from the aperture area of the reflector. Below this is listed the spillover loss, theamplitude taper loss, the phase error loss, the surface roughness loss, and thefeed blockage loss. The net result is the Estimated Gain of the reflector. Notethat several of these figures are only estimates when feed displacements are nonzero because of the complicated interaction between phase, amplitude, main
beam position, and the resulting gain, and the fact that these losses are computed
independently of each other. The gain figure listed on the left side of thewindow, however, is based on the rigorously computed far-field pattern, andshould be accurate. Note that both gain figures are for the gain at the main beam
position; when an axial offset is present, the main beam often has a "dip" so thatthe maximum gain does not occur at the center of the main beam. The beam
deformation factor, subtended half-angle of the dish, and the aperture efficiency(based on the maximum directivity of the aperture and the computed gain), is
also listed on the left side of the window.
Other results are available as listed in the Results tree. Plot the patterns of thereflector, or save the patterns to a data file, by clicking the appropriate item in
the Results tree. Click Co-pol Amplitude, X-pol Amplitude, or Co-pol Phase
to plot the corresponding data for the aperture distribution of the reflector. The
geometry of the reflector antenna may be viewed by clicking Show Geometry.
Information on the solution (including the number of term used in the JacobiBessel method, the CPU time, and similar data) can be viewed under Solution
78Notes. Solution time is fastest for the cos  and dipole feeds, and slower forhorn feeds, particularly for the circular horn feeds since these require numericalintegration to calculate their patterns.
qValidation
Consider a parabolic reflector with a diameter of 274.3 cm, f / D = 0.4, a circular
waveguide feed with a radius of 1.27 cm, operating at 7.9 GHz. The circular
waveguide feed can be modeled as a conical horn with a very long length. The
following results for beam position and gain are obtained when the feed is on
axis (  x  0 ), or with a lateral displacement (  x  4 ).

x / 

Beam Position

Gain

0.0
4.0

0.0
6.6º

45.8 dB
41.9 dB

Reference [7] gives a gain drop of about 4.0 dB for the displaced feed case.

79E.13. Offset Parabolic Reflector Analysis
This routine computes the patterns of an offset
parabolic reflector antenna using the JacobiBessel series method described in [29]. Thismethod is rigorous, but does not require
integration of the aperture for each patternangle, and therefore is extremely fastcomputationally. It provides accurate patterns
at wide angles, for a variety of feeds,
including displaced feeds. In addition tocomputing co- and cross-pol patterns, thisroutine can also provide plots of the aperture
amplitude distribution, the aperture phase
distribution, the reflector geometry, the antenna gain, and the loss associatedwith surface roughness. The user can choose from a set of built-in feed antennas,
including an ideal cos  pattern, a dipole, a pyramidal horn, or circular horns.
The feed pattern may also be specified using data files for the E- and H-plane
patterns. The analysis of the offset reflector uses the same routine as for thesymmetric reflector (where h = 0), but the symmetric reflector case allows fairly
accurate independent calculations of spillover, taper, and phase losses.
q

Begin by entering the frequency, the f / Dp ratio (where Dp is the diameter ofthe parent paraboloid), the actual dish diameter, the surface roughness for thereflector (the surface roughness dimension has a default value of zero), and theheight, h, of the center of the projected aperture above the axis of the reflector.
Next, select the feed antenna from one of the five choices using the pull-down
list, or select Feed From Data Files to use external feed pattern data.
Depending on the choice of feed, additional parameters will be specified for the
feed dipole or horn dimensions. For the ideal cos  (field) feed, specify either
the exponent, q>0, or specify the -10 dB angle of the feed (the half-angle, indegrees). When specifying the feed pattern from data files, the feed pattern data
must be in the format of (angle in degrees, pattern amplitude in dB), withdelimiters of either commas, spaces, or tabs, with an angle range that extends atleast from -90º to 90º. Optionally, feed pattern phase can be included as (angle
in degrees, pattern amplitude in dB, pattern phase in degrees). The step size ofthe feed pattern data file is arbitrary - numerical interpolation is used whennecessary. Pattern files generated by other PCAAD routines follow this format,
allowing other PCAAD routines to be used to generate feed patterns for directuse in this routine. For example, the array antenna module can be used togenerate E- and H-plane feed pattern files, which can then be used in this routine
to find the secondary patterns of the reflector.
q

Next, specify the displacement of the feed from the focal point of the reflector.
The feed may be displaced laterally (in the x or y directions), or axially (the z
80direction). The displacement is limited to less than 2λ in the lateral directions to
avoid long computation times (and because large displacements are generally
not used in practice due to large drops in gain). A lateral displacement will resultin a shift of the main beam in the opposite direction, while a axial displacement
will result in de-focusing of the main beam. Note that the coordinate reference
point for the feed is at the center of the dipole, or at the center of the aperture forthe horns. This point may not coincide with the actual phase center of the feed
antenna. The feed polarization can be chosen to be either vertical (y direction),or horizontal (x direction). The feed is assumed to be pointed at an angle toward
the center of the dish.
Select the pattern type and parameters with the Pattern Type select button.
Pattern plots can be made in the E- and H-planes of the reflector, or E-theta / Ephi or Co-pol / X-pol patterns can be made at an arbitrary azimuth angle. 3-Dvolumetric patterns are not available because the beamwidth of most reflectors
is too narrow to be plotted in volumetric form. Since most reflector antennas
have narrow beamwidths, the elevation step size should be small, typicallybetween 0.01º and 0.1º. Also specify the maximum angular range of theelevation pattern plot. Because of the narrow beamwidth of most reflector
antennas, the maximum angular range of the pattern calculation usually does notneed to exceed a few degrees. Unlike other methods of reflector antenna
analysis, the Jacobi-Bessel method does not use appreciably more computer
time as the pattern step size, or pattern angle range, is increased.
After clicking the Compute button, the patterns will be calculated and various
results will be presented. On the right side of the window the maximum
directivity that is available from the aperture of the reflector will be printed,
along with losses due to spillover, amplitude taper, and surface roughness. On
the left side of the window is printed the subtended angle from the horizontal
axis to the center of the dish, the beam deformation factor, the aperture
efficiency (based on the maximum directivity of the aperture), and the calculated
gain (based on the rigorously computed far-field pattern).
Other results are available as listed in the Results tree. Plot the patterns of thereflector, or save the patterns to a data file, by clicking the appropriate item in
the Results tree. Click Co-pol Amplitude, X-pol Amplitude, or Co-pol Phase
to plot the corresponding data for the aperture distribution of the reflector. The
geometry of the reflector antenna may be viewed by clicking Show Geometry.
Additional information on the solution (including the number of term used in the
Jacobi-Bessel method, the CPU time, and some useful geometrical parameters of
the offset reflector) can be viewed under Solution Notes. Solution time is fastest
for the cos  and dipole feeds, and slower for the horn feeds, particularly forthe circular horn feeds since these require numerical integration to calculate
their patterns.
q81Validation
An offset parabolic reflector has a diameter of 100λ, f / Dp = 70λ, and acos q  feed pattern with q = 13.09. The following results are obtained, andcompared with data from the reflector analysis software PRAC. The pattern isshown below.
Quantity

PCAAD 7.0

PRAC

Gain
Aperture efficiency
HPBW
First sidelobe

49.01 dB
80.7 %
0.65º-24.3 dB

49.01 dB
80.7 %
0.64º-24.3 dB

Peak X-pol level-28 dB-28 dB

Figure 6. Co-pol and X-pol patterns of the offset reflector antenna.

82

E.14. Spherical Reflector Analysis
This routine computes the patterns of aspherical reflector antenna using the JacobiBessel series method described in [29]. Thismethod is rigorous, but does not require
integration of the aperture for each patternangle, and therefore is extremely fastcomputationally. It provides accurate patterns
for a variety of feeds. In addition to computing
co- and cross-pol patterns, this routine canalso provide plots of the aperture amplitude
distribution, the aperture phase distribution,
the reflector geometry, the antenna gain, andthe losses associated with spillover, amplitude taper, phase errors, and surface
roughness. The user can choose from a set of built-in feed antennas, including
an ideal cos  pattern, a dipole, a pyramidal horn, or circular horns. The feedpattern may also be specified using data files for the E- and H-plane patterns.
Due to problems with numerical convergence, it is best to avoid reflectors thatare close to hemispherical - thus the program restricts reflector diameter to beless than 80% of the spherical diameter.
q

Begin by entering the frequency, the radius of the spherical reflector surface, thedish diameter, and the surface roughness for the reflector (the surface roughness
dimension has a default value of zero). Next, select the feed antenna from one of
the five choices using the pull-down list, or select Feed From Data Files to use
external feed pattern data. Depending on the choice of feed, additionalparameters will be specified for the feed dipole or horn dimensions. For the idealcos q  (field) feed, specify either the exponent, q>0, or specify the -10 dB
angle of the feed (the half-angle, in degrees). When specifying the feed patternfrom data files, the feed pattern data must be in the format of (angle in degrees,
pattern amplitude in dB), with delimiters of either commas, spaces, or tabs, withan angle range that extends at least from -90º to 90º. Optionally, feed patternphase can be included as (angle in degrees, pattern amplitude in dB, patternphase in degrees). The step size of the feed pattern data file is arbitrary numerical interpolation is used when necessary. Pattern files generated by other
PCAAD routines follow this format, allowing other PCAAD routines to be used
to generate feed patterns for direct use in this routine. For example, the array
antenna module can be used to generate E- and H-plane feed pattern files, which
can then be used in this routine to find the secondary patterns of the reflector.
Next, specify the axial displacement of the feed from the center of the reflector.
Typically a spherical reflector uses a feed located approximately halfway
between the reflector surface and the center of the sphere (the entry in this casewould be a positive value). Note that the coordinate reference point for the feed83

is at the center of the dipole, or at the center of the aperture for the horns. This
point may not coincide with the phase center of the feed antenna. The feedpolarization can be chosen to be either vertical (y direction), or horizontal (xdirection).
Select the pattern type and parameters with the Pattern Type select button.
Pattern plots can be made in the E- and H-planes of the reflector, or E-theta / Ephi or Co-pol / X-pol patterns can be made at an arbitrary azimuth angle. 3-Dvolumetric patterns are not available because the beamwidth of most reflectors
is too narrow to be plotted in volumetric form. Since most reflector antennas
have narrow beamwidths, the elevation step size should be small, typicallybetween 0.01º and 0.1º. Also specify the maximum angular range of theelevation pattern plot. Because of the narrow beamwidth of most reflector
antennas, the maximum angular range of the pattern calculation usually does notneed to exceed a few degrees. Unlike other methods of reflector antenna
analysis, the Jacobi-Bessel method does not use appreciably more computer
time as the pattern step size, or pattern angle range, is increased. Note that
because most spherical reflectors are under illuminated, the pattern at wide
angles will likely be inaccurate - it is therefore suggested to limit the patterncomputation range to a few beamwidths.
After clicking the Compute button, the patterns will be calculated and various
results will be presented. On the right side of the window a loss budget for thereflector will be given, starting with the maximum directivity that is available
from the aperture area of the reflector. Below this is listed the spillover loss, theamplitude taper loss, the phase error loss, and the surface roughness loss. The
net result is the Estimated Gain of the reflector. On the right side of the window
is listed the subtended half angle of the reflector, the aperture efficiency (basedon the maximum directivity of the aperture and the computed gain), and thecomputed gain (as found from the computed far-field pattern).
Other results are available as listed in the Results tree. Plot the patterns of thereflector, or save the patterns to a data file, by clicking the appropriate item in
the Results tree. Click Co-pol Amplitude, X-pol Amplitude, or Co-pol Phase
to plot the corresponding data for the aperture distribution of the reflector. The
geometry of the reflector antenna may be viewed by clicking Show Geometry.
Information on the solution (including the number of term used in the JacobiBessel method, the CPU time, and similar data) can be viewed under Solution
Notes. Solution time is fastest for the cos  and dipole feeds, and slower forthe horn feeds, particularly for the circular horn feeds since these require
numerical integration to calculate their patterns.
q84

Validation
A spherical reflector has a radius of 97λ, and a diameter of 48λ. The feed is located48.87λ from the center of the sphere, and has a cos  feed pattern, with q =17.09. PCAAD produces the following results. The pattern is in good agreementwith that given in reference [29].
qMaximum directivity
43.57 dB
Spillover loss
-0.06 dB
Amplitude taper loss
-1.31 dB
Phase taper loss
-0.02 dB______________________________
Directivity - Losses
42.2 dB
Calculated gain
42.3 dB

Figure 7. Pattern of the spherical reflector85E.15. Beam Efficiency
This routine calculates the beam efficiency ofan aperture antenna. Beam efficiency isdefined as the ratio of the radiated power overa fixed angular range to the total radiatedpower. The angular range is often chosen as
the -3 dB points or -10 dB points, but may bearbitrary. This quantity gives a measure of
how much power is radiated in the main beam
relative to the total power, and is useful in a
number of applications where the powerreceived off the main beam is important tosystem performance.
Enter the frequency of operation, the maximum angle for the beam efficiency
calculation, and the desired step size. Next, select the antenna type from one of
the five choices using the pull-down list, or select Feed From Data Files to use
external feed pattern data. Depending on the choice of feed, additionalparameters will be specified for the feed dipole or horn dimensions. For the idealcos q  (field) feed pattern, specify the exponent of the field pattern, q>0. Whenspecifying the feed pattern from data files, the feed pattern data must be in theformat of (angle in degrees, pattern amplitude in dB), with delimiters of either
commas, spaces, or tabs, with an angle range that extends at least from -90º to
90º. Optionally, feed pattern phase can be included as (angle in degrees, patternamplitude in dB, pattern phase in degrees). The step size of the feed pattern data
file is arbitrary - numerical interpolation is used when necessary. Pattern files
generated by other PCAAD routines follow this format, allowing other PCAAD
routines to be used to generate feed patterns for direct use in this routine. For
example, the array antenna module can be used to generate E- and H-plane feedpattern files, which can then be used in this routine to find the secondary
patterns of the reflector.
Click Compute to compute the beam efficiency over the selected range ofangles. The beam efficiency data will be listed versus angle in the list box. The
beam efficiency may be plotted by clicking Plot Beam Efficiency option in the
Results tree, or saved to a data file by clicking Save Data.
Validation

Consider a pencil beam antenna with a power pattern given by F  ,    cos  ,3

for 0     / 2 . For this case, q = 1.5. Direct integration gives the beam
efficiency as b  1  cos  0 . At  0  30 this gives an efficiency of 43.8%; at4 0  60 , the efficiency is 93.8%. These values agree with the data from the beam
efficiency routine of PCAAD 7.0.
86

F. The Microstrip Antennas Menu
This set of routines implement approximate solutions for rectangular and circular
microstrip antennas. Two different solutions are available for probe-fed rectangular
patches, as well as solutions for a microstrip line fed rectangular patch, a proximity
coupled rectangular patch, an aperture coupled rectangular patch, and a probe-fed
circular patch. In general, these solutions work well for microstrip antennas on thin
substrates, but fail for substrates thicker than about 0.02. Subject to this limitation,these routines can be used to get a reasonably good estimate of the resonant
frequency and input impedance for these antennas, but be aware that these routines
will not be as accurate as full-wave solutions. Use of the integrated Smith chartroutine gives quick results for tuning and matching microstrip antenna designs. The
routines also compute patterns and directivity.

F.1. Rectangular Probe-Fed Patch (Carver model)This routine analyzes a rectangular probe-fed
microstrip antenna using Carver's transmission
line model discussed in references [5] and [13].
It treats the patch as a transmission line withequivalent end admittances to account forradiation, and length extensions are used toaccount for fringing fields at the radiating edges.
The radiation patterns are found from theequivalent magnetic currents for the dominant
TM10 mode at the edges of the patch, including
the sidewall contributions. The sidewall currents
do not contribute to the principal plane patterns,
but do have an effect on cross-pol fields and directivity, which is calculated byintegrating the far-field patterns. This solution generally gives good results for
microstrip antennas on thin substrates with low dielectric constants.
Enter the patch length (in the resonant direction), the patch width, the dielectric
constant, the substrate thickness, the dielectric loss tangent, and the distance ofthe probe from the radiating edge of the patch. Select the pattern type andparameters with the Pattern Type select button. Pattern plots can be made in theE- and H-planes of the patch, or E-theta / E-phi or Co-pol / X-pol patterns canbe made at an arbitrary azimuth angle. The routine will then compute theapproximate resonant frequency, the input resistance, the approximate
bandwidth, the radiation efficiency, and the directivity. The specified patterns
may be plotted by clicking the appropriate option in the Results tree, or saved todata files.
See the following section for validation examples.

87F.2. Rectangular Probe-Fed Patch (cavity model)This routine analyzes a rectangular probe-fed
microstrip antenna using a cavity model similar
to that discussed in reference [7]. The patch istreated as a lossy cavity to account for radiation,and length extensions are used to account forfringing fields at the radiating edges. A parallel
RLC equivalent circuit is then used to computethe input impedance versus frequency. The
radiation patterns are found from the equivalentmagnetic currents for the dominant TM10 modeat the edges of the patch. The directivity is
calculated by integrating the far-field patterns.
This solution generally gives good results for microstrip antennas on thin substrates
with low dielectric constants.
Enter the patch length (in the resonant direction), the patch width, the dielectric
constant, the substrate thickness, the dielectric loss tangent, and the distance of theprobe from the radiating edge of the patch (the probe is assumed to be centeredalong the width dimension). The routine will then estimate the resonant frequencyof the antenna, and suggest a frequency step size. These values are displayed, alongwith the default number of frequency points, in three boxes to the right of theCompute button. Click the Compute button to accept these values for thefrequency sweep, or enter new values for the sweep center frequency, the frequency
step size, or the number of frequency points. Select the pattern type and parameterswith the Pattern Type select button. The routine will compute the input impedanceof the antenna over the frequency sweep and display the results in the list box. If
necessary, use the scroll bar at the right of the box to scroll through the list of
impedances. The routine also computes the approximate bandwidth, the radiation
efficiency, and the directivity of the antenna. From the Results tree you can plot
patterns or the impedance locus vs. frequency, and save patterns or impedance todata files.
Validation #1
Consider a rectangular probe-fed patch with a length of 4.92 cm, a width of 3.28
cm, a substrate with a dielectric constant of 2.32 and a thickness of 0.159 cm, and afeed probe positioned 1.0 cm from the edge of the patch. This example is given inreference [8], with the following results compared with Carver’s model and thecavity model from PCAAD:

88

Quantity

Reference [8]Carver Model

Cavity Model

Resonant frequency
Resonant resistance
Bandwidth
E-plane beamwidth
H-plane beamwidth
Directivity

2.00 GHz
n/a
0.7 %
102º
85º
7.0 dB

1.94 GHz
336 Ω
1.2 %
103º
86º
7.0 dB

1.97 GHz
192 Ω
1.7 %
101º
86º
7.0 dB

Validation #2
Consider a probe-fed rectangular patch with a length of 1.8 cm, a width of 2.505
cm, a substrate with a dielectric constant of 2.2 and a thickness of 0.159 cm. The
probe is positioned 0.5 cm from the edge of the patch. Results from the cavity
model of PCAAD are plotted on the Smith chart below, and compared withmeasured data. Agreement is very good, particularly near resonance.

Figure 8. Smith chart plot of calculated (red) and measured (blue) data for a probefed rectangular microstrip antenna.
89F.3. Rectangular Line-Fed Patch (t-line model)This routine analyzes a rectangular microstrip
line-fed microstrip antenna using thetransmission line model discussed in reference[8]. The patch is treated as a transmission linewith equivalent end admittances to account forradiation, and length extensions are used toaccount for fringing fields at the radiating edges.
The transmission line circuit is used to compute
input impedance versus frequency. The
radiation patterns are found from the equivalentmagnetic currents for the dominant TM10 modeat the edges of the patch. The directivity is
calculated by integrating the far-field patterns. This solution has been validated fora large number of practical designs, and generally gives good results for microstrip
antennas on thin substrates with low dielectric constants.
Enter the patch length (in the resonant direction), the patch width, the dielectric
constant, the substrate thickness, the dielectric loss tangent, and the width of the
microstrip feed line. The routine will compute and display the required feed line
width for a 50  line; enter a new value if your line width is different. The routine
will then estimate the resonant frequency of the antenna, and suggest a frequency
step size. These values are displayed, along with the default number of frequency
points, in three boxes to the right of the Compute button. Click the Computebutton to accept these values for the frequency sweep, or enter new values for the
sweep center frequency, the frequency step size, or the number of frequency points.
Select the pattern type and parameters with the Pattern Type select button. The
routine will then compute the input impedance of the antenna over this frequency
sweep, and display the results in the list box. If necessary, use the scroll bar at theright of the box to scroll through the list of impedances. The routine also computes
the approximate bandwidth, the radiation efficiency, and the directivity of theantenna. From the Results tree you can plot patterns or the impedance locus vs.
frequency, and save patterns or impedance to data files.
Validation
Consider a rectangular microstrip line-fed microstrip antenna with a patch length of
3.315 cm, a patch width of 3.317 cm, a dielectric constant of 2.2, a substrate
thickness of 0.079 cm, a loss tangent of 0.001, and a feed line width of 0.47 cm.
Measured results from [8] are compared with PCAAD:
Quantity
Resonant frequency
Resonant resistance
Bandwidth

Measured [8]3.00 GHz
278 Ω
1.1 %
90

PCAAD 7.0
3.01 GHz
241 Ω
1.1 %

F.4. Rectangular Proximity-Coupled Patch (t-line model)This routine analyzes a rectangular proximitycoupled microstrip antenna using a transmission
line model discussed in references [8], [20].
The patch is treated as a transmission line withequivalent end admittances to account forradiation, and length extensions are used toaccount for fringing fields at the radiating edges.
The reciprocity method is used to compute thecoupling term between the feed line and theedge of the patch, and the transmission line
circuit is used to compute input impedance
versus frequency. The radiation patterns arefound from the equivalent magnetic currents for the dominant TM10 mode at theedges of the patch. The directivity is calculated by integrating the far-field patterns.
This solution is not highly accurate, but generally gives reasonable results for
microstrip antennas on thin substrates with low dielectric constants.
Enter the patch length (in the resonant direction), the patch width, the total substrate
thickness (d), the dielectric constant, and the height (h) of the feed line above theground plane (this must be less than the substrate thickness). Next enter the widthof the microstrip feed line, and the loss tangent of the substrate material. Finally,
enter the stub length, as measured from the edge of the patch to the end of the stub.
The routine will then estimate the resonant frequency of the antenna, and suggest afrequency step size. These values are displayed, along with the default number of
frequency points, in three boxes to the right of the Compute button. Click theCompute button to accept these values for the frequency sweep, or enter newvalues for the sweep center frequency, the frequency step size, or the number of
frequency points. Select the pattern type and parameters with the Pattern Typeselect button. The routine will then compute the input impedance of the antenna
over this frequency sweep, and display the results in the list box. If necessary, use
the scroll bar at the right of the box to scroll through the list of impedances. The
routine also computes the approximate bandwidth, the radiation efficiency, and the
directivity of the antenna. From the Results tree you can plot patterns or the
impedance locus vs. frequency, and save patterns or impedance to data files.
Validation
Consider a proximity-coupled patch with a length of 2.5 cm, a width of 4.0 cm, anda substrate with a dielectric constant of 2.2 and a thickness of 0.316 cm. The feedheight is 0.158 cm, and the feed line width is 0.5 cm. The length of the stub is 1.25
cm. At 3.6 GHz, PCAAD gives an input impedance of 34 - j 3 , while measured
data from [5] gives an impedance of about 40 + j 3 .

91

F.5. Rectangular Aperture Coupled Patch (cavity model)This routine analyzes a rectangular aperture
coupled microstrip antenna [14], using a cavity
model solution for the patch combined with thereciprocity method [15] for treating the slot feed
and microstrip line. The patch is modeled as alossy cavity with magnetic sidewalls, and the Q
is found by integrating the radiated fields of thepatch. Length extensions are used to account forfringing fields at the radiating edges of thepatch, and closed-form approximations for shortslots are used for the slot self-conductance andsusceptance. The radiation patterns are foundfrom the equivalent magnetic currents for the dominant TM10 mode at the edges ofthe patch. The directivity is calculated by integrating the far-field patterns. It is
assumed that the coupling slot is centered under the patch, the feed line is centeredacross the slot, and that the feed line is terminated with an open-circuited stub.
First enter the parameters for the patch side of the antenna geometry: the substrate
thickness, dielectric constant, patch length (resonant dimension), patch width, slot
length (long dimension), and slot width (short dimension). Then enter theparameters for the feed side of the antenna: the substrate thickness, dielectric
constant, feed line width, and tuning stub length (measured from the center of theslot to the end of the stub). The routine will then estimate the resonant frequency of
the antenna, and suggest a frequency step size. These values are displayed, alongwith the default number of frequency points, in three boxes to the right of theCompute button. Click the Compute button to accept these values for thefrequency sweep, or enter new values for the sweep center frequency, the frequency
step size, or the number of frequency points. Select the pattern type and parameterswith the Pattern Type select button. The routine will then compute the input
impedance of the antenna over this frequency sweep, and display the results in thelist box. If necessary, use the scroll bar at the right of the box to scroll through thelist of impedances. The routine also computes the approximate bandwidth, theradiation efficiency, the front-to-back ratio, and the directivity of the antenna. From
the Results tree you can plot patterns or the impedance locus vs. frequency, andsave patterns or impedance to data files.
Validation
Consider a rectangular aperture coupled microstrip antenna with the following
parameters:
Antenna substrate dielectric constant:
Antenna substrate thickness:
Patch length:
Patch width:
92

2.54
0.16 cm
4.0 cm
3.0 cmFeed substrate dielectric constant:
Feed substrate thickness:
Slot length:
Slot width:
Feed line width:
Stub length:

2.540.16 cm
1.12 cm
0.155 cm
0.442 cm
2.0 cmCalculated data using the model of [15] are compared with PCAAD at f = 2.217
GHz:

Quantity

Reference [15]PCAAD 7.0

Input impedance

65 - j 17 
6.2 dB
23 dB

64 - j 0.8 
6.1 dB
25 dB

Gain (efficiency  directivity)
Front-to-back ratio

93F.6. Circular Probe-Fed Patch (cavity model)This routine analyzes a circular probe-fed
microstrip antenna using a cavity model similar
to that discussed in reference [8]. The patch istreated as a lossy cavity to account for radiation,and length extensions are used to account forfringing fields at the patch edge. A parallel RLC
equivalent circuit is then used to compute theinput impedance versus frequency. The
radiation patterns are found from the equivalentmagnetic currents for the dominant TM11 mode.
The directivity is calculated by integrating the
far-field patterns. This solution generally gives
good results for microstrip antennas on thin substrates with low dielectric constants.
Enter the patch radius, the radial distance to the feed probe, the substrate thickness,the dielectric constant, and the dielectric loss tangent. The routine will then estimate
the resonant frequency of the antenna, and suggest a frequency step size. These
values are displayed, along with the default number of frequency points, in threeboxes to the right of the Compute button. Click the Compute button to accept
these values for the frequency sweep, or enter new values for the sweep center
frequency, the frequency step size, or the number of frequency points. Select thepattern type and parameters with the Pattern Type select button. The routine willthen compute the input impedance of the antenna over this frequency sweep, anddisplay the results in the list box. If necessary, use the scroll bar at the right of thebox to scroll through the list of impedances. The routine also computes theapproximate bandwidth, the radiation efficiency, and the directivity of the antenna.
From the Results tree you can plot patterns or the impedance locus vs. frequency,
and save patterns or impedance to data files.
Validation #1
Consider a circular probe-fed patch with a radius of 6.7 cm, on a substrate with adielectric constant of 2.62 and a thickness of 0.16 cm, and a probe positioned 5.03
cm from the center of the patch. This example is given in [7] using a different
cavity model, and compared with the following results from PCAAD:

Quantity

Reference [7]PCAAD 7.0

Resonant frequency
Resonant resistance

793 MHz796 MHz

180 

219 

94

Validation #2
Consider a circular probe-fed patch with a radius of 2.78 cm on a substrate with adielectric constant of 2.32 and a thickness of 0.16 cm, and a feed probe at the edgeof the patch. Reference [8] gives the following data, compared with PCAAD:

Quantity

Reference [8]PCAAD 7.0

Resonant frequency

2.00 GHz

1.996 GHz

Directivity
Bandwidth
E-plane 3 dB beamwidth
H-plane 3 dB beamwidth

7.1 dB
1.1 %

7.1 dB
1.3 %

100
80

103
81

95

G. The Transmission Lines and Waveguides Menu
This set of routines provides solutions for the analysis and design of several typesof transmission lines and waveguides that are commonly used in microwave andantenna systems. Included are analysis of coaxial line, rectangular and circular
waveguides, and analysis and design of microstrip line and stripline (based on
quasistatic formulas). New in PCAAD 7.0 are several full-wave analysis routines
for planar transmission lines. These include multilayer microstrip line, multilayer
stripline, coupled microstrip lines, coupled striplines, and surface waves on single
and multilayer dielectric sheets. Also included is a routine that lists data forstandard rectangular waveguide.

G.1. Coaxial Line
This routine computes the characteristic
impedance and attenuation due to dielectric loss
and conductor loss for a coaxial line. It also
computes the cut-off frequency of the TE11
waveguide mode of the coaxial line. The
formulas used in this routine are standard
results, as found in reference [9].
Begin by entering the inner conductor radius,
the outer conductor radius, and the dielectric
constant. Click the Compute Zo button, and theroutine will compute and print the characteristic
impedance of the coaxial line and the approximate cut-off frequency of the TE11
waveguide mode. You can compute attenuation for the coaxial line by entering thefrequency, the loss tangent of the dielectric filling material, and the conductivity of
the coax conductors. The conductivity may be entered as a value in Siemens/meter,or a specific conductor material can be selected from the drop-down menu at theright of the conductivity box. Click the Compute Attenuation button, and theattenuation due to dielectric loss, conductor loss, and the total attenuation will be
printed in dB/cm.
Validation
Consider a copper coaxial line with an inner conductor radius of 0.5 mm, an outerconductor radius of 1.5 mm, a dielectric constant of 2.5, and a loss tangent of 0.01,
operating at 10 GHz. The formulas in [9] give the following results compared with
PCAAD:
Quantity
Characteristic impedance
TE11 mode cutoff frequency
Conductor attenuation
Dielectric attenuation

Reference [9]41.7 
30.2 GHz
0.0115 dB/cm
0.145 dB/cm
96

PCAAD 7.0
41.7 
30.2 GHz
0.012 dB/cm
0.144 dB/cm

G.2. Rectangular WaveguideThis routine computes the cut-off frequencies
and propagation constants for the five lowest
order modes of a rectangular waveguide, andthe attenuation due to dielectric and conductor
losses for the TE10 mode. Begin by entering theE-plane (narrow wall) and H-plane (broad wall)inside dimensions of the guide, the dielectric
constant of the material filling the guide, and theoperating frequency. Click the Compute button,
and the routine will compute and print the cutoff
frequencies of the (1,0), (2,0), (0,1), (1,1), and(0,2) modes; if the mode is propagating at the
specified frequency, the propagation constant will also be printed; otherwise it islisted as cut-off. The formulas used in this routine are standard results, as found inreference [9].
You can compute attenuation for the dominant TE10 mode, if it is propagating, byentering the loss tangent of the dielectric filling material and the conductivity of the
waveguide walls. The conductivity may be entered as a value in Siemens/meter, ora specific conductor material can be selected from the drop-down menu at the rightof the conductivity box. Click the Compute Attenuation button, and theattenuation due to dielectric loss, conductor loss, and the total attenuation will be
printed in dB/cm.
Validation
Consider a copper K-band waveguide of dimensions 1.07 cm  0.43 cm, operating
at 15 GHz. The guide is filled with Teflon (dielectric constant of 2.08, loss tangentof 0.0004). This problem is treated in Example 3.1 of [9], and the results arecompared with those from PCAAD below:

Quantity

Reference [9]PCAAD 7.0(1,0) mode cutoff frequency(2,0) mode cutoff frequency(0,1) mode cutoff frequency

9.72 GHz
19.44 GHz
24.19 GHz9.720 GHz
19.440 GHz
24.188 GHz(1,1) mode cutoff frequency
TE10 propagation constantConductor attenuation
Dielectric attenuation

26.07 GHz
345.1 rad/m
0.00434 dB/cm
0.0103 dB/cm

26.068 GHz
345.08 rad/m
0.00433 dB/cm
0.01034 dB/cm

97

G.3. Rectangular Waveguide Data
This routine lists data for standard rectangular
waveguide, including the WR-number, thestandard band letter designation, therecommended operating frequency range, thecut-off frequency for the TE10 mode, and theinner dimensions of the guide. The scroll barat the right side of the list box can be used toscroll the entries up or down. The source data
for this routine is stored in the ASCII file
RecWGData.dat (in the PCAAD user
directory), which you may edit to add orchange the data displayed by PCAAD 7.0. The
data for each waveguide is entered on a separate line, with spaces or tabs asdelimiters between the data elements.
The routine also allows you to send dimensions for a particular waveguide to therectangular waveguide analysis routine (Section G.2), for convenient calculationof propagation constants, higher-order mode cutoff frequencies, or attenuation.
Select a waveguide by clicking on the appropriate line in the list box (the line
will be highlighted), then click the Send to Rec. WG button. The window for
the Standard Rectangular Waveguide Data routine will close, and the
Rectangular Waveguide Analysis window will open, with the dimensions forthe selected guide automatically entered in the appropriate data boxes.

98G.4. Circular WaveguideThis routine computes the cut-off frequencies
and propagation constants for the five lowest
order modes of a circular waveguide, and theattenuation due to dielectric and conductor
losses for the dominant TE11 mode. Begin byentering the inside radius of the guide, thedielectric constant of the material filling theguide, and the operating frequency. Click theCompute button, and the routine will computeand print the cutoff frequencies of the TE11,
TM01, TE21, TE01, and TM11 modes; if the modeis propagating at the specified frequency, thepropagation constant will also be printed; otherwise it is listed as cut-off. The
formulas used in this routine are standard results, as found in reference [9].
You can compute attenuation for the dominant TE11 mode, if it is propagating, byentering the loss tangent of the dielectric filling material and the conductivity of the
waveguide walls. The conductivity may be entered as a value in Siemens/meter, ora specific conductor material can be selected from the drop-down menu at the rightof the conductivity box. Click the Compute Attenuation button, and theattenuation due to dielectric loss, conductor loss, and the total attenuation will be
printed in dB/cm.
Validation
Consider a circular waveguide with an inner radius of 0.5 cm, filled with Teflon(dielectric constant of 2.08, loss tangent of 0.0004). The waveguide is gold plated,
and is operating at 14 GHz. This problem is presented as Example 3.2 in [9], withresults compared to PCAAD below:

Quantity

Reference [9]PCAAD 7.0(1,1) mode cutoff frequency(0,1) mode cutoff frequency
TE11 propagation constantConductor attenuation

12.19 GHz
15.92 GHz
208.0 rad/m
0.00583 dB/cm

12.190 GHz
15.924 GHz
207.984 rad/m
0.0058 dB/cm

Dielectric attenuation

0.0149 dB/cm

0.0149 dB/cm

99

G.5. Microstrip Line (quasi-static)
This routine is used to find the characteristic
impedance of a microstrip transmission line,
given the substrate parameters and line width, or
to find the line width, given the substrateparameters and the characteristic impedance.
Attenuation due to conductor and dielectric loss
can also be calculated, if desired. These
solutions employ closed-form quasi-static
formulas that generally give good results formost practical design problems, as discussed inreference [9].
First choose either the Compute Zo option, or the Compute width option, by
clicking the appropriate radio button at the left side of the window. This will change
the input statements for the relevant data entry. When computing characteristic
impedance, you will enter the dielectric constant, the substrate thickness, and theline width. Click the Compute Zo button to compute and print the characteristic
impedance and the effective dielectric constant for the line. When calculating line
width for microstrip design, you will enter the characteristic impedance, thedielectric constant, and the substrate thickness. Click the Compute width button tocompute and print the required line width, and the effective dielectric constant for
the line.
You may compute the attenuation for the line for either the line analysis or the line
design case. Enter the frequency, the loss tangent of the dielectric filling material,
and the conductivity of the microstrip conductors. The conductivity may be enteredas a value in Siemens/meter, or a specific conductor material can be selected fromthe drop-down menu at the right of the conductivity box. Click the ComputeAttenuation button, and the attenuation due to dielectric loss, conductor loss, andthe total attenuation will be printed in dB/cm. Note that, unlike most other
PCAAD routines, this routine uses dimensions in millimeters.
Validation
Consider the design of a 50  microstrip line on a substrate with a dielectric
constant of 2.08 and a thickness of 1.59 mm, at a frequency of 5 GHz. The
conductors are copper and the dielectric loss tangent is 0.0004. This example
corresponds to Example 6.2 in [9], and results are compared with PCAAD below:
QuantityLine width
Effective permittivity
Conductor attenuation
Dielectric attenuation

Reference [9]5.08 mm1.80
0.00629 dB/cm
0.00208 dB/cm
100

PCAAD 7.0
5.08 mm1.806
0.0049 dB/cm
0.0021 dB/cm

G.6. Stripline (quasi-static)
This routine is used to find the characteristic
impedance of a stripline transmission line, given
the substrate parameters and line width, or tofind the line width, given the substrateparameters and the characteristic impedance.
Attenuation due to conductor and dielectric loss
can also be calculated, if desired. These
solutions employ closed-form quasi-static
formulas that generally give good results formost practical design problems, as discussed inreference [9].
First choose either the Compute Zo option or the Compute width option, by
clicking the appropriate radio button at the left side of the window. This will change
the input statements for the relevant data entry. When computing characteristic
impedance, you will enter the dielectric constant, the ground plane spacing, the line
width, and the strip thickness. Click the Compute Zo button to compute and print
the characteristic impedance and the cut-off frequency of the parallel-platewaveguide mode. When calculating line width for stripline design, you will enter
the characteristic impedance, the dielectric constant, the ground plane spacing, andthe strip thickness. Click the Compute width button to compute and print therequired line width, and the cut-off frequency of the parallel-plate waveguide mode.
You may compute the attenuation for the line for either the line analysis or theline design case. Enter the frequency, the loss tangent of the dielectric fillingmaterial, and the conductivity of the stripline conductors. The conductivity may
be entered as a value in Siemens/meter, or a specific conductor material can beselected from the drop-down menu at the right of the conductivity box. Click theCompute Attenuation button, and the attenuation due to dielectric loss,
conductor loss, and the total attenuation will be printed in dB/cm. Note that,
unlike most other PCAAD routines, this routine uses dimensions in millimeters.
Validation
Consider the design of a 50  stripline at 10 GHz on a substrate with a dielectric
constant of 2.2 and a ground plane spacing of 3.2 mm. The thickness of the strip is0.01 mm, the conductors are copper, and the dielectric loss tangent is 0.001. This
example corresponds to Example 3.5 in [9], and results are compared with PCAAD
below:
QuantityLine width
Conductor attenuation
Dielectric attenuation

Reference [9]2.66 mm
0.0106 dB/cm
0.0135 dB/cm
101

PCAAD 7.0
2.62 mm
0.0105 dB/cm
0.0135 dB/cm

G.7. Multilayer Microstrip Line (full-wave)
This routine implements a full-wave moment
method solution for the analysis of amultilayered microstrip line geometry. Up tofour dielectric layers below the strip
conductor, and four dielectric layers above thestrip conductor, can be treated. The effective
dielectric
constant,thecharacteristic
impedance, and the attenuation constant arecomputed. This is a rigorous spectral domain
solution using the exact Green's function for a
multi-layer dielectric medium, with thespectral perturbation technique for calculating
the attenuation constant [22].
Begin by entering the number of dielectric layers above the strip conductor.
Then enter the thickness, dielectric constant, and loss tangent for each layer,using the scroll bar to move between layers. Note that there must be at least one
layer above the strip, and that the topmost layer is always of infinite thickness.
Next enter the number of layers below the strip, and the corresponding
parameters for each layer. The routine plots a small graphic showing the actual
number of layers in the multilayer geometry. Then enter the frequency, line
width, and the conductivity of the line. The conductivity may be entered as avalue in Siemens/meter, or a specific conductor material can be selected fromthe drop-down menu at the right of the conductivity box. Click the Computebutton, and the effective dielectric constant, the characteristic impedance, andthe total attenuation (in dB/cm) will be displayed. The attenuation includes
dielectric loss and loss due to finite conductivity of the strip; loss in the groundplane is not included. Note that, unlike most other PCAAD routines, this routine
uses dimensions in millimeters.
Validation
Consider covered microstrip line, with one dielectric layer between the groundplane and the strip, and one dielectric layer above the strip (with air above that).
Let  r 1   r 2  2.53 , and d1  d 2  1.0 mm, with a loss tangent tan   0.001 ,and copper conductors, operating at 1 GHz. Results from PCAAD are compared
below with data from another commercial software package for various line
widths:102

W
1.0 mm
2.0 mm
4.0 mmOther Software

PCAAD 7.0

Z0

e

Z0

e

78
56
36

2.39
2.38
2.38

79
56
37

2.41
2.38
2.38

103

G.8. Multilayer Stripline (full-wave)
This routine implements a full-wave moment
method solution for the analysis of amultilayered stripline geometry. Up to four
dielectric layers below the strip conductor, andfour dielectric layers above the strip
conductor, can be treated. The stripline
geometry assumes ground planes at thebottom and top of the structure. The effective
dielectric
constant,thecharacteristic
impedance, and the attenuation constant arecomputed. This is a rigorous spectral domain
solution using the exact Green's function for a
multi-layer dielectric medium, with the spectral perturbation technique forcalculating the attenuation constant [22].
Begin by entering the number of dielectric layers above the strip. Then enter the
thickness, dielectric constant, and loss tangent for each layer, using the scroll bar
to move between layers. Next enter the number of layers below the strip, and thecorresponding parameters for each layer. The routine plots a small graphic
showing the actual number of layers in the multilayer geometry. Then enter thefrequency, line width, and the conductivity of the line. The conductivity may beentered as a value in Siemens/meter, or a specific conductor material can beselected from the drop-down menu at the right of the conductivity box. Click theCompute button, and the effective dielectric constant, the characteristic
impedance, and the total attenuation (in dB/cm) will be displayed. The
attenuation includes dielectric loss and loss due to finite conductivity of the
strip; loss in the ground plane is not included. Note that, unlike most other
PCAAD routines, this routine uses dimensions in millimeters.
Validation
Consider a stripline with two different dielectric layers,

 r 1  10.2 ,d1  0.635 mm,  r 2  2.2 , d 2  1.57 mm, and operation at 3 GHz. Results arecompared below with data from another commercial software package:W
0.5 mm
1.0 mm
2.0 mmOther CAD Software

PCAAD 7.0

Z0

e

Z0

e

49.8
35.0
22.2

7.047
7.386
7.776

51.2
36.0
23.3

7.069
7.372
7.749

104

G.9. Coupled Microstrip Lines (full-wave)
This routine implements a full-wave moment
method solution for the analysis of coupledmicrostrip lines, including a dielectric coverlayer. This is a rigorous spectral domain
solution using the exact Green's function forthe dielectric medium. The effective dielectric
constant and characteristic impedance arecalculated for even and odd propagation
modes. (Although it is straightforward tocompute attenuation for coupled lines, theattenuation constants for even and odd modes
are generally not useful in practice. This isbecause most applications of coupled lines involve a superposition of even andodd modes, and superposition does not apply to power loss.)
Begin by entering the dielectric constant and thickness for the substrate layer
below the strip, then the dielectric constant and thickness for the cover layer(enter values of 0 and 1, respectively, if there is no cover layer). Next enter thewidth of the lines and the (edge-to-edge) separation between the lines, followedby the frequency. Click the Compute button, and the effective dielectric
constant and the characteristic impedance will be displayed for the even and odd
modes of the coupled lines. Note that, unlike most other PCAAD routines, thisroutine uses dimensions in millimeters.
Validation
Consider coupled microstrip lines on a substrate with  r  10.2 , d  1.0 mm, aline width of W  1.0 mm, and operation at 3 GHz. The even and odd mode
impedances and effective dielectric constants from PCAAD are compared withresults from another commercial code, for various line separations:S
0.1 mm
1.0 mmOther CAD Software

PCAAD 7.0

Z0e

 ee

Z0o

 eo

Z0e

 ee

Z0o

 eo

67.0
55.0

7.50
7.66

29.3
41.4

5.91
6.17

67.0
55.1

7.51
7.65

29.3
41.6

5.91
6.16

105

G.10. Coupled Striplines (full-wave)
This routine implements a full-wave moment
method solution for the analysis of coupled
striplines, with separate dielectric layers aboveand below the strip conductors. This is arigorous spectral domain solution using theexact Green's function for the dielectric
medium. The effective dielectric constant andcharacteristic impedance are calculated foreven and odd propagation modes. (Although it
is straightforward to compute attenuation forcoupled lines, the attenuation constants foreven and odd modes are generally not usefulin practice. This is because most applications of coupled lines involve asuperposition of even and odd modes, and superposition does not apply to power
loss.)
Begin by entering the dielectric constant and thickness for the dielectric layer
below the strip, then the dielectric constant and thickness for the dielectric layer
above the strip. Next enter the width of the lines and the (edge-to-edge)
separation between the lines, followed by the frequency. Click the Computebutton, and the effective dielectric constant and the characteristic impedance
will be displayed for the even and odd modes of the coupled lines. Note that,
unlike most other PCAAD routines, this routine uses dimensions in millimeters.
Validation
Consider coupled striplines with a dielectric constant of 10.2, a total dielectric
thickness of 2.0 mm, and a strip width of 1.0 mm, operating at 3 GHz. The evenand odd mode impedances from PCAAD are compared with results from anothercommercial code, for various line separations:S
0.1 mm
0.5 mm
5.0 mmOther Software

PCAAD 7.0

Z0e

Z0o

Z0e

Z0o

40.75
35.7
30.8

20.9
26.0
30.8

40.8
35.9
31.0

21.1
26.0
31.0

106

G.11. Single Layer Surface Wave Modes (full-wave)
This routine computes TM and TE surface wave
propagation constants for a grounded dielectric
substrate. It first determines the number of
propagating surface wave modes on the slab,
then uses a Newton-Rhapson iteration techniqueto find the propagation constants. It is based onstandard results, as found in reference [9].
Enter the frequency, the substrate dielectric
constant, and the substrate thickness. Click theCompute button to print out the normalized(to k0) propagation constant for eachpropagating surface wave mode. The routine also computes and prints anapproximate value for the radiation efficiency of a printed antenna on thissubstrate. This efficiency is based on power lost to surface waves, and ismeaningful because it has been shown that this type of radiation efficiency isfairly independent of the type or size of the actual radiating element, depending
primarily on the substrate dielectric constant and thickness, as discussed inreference [16]. Note that, unlike most other PCAAD routines, this routine uses
dimensions in millimeters.
Validation
Consider the surface wave for a substrate with a dielectric constant of 2.55 and a
thickness of 1.9 mm, operating at 30 GHz. This case occurs in [12], where thenormalized propagation constant is given as  / k0  1.283 ; PCAAD gives a valueof 1.28249.

107

G.12. Multilayer Surface Wave Mode (full-wave)
This routine computes the TM0 (lowest order)
surface wave propagation constant for a
multilayer dielectric geometry with a groundplane. This is a rigorous spectral domain
solution using the exact Green's function for a
multi-layer dielectric medium [22].
Begin by entering the number of dielectric
layers above the ground plane. Note that there
must be at least two layers, and that the top
layer is of infinite extent. Next enter the
thickness and dielectric constant for eachlayer, using the scroll bar to move between layers. The routine plots a small
graphic showing the actual number of layers in the multilayer geometry. Thenenter the frequency, and click the Compute button to compute the propagation
constant of the surface wave mode. The propagation constant is also printed out
in normalized (to k0) form. Note that, unlike most other PCAAD routines, thisroutine uses dimensions in millimeters.
Validation
Consider the same case as in Section G.11, but constructed with two dielectric
layers having the same dielectric constant and the same total thickness. Thus, let r 1   r 2  2.55 , and d1  d 2  0.95 mm, with a frequency of 30 GHz. The
multilayer surface wave routine gives a value of  / k0  1.28249 , in agreementwith the single layer case.

108

H. The Miscellaneous Menu
This set of routines provide several solutions and data for a variety of topics related
to antennas and applications. Included are routines for calculating communication
link loss, the polarization mismatch between two antennas, the degradation in axial
ratio caused by amplitude and phase errors, graphs for atmospheric attenuation andantenna temperature, and a calculator for useful microwave and antenna functions.

H.1. Communication Link Loss
This routine computes the link loss for a radio
communications link using the Friis formula[1], [2], [9].
Enter the gains of the transmit and receive
antennas, the range between transmitter andreceiver, the frequency, the polarization
mismatch (enter 0 dB for no mismatch), and theatmospheric attenuation. The routine calculates
the link loss assuming impedance matchedantennas.

Validation
Example 14.4 of [9] describes the link loss of a DBS satellite, with a transmit
antenna gain of 34.0 dB, a receive antenna gain of 33.5 dB, a range of 39,000 km,
and an operating frequency of 12.45 GHz. PCAAD gives a link loss of 138.7 dB, inagreement with the result of [9].

109

H.2. Polarization Mismatch
This routine calculates the maximum andminimum polarization mismatch between two
arbitrarily polarized antennas using theformulation presented in [23].
Enter the axial ratio of each antenna, andspecify the polarization sense (right hand or lefthand). For an ideal linearly polarized antenna,
enter a large value, such as 100 dB, for its axial
ratio. The routine then computes the maximum
and minimum losses due to polarization
mismatch. Note that these values, being defined
as losses, appear as positive dB. The actual loss in practice will depend on therelative orientation of the polarization ellipses of the two antennas, but will always
be between the minimum and maximum values given by this routine.
Validation #1
Consider the mismatch between an ideal circularly polarized antenna and an ideal
linearly polarized antenna. By entering 0 dB for the axial ratio of the circularly
polarized antenna, and 100 dB for the axial ratio of the linearly polarized antenna,
PCAAD gives a minimum and maximum mismatch loss of 3.01 dB, as expected.
Validation #2
Consider a RHCP antenna with an axial ratio of 8 dB, and a RHCP antenna with anaxial ratio of 4 dB. PCAAD gives the minimum and maximum mismatch losses as
0.15 dB and 1.85 dB. These values are in agreement with an example in [23].

110H.3. Atmospheric Attenuation
This routine presents a graph of atmosphericattenuation versus frequency, along withattenuation due to rain, as given in [7]. The
atmospheric attenuation is at sea level, while
the rain attenuation is given for three different
rain rates.

Validation
At a frequency of 60 GHz, the attenuation rate of the atmosphere is 15 dB/km.
At 40 GHz, the attenuation due to rain at a rate of 1 mm/hr is 0.33 dB/km; rain
at the rate of 16 mm/hr increases to 4.9 dB/km.

111

H.4. Axial Ratio versus Errors
Many circularly polarized antennas areconstructed using two orthogonal linearlypolarized antennas fed with equal amplitude
excitations that are 90º out of phase. As
presented in [24], this routine gives theresulting axial ratio due to errors in the actual
amplitudes and phases.
Enter the amplitude error (in dB), and thephase error (in degrees). The resulting axial
ratio is calculated. Changing the sign of theamplitude error, or the phase error, does notchange the resulting axial ratio. A graph illustrating constant axial ratio contours
versus amplitude and phase errors is also shown - this can be useful for
estimating the amplitude and phase accuracies required for a given axial ratio.
Validation
For two orthogonal linearly polarized antennas having excitations with zero phaseerror and 3 dB amplitude error, PCAAD gives an axial ratio of 3 dB, in agreementwith the graph, and with the results in [24]. For the case of zero amplitude error anda phase error of 30, PCAAD gives an axial ratio of 4.8 dB, in agreement with thegraph, and with the results in [24].

112H.5. Antenna TemperatureThis routine presents a graph of the
background noise temperature for an ideal(lossless) antenna versus frequency andelevation angle (elevation angle is measured
from the horizon, so   90 is overhead). The
antenna is assumed to have a narrow pencil
beam, with no sidelobes pointed toward theearth. Results are given for various elevation
angles. The minimum and maximum noise
temperatures are also shown. This data istaken from [26].
Validation
At a frequency of 2 GHz, a narrow beam antenna pointed directly overhead will
see an apparent noise temperature of about 9 K. An antenna with a more
omnidirectional pattern will see a noise temperature as high as 100 K.

113

H.6. Calculator
This routine provides a calculator function forthree different types of conversions:conversion of dimensions (between meters,
centimeters, millimeters, inches, and mils),
conversion of return loss and VSWR (between
return loss, reflection coefficient magnitude,
VSWR, and mismatch loss), and conversionof dB and ratios (between ratios in dB, nepers,
power ratios, and voltage ratios). Each ofthese functions operate in the same way.
Simply enter the known value in theappropriate text box, press Enter, and theconverted values will appear in the remaining boxes. Note that all dimensions
must be greater than zero; return loss, reflection coefficient magnitude,
mismatch loss, voltage ratio, and power ratio must be non-negative; and VSWR
must be unity or larger.
Validation
Consider an antenna having an input VSWR of 2.0. Entering this value in the
VSWR box of the calculator routine and pressing Enter shows that the input
reflection coefficient magnitude is 0.3333, the input return loss is 9.54 dB, andthe mismatch loss is 0.512 dB.

114

I. The Help Menu
PCAAD has a comprehensive Help file system, based an HTML compiled help
system. The Help file is named PCAAD7.CHM, and is located in the application
directory.

H.1. Help Table of Contents
This menu option shows the Table of Contents of the Help file, with all routines
listed according to type. The Help index can also be accessed.

H.2. Help Index
This menu option leads directly to the index of the Help file.

H.3. Context Help (F1)Context Help provides assistance for the routine that is currently being used. You
can also access context help by pressing the F1 key.

H.4. Short Course and Tutorials
The short course on antennas can be accessed from this menu option, along withtutorials on transmission lines, the Smith chart, and the design of electrically small
antennas. This material is given in PDF format, and requires a PDF reader.

H.5. About PCAAD
This menu option shows the main and sub versions of PCAAD. Also shown are thedirectory path for the PCAAD application directory, the location of the bitmap files
used by PCAAD, the current default directory for user data files, the Windows
application directory for user data files, the path for the PCAAD7.INI file, the pathfor the Short Course and Tutorial files, and the path for the PCAAD Help file.

115

V. References[1] C. A. Balanis, Antenna Theory: Analysis and Design, 3rd edition, John
Wiley & Sons, New York, NY, 2012.
[2] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 3rd edition,
John Wiley & Sons, New York, NY, 2012.
[3] J. D. Kraus and R. J. Marhefka, Antennas, 3rd edition, McGraw-Hill, New
York, NY, 2001.
[4] T. Milligan, Modern Antenna Design, 2nd edition, McGraw-Hill, New
York, NY, 2005.
[5] D. M. Pozar and D. H. Schaubert, Microstrip Antennas: The Analysis andDesign of Microstrip Antennas and Arrays, IEEE Press, New Jersey, 1995.
[6] A. W. Rudge, K. Milne, A. D. Olver, and P. Knight, editors, Handbook of
Antenna Design, Vol.2, Peter Peregrinus Press, London, 1983
[7] Y. T. Lo and S. W. Lee, Antenna Handbook, Van Nostrand, New York,1988.
[8] J. R. James and P. S. Hall, Editors, Handbook of Microstrip Antennas,
Peter Peregrinus Press, London, 1989.
[9] D. M. Pozar, Microwave Engineering, 4th edition, John Wiley & Sons,
New York, NY, 2012.
[10] J. H. Richmond, "Computer Program for Thin-Wire Structures in a
Homogeneous Medium", Technical Report TR-2902-12, ElectroScience
Laboratory, Ohio State University.
[11] M. Kluskens, "A New Computer Algorithm for the Complex Exponential
Integral in the Method of Moments", IEEE Trans. Antennas and Propagation,
vol. 47, pp. 803 - 806, May 1999.
[12] D. M. Pozar and D. H. Schaubert, "Scan Blindness in Infinite Arrays of
Printed Dipoles", IEEE Trans. Antennas and Propagation, Vol. AP-32, pp. 602610, June 1984.
[13] K. R. Carver and J. W. Mink, "Microstrip Antenna Technology", IEEE
116

Trans. Antennas and Propagation, vol. AP-29, pp. 2-24, January 1981.
[14] D. M. Pozar, "A Microstrip Antenna Aperture Coupled to a Microstrip
Line", Electronics Letters, Vol. 21, pp.49-50, January 17, 1985.
[15] D. M. Pozar, "A Reciprocity Method of Analysis for Printed Slot and Slot
Coupled Microstrip Antennas", IEEE Trans. Antennas and Propagation, Vol.
AP-34, pp.1439-1446, December 1986.
[16] D. M. Pozar, "Rigorous Closed-form Expressions for the Surface Wave
Loss of Printed Antennas", Electronics Letters, vol. 26, pp. 954-956, June 1990.
[17] E. Jull, Aperture Antennas and Diffraction Theory, Peter Peregrinus,
London, 1981.
[18] A. D. Bresler, "A New Algorithm for Calculating the Current Distributionsof Dolph-Chebyshev Arrays", IEEE Trans. Antennas and Propagation, vol. AP28, pp. 951-952, November 1980.
[19] A. T. Villeneuve, "Taylor Patterns for Discrete Arrays", IEEE Trans.
Antennas and Propagation, vol. AP-32, pp. 1089-1093, October 1984.
[20] S. M. Duffy and M. A. Gouker, "A Modified Transmission Line Model for
Cavity Backed Microstrip Antennas", 1996 IEEE Antennas and Propagation
International Symposium Digest, pp. 196-199, July 1996.
[21] E. A. Swanson, P. Elliot, and D. M. Pozar, "Design of a Broadband
Corrugated Horn Antenna", Microwave Remote Sensing Laboratory Report
MIRSL-82-1, University of Massachusetts, 1982.
[22] N. K. Das and D. M. Pozar, "Full-wave Spectral Domain Computation ofMaterial, Radiation, and Guided Wave Losses in Infinite Multilayered Printed
Transmission Lines", IEEE Trans. Microwave Theory and Techniques, pp. 5463, January 1991.
[23] A. Simmons, “Polarization Mismatch Loss”, IEEE Antennas andPropagation Newsletter, pp. 15-16, August 1984.
[24] D. M. Pozar and S. Targonski, “Axial Ratio of Circularly Polarized
Antennas with Amplitude and Phase Errors”, IEEE Antennas and Propagation
Magazine, pp. 45-46, October 1990.
[25] R. J. Mailloux, Phased Array Antenna Handbook, 2nd edition, Artech117

House, 2005.
[26] L. Blake, “Antenna Noise Temperature”, IEEE Antennas and Propagation
Newsletter, pp. 8-9, December 1984.
[27] A. W. Love, “The Diagonal Horn Antenna”, Microwave Journal, pp. 117122, March 1962.
[28] D. L. Waidelich, “The Phase Center of Aperture Antennas”, IEEE Trans.
Antennas and Propagation, vol. AP-28, pp. 263-264, March 1980.
[29] Y. Rahmat-Samii and V. Galindo Israel, "Shaped Reflector Antenna
Analysis Using the Jacobi-Bessel Series", IEEE Trans. Antennas andPropagation, vol. AP-28, pp. 425-435, July 1980.

118