NBSIR 79-1601

PUBLICATIONS

A111D4 S 1 3 T fi 2

THE EFFECTS OF RESISTIVE LOADING ON TEM HORNS

Motohisa Kanda

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

August 1979

National- iffifaaa of SftfffdgA®* JAN 3 | 1980'

NBSIR 79-1601

THE EFFECTS OF RESISTIVE LOADING ON TEM HORNS

Motohisa Kanda

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

August 1979

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Contents

£iae

1. INTRODUCTION 1

2. THEORETICAL CONSIDERATIONS 2

2.1 A Resistively Loaded "TEM" Horn 2

2.2 Conductive TEM Horns 6

3. CHARACTERISTICS OF RESISTIVELY LOADED "TEM" HORNS 10

3.1 Loading Profile ' 10

3.2 Current Distribution 10

3.3 Driving-Point Impedance 11

3.4 Reflection Coefficient 11

3.5 Radiation Power Pattern 11

4. FREQUENCY DOMAIN RESULTS 12

5. TIME-DOMAIN RESULTS 13

6. CONCLUSION 14

7. References 15

Figure Captions 16
The Effects of Resistive Loading of "TEM" Horns

Motohisa Kanda

Electromagnetic Fields Division

National Bureau of Standards

Boulder, Colorado 80303

For directional reception or transmission of picosecond pulses with

minimal distortion, a short transverse electromagnetic (TEM) horn with

continuously tapered resistive loading was developed and found to be broadband

and nondispersive with a low VSWR. The receiving transient response of the

resistively loaded "TEM" horn indicates that the shape of a 70-ps impulse is

well preserved. The theoretical analyses using the method of moments and the

fast Fourier transform (FFT) technique were performed and agreed well with

time-domain measurements.

Key words: Broadband; directivity; effective length; FFT: method of moments;

nondispersive; picosecond pulse; resistive loading; TEM horn; transfer function

transient.

1 v
1. INTRODUCTION

Recent study related to electromagnetic pulse ( EMP ) phenomena has

focused strong attention on the subject of transient electromagnetic (EM)

fields. Antenna structures able to preserve the time-domain waveform of EMP

must be inherently broadband and nondispersi ve. One such antenna, which has

been successfully fabricated, is a dipole with continuously tapered resistive

loading [1 ,2]

.

In an effort to attain increased directivity or increased antenna gain

for a broadband and nondispersive antenna, many researchers have considered

a transverse el ectromagnetic "(TEM) horn, which is a two-conductor, end-fire

traveling-wave structure. If the flare angle and the plate widths of a TEM

horn are properly chosen so that a constant, characteristic impedance can be

maintained, the horn will guide an essentially TEM mode into free space.

Thus, a TEM horn can be considered as a transition section which transfers EM

energy from a transmission line to free space. In order to achieve a "smooth"

transition, i.e., a transition with low reflection, the length of a conventional conductive TEM horn has to be at least one-half wavelength long

at the lowest frequency of interest. This means that, if the lowest frequency

of interest is 100 MHz, a TEM horn may be as long as 1.5 m, which is too long

to be practical.

The Cornell Aeronautical Laboratory (CAL) designed a TEM horn with

nonuniform-line matching from 50 ft at the antenna throat to 377 ft at the

aperture. The nonuniform-line matching was achieved by forming the TEM horn

plates empirically into tear-drop shapes. A small resistance card termination

was placed at the tip of the aperture to provide adequate current attenuation

for a traveling wave. With these empirical modifications, the length of the

TEM horn was reduced to 1 m with a reasonable reflection coefficient (less

than 0.48) for the frequency range of 100 MHz to 2 GHz.

In this paper, a "TEM" horn with continuously tapered resistive loading

is considered for the purpose of developing a relatively short, broadband and

nondispersive antenna with high directivity. One-dimensional, theoretical

analysis for a resistively loaded "TEM" horn using the method of moments [3]

has been performed in the frequency domain. Using the fast Fourier transform
(FFT) technique then allows the determination of transient radiated EM fields

for a known input pulse waveform. Comparison between theory and time-domain

measurements is also given in this paper.

2. THEORETICAL CONSIDERATIONS

In this section, the theoretical considerations for a one-dimensional

model of a resistively loaded "TEM" horn, as shown in figure 1, are given

first. A one-dimensional analysis simplifies the mathematics involved, yet

gives good physical insight for evaluating the effects of resistive loading on

a TEM horn.

To analyze a conductive TEM horn, a biconical antenna model given in

figure 2 is used. By adjusting the apex angle and the lengths of the cones,

this model gives good physical understanding for analyzing conductive TEM

horns.

2.1 A Resistively Loaded "TEM" Horn

Because of the presence of loss in TEM horn plates, the field patterns

for EM waves propagating between lossy plates deviate from a pure TEM mode.

Because a resistively loaded "TEM" horn cannot support a pure TEM mode, the

term "TEM" horn may not be truly appropriate but will be used throughout this

paper.

If there are abrupt changes in the characteristics of the boundary

(i.e., air to lossy TEM horn plate), the problem can be solved by finding

general solutions for each of the regions and evaluating unknown constants by

satisfying the boundary conditions across plate interfaces. A transcendental

matrix equation derived by matching the field across plate interface is not,

however, expected to be easy to solve in general cases. For this reason, the

analysis used in the paper is a one-dimensional model given in figure 1* which

ignores any transverse current components on the lossy plates. When the horn

angle and the plate widths are so chosen that they vary smoothly, it is a reasonably good assumption to neglect transversal components of current on the

lossy plates. The shape for horn plates in the study is, therefore,

chosen to be triangular.

Using the one-dimensional model which neglects any transverse components

of current on the lossy plate, we calculate numerically the longitudinal

2
component of the current by using the method of moments. In this paper, we review briefly a general theoretical development for a one-dimensional,

resistively loaded antenna structure, which can be bent and can have step

discontinuities in radius. More detailed discussion on the theory is given

elsewhere [3,4].

Figure 1 shows a typical one-dimensional structure of a TEM horn modeled

by straight sections with a bend at a junction. Using a one-dimensional

model, the current is assumed to be uniform perpendicul ar to the figure and to

flow in one direction on each plate. Then, the incident electrical field

F associated with the current I and the charge density p on a inc

one-dimensional plate are given in terms of usual vector and scalar potentials

•fA and

if. = -JuiA - v$>,

inc ( 1 )

( 2 )

and

(3)

where R is defined to be:

R = r-r' (s' )| 2 + a

2 (s' )

.

(4)

One-dimensional charge density p(s) is related to the current I(s) through

the equation of continuity:

p(s)

dl ( s)

j w ds

( 5 )

The unit direction vector (T, which is parallel to the axis of each segment,

is defined as:

3
( 6 )

4- 4-

Using the pulse-testing function, expanding the current in pulses, and

applying a finite difference approximation to compute charge density p, we can rearrange eq (1) in terms of the usual impedance matrix Zmn associated

with the current and voltage matrix I n and V m , i.e.,

N

l

I Z = V .

, n mn m

n=l

The matrix element Zmn associated with the nth current at the

observation s mis given by [4]:

(7)

Zmn

-1

4uj we

k 2 (r

m+i

-r -r rm-§

* ^n+^

4*m+ j,n,n+l ^

J m+| ,n-l ,n ^m-4 ,n,n+l

s - s s - s , s . - s n+1 n n n-1 n+1 n

^m- jn-1 ,n ~

( 8 )

+ Z(s ) m

),

where Z(sm ) is the internal resistance per unit length due to resistive

loading. Both the vector and scalar potential terms involve the integral of

the form:

4/ m,u ,u

u m

where

Rm

r'(s')|

2 + a2

(s').

The matrix element V mis simply given by:

(9)

( 10 )

4
( 11 )

The resistive loading profile l{l) in ohms per meter of a "TEM" horn is

expressed as:

where Z0 is the resistance per unit length (ft/m) at the driving point, and

L is the length of the "TEM" horn. Equation (12) predicts that the resistive

loading of the "TEM" horn increases continuously from the value Z0

(ft/m) at

the driving point to infinity at the end of the "TEM" horn. The choice of

this particular resistive loading profile, which enables a TEM horn to handle

extremely wide bandwidth signals without dispersion distortion, has been given

by many researchers [5, 6, 7, 8] as well as by the author [1,2]. In essence,

there exists a critical value for Z0 , for which a "TEM" horn can sustain a traveling-wave current from the driving point toward the end of the "TEM"

horn. A traveling-wave structure supporting TEM mode propagation is essential

for transmitting and receiving a signal with large instantaneous bandwidth

without serious pulse broadening or wide angle sidelobes.

Once the current distribution of the resistively loaded "TEM" horn is

determined, the effective length h e (f) of the antenna can be calculated from

the moment of its current distribution divided by the driving-point current,

i .e.

The effective length and the driving-point impedance of the antenna are required later to evaluate its transfer function.

A formal solution to the resistively loaded "TEM" horn problem can be

formulated by modeling solid plate surfaces with loaded wire grids or meshes.

This extends the one-dimensional problem to a two- or three-dimensional

problem by taking into account the transverse current components on horn

plates. The moment method technique will give a reasonable solution in the

frequency range in which each surface is smaller than a few square

Z(s) = ft/m, o<s<L,

s

Z o

( 12 )

(13)

5
wavelengths. Above those frequencies, the moment method unfortunately needs

many loaded wire segments and therefore requires many unknown currents to

accurately model a solid surface. In this case, perhaps the geometrical

theory of diffraction (GTD) technique would provide more efficient solutions

to this problem. These techniques will be pursued for better understanding of

a resistively loaded "TEM" horn.

In the present study, the one-dimensional theoretical analysis for the

resistively loaded "TEM" horn using the method of moments [3] has been

performed in the frequency domain. Using the FFT then allows the

determination of transient characteri sties of the antenna.

2.2 Conductive TEM Horns

In a previous paper by the author [9,10], a simple theoretical model was developed using the assumed aperture field. In this model the horn flare

angle and the plate widths are chosen so that the TEM horn guides only the TEM

mode by maintaining a constant impedance. If the edge diffraction effect and

fringe fields are neglected, the aperture field of the TEM horn is assumed to

be a linearly polarized, spherical field. Once an aperture field is

established, the radiated EM field at any distance can be evaluated using the

plane-wave spectrum analysis technique.

As discussed in [9,10], a number of major limitations of the simplified

theoretical model still remain, although some useful engineering design

concepts were obtained. For example, the assumption that a TEM mode is

basically guided from the throat to the aperture by the nondi spersive TEM horn

is highly questionable. Particularly at the high frequency range of the

spectrum, above 1 GHz for example, the aperture field may be quite different

from a basic TEM mode due to higher modes. Even at the lower frequency

ranges, below 1 GHz for example, the magnitude of the TEM mode at the aperture

may not remain constant due to a high reflection coefficient, e.g., 0.98 at

100 MHz.

In an effort to treat these aspects more rigorously, a formal solution

to the TEM horn problem using a vector integral equation technique was proposed. Using the equivalence principle [11], the electric field if in the

free space generated by an unknown set of electric currents if on the TEM horn

plates is:

6
( 14 ) e" = - V X F - j

(41 A + — v( V , A)

,

J we

where the electric vector potential F is given in terms of the known

excitation equivalent magnetic current by M:

F

l-ff 4iry J s

-jkR

source R ds

,

(15)

and the magnetic vector potential A is given in terms of the unknown current

>

J on the TEM horn plates by:

1 - vjl J

pi ates

-jkR

ds, (16)

with R = | r-r'| . Boundary conditions are such that the tangential electric field at the

TEM horn plates is zero, i.e.:

n x E = 0 on the plates.

Substituting eqs (14), (15), and (16) into eq (17) gives:

(17)

->n x (-v ds) + n x ds

on the plates.

(18)

The above electric field integral equation may be solved for the unknown J.

f

Once J is determined, the other EM fields everywhere may be determined by use of eqs (14), (15), and (16).

The derivation of the electric field integral equation given in eq (18)

is complete and straightforward. The solution may also be obvious using the

method of moments technique. The horn plates are divided into small patches.

7
After the vector integral equation given in eq (18) is decomposed into

appropriate coupled scalar integral equations, two orthogonal components of

current J with two unknown constants over each patch must be forced to satisfy

the boundary condition. Although the matrix formulations of the problem are quite straightforward, their solution can get extremely formidable,

particularly at higher frequencies where each patch has to be divided into

smaller ones compared to wavelength. Although some symmetry arguments may be

used to keep the matrix sizes tractable, there is no easy way out except to

perform a very large matrix computation. In addition, because the FFT is used

to obtain the transient characteristics of the TEM horn, the above electric

field integral equation has to be solved for many frequency points, e.g., on the order of one thousand from 10 MHz to several GHz. This is a very

expensive process.

In this paper, a simple model, modified from one used in previous papers

by the author [9,10], is adopted to analyze a conductive TEM horn. The model

used is a biconical antenna structure, where the apex angle and the length of

a bicone are adjusted to fit a TEM horn. The biconical model of a conducting

TEM horn is shown in figure 2. A knowledge of both the driving-point

impedance and the effective length of the antenna for the frequency range over which the spectrum of the excitation has significant amplitude is required to

discuss quantitatively the transient response of a transmitting and receiving

TEM horn using the FFT technique.

The effective length h e (f) and the driving-point impedance Z0(f) of

a wide-angle conical antenna, studied by many workers [12] as well as by the

author [9,10], are given respectively by:

( 19 )
and

z ( f ) = i o c

( 20 )

The symbols have the following meanings:

l is the length of the antenna,

P

n (cos 9) is the Legendre polynomial of order n,

h

n ^

(la) is the spherical Hankel function of the second kind,

Z = 60fcn cot — , c 2

( 21 )

_3 _ -j2ka

= e

r. .60 r 2n + 1 „ A 2 , , N 1 + J l "f'T'u [P cos e ) ? (H)

c n=l 2

.60 - 2n + 1 L , „ A 2

J

1 + J F l n(nTT)(P

n (c0S

o')

?n (k‘>

C

n=l

J

( 22 )

and

cn (ka)

h

(2)

(k*)

n

h

( 2 ) (k*) - ~ h

(2)

(ka.)

n-1 ka n

(23)

Then the far-field electric field is given by:

E(f) = j

60

Z ( f ) + Z o g

F(f) e -jkr

(24)

where the field characteristic F(f) is related to the effective length

h e (f) through the Rayl eigh-Carson reciprocity theorem [13]:

F(f) = kh (f).

e (25)

9
3. CHARACTERISTICS OF RESISTIVELY LOADED "TEM" HORNS

3.1 Loading Profile

In the present study, the one-dimensional theoretical analysis for a triangularly shaped "TEM" horn with resistive loading has been performed to

solve for the current distribution using the method of moments. The physical

dimensions of the TEM horn are shown in figure 3.

If Z

0 in eq (12) is chosen to be about 14 ft/m, then a 36-cm long "TEM"

horn can sustain a traveling-wave current along the antenna for the frequency

range of 100 MHz to 8 GHz. When Z 0 is lower than 14 ft/m, the current

distributions along the antenna are similar to standing waves. On the other

hand, when Z0 is much higher than 14 ft/m, the current distribution is

overdamped, and the radiation efficiency of the antenna is expected to be very

low because the antenna is acting like a load termination.

Several resistively loaded "TEM" horns have been made by sputtering

copper on polycarbonate substrates (£r=3). The required resistive-loading

profile was obtained by moving the substrate through a stationary mask.

3.2 Current Distribution

The current distributions on the resistively loaded, 36-cm long "TEM"

horn are calculated numerically using the method of moments for the frequency

range of 10 MHz to 5 GHz. The discussion of the numerical technique used to

calculate the current distribution on the resistively loaded "TEM" was given

briefly in section 2.1.

The current distribution at frequencies above 100 MHz is a traveling

wave, whereas that below 100 MHz exhibits some standing-wave component due to

a reflection from the end. Figure 4 shows the current distribution at 1 GHz

along with the experimental results. The current distribution measurement was made using a 1-cm diameter loop with a beam lead Schottky diode. The

discrepancy between theoretical and experimental results is mainly due to

experimental difficulties encountered in measuring current distribution using

the electrically small loop antenna.

10
3.3

Driving-Point Impedance

Figure 5 shows the driving-point resistance and reactance obtained by

the method of moments along with the experimental results. The experimental

results were obtained using an automatic network analyzer. The impedance of

the resistively loaded "TEM" horn typically has a resistance of about 70 a and

a capacitance of about 27 pF in a series configuration.

3.4

Reflection Coefficient

The input reflection, coefficient of the 36-cm long resistively loaded

"TEM" horn is shown in figure 6. The reflection coefficient typically stays

below 0.5 for the frequency range from 100 MHz to 8 GHz as shown in this

figure. For comparison, the reflection coefficients of a 36-cm long

conducting TEM horn and a 1-m long CAL TEM horn are also shown in figure 7.

This figure indicates that the reflection coefficient of the TEM horn has been

significantly improved through resistive loading, and that the reflection

coefficient of the 36-cm long resistively loaded "TEM" horn is comparable to

that of a 1-m long CAL TEM horn. On the other hand, the reflection

coefficient of a conducting TEM horn is very high, particularly at the

low-frequency range (0.98 at 100 MHz), and shows an oscillatory nature above

1 GHz due to multiple reflections between the throat and the aperture as shown

in figure 7.

3.5

Radiation Power Pattern

To obtain the far-field radiation power pattern of the resistively

loaded "TEM" horn, it is assumed that the current flows in the direction of

the axis of the antenna, and that transverse components of current are ignored. Once the current distribution of the antenna is determined, the

far-field radiation power pattern in the E plane (EG i ls Qiven by:

11
( 26 )

ii -jkr

E (e) = jw sin (e - A/2) —

ii 4irr / I (z‘ ) e-jkZ ' C0s (6 - i/2)

dz'

% e f

,

, 1% -jkz ' cos (6 + a/2) . , -Joo sin (6 + a/2) ——

j

I z (z ) e dz .

The far-field radiation power pattern in the H plane (Ej^ is given by:

E r

, (e) = 2 sin (a) E r

, .(e). (27)

where

sin (a) = sin (a)

1 2 2

1 - cos 6 . cos (a)

(28)

The geometry considered is shown in figure 8. The theoretical results of

far-field power patterns in the E and H planes are shown respectively in

figures 9 and 10.

Experiments to measure radiation power patterns of the antenna in both

the E and H planes were performed in an anechoic room using a standard horn as

a transmitting antenna. The results are also shown in figures 9 and 10. It

is found from these figures that the half-power beamwidths of the antenna are typically 100° in both E and H planes at 1 GHz. The directivity of the

antenna is then roughly estimated to be about 6 dB at 1 GHz.

4. FREQUENCY DOMAIN RESULTS

The frequency-domain representation of the receiving transfer function

S r (f) of the resistively loaded "TEM" horn is given by:

V .(f) -h (f) Z (f)

L e L E. (f)

= Z (f) + Z. (f)

* inc o L

(29)

where V|_ ( f ) is the load voltage (V), E^ nc

i s normal incident

electric field (V/m) , he(f) is the effective length of the antenna (m),

Z 0 (f) is the driving-point impedance of the antenna (ft), and Z|_(f) is the

load impedance (ft).

12
Using the effective length of the antenna (which is defined as the

moment of its current distribution derived from the input current) and the

driving-point impedance of the antenna, we calculate the frequency-domain

representation of the receiving transfer function of the antenna using

eq (29). The receiving transfer functions of the resistively loaded "TEM"

horn and the conductive TEM horn are shown in figures 11 and 12,

respectively.

Experiments were performed using a time-domain antenna range with a time-domain automatic network analyzer. The experimental results of the

receiving transfer function of the resistively loaded "TEM" horn and that of a conductive TEM horn of the same size are also shown in figures 11 and 12,

respectively.

The theoretical and experimental results for the receiving transfer

function of the resistively loaded "TEM" horn agree well. The receiving

transfer function of the antenna is flat to within ±3 dB from 20 MHz to 7 GHz.

On the other hand, the experimental results of the transfer function for a conducting TEM horn indicate that there are strong resonances in the horn and

that its transfer function is not nearly as flat as that of the resistively

loaded "TEM" horn.

5. TIME-DOMAIN RESULTS

Once frequency-domain solutions are determined, transient fields for a known input waveform can be found using the FFT technique. The experiments

were performed using a time-domain antenna range with a time-domain automatic

network analyzer. The impulse generator generates extremely narrow (70 ps)

duration impulses with flat spectrum amplitudes greater than 60 dB V/MHz up to

5 GHz, as shown in figure 13. 70 ps was used both as a driving voltage for

the investigation of transmitting transient responses and as an incident

impulse field for the investigation of receiving transient responses. The

theoretical and experimental transient characteristics of receiving and

transmitting responses for the resistively loaded "TEM" horn are shown in

figure 14. As this figure indicates, there is an agreement between theory and

experimental results of the receiving and transmitting responses.

13
6. CONCLUSION

For directional reception or transmission of picosecond pulses with

minimal distortion, a short "TEM" horn with continuously tapered, resistive

loading was developed, and was found to be broadband and nondispersi ve with a low VSWR. The receiving transient response of the resistively loaded "TEM"

horn indicates that the shape of 70 ps is well preserved. Theoretical

computations using the method of moments and the FFT technique were performed

and agreed well with time-domain measurements. The short "TEM" horn with

continuously tapered resistive loading measures fast, time-varying, transient

fields with minimal pulse-shape distortion due to nonlinear amplitude or phase

characteristics of the transfer function. Although the antenna described in

this paper was designed for a particular application, the theoretical design

technique presented indicates that the approach can be used in other

applications if extremely wide bandwidth and extremely low reflection

coefficients are required.

14
References

[1] Kanda, M., The characteristics of a relatively short, broadband linear

antenna with tapered resistive loading, International Symposium on Antennas and Propagation, Digest, 230-233, Stanford Univ., CA

(June 1977).

[2] Kanda, M., A relatively short, cylindrical broadband antenna with tapered

resistive loading for picosecond pulse measurement, IEEE Trans. Antennas

Propagat. AP-26 , No. 3, 439-447 (May 1978).

[3] Harrington, R. E., Field Computation by Moment Methods (New York: The

MacMillan Company, 1968).

[4] Wilton, D., Digest of numerical and asymptotic techniques for

electromagnetics and antennas. University of New Mexico (March 1978).

[5] Wu, T. T., and King, R. W. P., The cylindrical antenna with nonreflecting

resistive loading, IEEE Trans. Antennas Propagat. AP-13 , No. 3,

369-373 (May 1965).

[6] Shen, L. C., and Wu, T. T., Cylindrical antenna with tapered resistive

loading. Radio Science 2 , No. 2, 191-201 (Feb. 1967).

[7] Taylor, C. D., Cylindrical transmitting antenna: Tapered resistivity and

multiple impedance loading, IEEE Trans. Antennas Propagat. AP-16 , No. 2,

176-179 (March 1968).

[8] Baum, C. E., Resistively loaded radiating dipole based on a transmission

line model for the antenna, AFWL EMP1-6 , 6., SSN-81, 1-27 (1970).

[9] Kanda, M., Transients in resistively loaded antennas and their comparison

with conical antennas and TEM horns, International Symposium on Antennas

and Propagation, Digest, 13-16, Univ. of Maryland, MD (May 1978).

[10] Kanda, M., Transients in resistively loaded antennas and their comparison

with conical antennas and TEM horns, NBSIR 78-876, National Bureau of

Standards, Boulder, CO (March 1978).

[11] Harrington, R. F., Time-Harmonic Electromagnetic Fields (McGraw-Hill Book

Co., 1961).

[12] Harrison, C. W., Jr., and Williams, C. S., Jr., Transients in wide-angle

conical antennas, IEEE Trans. Antennas Propagat. AP-13 , 236-246,

(March 1965).

[13] King, R. W. P., The Theory of Linear Antennas (Harvard University Press,

Massachusetts, 1956).

15
Figure Captions

Fig. 1 One-dimensional model for a resistively loaded "TEM" horn.

Fig. 2 Biconical model for a conductive TEM horn.

Fig. 3 Resistively loaded "TEM" horn.

Fig. 4 Current distribution of a resistively loaded "TEM" horn.

Fig. 5 Driving point impedance of a resistively loaded "TEM" horn

(a) Resistance;

(b) Reactance.

Fig. 6 Reflection coefficient of a resistively loaded "TEM" horn.

Fig. 7 Reflection coefficients of various TEM horns.

Fig. 8 Geometry for a resistively loaded "TEM" horn.

Fig. 9 Radiation power patterns in the E plane.

Fig. 10 Radiation power patterns in the H plane.

Fig. 11 Transfer function of a resistively loaded "TEM" horn.

Fig. 12 Transfer function of a conductive TEM horn.

Fig. 13 Time-domain measurement:

(a) Time-domain picosecond impulse;

(b) Spectrum amplitude of picosecond pulse.

Fig. 14 Time-domain response of a resistively loaded "TEM" horn.

16
Fig. 1 One-dimensional model for a resistively loaded "TEM" horn.

17
Fig. 2 Biconical model for a conductive TEM horn.

18
Fig. 3 Resistively loaded "TEM" horn.

19
COCO

( a/vlu ) Noiinamisia iNBdanG

20

Current

distribution

of

a

resistively

loaded

"TEM"

horn
REACTANCE

(fl|

FREQUENCY

(a) Resistance

3 -10 r

-10 -

i -io -

o -10 1 I

i 10 MHz 100 MHz l GHz FREQUENCY

(b) Reactance

Fig. 5 Driving point impedance of a resistively loaded "TEM" horn.
RESISTIVELY

LOADED

'TEM'

HORN

1N3 10 Idd 3 00 3All03T33b

<£>

cn

22

Reflection

coefficient

of

a

resistively

loaded

"TEM"

horn
^

RESISTIVELY

LOADED

TEM'

HORN

Fig. 7

Reflection

coefficients

of

various

TEM

horns.
IN

PLANE

OF

YZ

>-

24

Fig. 8

Geometry

for a

resistively

loaded

"TEM"

horn.
THEORY

E PLANE PATTERN

1 GHz

EXPERIMENT

Fig. 9 Radiation power patterns in the E plane.

25
H PLANE PATTERN

1 GHz

THEORY — EXPERIMENT

Fig. 10 Radiation power patterns in the H plane.

26
RESISTIVELY

LOADED

TEM

HORN

(THEORETICAL) CDo

CD

CD

>-CD

r*si

I I i_l I I 1

CD CD CD CD CD

*— OJ CO ”3-

I

I I I

lap) NOliONOd HddSNVdi do dOOilNOVIAI

27

Fig.

11

Transfer

function

of

a

resisti'vely

loaded

"TEM"

horn.
TEM

HORN

RECEIVING

CHARACTERISTIC

N

(9P) NO I iONflJ HddSNVHi

28

Fig.

12

Transfer

function

of

a

conductive

TEM

horn.
(a) Time-domain picosecond impulse

Fig. 13 Time-domain measurement.

29
30

Fig.

14

Time-domain

response

of

a

resistively

loaded

"TEM"

horn.
NBS-1 14A (REV. 5-78)

U.S. DEPT, of COMM. PUBLICATION OR REPORT NO.

BIBLIOGRAPHIC DATA , SHEET 1 NBSIR 79-1601

2. Go\ recession No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

The Effects of Resistive Loading on TEM Horns

5. Publication Date August 1979

6. Performing Organization Code

723.03

7. AUTHOR(S)

Motohisa Kanda

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 7233281

11. Contract /Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) 13. Type of Report & Period

Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

For directional reception or transmission of picosecond pulses with minimal

distortion, a short transverse electromagnetic (TEM) horn with continuously tapered

resistive loading was developed, and found to be broadband and nondispersive with

a low VSWR. The receiving transient response of the resistively loaded "TEM" horn

indicates that the shape of 70-ps impulse is well preserved. The theoretical

analyses using the method of moments and the fast Fourier transform (FFT) technique

were performed and agreed well with time domain measurements.

17. KEY WORDS (sin to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) ^ . rc - . . T-.T-.rr. j r Broadband; directivity; effective length; FFT; method of

moments; nondispersive; picosecond pulse; resistive loading; TEM horn; transfer

function; transient.

18. AVAILABILITY Unlimited

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19. SECURITY CLASS

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20. SECURITY CLASS

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UNCLASSIFIED

21. NO. OF PAGES

22. Price

U.S. GOVERNMENT PRINTING OFFICE: 1979-0-677-072/1299

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