NATL INST. OF STAND & TECH

AlllDb 33^flM7

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"'"tSAM Of * NBS TECHNICAL NOTE 1090

Reference

NBS

PUBLICATIONS

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards
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„ MBS CO

Finline Diode Six-Port: /^^T

Fundamentals and Design Information

e^ 9 ^

M. Weidman

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued December 1985
National Bureau of Standards Technical Note 1090

Natl. Bur. Stand. (U.S.), Tech Note 1090, 40 pages (Dec. 1985)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1985

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
CONTENTS

Page

1. Introduction 1 2. Preliminary design 2 2.1 Materials and fabrication techniques 2 2.2 Six-port geometries 2 2.3 Transmission line type 5 3. Initial hardware and testing 6

3.1 Waveguide-finline-waveguide (WFW) transition 6

3.2 Beam lead diode sensitivity and linearity tests 9

3.3 Series slot tests 14

4. Redesign 15

4.1 Leakage correction 15

4.2 Waveguide housing 16

4.3 Taper design 17

4.3.1 Dielectric taper 17

4.3.2 Finline taper design....,.,..,.. 24

4.3.3 Soft substrate designs 29

5. Summary and future work 32

6. Ack nowl edgment 32

7. References 32

m

Finline Diode Six-Port: Fundamentals and Design Information

M. Weidman

Electromagnetic Fields Division

National Bureau of Standards

Boulder CO 80303

The preliminary design and testing of a planar circuit six-port

with diode detectors is described. The planar circuit medium was chosen to be finline, and all preliminary work was done in WR-42

waveguide (18-26,5 GHz). The finline substrate was alumina, and

initially commercial beam-lead diodes were bonded to the finline

metal izati on. The goal is to design an integrated circuit which

could be fabricated on one chip (with diode detectors) and used as part of a six-port network analyzer in the waveguide bands above

18 GHz. Initial designs proved to be unsatisfactory because of

high losses and reflections. Most of the problems have been

solved, and a usable integrated finline circuit is a good possibility for a millimeter wave six-port.

Key words: diode six-port; finline; integrated circuit; millimeter

wave; network analyzer; planar circuit; six-port.

1. Introduction

A six-port is a linear passive network having six ports. It is used to measure the complex scattering parameters of devices from submicrowave to optical frequencies. One of the ports is connected to a signal source, another

to the device under test, and the remaining four ports to power detectors.

Present six-port work in the millimeter wave region has shown a need for sen- sitive detectors and smaller size six-port networks. Broadband power sources

above 40 GHz have very limited (1 mW to 50 mW) power outputs. Thermistor

power detectors on a dual six-port system would have less than tenths of

milliwatts to work with, and this seriously degrades the performance of the

system. Diode detectors would reduce source power requirements by 10-15 dB

but would require additional calibration steps to characterize their nonlinear

power response. The size of the six-port network plus detectors is critical

because of the need for temperature control and problems with flange alignment

and repeatibi 1 ity. Temperature control is accomplished by housing the network

and detectors in a proportionally controlled heat sink. A physically large
six-port, with the heat sink, is heavy and creates problems with flange alignment. An integrated diode finline six-port would be at least an order of

magnitude smaller than existing designs.

Some of the early designs with finline on alumina pointed out loss and

reflection problems. Most of these problems have now been solved, and the

next step is to build a prototype six-port using beam-lead diodes bonded to

the finline.

2. Preliminary design

2.1 Materials and fabrication techniques

It was decided that if the final design were to have diodes integrated

into the microwave-millimeter wave circuit, a hard substrate such as alumina

(AI2O2) should be used for preliminary microwave design and testing. NBS fabrication facilities were used as much as possible during the development

stages. Metal ization of the alumina was a thin layer of chrome (0.05 ij,m) and

then gold built up to several skin depths (0.15 lam evaporated plus 3 ^im plated). Quartz or glass could also be used as a substrate, but the initial

idea was to eventually use silicon on sapphire technology, and alumina was chosen because of its similarity to sapphire.

2.2 Six-port geometries

Two types of six-port geometry were considered (fig. 1). The first uses three nondi rectional probes along with one directional coupler to make a sixport network. The spacing of the three nondi rectional probes should be approximately \q/6 where \^ is the guide wavelength [1]. The second geometry

can be realized by placing short circuits on the side arm of three directional

couplers where there would normally be a matched termination [1]. The proper

phase relationships between the detectors at the other side arm ports are obtained by making the relative distances to the three short circuits differ

by ^q/6. A series slot six-port is equivalent to the one using three non- directional probes. The diodes are placed in series with the finline and

spaced \q/6 apart. Figure 2 shows the two types of six-ports realized in finline. The series slot configuration has already been proven useful in a WR-42

waveguide six-port.
P4) (Ps) (Pe

G>

-^^A^

["— f "I* f-»^

-AWfl=Ag/6

(a) Three nondirectional probes plus one directional coupler.

&

<$'^i .1

ww-

(b) Equivalent to (a) with shorted couplers.

Figure 1.Two convenient six-port realizations.
Waveguide

Housing

A' '^ I ^Substrate

Finline Circuit

Reflecting Cavity

Waveguide

A-A' Narrow

Dimension

Substrate

Load

(a) Shorted coupler six-port

dc Lead

Waveguide

Directional Coupler Lossy Material

A-A' Narrow

Dimension Spaced

(b) Series slot six-port

Figure 2. Finline substrate metalization for two six-port geometries.
2.3 Transmission line type

After doing an extensive literature search, it was decided that finline

would lend itself to the realization of a six-port with diode detectors.

Finline, proposed by Meier [2], is a printed or metalized substrate circuit

placed in rectangular waveguide in the E plane, or parallel to the electric

field. In its simplest form it is a dielectric loaded, ridged waveguide with

very thin ridges. Finline was chosen for its adaptability to rectangular

waveguide and the integration of the diode detectors. The six-ports will be

used mainly for rectangular waveguide measurements above 18 GHz. Two other

types of transmission line which were considered for an integrated six-port

are microstrip and suspended substrate, but they are not as easily adapted to

waveguide as finline. Reference [3], with 94 references, gives a good summary

of E plane millimeter wave technology.

After the decision to use finline, some initial design parameters were estimated using the available literature [4,5]. It was decided to do all the

preliminary work in the WR-42 waveguide band (18-26.5 GHz). This is the

lowest frequency band in the range of interest, and an existing single sixport could be used to make measurements on preliminary hardware. The main

parameters of interest for designing the six-port in finline are X^ (guide

wavelength) and impedance. Impedance in finline or rectangular waveguide can

be defined in more than one way, so care must be taken to understand which

definition is used in the literature. Generally impedance can be defined as

2 2

wave, voltage/current, (voltage) /power, or power/ (current ) .

The parameters X and Z (impedance) are a function of waveguide dimensions (a and b), substrate thickness (s), substrate dielectric constant (er),

and slot width (d), all shown in figure 3. For alumina, e^ is approximately

10. The thinnest practical substrate is about 0.1 mm, and if the design is to

be scaled over the frequency range from 18 to 100 GHz, the substrate for WR-42

would be about 0.6 mm thick. The guide wavelength in a typical finline on 0.6 mm alumina substrate is approximately one half the free space wavelength {Xq) . A typical range of impedances is 100-400 ohms, depending on slot width (d) and

impedance definition. From these initial rough estimates, some preliminary

hardware was built and tested.
Dielect

Substrate

(£r)

Metalization (Fins)

—\ Rectangular

X

Waveguide

Figure 3. Unilateral finline cross section with relevant dimensions.

During the literature search on finlines, several papers were found on the design of finline and slotline directional couplers [6-12], Finline is a special case of slotline, and for narrow gaps there is little difference

between the two. Most of the finline papers give theory and data based on finlines built with soft duroid [e^ = 2.22) substrates. The results from the

literature were modified to approximate parameters for alumina substrate. An

initial design for a finline directional coupler has been completed, but no fabrication or testing has been done to date.

3. Initial hardware and testing

3.1 Waveguide-finl ine-waveguide (WFW) transition

Since the six-port will be used to make measurements in rectangular waveguide, a transition to finline is necessary. Also, the only way to use the

existing six-port to make finline measurements is at a rectangular waveguide

port. Two transitions were fabricated on one 5 cm x 5 cm substrate. Figure 4

shows the two circuits. One finline has a center gap of 0.381 mm and the

other 0.762 mm. The taper from the narrow waveguide dimension (4.318 mm) to

the final finline gap is linear and approximately 20 mm long. The metalized

substrate was placed through two 0.7 mm wide, longitudinal slots milled into

the center of the broad walls of a WR-42 straight section of waveguide. The
metal ized side was prevented from touching the waveguide by a thin (0.08 mm)

sheet of Mylar. This was done so that all metalized sections are dc isolated.

After centering the circuit in the waveguide, the narrow walls were squeezed

with clamps to hold the substrate in place.

Initial loss and reflection tests showed much higher loss and reflection

than anticipated (3-10 dB loss and reflection coefficient > 0.4). It appeared

that there was considerable leakage from the finline where it protruded from

the waveguide.

Initial loss measurements were made by placing a thermistor mount at the

input and output of the transition and calculating Pout''''^in* Reflection coefficient measurements were made using the single six-port looking into one port

of the transition with the other port terminated in a matched load. More

accurate but time consuming sliding short loss measurements [13],

Metalization

^^AIunnina Su

0.762 mm gap

1

0.381 mm gap

bstrate

Figure 4. First finline fabrication (two waveguide-finline-waveguide transitions).
showed the loss of the waveguide-f inl i ne-waveguide transition (WFW) to be in

the range of 3-5 dB for the 0.762 mm finline and 6-10 dB for the 0.381 mm finline.

The loss in dB measured with a sliding short is 10 log ti^, where ti^ (twoport maximum efficiency) is

a and

n. =—?I (1)

1 + /I - 4T2

T =T-r-r^

Z7 , (2)

1 + r'

r + r

' 'max I 'mi n ,^.

r = 2

' ^^^ and 1^1 - Irl

' ' ma X I ' mi n , .. r, = 2 • (^)

The quantities IrL^^ and I rL^ „ are the maximum and minimum reflection ' I I iild A I I 111 I II coefficients as measured by the six-port at the input to the WFW transition

with a sliding short moved at the output.

Other loss parameters such as |S2i|^ and r\ J_ _ r. (efficiency of twoport with matched load) are

|S2iP = r(l - |Sn|)2, (5)

and

The loss varied considerably depending on finline orientation and clamping

pressure. Additional plating was done on the metal ization to assure enough

skin depths of conductor, but the lowest loss achieved on the 0.762 mm finline

was still in the 2-3 dB range. Later it was discovered that the metalization

should extend only to the outside of the broad waveguide wall and not beyond

it. Waves propagating at right angles to the normal transmission line mode

will then see an open circuit \j/4 from the inside of the waveguide wall--Xj

is wavelength in the dielectric (eq ~ 10), and the standard waveguide wall

thickness is approximately X^/4 (1 mm).
The reflection coefficient looking into the transition was in the range

0.1-0.5 across the band. Both loss and reflection were an order of magnitude

worse than expected.

At this time tests were also made with a thin, lossy material placed so

as to terminate the finline in the center of the finline section. This type

of material would be used to terminate the side arm of a directional coupler

or a broadband diode detector mount fabricated in finline. The lossy material

was placed on either side of the substrate in the form of a tapered wedge between the two metal ized fins. Location of the lossy material did not seem to

affect the loss very much. The loss in this case was not nearly high enough.

The terminated finline should have had a very high loss (> 40 dB). The

primary loss and termination problems appeared to be caused by leakage out of

the structure and leakage around the termination. The high reflection coefficient was caused mainly by the abrupt change from air filled waveguide to

slab loaded waveguide.

3.2 Beam lead diode sensitivity and linearity tests

After completing the transition loss and reflection tests, a beam lead

diode was attached across the 0.762 mm gap finline (using an ultrasonic

bonder). One of the original ideas was to compare the reflection coefficient

of the plain finline transition to the diode loaded finline. This would give some idea of the impedance relations between the finline and the diode.

However, since the finline reflection was initially so high, no usable imped- ance information was obtained for the diode mounted in the finline.

Sensitivity and power linearity of the diode mounted in the finline

structure were measured. The transition, with diode in place, was terminated

by an adjustable short circuit at one of the ports. The other port was then

the input of a tunable diode detector mount. Both direct dc detection (using

a digital nanovoltmeter) and ac (source amplitude modulation with synchronous

receiver at diode) were used. During these tests it was noted that since the

diode was a low to medium barrier Schottky diode, dc bias (approximately 3 \l^)

had to be applied to the diode to achieve the lowest noise level. Sensitivity

was determined by setting up a known amount of input power with a calibrated

thermistor mount and then using a combination of level set and rotary vane
attenuators to reduce this power from +10 dBm to -60 dBm. The sliding short

tuner on the output of the finline detector was adjusted to give maximum sen- sitivity at each frequency.

The noise level was near the predicted -50 dBm level. The actual specifications for Schottky diodes are in terms of TSS (tangential sensitivity)

which is approximately 4 dB above the noise level. This compares to a bolometric detector (thermistor mount), more commonly used with six-port systems,

of about -45 dBm using the best instrumentation (1 p,V resolution voltmeter and

low thermal relay scanner). Signal levels at the six-port detectors should be

40 dB above this noise level for 0.01 percent power resolution in order to

fully utilize the six-port capability for measuring reflection coefficient.

Improved diode and mounting design can probably improve the diode detector

performance, at best, another 10 dB for an improvement of 15 dB over the

thermistor detector. This means 15 dB less power required from the source.

Sources in the range of 10-50 mW would be satisfactory.

Power linearity, or diode square law response, was measured using the

same techniques described above. The linearity was compared with the rotary

vane attenuator, which is accurate to within 0.02 dB in the lower portion of

its range. The diode must be loaded (resistor in parallel with diode outside

of waveguide) in order to even approach a square law response. The results of

these measurements are shown in figures 5-7. Figure 5 shows the diode re- sponse with a 200 kQ load resistor over a range of input power levels from

dBm to -50 dBm. The straight line is a perfect square law response. Figure 6

shows diode response for different values of load resistor. Figure 7 is an expanded vertical scale plot with both 100 kQ and 200 kQ load resistors. In the region of power levels in figure 7 (-48 dBm to -20 dBm), the diode detector should exhibit much better linearity. Perfect square law response would

be a straight horizontal line. Any deviation from a straight line (>0.01

percent) adds an additional step to the six-port calibration. As can be seen from figure 7, there is an overall vertical spread of approximately 8.3

percent for the 100 kQ load and 11.3 percent for the 200 kQ load. This non- linearity does not prohibit the use of the diode detector in a six-port

system; but the smaller the correction the better. More work will be needed

in the area of detector design (diode parameters and mounting in finline).

10
100

I

O)

OS

O

10

1.0

0.1

0.01

X —

X _

LEGEND

X =200kQ Load

3 ^A bias —Square Law

Response

-40 -30 -20

Input Level (dBm)

-10

Figure 5. Finline diode detector response over the power range dBm to -50 dBm (200 k Q load).

11
0.01

LEGEND

X —No Load Resistor

O—82.5 k Q Load —200kQ Load • —1 MQ Load

-30 -25 -20 -=15 -10 -5

Input Level (dBm)

Figure 6. Finline diode detector response using different values of load resistors.

12
1450

-35 -30

Input Level (dBm)

Figure 7. FinMne diode detector response with expanded vertical scale.

13
3.3 Series slot tests

A second substrate was metalized with two different circuits, each having

three slots, as shown in figure 8. One circuit had a finline gap of 0.762 mm

and the other 0.381 mm. These circuits were built to test the three non- directional probes which make up the correlator or phase information part of

the six-port. The longitudinal spacing of the three slots was the estimated

X /6. The width of the three slots was 0.762 mm. Ream lead diodes were

ultrasonical ly bonded across each of the slots. This places three impedances

(diode impedance) in series with the finline and with X /6 spacing along the

finline. The nondi rectional voltage coupling to each diode will be the ratio

of the real part of its impedance to the impedance of the finline. If the

coupling is weak (approximately 10 dB), each diode will detect approximately

the same level

.

Measurements on the series slot arrangement showed coupling to be relatively close to that estimated by typical models for the Schottky diode impedance and the previously estimated finline impedance. For the 0.762 mm finline, the impedance is approximately 200 ohms. The real part of the diode

impedance should be around 20 to 30 ohms.

Alumina Substrate

Metalization Connection Pads

Figure 8. Series slot finline metalization.

14
Phase measurements were done by looking at the output from each diode,

sliding a short at the output port of the finline circuit, and noting the

position of the short (micrometer readout) for a null at each diode. Converting from distance to phase is a simple matter of knowing the guide wavelength in the rectangular waveguide, since the sliding short was mounted in

WR-42 waveguide. The phase relationships between diodes were not anywhere

near the 120° electrical spacing predicted. The probable cause of the problem

in the phase measurements is multiple high reflections within the network.

4. Redesign

At this point in the work several things became apparent.

a) The leakage/loss problem had to solved.

b) The waveguide housing needed to be redesigned.

c) Multiple reflections within the WFW transition were masking effects

which needed to be measured.

4.1 Leakage correction

Several of the finline papers [14-16] suggested putting serrations or transverse slots along the metalization where it passes through the broad wall

in the rectangular waveguide, as shown in figure 9. This is done to suppress

TEM propagation in the waveguide wall region. This technique is based on an old idea for probing fields in rectangular waveguide without disturbing the

fields inside the guide [17], This technique was tried on the next finline

circuit, but an important point was missed. The metalized serrations should

not extend beyond the outside of the waveguide wall. The serrations are merely open-circuited, quarter-wave transmission lines, sandwiched in the slot

in the waveguide wall. If they protrude beyond the wall, they act like

antennas, coupling energy out of the waveguide. Future fabrication will

correct this problem.

15
Rectangular

Waveguide Wall

•Finline Metalization

Waveguide

1.02 mm Wall

Thickness

Direction of Propagation in Waveguide

Figure 9. Serrations in finline metalization in waveguide wall region.

4.2 Waveguide housing

The waveguide housing was redesigned to more accurately and consistently

locate the finline substrate within the waveguide. The new housing consists

of two waveguide halves split down the center of the broad waveguide walls.

Two slots the same length and width of the substrate are milled into one of

the halves. The two halves are held together by screws which go through thick

plates which form the narrow walls of the waveguide, as shown in figure 10.

I

JL

Screw Slot in one

half of housing

both top and

bottom.

Partial Top View of Housing

p.l.l.l.M.l.l J

m.Mm ^

#6-32 Screws

4 Places

End View of

Waveguide

Figure 10. Waveguide housing for finline substrate.

16
4.3 Taper design

High reflections in the first two finline circuits led to a very intensive study of the propagation characteristics (X^, Z) for finline on alumina

substrate. This resulted in two taper designs. The tapers are used for

impedance matching at transmission line discontinuities. The two tapers are

1) for open waveguide to alumina slab loaded waveguide, and 2) for slab loaded

waveguide to narrow gap finline.

4.3.1 Dielectric taper

Waves propagating down the open rectangular waveguide first encounter a discontinuity at the alumina substrate in the WFW transition. The high dielectric constant of the alumina, even in a very thin slab, concentrates the

fields in the center of the guide and has the same effect on propagation that

ridges or finline have. This effect lowers the cutoff frequency (f ) and, as

a result, increases the bandwidth of the waveguide. The slab also lowers the

impedance of the waveguide, thus creating a high reflection. In order to

study this problem, the transverse resonance method was used [18]. Consideration of a slab, parallel to the E field, centered in the waveguide leads to

the transcendental equation,

Ol.lli/x .It /-7\ tan T— (a-s) = cot t— s, (7)

02 c, c^

where Zqi and Z02 are the respective impedances in the open and dielectric

portions of the transverse section of waveguide; X^. and X^ the cutoff wavelengths in the open and dielectric sections; a, the waveguide width; and s,

the dielectric slab thickness. X^ can be obtained by using the relationship

(8)

along with eq (7). The quantity e^ is the slab relative dielectric constant

and Xq the free space wavelength. The Newton-Rapheson technique was used with

a computer to solve eqs (7) and (8) for Xq/X and X-j (cutoff wavelength of

g ^^ slab loaded waveguide). Figure 11 shows the effect of different dielectric

17
1.5

D5

CD

11 13 15 17 19 21 23 25 27

Frequency (GHz)

Figure 11. Guide wavelength and cutoff frequency effects for different

slab loaded waveguides.

18
slabs on the guide wavelength and cutoff frequency (intersection with frequency axis). One additional complication arises when Xq/\ is greater than

unity, because eq (8) becomes complex and the use of hyperbolic functions in

eq (7) is necessary. The computer program written to solve eqs (7) and (8) is

versatile enough to handle a variety of slab loaded waveguide problems.

Once \q and \^^ have been determined, the taper problem can be solved.

The technique used is a numerical one, and is based on the first part of a paper by Johnson [19]. The assumptions are that multiple reflections and ex- citation of higher order modes are ignored. The taper is broken up into N sections and the reflection coefficient looking into the taper is (see fig. 12)

I n=l

r exp[

n-1

2 I m=0

Y Axl

'm -' (9)

where

^n -I

n-l

n n-l

(10)

Y^ is the propagation constant of the mth section (y

assuming losslessness (a = 0),

= a + jp ) and

m ^m

Ym = J 2%

gm

(11)

—^ AxM- ^^

Narrow

Waveguide

Dimension

x =

n =

Figure 12. Physical representation for numerical solution of dielectric taper.

19
where \„^ is obtained from eqs (7) and (8). Ax is L/N where L is the length

of the taper. The impedances in eq (10) were calculated using the wave impedance definition

^0

Z

= (12)

f

2 Cs

where f^, is the cutoff frequency for an open waveguide and f is the frequency

of interest. The parameter k^ varies from 1 in the open waveguide to a final

value

k Xo 2 f

2 (13)

where X^ is the guide wavelength for the fully loaded guide. The intrinsic

impedance, t]q, is the impedance at infinite frequency for an open waveguide

(rio =377 ohms). For a linear taper, the assumption was made that k^ in eq

(12) varies linearly from 1 to a value (kg calculated using eq (13)), as x varies from to L. In the case of an 0.635 mm alumina substrate, k = 2.524.

Equations (7) through (12) were incorporated into a computer program to solve

for taper reflection coefficient, r, for variable taper lengths, functional

shape, and frequency. Figure 13 shows the results of this analysis. A linear

taper (pointed triangle cut from alumina) 2.54 cm long was added to each end

of the WFW transition, and the improvement in reflection agreed with the

analysis.

The analytical approach, later in the Johnson paper [19], was also used

to analyze different tapers. This involved considerable analytical work along

with numerical approximations, and yielded similar but less accurate results.

Figures 14 and 15 show results from this analysis. This approach takes the

limit in eq (9) as Ax -> 0, which then leads to an integral equation for r (eq

(14)). Integrating by parts leads to an expression for r containing three

parts (eq (15)), the third of which is a difficult expression to evaluate.

The third term is usually negligible. The name, two-term analysis, comes from

the fact that the third term in eq (15) for r is negligible (for longer taper

lengths )

.

20
0.3

0.25

0.2

in 0.15

0.1

0.05

irimax =0.38

(zero length taper)

.5

Tapered Slab-Loaded Waveguide

WR-42, s = 0.635 mm, £r=10

18 GHz

1 1.5 2

Taper Length L/Aq

2.5

and

Figure 13. Numerical solution for reflection coefficient magnitude (|r|)

for a linear dielectric taper.

L

1 H ^ ^ = / 7 (hV ^nZ) exp[-2 / YdT]dx, (14)

^ ax

L , , , X

•' dx ^4y dx ^ ^^

The subscripts and 1 refer to evaluation of the expression at x = and x =

L, and y is the propagation constant (a + jp), which in general is a function

of X.

21
^ »''~~' CD \ / \ T3 \ y f O 1 X 1

':3 1 / \ en

"^ J f \

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4.3.2 Finline taper design

The finline propagation characteristics and taper analysis follow the

same general ideas as the dielectric taper. There is the added complication

of fins or ridges superimposed on a slab loaded v;aveguide. In the case of

finline, it is necessary to solve three transcendental equations before obtaining \q and kg. The physical dimensions occuring in the following equations are shown in figure 3. A transverse resonance solution is described in

[20] and [21]. The sequence of solution for \ starts with an approximate,

closed-form equation (16) for k^^ which is the cutoff wave number for air

[22]. k^g can a tion from [20].

filled finline [22]. k^, can also be solved for with a transcendental equa2tx ca X a ca

= l[l.i(l,0.2 A)^.ncsc(i^)]

_ 1/2

2 b- (16)

\^, is the cutoff wavelength of air filled finline (no substrate). The next

ca ^ step is to solve eq (17) for k^^, the cutoff wave number for dielectric filled

finline [20].

a k cd

] -cot [k,, (f cot _ s)] +/= 0. [- 2 ^ " "^" L-cd ^2 - "^J Y (17)

In eq (17),

Y, -n: cd '- w R^ d b^ -' (18)

where

and

^ = ^n [esc [^]]

-arc tan (-] + in /l + fd s d' — arc tan — + Jin /I

b 's

(19)

(20)

(21)

Then, with k^.^ from eqs (17)-(21) and k^^ from eq (16), the constant k^. can be

sol ved using eq (22)

k

2

cd

(22)

24
The constant k^ is the equivalent dielectric constant at cutoff. The

parameter k ([2]) is the equivalent dielectric constant, which in general is

a function of frequency, kg is used to calculate guide wavelength, \ , using

eq (23)

^ = /( - (%) . (.3,

where k^ is t—. If the dielectric is very thin [-r- << 1], and/or the dielectrie constant is low {e^ » 1), then k^ is not a function of frequency and is

approximately k^. No more computation is necessary in this case to determine

\q. If, however, alumina substrates are used, more computation is necessary.

After determining k^, eqs (24)-(26) are used to get \ [21]. Solve for x in

eq (24)

cot [| X /—) - /e^ tan [^ (1 - x) / j^ ] = 0.

c c (24)

Then solve for ep(f) in eq (25)

cot (I X —^ /ej - y^ ^tan [$ (1 - x) -r^ /I - e ] = (25) V X K^ 1-e '-2 \ 0-' e X k 2 where —r— = -r— from eq (16) and k = —. Equation (26) shows the relationca ° ship between e , kg, and X

g ca

The process from eqs (16)-(26) has been computerized to obtain X as a function of waveguide dimensions -a and b, gap width -d, substrate thickness -s

,

dielectric constant -e^^ and frequency.

In order to completely characterize finline, an impedance needs to be

defined and calculated. One definition and method of solution is given in

[22]. This definition is a voltage-current definition, but as long as the

same definition is used throughout an analysis (for example, throughout a taper in a taper analysis), the results should be accurate. The impedance

(Zq) from [22], is

25
Zo =

Xf

^0

ca

(27)

where k^ and -r-— have already been calculated, and Zq^ is the impedance at

ca infinite frequency from eqs (28)-(31).

where

120 tc2 ca

d''"" X

US r ° _L 4. "n: (a - S ) 1 It? [y- + tan -p -^-^^ ^J cos Yca ca ca

(28)

X

^^ [^ CSC a + ,^^°^^;^ 4- 16 (—)^

[1 - 3sin2a)^ cos^a] (29) ca l+Osin'+a ca

_ 71 d

and

Q = [1 - (t^) ]

- V.

- 1. ca

A simpler approximation for tt- is

'0Bo 2b

X

In CSC a. ca

(30)

(31)

(32)

At this stage, a taper can he analyzed by using either the two-term or numerical technique described in the preceding section. After programing the

X and Zq solutions and doing a two-term analysis, figures 16 and 17 show the

results for various finline tapers on alumina substrate, plotted using a computer.

An exponential finline taper, along with a linear dielectric taper, was fabricated for a waveguide-fi nl

ne-waveguide transition and a series slot

configuration. The serrations were also included, although they protruded

from the waveguide. Measurements showed that the reflection problems were

solved, but the high loss was still there. The loss can be removed as described in 4.1. The reflection coefficient of the WFW transition was less

than 0.2 across the band (Irl < 0.1 over most of the band). The WFW

26
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transition has four discontinuities or tapers, and the results agree well with

the analyses in 4.3.1 and 4.3.2.

The internally terminated WFW transition measured jSnj < 0.07 with loss

> 25 dB. The internal load removes two tapers from the measurement leaving

the result from one dielectric taper and one finline taper. The > 25 dB loss

is an improvement over initial designs and will be improved more by trimming

the metalization outside the waveguide.

4.3.3 Soft substrate designs

An alternate approach to using alumina as a substrate would be to use teflon-fiberglass {e^ = 2.22). One reason for using teflon-fiberglass is that

fabrication (using commercially available, metalized substrates)i s easier.

The lower dielectric constant of teflon-fiberglass also simplifies the analysis of the propagation characteristics of the finline and reduces the effects

of the high dielectric constant of alumina. The diodes would have to be

attached after fabrication of the finline circuit. A design analysis was done

for teflon-fiberglass substrate in order to come up with a prototype six-port

sooner than the work with alumina would allow. No hardware was fabricated,

but a description of the analysis is included here for possible use in future

work. Recently available, empirical equations for \^ and Z were used to

analyze the soft substrate finline [23].

Another recent paper [24] describes a geometric taper design for finline.

This design involves two tangential circles to form the functional shape of

the taper. It is a simple geometric design, and a pattern for finline on teflon-fiberglass was drawn using a computer graphics package. This design

has not yet been implemented. Figure 18 shows the geometry of the two-circle

taper, and figure 19 shows the results of a numerical analysis of the reflection coefficient of this taper compared to a linear and exponential taper

(teflon-fiberglass substrate). The object of the design is to make the point

of tangency of the two circles such that the impedance at L/2 (half the taper

length) is equal to the average of the impedance at either end of the taper.

The impedance calculations were done using the closed form equations [23],

This calculation then gives the gap width at L/2 or P^ in figure 18. The

impedance does not follow the same curve as the physical dimensions, so the

29
Dielectric

Loaded

Waveguide

Region

Narrow Gap

Finline Region

s(x)=taper shape (finline gap spacing)

MH=center of first circle

fh =radius of first circle

Mp^center of final circle

rprrradius of final circle Ps = point of tangency

Z|n+Z Pm=point where z =

s =final finline gap width

out

Figure 18. Two-circle taper showing the geometry of one-half of the taper

(full taper would include mirror image of curve shown).

30
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31
tangency point tends to be toward the open end of the taper (radius rp is much

larger than radius r|^). The slope of the taper at either end is zero, so a two-term analysis would give a reflection coefficient of zero; the derivative

-7— (J?nZ) in eq (15), evaluated at either end would be zero. Figure 19, which

comes from a numerical analysis, does not yield a zero reflection coefficient

(the two-term analysis is only approximate). The two-circle taper appears to

be as good or better than the exponential taper for matching. It is also

easier to make a pattern for the two-circle taper than it is for the exponential taper.

5. Summary and future work

Initial designs of finline circuits which could lead to the fabrication

of integrated diode six-ports for use above 18 GHz were unacceptable. High

losses and reflections led to improved designs. A great deal of effort was

put into analyzing slab loaded waveguide and finline. This effort led to the

design of tapers for finline on alumina. Work was also done on the design of

finline on teflon-fiberglass.

Future work should start with the fabrication and testing of finline on alumina with no protrusion of the metalization from the waveguide. If all

goes well, a directional coupler can be built and tested, and finally a sixport with beam lead diodes in WR-42 waveguide built and tested. In the event

that alumina still gives problems, a teflon-fiberglass substrate can be used

to build a six-port. Ultimately an integrated diode six-port still has a good

probability of realization.

6. Acknowledgment

The author wishes to thank R. Ginley for his work in fabricating the finline circuits and also members of the NBS Cryoelectronics Metrology Group for

their suggestions and the use of their fabrication facility.

7. References

[1] Russell, D. H.; Weidman, M. P. Millimeter wave six-ports. Wiltse, J. C, ed. Proceedings of the International Society of Photoptical

Engineering (SPIE); Vol. 544:162-168; 1985 April 9-10; Arlington, VA.

32
[2] Meier, P. J. Integrated fin-line millimeter components. IEEE Trans.

Microwave Theory Tech. (U.S.) 22(12): 1209-1216; 1974 December.

[3] Solbach, K. The status of printed millimeter-wave printed E-plane

circuits. IEEE Trans. Microwave Theory Tech. (U.S.) 31(2): 107-121;

1983 February.

[4] Gupta, K. C; Garg, R.; Bahl , I.J. Slotlines I, chapter 5 in Microstrip

lines and slotlines. Massachusetts: Artech House, Inc.; 1979. 197-223.

[5] Knorr, J. B.; Shayda, P. M. Millimeter-wave fin-line characteristics.

IEEE Trans. Microwave Theory Tech. (U.S.) 28(7): 737-742; 1980 July.

[6] Gupta, K. C; Garg, R.; Bahl, I.J. Slotlines I, chapter 8 in Microstrip

lines and slotlines. Massachusetts: Artech House, Inc.; 1979. 303-313,

352-362.

[7] Knorr, J. B.; Kuchler, K. D. Analysis of coupled slots and coplanar

strips on dielectric substrate. IEEE Trans. Microwave Theory Tech.

(U.S.) 23(7): 541-548; 1975 July.

[8] Rudokas, R.; Itoh, T. Passive millimeter-wave IC components made of

inverted strip dielectric waveguides. IEEE Trans. Microwave Theory

Tech. (U.S.) 24(12): 978-981; 1976 December.

[9] Kpodzo, E.; Schunemann, K.; Begemann, G. A quadraphase fin-line

modulator. IEEE Trans. Microwave Theory Tech. (U.S.) 28(7): 747-752;

1980 July.

[10] Sharma, A. K.; Hoefer, W. K. Propagation in coupled unilateral and

bilateral finlines. IEEE Trans. Microwave Theory Tech. (U.S.) 31(6):

498-501; 1983 June.

[11] Mariana, E. A.; Agrios, J. P. Slot-line filters and couplers. IEEE

Trans. Microwave Theory Tech. (U.S.) 18(12): 1089-1094; 1970 December.

[12] Levy, R. Directional couplers. Chapter 3, Advances in microwaves. Vol.

1. L. Young, ed. New York: academic Press; 1966. 115-209.

[13] Engen, G. F. Theory of UHF and microwave measurements using the power

equation concept. Nat. Bur. Stand. (U.S.) Tech. Note 637; 1973 April.

63 p.

[14] Meier, P. J. Millimeter integrated circuits suspended in the E-plane of

rectangular waveguide. IEEE Trans. Microwave Theory Tech. (U.S.)

26(10) :726-733; 1978 October.

[15] Meier, P. J. New developments with integrated fin-line and related

printed millimeter circuits. IEEE MTT-S International Symposium Digest

(U.S.). 143-145; 1975 May 12-14; Palo Alto, CA.

[16] VanHeuven, J. H. C. A new integrated waveguide-microstrip transition.

IEEE Trans. Microwave Theory Tech. (U.S.) 24(3) :144-147; 1976 March.

33
[17] Tomiyasu, K.; Bolus, J. J. Characteristics of a new serrated choke.

IRE Trans. Microwave Theory Tech. (U.S.) 4(1): 33-36; 1956 January.

[18] Marcuvitz, N. Propagation in composite guides. Chapter 8.1 in

Waveguide handbook. Vol. 10 of Rad. Lab. Series. N. Marcuvitz, ed. New

York: McGraw Hill Book Co., Inc.; 1951. 388-391.

[19] Johnson, R. C. Design of linear double tapers in rectangular

waveguides. IRE Trans. Microwave Theory Tech. (U.S.) 7(3): 374-378;

1959 July.

[20] Piotrowski, J. K. Accurate and simple formulas for dispersion in finlines. IEEE MTT-S International Symposium Digest (U.S.) 333-335; 1984

May 30-June 1; San Francisco, CA.

[21] Pramanick, P.; Bhartia, P. Analysis and synthesis of tapered finlines. IEEE MTT-S International Symposium Digest (U.S.) 336-338; 1984

May 30-June 1; San Francisco, CA.

[22] Hoefer, W.J.R.; Burton, M. N. Closed form expressions for the

parameters of finned and ridged waveguides. IEEE Trans. Microwave

Theory Tech. (U.S.) 30(12): 2190-2194; 1982 December.

[23] Pramanick, P.; Bhartia, P. Accurate analysis equations and synthesis

technique for unilateral finline. IEEE Trans. Microwave Theory Tech.

(U.S.) 33(1): 24-30; 1985 January.

[24] Beyer, A.; Wolff, I. Finline taper design made easy. IEEE MTT-S

International Symposium Digest (U.S.) 493-496; 1985 June 3-5; St. Louis,

MO.

34
NBS-n4A IREV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS TN-1090

2. Performing Organ. Report No. 3. Publication Date

December 1985

4. TITLE AND SUBTITLE

Finline Diode Six-Port: Fundamentals and Design Information

5. AUTHOR(S)

M. Weidman

6. PERFORMING ORGANIZATION (If joint or ather than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State, ZIP)

10. SUPPLEMENTARY NOTES

Q^ Document describes a computer program; SF-185, PIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most si gnificant information. If document includes a si gnificant

bibliography or literature survey, mention it here) The preliminary design and testing of a planar circuit six-port with diode detectors is

described. The planar circuit medium was chosen to be finline, and all preliminary work

was done in WR-42 waveguide (18-26.5 GHz). The finline substrate was alumina, and

initially commercial beam-lead diodes were bonded to the finline metal ization. The goal

is to design an integrated circuit which could be fabricated on one chip (with diode

detectors) and used as part of a six-port network analyzer in the waveguide bands above

18 GHz. Initial designs proved to be unsatisfactory because of high losses and reflections. Most of the problems have been solved, and a usable integrated finline circuit

is a good possibility for a millimeter wave six-port.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

diode six-port; finline; integrated circuit; millimeter wave; network analyzer; planar

circuit; six-port.

13. AVAILABILITY

QQ Unlimited

I I For Official Distribution. Do Not Release to NTIS

[X] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C

20402.

Q3] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

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PRINTED PAGES

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15. Price

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