CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
A MICROSTRIPLINE 8-WAY POIVER DIVIDER
.1\
A thesis submitted in partial satisfaction of the
requirements for the degree of Master of Science in
Engineering
by
Garin Sandford Bircsak
June, 1978
The Thesis of Garin Sandford Bircsak is approved:
-~-\T;-'1'::'\-~-~
Vaugh'R.;r. Cao':!e
Edmond
s.
Gillespie
~hairman
California State University, Northridge
ii
TABLE OF CONTENTS
SECTION
PAGE
LIST OF ILLUSTRATIONS •••.•••••••••••••••••••••••
iv
A'BS,TRACT • •••••••••••••••••••••••••••••••••••••••
vii
I.
N-WAY POWER • ••••••••••••••••••••••••••••
1
II.
TWO-WAY N-SECTION POWER DIVIDER •••••••••
2
III.
BINARY POWER DIVIDER ••••••••••••••••••••
4
IV.
MICROSTRIPLINE •••••••••••••••••.••••••••
8
v.
FILM RESISTORS ••••••••••••••••••••••••••
11
EFFECTS OF
13
VL
VII.
PARA~~ER
VARIATIONS •••••••••
THE MICROSTRIP EIGHT-WAY POWER
DIVIDER. • • . • . • • • • • . • • • • . • • . . • • . . . • • • • • • •
35
CONCLUSIONS • ••••••••••.••••••••••••••••••
44
BIBLIOORAPHY. • • • • . • • • • • . • • • • • • . • • . • • • • . • . • • • • • • •
46
APPENDIX: COMPUTER PROGRAM......................
48
VIII.
iii
LIST OF ILLUSTRATIONS
FIGURE
PAGE
1.
N-Way Power Divider ••••••••••••••••••••••••
3
2.
2-Way N-Section Power Divider ••••••••••••••
3
3.
Binary 4-Way Power Divider •••••••••••••••••
7
4.
Binary 8-Way Power Divider •••••••••••••••••
7
5·
Microstripline Cross Section...............
9
6.
Divider Gain Response......................
14
7•
Input Reflection Response..................
14
8.
Output Reflection Response.................
15
9.
Isolation 1 Response.......................
15
10.
Isolation 2 Response.......................
16
11.
Isolation 3 Response.......................
16
12.
Gain Variation with Dielectric Constant....
18
13.
Gain Variation with Substrate Thickness....
18
14.
Component Location on Substrate............
20
15.
Gain Variation with Substrate 3 Dielectric
Constant • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . • •
16.
21
Gain Variation with Substrate 2 Dielectric
Constant • •........••.....•... ~ . • • . . . . . . . • • •
21
17.
Gain Variation with Substrate 3 Thickness ••
22
18.
Gain Variation with Substrate 2 Thickness ••
22
19.
Input Reflection Variation with
Dielectric Constant ••••••••••••••••••••••••
24
20.
Input Reflection Variation with Substrate
Th.ickness • •••••••••••••••••••••••••••••••••
iv
24
LIST OF ILLUSTRATIONS
FIGURE
21.
22.
23.
24.
25.
PAGE
Output Reflection Variation with
Dielectric Constant........................
25
Output Reflection Variation with
Substrate Thickness........................
25
Isolation 3 Variation with Dielectric
Constant for Substrate l Only..............
27
Isolation 3 Variation with Substrate
Thickness for Substrate l Only.............
27
Isolation 3 Variation with Dielectric
Constant·. • . . • . . . • . . . . . . . . . . . . . . . . . . . . . . • • • •
26.
Isolation 3 Variation with Substrate
Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • •
27.
28.
29.
28
28
Isolation 3 Variation with Isolation
Resistivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . •
30
Output Reflection Variation with
Isolation Resistivity......................
30
Isolation 3 Variation with Shunt Line
Length. • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • • •
31
30. Gain Variation with Shunt Line Length......
31
31.
Input Reflection Variation with Shunt
Line Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • •
32.
Output Reflection Variation with Shunt
Line Length. . . . • . . . . . . . . . . . . . . . . . . . . . . . . . • •
33.
34
Binary 8-Way Power Divider Substrate l
I.a.you t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.
32
Isolation 3 Variation with Shunt Line
Width......................................
34.
32
Binary 8-Way Power Divider Substrate 2
layout • ..................................••
v
37
LIST OF ILLUSTRATIONS
PAGE
FIGURE
36.
Measured Gain Response......................
4o
37· Meastrred Input Reflection...................
40
38. Measured Output Reflection..................
41
.......................
.......................
41
39·
Measured Isolation l
4o.
Measured Isolation 2
41.
Measured Isolation 3
42
A-1.
Housekeeping Flowchart......................
50
A-2.
Analysis and Printout Flowchart.............
51
A-3·
Program Listing.............................
52
A-4.
2-Way Divider Used in Computer Analysis.....
57
A-5. Computer
42
Run • •••••••••••••• • • • • • • • • · • • • • • • • •
59
A-6.
Computer Tabulation of Computer Input •••••••
61
A-7·
Computer Tabulation of Computer Input •••••••
62
A-8.
Computer Tabulation of Computer Input •••••••
64
vi
ABSTRACT
A MICROSTRIPLINE 8-WAY POWER DIVIDER
by
Garin Sandford Bircsak
Master of Science in Engineering
~Power
division can be realized in many ways but
the method suggested by Chapell lends itself to wide
bandwidth microstripline techniques and is closely examined here.
The fundamentals of N-way power dividers are briefly
reviewed and broadband 2-way power division is introduced.
Binary power division is discussed·and a binary 8-way
power divider is studied in detail.
introduced.
Film resistors are
A new method is described for tuning out the
capacitance effects of the film resistors.
A computer
program is used to simulate the response of the divider
to various modifications of design and design tolerances.
vii
A microstrip 8-way power divider using
beryllia
substrates and tantalum isolation resistors was constructed
and tested.
In the band of 960 to 1215 Mhz, the divider
exhibited a loss of
0~7
dB, a ripple of 0.15 dB, a VSWR
less than 1.2, and isolation greater than 15 dB.
viii
I.
N-WAY POWER DIVIDER
The N-way power divider considered in this paper
is equivalent to N-equal transmission lines shunted together at one end, as seen in Figure 1.
Power entering
at the shunt end emerges with equal amplitudes and phases
at the other ends of the N-transmission lines.
Power
entering any one of the non-shunted ends is isolated
from any of the other N-1 non-shunted ends by use of an
arrangement of isolating resistors (R1 ).
Wilkinson
(lJ*
has derived the matching and isolating
characteristics of this power-divider, shown in Figure 1.
If the source and load impedances connected to the N-way
power divider are
Ro,
then perfect match and isolation
occurs when the following conditions are met:
a)
transmission line lengths
=~
wave
length
b)
c)
= Ro
z1 = INRo
Rl
The Wilkinson power divider is a narrow band device since
matching between the generator and the load is achieved
using a single quarter-wave transformer.
* The numbers in brackets correspond to numbered references
in the bibliography.
1
II.
2-WAY N-SECTION POWER DIVIDER
Cohn (2] describes a circuit used to increase the
bandwidth of two-way power dividers with equiamplitude
output as shown in Figure 2(a).
He derived a relation-
ship between the transmission lines used in this power
divider and Young's
formers.
(3,4} cascaded quarter-wave trans-
This observation can be easily demonstrated by
noting that when equiamplitude and equal phase signals are
traveling down the two arms of the divider, as seen in
Figure 2(a), without any signal changes, the arms may be
joined together to form a series of cascaded quarter-wave
transformers whose impedances are the resultant parallel
impedances of the joined arms, viewed in Figure 2(b).
But it is not as obvious how to select the isolation
resistors.
For a single section, however, the results
given for the N-way power divider previously discussed are
the same, ie., Z1
= /2 Ro
AND R1
= 2 Ro·
For a greater
number of sections, the isolation resistors can be selected
by using the calculations of Cohn (2}.
2
p
1
2
3
4
5
zl
zl
zl
zl
zl
NON-SHUNT
ENDS l TO N
N
zl
N-EQUAL
TRANSJ',IISSION
LINES
SHUNT END
N+l
FIGURE 1.
N-WAY roWER DIVIDER MADE FROM
TRANSMISSION LINES ANTI RESISTORs·
zN
_,- - _z_:2=---.,_--z-=l"---_..,...--:O
RN
3
ZN
---
Rl
R2
Z2
l
a) GENERAL DIVIDER
3
lRo
-
<
2
zl
Zl
Zn
ZN
b) JOINED DIVIDER FOR
IMPEDANCE EVALUATION
FIGURE 2.
2-WAY N-SECTION POWER DIVIDER
-- --
'
III.
BINARY POWER DIVIDER
The basic Wilkinson N-way power divider for N greater
than two, illustrated in Figure 1, is a three dimensional
device and is difficult to build.
is binary, ie., N
= 2n,
If the power division
then a planar device can be built
using the method proposed by Chapell
[5]·
He suggests that
a binary power divider can be designed using several 2way power dividers, as shown in Figures 3 and 4.
The
impedances Z1 through Z4 are picked using Young's tables
[3,4] for cascaded quarter-wave transformers.
Chapell,
however, did not give a method to select the isolation
resistors R1 through R4.
One way to solve this isolation
problem is to use the table given by Cohn [2] for a 2way power divider by realizing that each 2-way can be
analyzed alone and then cascaded.
The values of the
resistors derived give good isolation at the band center
but it is not clear what happens at the band edges since
the 2-way power divider source and load impedances are not
constant.
The binary eight-way power divider shown in Figure
4 is the design used in this project.
It is made from
seven 2-way single section power dividers and one matching
quarter-wave transformer.
The extra quarter-wave line
was added to the circuit to decrease impedance steps
4
5
which could cause, in practice, discontinuities.
The
line impedances were calculated using Cohn's [2] analysis
of power dividers and Young's [4] tables for a four-section
quarter-wave transformer giving a Chebyshev response for
a forty percent bandwidth.
The values of Zl through Z4
z1 = 58.0 ohms, Z2 = 48.8 ohms, Z3 =
Z4 = 43.1 ohms. Isolation resistors Rl
were found to be
51.3 ohms, and
through R were computed using the transmission line
3
equation for a quarter-wave length transmission line of
impedance Zn and load ZL,
Z
0
=Z
ZL
+
Zn
j Zn
j ZL tan {fo ~ )
+
and the 2-way single section power divider isolation
n
resistor equation Rn
= 2(load
impedance).
The load for the first isolation resistor is 50
ohms.
Consequently,
R1
= 2(50
ohms)
= 100
ohms.
The Z1 line transforms the 50 ohm load to 67 ohms,
ZL = (58 ohms) 2/50 ohms = 67 ohms.
But two
z1
33·5.ohms.
lines are joined together forming a load of
Therefore,
R2
= 2(33·5
ohms)
= 67
ohms.
Similarly, the Z2 line transforms the 33.5 ohm load to
71 ohms.
ZL
= (48.8
ohms)2/33·5 ohms
= 71
ohms.
When two
6
z2 lines are tied together it follows that
R3
=2
~(71
ohms)
= 71
ohms.
r
zl
z3
4
Rl
Zl
R3
Zl
3
2
Zl___...--() 1
.___.._ _
FIGURE 3.
BIHARY 4-WAY POWER DIVIDER MADE
FROM THREE 2-WAY 2-SECTION FO\'/ER DIVIDERS
1
6
--------o 5
,.-----t----o 4
------4----o
3
r-;:;::----t----o
2
_ _ _......__--o 1
BINARY 8-WAY POWER DIVIDER MALE FROM
SEVEN: 2-WAY SINGLE SECTION PO'fiER :DIVIDERS
AND ONE INPUT
1L~TCHING
QUARTER-i'lAVE TRANSFORraF.R.
IV.
MICROSTRIPLINE
One class of transmission lines that is pa!ticularly
suited for realization of microwave circuits is microstripline, shown in Figure 5·
Microstripline [6,7] consists
of a dielectric substrate with.a ground plane on one side
and a thin metallic conductor on the other side.
Circuitry
of such lines can be fabricated by photo-etching techniques
applied to metallized substrates, allowing precise control
of line widths ru1d spacings.
The electric field of micro-
wave energy on the lines tends to concentrate near the
conductors allowing for small, simple planar structures
that are easily packaged.
The same processes used to put
metalic conductors on the substrate can also be used to
make film isolation resistors.
Beryllia substrates with gold conductors and tantalum
resistors were used to construct the binary 8-way power
divider discussed here.
Beryllia was chosen for its high
thermal conductivity [6] and the tantalum for its high
resistivity
[6].
The microstripline parameters used in the binary
8-way power divider were found using equations tabulated
by Kwan
[8,9].
For a beryllia substrate with a dielectric
constant of 6.8 and a thickness of 0.050 inches, the
conductor widths and quarter-wave lengths for zl, z2, z3,
8
C01TDUCTOR
,
••
• "'
.-..
I
• •
I
.
0
• •
ol
•
~
•
•
•
I
SUBS~RATE .
'•
•
.
•
"
:
•.,
•
•
.
'
.
• I''
•
,
•
I
I
o
I
. · ·• ' •• :·: ~
,.
.
.. .. . . . .. . . .:
.
.
# •••
.. .
•
•
·~
r :. ,
•
.,
.
..,
•
•
'
-.
ol
..,
•
'
•
..
1
l
h
GROUND PLANE
FIGURE
5.
MICROSTRIPLINE CROSS SECTION
SHOWING SUBSTRATE THICKiTESS, COKLUCTOR
WIDTH,. AND COl\1JJUCTOR THICt""NESS.
and Z4 are respectively 0.050 in. and 1.25 in., 0.070 in.
and 1.23 in., 0.063 in. and 1.24 in., and 0.088 in. and
1.22 in ••
V.
FILM RESISTORS
Film resistors, for all practical matters, are two
dimensional devices.
The film thickness is set when the
resistor substrate is manufactured and cannot normally be
varied by the designer.
Therefore, film resistor design
is simply a matter of determining film length and width,
allowing for heat dissipation and film resistivity.
The
ease of fabrication makes these film resistors practical
components.
But they exhibit capacitive effects to the
ground plane at microwave frequencies.
This capacitance
causes a phase shift across the film resistor which affects
the isolation properties of the power divider.
Shorted
stub transmission lines were joined to the center of the
film resistors to tune out the capacitive effects.
The
film resistor was modeled as a transmission line with
resistance per unit length and a computer program (Appendix)
was used to pick the shorted stub values.
The tantalum film resistivity was chosen to be
100 ohms per square and it was felt that a 100•c temper-
ature rise could be tolerated for the short period of time
by the beryllia.
the equations WL
The resistor sizes were calculated using
==
P/(KAT) and R
= RsL/W
where W, L, and
R are resistor width, length, and resistance.
The thermal
conductivity of beryllia, written as K, is given in the
11
literature as 16 watts per square inch per degree centigrade [6). 6T is the temperature rise and Rs is film
resistivity.
The resistor lengths and widths were calculated
to be 0.100 in. by 0.100 in. for R1, 0.100 in. by 0.125 in.
for R2, and 0.164 in. by 0.231 in. for R3.
VI.
EFFECTS OF PARAMETER VARIATIONS
A Computer Aided Design (CAD) program which simulates
an eight-way power divider was written for the Com-Share
time-share system in Com-Share FORTRAN.
The program is
described in Appendix and could be adapted to other microwave circuits.
The computer simulation was used to varify the
response of the divider and to check the tolerance sensitivity of the various circuit elements.
The quantities
examined by the program are the coupling, the input reflection coefficient, the output reflection coefficient,
and the isolations associated with R1 , R2, and R3.
The predicted response of the power divider as
generated by the simulation is shown in Figures 6 through
11.
These results show a coupling coefficient of 9.17
dB ± 0.05 dB, input and output reflection coefficients
of 0.06 or less and isolation greater than 24 dB with the
selected circuit values.
The results also indicate that
all of the isolation peaks are shifted above band center
frequency.
The power divider was designed to incorporate
long shunt line lengths in order to facilitate the tuning
of the isolation peaks to mid-band.
It was possible to
shift the peaks from above-band center frequency to midband by shorting out one or more loops of the shunt line.
13
9.3
I
/
r--
9.1
--
1---
1020
950
[__-------
e-::::--<
1090
~
v
t
I/
;
1160
1230
FREQUENCY (ii12GAHERTZ)
FIGURE~.
GAIN VARIATION WITH
FREQUENCY
0.12
. 0.10
~0.08
·Z
0
H
E-!Q .06
r:::!
(,)
L-----
...::!
IX!
~0.04
0.02
o.oo
1'---- t----
950
~
1---
1020
---
_./
t----'
v
1090
v
1160
· FREQUENCY (i.1EGAHERTZ)
FIGUrtE 7.
INPUT REFLECTIOl'l VARIATION 'NITH
FREQUENCY
l.----
•
1230
0.12
0.10
Q.,o. 08
.z
0
H
E-10. 06
~
1'--
H
fr-1
l="il0 •.04
~
0:::
~
0.02
o.oo
950
~
~
1---
1020
1090
--
v
v
~
_)........-
1230
1160
· FREQUENCY ( r.1EG AHER T Z )
FIGURE 8.
OUTPUT REFLECTION VARIATION
V/ITH
]'REWUE.NCY
54
1
48
\
:1
J
z
~36
E-1
<
H
0
/'
Cl130
H
24
1-- l-----
950
-- ~
L----
1020
~
v
/
1090
1160
FIGURE 9.
VARIATION
FREQUENCY
~
"""
·-
FREQUENCY ( r::EG All2RT Z)
ISOLATION 1
\
WITH
1230
60
54
1/ \
30
~-
v
24
950
~
v
v·
1020
1\
/
~
1090
~
1160
~
r--
1230
FREQUENCY (IvEGAH.2RT Z)
FIGURE 10.
ISOLATION 2 VARIATION '.VITH
FREQF3NCY
66
7
60
........
~54
-
36 1---
30
l.-----
950
L______.-
_:;;-
1020
/
v
/
\
\
\
I
v
\
""' ~ ~
1090
1160
FREQUENCY (MEGAHERTZ)
FIGURE 11.
ISOLATION 3 VARIATION
FREQUENCY
~ITH
..........
I'-
1230
17
The shunt line sections or loops were produced in a meandering pattern so they could be tied together to give the
correct length necessary to reach mid-band frequency.
The responses also appear asymmetrical to band center
because of these same lines.
Tolerance studies were conducted on all of the
circuit elements.
The dielectric constant, substrate
thickness, and resistance have the greatest tolerance
variation and these also appear to have the greatest effect
on the circuit.
The dielectric constant of beryllia is
a function of the density and purity of the material.
The
material used had a density of 2.88 gm/cc (5% less than
the theoretical maximum of 3.01 gm/cc) and a purity of
99.5%.
The dielectric constant was 6.8± 3%.
The beryllia
substrates were lapped to 0.050 inches ± 0.001 inches
(±
2%)
thickness.
The film resistors were etched to
within 10% of the design value.
Various line lengths were
also investigated since the shunt line lengths were to
be adjusted.
The effects of varying the dielectric constant and
substrate thickness are shown in Figures 12 and 13.
A
± 5% variation causes, in both cases, approximately 0.05
dB variation in coupling at the high end of the band.
The parameter changes in these two examples were considered
uniform for the different sections of the power divider
9.3
I
v
/
//
?
v v r
~
~
!'---~
~
k
L-----~=
t:::---_
~
9.1
v
/
v---
_..-/
'
c:
~~
-- r=--
~~
v
r:,.'t~ v
/
[------ ~
.....
1020
1090
1160
FREQUENCY {IiiEGAHERTZ)
FIGURE 12.
GAIN VARIATION WITH
DIELECTRIC CONSTANT
950
v
/
~ v11.~17
v·
17
v
v--
1230
9.3
v
_./ 7
,y---/ /
"
~ ~. :::--- --:::.
9.1
950
..
-
=
--
k
l---::=
-·
..
vL------:
~-
v
/
~1~
V~~ ~
s?:bc..
.
~ ~ ~~
~~
~,:,
r::
~-
1020
1090
1160
FREQUENCY (MEGAHERTZ)
FIGURE 13.
GAIN VARIATION WITH
SUBSTRJ\TE THICKNESS
1230
19
but this is not true in the practical case since the
power divider is made up of three different substrates,
each of which could have its own characteristics.
Figure
14 shows the three beryllia substrates plus the alumina
substrates used for the interconnected system.
The greatest
"theoretical" coupling imbalance would occur if substrates
two and three are not the same.
Figure 15 shows that
coupling from port 9 to port l is affected very little
by dielectric constant changes in substrate three.
Any
power reflected from substrate three would be isolated
from substrate two by the isolation action of R1 •
This
is not the case for substrate two since reflection of
power here represents power lost.
Figure 16 shows this
loss as a variation of 0.05 dB for a ± 5% variation of
dielectric constant.
This same dielectric variation
causes a 0.05 dB imbalance in the coupling between the
input and output ports.
A similar variation exists for
the differences in substrate thickness, as viewed in
Figures 17 and 18.
The coupling coefficients between the input port and
output ports are fairly insensitive to parameter changes
and are, with close approximation, equal.
The equal
power output is a desirable attribute that makes the
Wilkinson power divider useful.
However, input and output
I
FIGURE 14.
EIGHT-WAY POWER DIVIDER SHOWING
LOCATION ON SUBSTRA.TES
COMPONENT
9.3
I
~
~
~
-f..-!J..
"
~
~ ~.
7."f! I
j
9.1
1020
950
~
~
1090
~
/
1160
~
1230
FREQUENCY (i,1EGAHERTZ)
FIGURE 15.
GAIN VARIATION WITH
DIELECTRIC CONSTA~T
FOH SUBSTRATE 3
ONLY
9.3
.~
/~
/
/
->
1-t:::--
9.1
r---
950
-
-
~-
-
v
~
/
./
.
~
l------- ~ l----- ~
~
,...--
------
1020
1090
1160
FREQUENCY (MEGAHERTZ)
FIGURE16.
GAIN VARIATION WITH
DIELECTRIC CONSTANT
FOR SU3S1'RJ':.TE 2 ONLY
1230
9.3
I
~~
~~
/"'
.·
J__
~-
-=--
~
--===..~
~?
::::::---
~
"'
9.1
1020
950
1090
1160
1230
FREQUENCY (i.1EGAHERTZ)
FIGURE 17.
GAIN VARIATION WITH
ONLY SUBSTRATE 3 THICKNESS
9.3
_./
r--
f:::: ~
------=
9.1
950
[__---'
1--
~
::::::::---
1020
1090
v
v
-- ~
FREQUENCY (l.~EGAHERTZ)
/
------
1160
FIGURE 18.
GAIN VARIATION ~ITH
ONLY SUBSTR~TE 2 THICKNESS
v
..
-~
~
/
/
~
....~
/
1230
VSWR can be a problem.
Variation in parameters cause changes
in line impedances which give rise to power losses and high
reflections.
Figures 19 and 20 illustrate that a ± 5% variation
in dielectric constant or substrate thickness can cause
the input reflection coefficient to change over the range
of 0.03 to 0.10 which represents a VSWR change of 1.06
to 1.22.
The output reflection coefficient, Figures 21 and 22,
shifts with dielectric constant and substrate thickness
and this causes an increase in the coefficient at the
band edges.
The output coefficient changes from 0.02 to
0.06 and the VSWR changes from 1.04 to 1.10 for a
±
5%
variation in these respective parameters.
Three different levels of isolation exist in the
power divider investigated here.
The first level of
isolation occurs when power flowing back from one of the
output ports interacts with one of the R1 isolation resistors.
Half of the power is dissipated in R1 •
The
other half continues on to R2 where half of that power is
dissipated.
This is the second levei of isolation.
One
fourth of the original power travels to resistor R3 where
again half of the power is dissipated in the third level
of isolation.
All three levels have about the same response
.
0.12
0.10
~0.08
.z
/
0
H
80.06
0
~
..:I
i'--.
rzlO •.04
F.!
~
0.02
o.oo
v
!'--. ~
I'- t>;
K
I//
~~
1-----
r-
950
/
~
1020
.---
v
v
/
L---~
v
/
~
,/
l.-----
---
t-------
£.;>7,"1g-
~.11
t-------
---· ------
~
~
- ~l - - '
1090
.-f-.--
€; .. ".I).
1230
1160
· FREQUENCY (r;IEGAHERTZ)
FIGURE 19.
INPUT REFLECTION VARIATION WITH
DIELECTRIC CONSTANT
0.12
0.10
/
o_0.08
-
~
v
v v
v
v/
v
---~ v--- vc.------
------
:--
..,_,..j].!!- t - -
~
/
/
~ t--..
~~ r;:::_::t--
0.02
t--
o.oo
950
1020
v
/
.---.---
t-------
~. ...
~
l---
1---
-----
1160
FREQUENCY (l\:EGAHERT z.)
FIGURE 20.
INPUT REFLECTION VARIATION WITH
SUBSTRATE THICKNESS
1--
s1.r
1-J-'-
-h'"';
~
1090
~
s;,..- -....
1230
~o.os~r-----~--~--~~----4-----+----+----~----4-~
·Z
0
H
80.06
~~~--~~~~---4-----+-----+--~~~--~--~~
0
rr:t
H
~0.04~+---~+-----~~~~--~~~-+--~~----+---~+-4
~
950
1020
1090
1160
1230
· FREQUEN9Y (MEGAHERTZ)
FIGURE 21.
{)UTPUT REFLECTION VARIATION WITH
DIELECTRIC CONSTANT
950
10~0
1090
1160
FREQUENCY (i,:EGAHERTZ.)
FIGURE 22 •
OUTPUT REFLECTION V P.RIATION WITH
SUBSTRAT.S THICKi~ESS
. 1230
zo
to component tolerances.
The third level isolation was
produced on an individual beryllia substrate.
Insofar as
the two remaining isolation levels are not separately constructed, the parameter variations are best studied in
detail by examining the third level isolation.
When the
dielectric constant is varied, the third level isolation
response shifts in frequency.
change causes about a
5%
A 10% dielectric constant
frequency change.
Figures 23
and 24 demonstrate the results of uniform variation in
all three substrates.
Figures 25 and 26 illustrate the
results of parameter changes applied to a single substrate.
The shift in the peak of isolation is related to the
effective shunt line length connected to the isolation
resistor, which affects the phase of voltage crossing the
isolation resistor.
Compensation for the shift can be
made by changing the shunt line length.
The isolation is
hardly affected by varying the substrate thickness (see
Figure 26) and is _shown only to demonstrate that good
isolation will result if all three substrates have the
same thicknesses.
But by looking at Figures 23 and 24,
the effects of varying just the thickness or the dielectric
constant in the first substrate alone can be seen to radically affect the peak of isolation.
This drop in the peak
isolation is because of mismatching between the first
66
60
,.......
~54
ro
_...
:q
0
H48
E-1
<!
H
&542
H
36
30
950
1020
1090
FREQCENCY
(r.~EGAHERTZ)
1160
1230
FIGURE 2J.
ISOLATION 3 VARIATION WITH
.-·DIELECTHIC CONSTI1.NT
SUBS'rHATE 1 ONLY
FOR
,,r \
66
60
II;\'''\
,.......
!d 54
_...
~
/
0
~ 48
lfl
H
/
·-·-~-
~
42
36
'\
w~
k=S5"
::..--~---~
,.-i:"::-45---/~
<
H
0
v// -\\:~
~ ~~-
~~
~
~
=:::::::: ~ r.::;;
r----==:: ~
~~
v'-
30
950
1020
1090
1160
(WEGAHERTZ)
FIGURE 24.
ISOLATION 3 VARIATION WITH
FREQUENCY
SUBSTRATE THICKNESS
FOR SUBSTRATE 1 O~~LY
1230
66
60
~
P-154
ro
...........
z
0
H48
E-1.
<!
1-l
242
H
36
30
950
1020
1090
1160
1230
FREQUENCY (KEGAHERTZ)
FIGURE 25.
ISOLATION 3 VARIATION WITH
DIELECTRIC CO~S~ANT
66
60
~
~ 5.4
.........
~
0
H
48
E-1
<
H
0
(/)
H 42
36
30
950
1020
1090
1160
FREQUENCY ( i.1EG AHERT Z )
FIGURE 26.
ISOLATION 3 VARIATION WITH
SUBSTRATE THICKNESS
1230
29
substrate and the subsequent substrates.
Notice that the
average isolation still remains high as the dielectric
constant or the substrate thickness is varied.
The peak isolation drops also when R1 resistivity
is varied.
A 10% change in resistivity lowers the peak
isolation from infinite isolation to
45 dB of isolation,
but again the average isolation remains high so that the
divider is still quite useful.
Varying R1 by 20% affects
the output reflection coefficient by 0.02.
These effects
can be seen in Figures 27 and 28.
The results of using a shunt line to tune the isolation resistor are visible in Figures 29 through 32.
It
is apparent from these Figures that the greatest effect
is the shifting in frequency of the peak isolation; a
20% change causes a
40 megahertz shift.
Coupling, input
reflection, and output reflection are changed slightly,
but not enough to discredit the use of a shunt line.
Shunt line tuning by 20% increased the coupling 0.08 dB
at the low end of the band and caused the input and output
reflection coefficient to shift but not to increase in
amplitude.
Etching tolerances are a factor since the
shunt line widths were kept small.
typical in thin film work.
A one mil error is
The ten mil line width was
varied from 8 mils to 12 mils and Figure 33 shows that
30
66
\
/ \
I
60
............
~54
p
e.
/
~
--------.---·-.
~
~
.-·-:I-;:::--
~·- 1-
--- --
".......
. . J~ ~h:J
\"
IV
;.
-
~ -·-·-'
36
v
----·-·
.12~·1!·-:YE.:.
'{~ .,.~·/c
\
~
......._
-
~
- ----=::::-- ~
·-·-._. . --·-.. .
,__-
30
1020
950
1090
::::::
--·- --~
1160
1230
FREQUENCY (;~EGAHERTZ)
FIGUHE 27.
ISOLATION 3 VARIATION \VITH
ISOLATIOK RESISTIVITY R
3
0.12
0.10
~0.08
z
0
H
E-10.06
0
~
H
~0.04
p::
t::·
t=:2
r--: ~-
~----~·~~
~
0.02
~~ 1-- t '
·~ -------- q'""'i'cl
~
o.oo
"''<Jhlv-
f-C-'-'- _ _ _
/~-
$
.---;'
7~
~
~ ::..----v-
~----= ~
~
~~~If'--:
~ _--:----;?
~~~£!'::1 r.·. '-':~
950
1020
1090
1160
FREQUENCY (t.1SGAHERTZ)
FIGURE 28.
OUTPUT REFLECTIO=·: VARIATION WITH
ISOLATION RESISITIVITY R3
1230
.)..I.
66
60
,-....
~54
........
:z;
0
H48
E-l
.....:!
H
g42
H
36
30
1020
950
1090
FREQUENCY (ri~EGAHERTZ)
1160
1230
FIGURE 29.
ISOLATION 3 VARIATION WITH
SHUNT LINE LSHGTH L
3
9.3
t
>-.....
"~
I'--
r--..
9.1
1-----
r----
/?
~f?o
-r---
--- :;.~v
L------/ v
CJ:: (;Jo
~---:·
:--(J:::-700
--
'-3=770
f---:;::::.·
r---·-·- ·-·-·--
,.,Q
---- ....LJ::---
950
~
~~
/'""'
/
1020
--
~---
_.;.
-----.:
~-·
~
1090
1160
FREQUENCY UtEGAHERTZ)
FIGURE 30.
GAIN VARIATION WITH
SHill-IT LINE LENGTH L
3
1230
0.12
0.10
I - - 1-·
Q....0.08
~
77
·Z
0
H
E-iO. 06
~
H
!'----
r:r..
~0.04
I~
~
~
0.02
-.'.><
t-!'----
o.oo
~
~-~
k
____:.>< ,_
~
:;:;=:---.
---
/
__;-.-...r---. ___ ' ~£:...
r:------
~v
v v---~
~--
~
---
~
~-------
<
L..~
-
.-700 [___--- 1--~_;.-~--(9(/
~
LJ_;:2:>·
v·
-
p
;
-------- ----
~-------
1230
1020
1090 .
1160
· FREQUENCY (MEGAHERTZ)
950
L------1-:--
FIGURE 31.
INPUT
REFLECTION VARIATION WITH
LINE LEj\GTH IJ3
SHUl'~T
0.12
0.10
~0.08
z
0
H
E-lO. 06
~
H
f;.lo. 04
_.._L3;~
~
r:::~ ~
.
.........
........
~
--L3•7do
-L:):5(,o
./
..............
~~
.................
..........
. 0.02
o.oo
~
-.......·....:
......
950
:::::· ~
~
....-;--:: 1-"
~
1020
-~~
1090
FREQUENCY
~-
(I~::EGAHERTZ)
1160
FIGURE 32 •
OUTPUT
':.;:::"
REFLECTION VARIATION WITH
SHUNT LINE LEl\'GTH LJ
1230
this variation has little effect.
Computer simulation was particularly suitable for a
clear understanding of its tolerance sensitivity parameters,
due to the complexity of the frequency responses of the
binar~
eight-way power divider as compared to the Wilkinson
power divider.
34
66
.;...----WI"'" ;?~ll Jl
30
9")0
1020
1090
1160
FREQUENCY (WiliGAHERTZ)
FIGURE J3.
ISOLATION 3 VARIATION WITH
SHUNT LINE WID1'H W3
.1.230
VII.
THE MICROSTRIP EIGHT-WAY POWER DIVIDER
It was critical in developing the Microstripline
8-Way Power Divider to meet the criteria of designing a
device that was compact, small, and at the same time,
capable of dissipating a large quantity of power.
The
resultant 8-way power divider was constructed in a developmental program at RCA, Van Nuys, California using tantalum
resisters and gold conductors on beryllia substrates which
were aoldered.onto a brass headsink.
Specific line length and line widths were maintained
in planning the layout.
The line lengths were dictated
by quarter-wave Chebyshev matching transformers at the
band center of 1088 megahertz, with a 40% bandwidth.
Four quart.er-wave sections of 1.24 inches were used with
line impedances of 43 ohms, 51 ohms, 49 ohms, and 58 ohms
(see Figure 4).
The line widths were determined by the
line impedances, the substrate dielectric constant (E~6.8)
and the substrate thickness (0.050 inches).
The line
widths were 0.088 inches, 0.063 inches, 0.070 inches, and
0.050 inches, with the largest width representing the
lowest impedance.
A line spacing of two line widths was
attempted but had to be relaxed to 1.6 line widths because
of space restrictions.
Beveled right-angled corners were selected.
35
The
36
'
resistor values were found from isolation requirements to
be 100 ohms, 65 ohms, and 71 ohms.
Resistor sizes were
selected to have lengths and widths of 0.100 x 0.100 inches,
0.100 x 0.154 inches, and 0.164 x 0.231 inches so that
power dissipation temperature rise on the beryllia will be
less than 100 degrees centigrade.
Small gaps were placed
at strategic points in the gold conductors to facilitate
resistor adjustment, using an ohm meter.
soldered closed as a final assembly step.
These cuts were
Meandering
lines of five· and ten mils were used for the isolation
resistor shunt lines; ten mils for R3 and five mils for
the others.
Three beryllia substrates were used in the final
design.
A copy of the negative used to etch the divider
is available in Figures 34 and 35.
Substrate 2 and substrate
3 were etched with the same negative, except the negative
was reversed to give the mirror image on substrate 3.
The tantalum was vapor deposited to a resistivity
value of 50 ohms per square and had to be etched to the
final value of 110 ohms per square.
sodium hydroxide solution
10 •
The
~chant
was a hot
Beryllia is dissolved by
acid solutions, forming poisonous salts.
To alleviate
this problem, a 30% sodium hydroxide solution at 45°C
for three minutes proved successful.
An accelerating rate
'
FIGURE 34.
BINARY 8-WAY POWER DIVIDER SUBSTRATE 1 LAYOUT
FIGURE 35.
·,
BINARY 8-WAY POWER DIVIDER SUBSTRATE 2 LAYOUT
39
of etching was observed, making it important to monitor the
resistance during the process.
The measured resistance
was 10% higher when dry.
The final assembly of substrates were soldered onto
a brass baseplate and measurements of the eight-way power
divider were taken.
In Figure 36 the measure coupling of the different
ports can be seen to be 9.65 dB
~
0.25 dB.
This repre-
sents a loss of 0.5 dB when compared to the computer
simulated response of 9.17 dB
design limits.
~
0.05 dB, but is within
The measured maximum input and output
reflection coefficients, observed in Figures 37 and 38,
were 0.07 and 0.13, respectively, as compared to the
computer model's reflection coefficients of 0.06 and 0.06.
The three levels of isolation are shown in Figures 39,
40, and 41 and were measured having minimum values of
15 dB, 27 dB, and 30 dB.
When evaluated with the computer
model's isolations, these values are approximately 6 dB
lower.
These discrepancies are probably the result of
the many sharp bends and the compaction of the conductors
caused by the small package limitations.
It is possible
that the losses and reflections could be reduced in
...,. .....
950
1020
1090
FREQU~NCY
1160
1230
(~EGAHERTZ)
FIGURE 36·
GAIN RESPONSE
MEASURED
0.12
0.10
<L
g;
0.08
0
H
E-1
0
0. 06
r::::l
H
~
--
:------ r--b-,1
f;1 0.04
~
/
7
~
0.02
o.oo
950
1020
1090
1160
FREQUENCY (i.1EGAHERTZ)
FIGURE 3 7.
MEASURED INPUT REFLECTIOH
1230
~
o:rs
0.1/
~
O.D'f
z
0
H
Q.07
E-i
0
~
H
FJ
o.o~
r=l
0:::
Q,OJ
o.ol
1020
1090 .
1160
FREQUENCY ULEGAHERTZ)
FIGURE J8.
MEASURED OU~ePUT REFLECTION
960
21
20
~
j:Q
ItO
"d
...__..
~
0
H
18
E-i
<J:!
H
0
(/)
vv
17
H
~~
L_
~
/
//
/
/
/
v
~
v
1~
v-~~
/
/
~
v ~v
-~
--- --
1230
-- -·
i--
~
~
[-----
l--~
]3 sG/
-
:---
v
IS'
960
1020
1090
1160
FREQUENCY (l',1EGAHERTZ)
FIGURE 39·
MEASURED ISOLATION 1
1230
- 3s
36"
............
fTl
rz:j
........
34
/
v
2
0
H
8
32
~
/
H
0
en 30
H
2B
~6
1.-- 1/7
~
r---
~
v
..-!-
~
~j~l
~
'IS1d
-
~-.
~
~
~
~
v
1020
960
1090
~
I~ "'I
1160
1230
FREQGENCY (~EGAHERTZ)
FIGURE 40.
MEASURED ISOLATION 2 ·
35
............
·p::
"0
...........
34-
z
0
H
E-l
33
<
H
0
Ui
H
32
vv
960
/
v
/
v
1020
v
I~
v
~
~
?~
./'
1090
FREQUENCY (MEGAHERTZ)
FIGURE 41·
MEASUR.C:O ISOL1.\.TIO N 3
1160
1230
'
future designs by easing the size requirements.
'
VIII.
CONCLUSIONS
The binary eight-way power divider is simple and
easy to construct, and exhibits good performance characteristics.
It is particularly suited for applications in
microstripline circuits because of its planar geometry.
A model for this power divider was developed taking into
account the effects of capacitance upon the isolating thin
film resistors.
The resulting model was used to study the
response of the divider to variations of certain key parameters.
It was found that non-uniform substrates affect
the isolation of the divider and can cause degradation in
the divider.
It was also shown that a shunt line connected
to the middle of the isolation resistor can compensate
for some of the parameter variations.
The binary eight-way divider was fabricated in stripline and shown to have good power divider performance over
the band of 960 MHZ to 1215 MHZ.
It is interesting to note that the isolation performance of the binary power divider is not the same between the various ports.
The isolation improves as more
2-way dividers are involved, since 3 dB of loss occurs
at each junction with an isolation resistor.
In the binary
eight-way power divider, it is possible to gain 3 dB of
isolation at four 2-way isolation resistors.
Approximately
4.7 dB additional isolation results at the turn around
junction where power is lost to the input port.
This re-
sults in a total of a 16.7 dB improvement in isolation.
These effects can be used to simplify the design of a wide
band, high isolation, binary power divider since only the
first levels of two-way dividers are required to have wide
band isolation multisection circuits.
BIBLIOORAPHY
.1.
Wilkinson, E.J.
"AnN-Way Hybrid Power
Divider, 11
IRE Transactions on Microwave
..;;;T;.;;;h;..;;e..;;;o~r,J/.y-..:,a;.;;;n~d;....;;;;T..;;;e..;;;c.;.;;hn=i..;.tq~u..;.e..;:..s, HTT -8 :116-118,
Jan. 1960
2.
Cohn, S.B.
"A Class of Broadband Three-Port
TEM-Mode Hybrids, 11
IEEE Transactions on
Microwave Theor~ and Techniques,
MTT-16:110-116,
Feb. 1968
3.
Young, L.
"Tables for Cascaded Homogeneous
Quarter-Wave Transformers, 11
IRE Transactions on Microwave Theory and
Techniques,
HTT-7:233-238,
Apr. 1959
4.
Young, L.
"Correction,"
IRE Transactions on
Microwave Theor and Techni ues,
MTT- :243-244,
Mar. 1960
5.
Chapell, H.F.
"Binary Power Divider Design
·Approach,"
IEEE Transactions on Microwave Theory and Techniques,
MTT-22:580-581,
May 1974
6.
Altman, L.
"Hybrid Technology Solves Tough
Design Problems,"
Electronics, p 89=104,
June 1973
7.
Goodman, P.
"Microwave Integrated Circuits
Expand Options and Reduce Package Size,"
Electronic Products Magazine, p 39-45,
21 Jan. 1974
8.
Kwon, A.H.
"Design of Microstrip Transmission
Line,"
Microwave Journal, 19:1:61-63,
Jan. 1976
Kwon, A.H.
"Errata,"
May 1976
19:5:71,
10.
Microwave Journal,
Grossman, J.
"A New Etchant for Thin Films
of Tantalum and Tantalum Compounds, 11
Journal of the Electrochemical Society,
116:674,
1969
46
"t{
11.
Parker, W.N.
"DIPNET, A General. Distributed
Parameter Network Analysis Program,"
IEEE Transactions on }ucrowave Theory and
Techniques,
M~r-1?:495-505,
Aug. 1969
APPENDIX
The equations describing the frequency responses
of the various elements used in the power divider were
combined to form the total model and were programmed in
FORTRAN for the use on the Com-Share time-share system.
Flowcharts of the program are given in Figures
A-1 and A-2.
A complete listing of the program is given
in Figure A-3·
Each box in the flowchart contains numbers
to identify the computer program line number to which the
box refers.
The program is an adaption of the CAD program
DIPNET [11) •
The program was written to accept descriptive numbers to describe the circuit to be simulated.
A general
housekeeping main program, charted in A-1, is used to
accept the descriptive data and act upon this data according to instructions given it by the operator.
Typing
"execute" starts the calculation and prints out the program
as illustrated in Flowchart A-2.
The two-way power divider shown in Figure A-4 was
analyzed by the computer.
A copy of the computer run is
given in A-5 and demonstrates how the program is used.
A-6, A-7, A-8, and A-9 are computer tabulations of the
computer inputs used to analyze the coupling, reflections
48
and isolation responses of the eight-way power divider.
t
I
sJ
10
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DATA
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GLNE~RATOR
LATA INPUT
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LOJ'JJ D1iTA INPUT
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2-WAY DIVIDER USED IN CO:MPUTER ANALYSIS
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MAX• DISC1ltPT:Jtl TYPE o'IUMAER=..;l_
DISCRIPTOR SU9-NIJM9ER=2_
PERCENT V!\Rl<'\T!fl:-1=5
!'HAT 0'3 YOU .,..A·'H D·J'lE? ..L
DC l . 3>= 45.000
.011-125.462
-3 .t 77 -73.073
ol02 124.353
o950
.02S-ItR.357
-3 .t 3 6 -RO.Q77
.093 126.030
1.020
.038-115.43:1
-3. I OR -87.017
.082 125.178
t.O<JO
.047-111.446
-3·0R9 -93.9?0
.067 121.787
lol 60
.QS6-I05.901
-J.079-IQQ.Ili2
.048 II 5.206
1.230
DC I~ 3)= 47.500
,QOFo -3fl.21,0
-3.170 -72.719
.095 I l l . 502
.950
.QI9 -9?.. 600
-3.128 -79.711
.OR3 112-279
•• 020
.031 -9'l.l OA
-J.09!) -fl6.640
.070 110.275
lo090
.041 -97.353
-3.080 -93.531
.054 104.228
I .t 60
.052 -93.961
-J.Q71-IOO.,l06
90.017
.oJ6
1·230
DC I I 3)" S2.500
13.R53
.025
-3.1 71 -1?. .t I 5
••)9 7
R6. SOl
.950
.022 -27.421l
-3.(25 -79.075
R2.274
.080
1.020
.029 -54.490
-3.094 -R5.976
74.255
.065
l .090
.039 -65.710
-3.076 -92.836
59.337
I .160
.052
.os1 -69.7fl7
-3.069 -99.672
33.484
.045
lo230
DC l . 3)= ss.ooo
.034
I 7. 631
-3.176 -7!".1')56
76.422
.104
.950
.031) -t2 •.1Rl
69.784
-3. 129 -7R.798
.086
t.020
.033 -37.725
-J.09R -85.6:<2
59.366
.072
•• 090
.04?. -52.147
-3.079 ·92.524
43 .oo 6
.062
lol60
.osJ -S9.34ii
-J.072 -9?.:::29
19.780
o058
1.230
••
FIGURE A-5 (b).
CO:MPUTER RUN
-3-~11
-1.1 57
-·l.tl9
-.1.095
-3-0RI
-67.967
-14.64'1
-RI
.~6>;
-'n.R42
-94-J'D
-.1.1R6 -70.?.07
-3.13 7 -..77.1)40
-3 .t 1)3 -RJ.fH2
-3.0'!~ -9o. sv~
-3.0 72 -97.239
-3.158 -74.551
-3.11 R -Rl. 664
-3.091 -RR.71'l
-3.074 -95.7:19
-J.O.S'l-102. 749
-3 ·153 -76.65:1
-3.1 I 6 -!l3.R9:>
-3.0"2 -91 .')33
-3.0 7 7 -9R.247
-3.073-105.411)
-3.177 ~73-073
-1.1 3 6 -8().077
--1.1 ')'l -'l7.'11 7
-3 .Oil9 -93.9"'1
-J.079-IOO.Rl?.
-3 .t 70 -7?.719
-3 .t "!'l -79.711
-3.099 -R (,, 640
-3.00<0 -9:1.511
-3.071-101).4;)6
-3 .t 71 -7~. liS
-3 .t 25 -79.1)75
-3.094 ->;5.971;
-3 .f) 76 -9~. f{1.S
-3.069 -99. 672
-3 .t 76 -71 .R'>6
- 7<{. 79 8
-3.Q<J'l -~s ..-;....;2
-). 0 7'7 -'12.5:04
:..1.07?. -99.;139
-J.J?O
FIGURE A-6.
--
EIGHT WAY POW'ER DIVIDER ELEl.1ENT TYPE ASSIGNMENTS
TYPE 20 IS A 50 OHM TERMINATION
~-.-
FIGURE A-7 {a).
EIGHT
WAYJ~
POWER DIVIDER ELEMENT PLACE ASSIGNMENTS.
FOR COUPLING CALCULATIONS
t.oon
.950
FR£.JliE'IC"fSCGHZl
H-IG-1 V
0
2
0
-2 41 4:)
1 0 0
-2 I 7 16
-I 20 0
0
0
3
2,) 0
0
18 0
0
7 0 0
0
1
0
6 0
0
11 0 0
0
10 0
0
8
0
10 0 0
0
0
0
0
0
20
1
0
0
0
0
0
0
13
16
13
17
0
0
0
0
0
0
0
0
0
0
0
0
12
14
-I
0
0
67
0
15
0
17
19
0
0
3
0
19
12
0
0
0
0
0
0
0 3
IS 0
6 0
4 0
-I 57
19 0
17
0
15 0
16
20 0
0
12
-2 71 70
17
0
20 0
19
0
13 0
0
SU<l~
SUB I
6.800
2.000
6·800
2.000
6.800
2.000
6.800
3.000
6.soo
4.000
0
0
0 4
0 5
-2 24 23
-I 13 0
9
0 0
20 0
0
-2 34 33
0
0
0
0
0 I
D 2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-I 37
6 0
0
II
18 0
0
3
7
II
5
3
13
0
0
6
11
IS
2
12
-I 30 0
0
9 0
0
20 0
-2 61 60
-I sa
0
0
0
0
1 .230
I .160
t.090
0
0
5 0
0
-2 54 53
20 0
0
0
0
0
0
0
SIJ84 ·
SIJ"l'5
511'13
"lR.OOO
so.ooo 1220.000
63.000
so.ooo 12·1.11).000
"12.001
so.ooo 12so.ooo
7<10 .ooo
ta.ooo
so.ooo
82.000 254.01)0
so.ooo
SU"l6
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.ooo
.coo
110-000
.{).)0
010
2.ooo
2.000
3.000
3.000
4.000
6.800
6.81)0
6.800
6-800
6.800
so.ooo 1210.00!)
so.ooo
t.JO.OO'l
so.ooo 1?.00.0·)0
so.ooo lllOO.Q:)Q
so.ooo
5o.o·10
5!.000
60.000
s.ooo
s.ooo
111).000
.ooo
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110.()00
011
012
013
014
015
4.000
2·000
2.000
3.000
3.000
6-800
6.800
6.800
6.800
6.800
so.ooo
so.ooo
so.aoo 1270.000
410.000
50.000
so.ooo 1200o000
50.000 1400.000
110.000
51 .ooo
60.000
s.ooo
·s.ooo
IIOoOOO
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016
017
U!3
4.000
4.001)
2.000
2.000
t.ooo
6.800
6.81)0
9.700
9.700
50.000
so.ooo
so.ooo
25.000
?.5.000
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50.000
50.01)0
50fJ.OOQ
500.01)0
.Q•)O
1 70 .ooo
II n .000
25.000
25.000
.ooo
110·0·10
IIO.OQO
.ooo
.ono
.ooo
.ooo
.ooo
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0 6
D 7
0 8
D9
Dl9
020
021
022
0
WHAT
qo
YOU
~il\i>lT
DONE?
..s.
F'GR~.'I\RD
F'REO
.950
1·020
1·090
1 • I 60
1·230
RErL
A:-JG
.023-173.231
.009-!33.3>ll
•• 026-110.056
.044-133.024
.056-172.998
GAIN
A·'IG
-9.!50 -18.61',4
-9.t39 -49.733
-9.147 -P.0.712
-9.t69-l11.645
-9.204-142.586
~ErL
.oso
.Q;>!J
.009
.023
.042
FIGURE A-7 (b).
REVERSE
G'll 'I
ANG
-23.S22
-31 • 431
7.153
15. 731
72,851
''"~G
-9. I S<J -I:::. 56.4
- 0 .141)
-49.7.1)
-9 ol4 7 -KO .112
-9. I 69-1 I I • 6'l <;
-9.205-142.5136
I
I
I
I
I
I
I
l
I
I
I
I
22
I
9 23,
I
I
101
1
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I
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I
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I
- - .._ -'- - - - -- - - i
I
1---- ---·
PEN~R-
1
:
lATOR
I
liNPUT .,
_j_ ___ _j
FIGURE A-8 (a).
EIGHT WAY POWER DIVIDER ELEr:S1TT PLACE ASSIGNMENTS
FOR ISOLATION 3 CALCULATIONS
FREOUE:-ICYS CGHZ >
.IT-IC-lV
13 0
19 0 0
-I 10
0
17 0
12 0
0
12 0
-I 30
·16 0 0
19 0
0
13 0
0
I
I)
s
0
6
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
17
3
0
18
3
18
6
D
0
0
D
0
2
3
4
s
.950
lo020
lo090
0
-2 12 II
I3 0
0
-2 32 31
-2 27 26
0
20 0
17
19.
16
12
17
0
12 0
0
3 0
20 0
0
-2 61 60
-I so 0
0
13 0
-2 41 38
0
2
0
0
3
0
0
7 0
19
2
s
0
9
20 0
-2 71
20 0
7 0
SUB I
2.000
2.000
2.000
3.000
4o000
0
0
0
0
0
0
10
0
0
SUB2
6.800
6.800
6o800
6o80Q
6.800
11
10
6
II
18
0
0
0
0
0
I • 160
0
0
0
0
0
0
0
0
0
0
0
-I 57
IS
0
0
0
Is 0
20 0
14 0
-I 23
I5 0
1·230
0
0
0
0
0
20 0
0
-I 37 0
4 0
0
-2 54 53
20 0
0
7 0
6
0
0
0
0
10 0
0
8
0
7 0
-I 67
0
0
0
0
9 0
0
IJ
0
0
0
0
SUAS
SUA4
SUB3
ss.ooo
50.000 1220.000
63.000
50.000 1240.000
72.000
so.ooo 1250.000
1o.ooo
700.000
so.ooo
82.000 254.000
50.000
0
0
0
0
0
0
SUB6
.ooo
.ooo
.ooo
.ooo
tto.ooo
0 6
D 1
0 8
0 9
010
.~.000
2.000
3.000
3.000
4o000
6.800
6.800
6.800
6.800
6.800
so.ooo 1270.000
4\0.000
so.ooo
so.ooo 1200.000
so.ooo 1400.000
so.ooo
so.ooo
51.000
60.000
s.ooo
s.ooo
170.000
.ooo
.ooo
.ooo
.ooo
110.000
011
015
4o000
2.000
2.000
3.000
3.000
6.800
6o80Q
6.800
6.800
6o8QO
so.ooo
so.ooo
50.000 1270.000
410.000
so.ooo
so.ooo 1200.000
so.ooo 1400.000
110.000
51.000
60 .ooo
s.ooo
s.ooo
110.000
.ooo
.ooo
.ooo
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016
017
018
019
020
4.000
4o000
2.000
2.000
a.ooo
6o800
6.800
9.700
9o700
so.ooo
so.ooo
50.000
25.000
25.000
.ooo
50.000
50.000
500.000
soo.ooo
.ooo
170.000
110.000
25.000
25.000
.ooo
liO.OOO
110.000
.ooo
.ooo
.ooo
.ooo
.ooo
.ooo
.ooo
.ooo
.ooo
.ooo
.ooo
012
013
014
.ooo
.ooo
021
.oco
.ooo
022
WHAT 0<3 YOU WI\ NT 00NE? E
fREQ
.;so
1.020
lo090
I ol 60
lo230
I"0R lo/.1\ R 0
REFL
ANG
G.'I!N
A"'G
.050 -23.823 -36.987-173.402
.023 -31.432 -41.39"> 149.764
.009
7.152 -50.167 II 7.230
.023
75.730 -52.160-118.202
.042 72.851 -•Ho631-l-49o456
REVERSE
G-. [ .~
ANG
REFL
A"'G
.oso -23.1!22 -36.'11"()-1 73.?.91
.02>3 -31.432 -41.41 6 t.t,9. 694
.009
7.154 -50.022 120.09'3
7">. 730 -">2.331-tt7.74f>
.023
.042 72.851 -41.658-149.344'
FIGURE A-8 (b).