New for February 2025. This information came from Max Passion, who noticed we did not offer a solution to calculating optimum resistor values for multi-section Wilkinsons on this ancient Microwaves101 page. Thanks!! Below, when we quote (or paraphrase) Max Passion we will put the text in italics. We added some possibly kibbitzing content that is not in italics.
When we say "ideal" resistors, bear in mind that ideal is in the mind of the beholder. If you only need 16 dB return loss across your band and are willing to trade that for fewer sections (and lower loss) you will need to dive into the math yourself.
The ideal resistor values may have to be rounded up or down which could affect results. And in the case of diamond resistors for high-power combiners, you are out of luck because here are only a few values commercially available!
Background - Seymour Cohn's 1968 article
Mr. Cohn offered a method for calculating isolation resistors; the math he used is beyond our attention span so we never tried to figure it out. However, Cohn provided a table of Z and R values for two-section, three-section, four-section and seven-section Wilkinsons. Below is a snippet from his paper showing the values.
Seymour Cohn is featured in our Microwaves Hall of Fame!
Don't worry about having to type the data yourself, we will eventually offer an Excel file that has all of the data for 1 to 15 section Wilkinsons that you can cut and paste into your favorite design tool. Now, onto the new content!
New work on Wilkinson resistors by Max Passion
The work I have done is an extension of Seymour B. Cohn's work, i.e., the number of sections of the Wilkinson power divider has been further extended to 8-15 sections. The extension of the design form is not simply a natural extension of the data, but a modification of Seymour B. Cohn's design formula by introducing the F-factor.
The calculation formula for the isolation resistors of a multi-section broadband Wilkinson power divider was first proposed in Cohn's paper [1]. However, when the number of sections is large, the calculation based on his formula will encounter problems. To solve this issue, an F factor can be introduced into the formula.
Although simulation software, such as ADS and AWR, are now very popular and widely used, and Wilkinson power divider design parameters with more sections can be obtained by software optimization, in practice, when there are particularly many optimization variables, it is not easy to optimize with the simulation software. Therefore, I think this design data table is still helpful for designers.
Next, I explain to you how to use this table. The parameters of this table are impedance normalized like Seymour B. Cohn's table. Taking 10-section as an example, N is the number of sections, f2 is the upper limit of the operating frequency, f1 is the lower limit of the operating frequency, S1 is the standing wave at port 1, S2 and S3 are the voltage standing wave ratio at ports 2 and 3, respectively, and I is the isolation of ports 2 and 3 in dB format. F is the tuning factor, which is used to correct the Cohn's formula.
The calculation tables for the isolation resistors of 5 to 15 section Wilkinson power dividers are shown in Table Ⅰ (a) and (b). The data are normalized.
Table A: Design data for 10-section power divider (includes data for 50Ω port impedance)
|
N
|
10
|
|
f2/f1
|
14
|
|
S1(max)
|
1.19
|
|
S2,S3(max)
|
1.056
|
|
I(min),dB
|
22.5
|
|
F
|
1.3
|
|
|
Z (normalized)
|
Z*50（50Ω port）
|
R (normalized)
|
R*50（50Ω port）
|
|
1
|
1.1136
|
55.68
|
9.8044
|
490.22
|
|
2
|
1.1641
|
58.205
|
24.3713
|
1218.565
|
|
3
|
1.2247
|
61.235
|
19.4834
|
974.17
|
|
4
|
1.2948
|
64.74
|
15.7916
|
789.58
|
|
5
|
1.3733
|
68.665
|
12.8366
|
641.83
|
|
6
|
1.4580
|
72.9
|
10.3484
|
517.42
|
|
7
|
1.5463
|
77.315
|
8.1397
|
406.985
|
|
8
|
1.6349
|
81.745
|
6.1132
|
305.66
|
|
9
|
1.7200
|
86
|
4.2122
|
210.61
|
|
10
|
1.7980
|
89.9
|
4.0317
|
201.585
|
Based on the data in Table A, the ADS simulation schematic is built as shown in Figure 1 and the simulation results are obtained as shown in Figure 2 and Figure 3.
Figure 1. Schematic diagram of the ten-section Wilkinson power divider.
Figure 2. Simulation results of VSWR at each port of the ten-section Wilkinson power divider.
Figure 3. Isolation simulation results for port 2 and port 3 of the ten-section Wilkinson power divider.
Free download
We put all of resistor and impedance values for two through 15 sectio Wilklinsons into a handy Excel file, where you can compare bandwidths, VSWRs, isolations and return losses. Excel is perfect for cutting and pasting values into ADS or Microwave Office. Look in our download area.
References
[1] S. B. Cohn, “A class of broadband three port TEM-mode hybrids,” IEEE Transactions on Microwave Theory and Techniques, vol. MTT-16, no. 2, pp. 110–116, February 1968.