Multistage Wilkinsons
Updated December 9,
2012
Click
here to go to our main page on Wilkinson power splitters
Click
here to go to our page on designing Wilkinson splitters with
Excel
New for December 2012! Here's a link to a UK college web site that is showing students how to design multisection Wilkinsons, including detailed schematics and artwork. Thanks to Alan. Bravo!
Multistage (or multisection)
Wilkinson power splitters can perform remarkably well over more
than a decade of bandwidth. On this page we will show you a procedure
that will help you design a multisection Wilkinson quickly and
efficiently, instead of using guesswork and optimization. Then you
can cheaply build your own splitters instead of buying them from
Narda for thousands of dollars!
Example 2 presents info on the
exact design of Chebyshev and maximally flat multistage Wilkinson
splitters, using our impedance transformer spreadsheet that you
can download! Does Agilent
offer this in ADS? Heck no, Dude!
Recently a question came up about what to use as center frequency for a broadband design. Should lambda/4 represent the arithmetic mean (the average), or something else, like the geometric mean. The answer is arithmetic, my dear Watson... for 6 to 18 GHz, the center frequency is 12 GHz, and all the sections should be a quarterwavelength at 12 GHz. Thanks for asking, Tamas!
Calculating
isolation resistors
For
a multistage Wilkinson, we haven't (yet) developed a detailed method
for determining isolation resistors along the chain. Harlan
Howe's book on stripline design has some nice tables that can
help, he also shows some equations. Seymour Cohn wrote an excellent
article on the subject way back in 1968, you can download it from
IEEE Explore if you are a member. Sorry,
we try to respect restrictions on copyrighted material so we won't
post the article. Here's the exact reference:
A Class of Broadband ThreePort
TEMMode Hybrids
Cohn, S.B., Microwave Theory and Techniques, IEEE Transactions
on
Volume 19, Issue 2, Feb. 1968 Page(s): 110  116
Thanks to Tim for this IEEE reference!
Table 1 gives normalized quarterwave line impedances and resistor
values for various bandwidth designs. Cohn does give closedform
equations for the two resistors in a twostage Wilkinson for equalripple
response, then shows some approximations for cases higher than N=2.
In the end, you will probably have to use an optimizer such as you'll
find in Agilent's ADS to squeeze out the maximum isolation over
your design bandwidth.
Isolation resistors are sometimes
referred to as "dump" resistors, an example of microwave
slang. Also thanks to Tim!
New for August 2008! We
created a spreadsheet that will allow you to analyze multisection
Wilkinsons in Excel, including isolation between the split ports.
It's explained on this
page.
Example 1: designing the hard
way...
We put together
the twostage Wilkinson combiner below to illustrate the extra bandwidth
that you have achieve with a second set of quarterwave sections.
The values for the line impedances and isolation resistors were
obtained by shamelessly using the optimizer in our ancient old copy
of Eagleware Superstar... sorry to disappoint anyone that thought
we would derive equations for the optimum values!
Example of twostage
Wilkinson with input transformer

Sparameters of above
2stage Wilkinson with input transformer

Example 2A, twostage, 75 ohms,
the easy way!
This two stage divider was calculated
using our transformer spreadsheet located in the download
area. The arm impedance has to be twice that of the transformer
solution, because two arms are in parallel.
The circuit is a two stage, Chebyshev
Wilkinson, with characteristic impedance 75 ohms (instead of the
usual 50 ohms, just for fun).
The required frequency band was
950 to 2025 MHz, because that's what a Microwaves101 reader requested.
The center frequency is 1.488 GHz (=(F1+F2)/2). The load and source
resistance that the transformer is matching to is 75 ohms (the common
port) and 37.5 ohms (the split ports, two 75 ohm loads in parallel).
The Chebyshev transformer spreadsheet calculates 61.248 and 45.920
ohms for the two sections; you need to double these values to 122.5
and 91.8 ohms, as we stated before, because the two arms are in
parallel. Note that the impedances are a function of the percentage
bandwidth as well as the termination impedances. You can view the
VSWR of the input port from within the spreadsheet, this is very
handy and will help you decide how many sections to use for your
application.
The isolation resistors values
were found by referring to a graph in Harlan Howe's book "Stripline
Circuit Design". You can find this book in our page on microwave
engineering books. Note that more than one solution exists for
the resistors, depending on what you want to optimize (isolation
at center frequency, bandwidth of S22, etc.)
Example 2B, twostage, 75 ohms,
with transformers
In the next example, we added
a pair of transformers to reduce the 75 ohm terminations to 50 ohms
at each port (61.2 ohm quarterwave three transformers did the job).
This reduces the maximum impedance of the arms, they are now Z1=61.2
and Z2=81.7 ohms (exactly 2/3 what they were before, because we
reduced 75 ohms to 50 ohms). Z2 at 122.5 ohms might have been unrealizable
previously. The isolation resistors were also scaled by 2/3 from
the previous example. The resulting input impedance (S11) stays
close to equalripple in the passband.
Example 2C: 950 to 2025 MHz,
three stages
Below we designed a three stage
Wilkinson, this time with a "physical" model. The transmission
lines are microstrip on Rogers 4003 (ER=3.38), 32 mils thick with
halfounce copper (0.7 mils). Again, we are looking for 950 to 2025
MHz bandwidth, but we want more isolation (hence three stages).
We used the starting values for line impedances from our transformer
and microstrip calculators, took the isolation resistor values from
Harlan Howe's book, then did a little optimization using Agilent
ADS. The next two plots show the model and predicted performance.
We rounded off the resistors to 1% RETMA
values. The isolation that you get will probably be six dB worse
than the prediction (which was greater than 30 dB), because the
resistors won't act ideal.
Example 3
Yet another request from the
Microwaves101 message board. This is for 800 MHz to 6 GHz. We arbitrarily
chose four sections because we don't have a specification to go
by.
If you download the transformer
calculator to use as a multisection Wilkinson 2way design, we recommend
you start with the equal ripple page, enter input impedance = 50
ohms, output=25 ohms (Z0/N, where N=number of outputs...) for a
threeway, output=16.7 ohms etc.
Then enter the frequency range, 0.8 to 6 GHz for this example. The
number of sections can be traded for VSWR (more sections=lower VSWR
ripples).
The calculator will give you the section impedances, for example
if you have a twoway divider (50:25 ohms) with four sections, the
transformer spreadsheet will give you these impedances:
41.243
37.299
33.513
30.308
These you will use as the arms for the Wilkinson. But first you
have to double them because the two arms will be in parallel. The
low values go toward the 2way side, the high values toward the
50 ohms side.
The "magic" you will have to perform on your own is to
calculate isolation resistors,
Next we simulated the Wilkinson
on ADS, and used 200 ohm isolation resistors. Why 200 ohms? It's
a pidooma!
Here's the schematic and the
response:
The isolation is pretty good
at 17 dB, but it could be better.
We used the ADS optimizer and
came up with 20 dB isolation across the band:
That took all of 15 minutes!
Here's the group delay of the
splitter:
Coming soon! Maybe a layout of
a Wilkinson, and maybe some EM analysis!
