Updated July 10,
here to go to our main Wilkinson page
here to go to our N-way Wilkinson page
here to go to our multi-section Wilkinson page
Improved for July 2007!
This Wilkinson design example was provided by Kjer Andresen, who
designed it as part of his part of his Diploma Thesis, auf Deutschland.
He used calculations he found here on Microwaves101; this is exactly
how Microwaves101 is supposed to work, you stop here, get smarter,
and then contribute more content so the rest of us get smarter too.
Kjer gets it, do you?
This 50-Ohm combiner (shown below)
was developed on Duroid 5870 and Ultralam 2000 (both Rogers products).
Kjer used Agilent's Advanced Design System (ADS) to design the splitter,
and a Rhode & Schwartz network analyzer to verify the design.
Say, that smells like free advertising, enjoy it while it lasts,
This is a good example of a microstrip,
Wilkinson design with equal amplitude outputs. Ideally the outputs
are 9 dB below the input signal due to the cascade of three 3-dB
splits. Such a cascade of two-way splitters to achieve 2N
outputs is called a corporate splitter.
Now we'll let Kjer
discuss his work (with editorial comments here and there when
we can't resist...)
I've been working
on a Wilkinson combiner project for my diploma thesis at the Institute
of Measurement Technology at the Technical University of Hamburg
for about two months and found a lot of helpful information on Microwaves101.
Now I want to share my results with you.
I designed an eight-way Wilkinson
combiner (three stages) with the following performance goals:
- Substrates: Rogers Duroid
5870, 1.5 mm thick, 35 um copper on both sides
- Attenuation from input to
output: nominally -9 dB (ideally, cascade of three -3 dB splitters)
- Isolation between splitter
ports: minimum -20 dB
- Bandwidth: 30 MHz to 3 GHz
- Center frequency: 2 GHz
First I looked at the other examples
at Microwaves101 and simulated them myself with the Advanced Design
System by Agilent. Gradually I changed some parameters so that they
fitted my constraints.
First Step: I downloaded the
The Professor's N-section impedance transformer spreadsheet from
the download page and calculated
arm impedances for the three-section, two-way transformer (or in
this case, combiner!) over the required bandwidth. Later these two-way
splitters were cascaded to provide the eight-way corporate combiner.
Here are the results from the spreadsheet:
- Z1=45.74 Ohms
- Z2=35.36 Ohms
- Z3=27.33 Ohms
You will need to double these
impedance values, because there are two arms (transformers) in parallel.
Next I set the three isolation
resistors to 300 Ohms and made them tunable in ADS. I also tried
to exercise the optimization function of ADS, but the solutions
were extremely different from calculation to another, so I decided
to tune the resistor values by hand. Nice to know: when you set
up your ADS simulation with variables you can tune them and watch
the S-parameters change. I used this for optimization of the resistors
as well as the center frequency. For example, set L1=L2=L3 and move
the slider to change the value, you will see how the center frequency
moves left or right.
I found the following isolation
values to be good:
- R1=120 Ohm
- R2=220 Ohm
- R3=470 Ohm
Editors note... 300 Ohms is
a good pidooma for a starting value
for the isolation resistors. If anyone knows a better way to determine
isolation resistors for a multi-section Wilkinson than hand-tuning,
please let us all know about it so we can share this knowledge!
We agree with Kjer that optimization of these value in ADS is not
as satisfactory as you might guess...
To know how wide the microstrip
lines should be to meet Z1, Z2 and Z3 you can use the tool Lincalc,
included in ADS, but there are other microstrip calculators available
on the net. (There's even one here
After the simulations looked
good, I built a two-way combiner to verify the simulated results.
(I did the etching myself in one of our University labs. No big
I found a good measured/modeled
match over most of the frequency band, as you can see below:
red, measurement in blue
S12 is about -4 dB, as opposed
to -3 dB for the ideal case. This one dB additional loss I believe
is caused by the connectors and the resistor tolerances. (There
appears to be some unexplained losses above 3 GHz which require
One other problem is the output
isolation for small frequencies (smaller than 500 MHz), but that's
only a problem for my application. I want to use it between 30 MHz
and 3 GHz, if I used the splitter from 1 to 3 GHz I'd meet my -20
dB isolation design goal. (Isolation of -20 dB at 30 MHz might
require quite a few more transformer sections...)
Here is a picture of a four-to-one
combiner I developed by cascading two stages of the two-way splitter
i developed. All of the important paths have the same physical lengths
and it works very nice with my goals. I needed to place two connectors
on the long side which disturbs the equal path lengths somewhat,
because of the big N-connectors of our network analyzer. If you
need phase matched outputs you'll need to make all paths have the
same physical length.
Now I cascaded three stages of
two-way/three-section combiners to get my eight-way combiner, shown
below with the port numbers labeled for discussion. What did I expect
to get? S12, S13 ... S19 parameters should all ideally be close
to -9 dB, because the signal goes through three -3 dB combiner losses.
The isolation is not the same between all outputs, because there
may be different numbers of combiners between them. For example:
ports 2 and 3 are neighbors and connected to that same combiner,
so expect -20 dB isolation. But between ports 2 and 5 is an additional
combiner, which adds -20 dB, so we can achieve -40 dB isolation
(We really like the compact
layout that Kjer achieved by reversing the direction of the second
splitter stage, based on this feature alone we award him an "A"
letter grade. Note that to test this Bad Boy, you'll need to screw
seven 50-ohm terminations onto all of the unused ports, or your
data will be a mess!)
Let's see some measured results:
(Sorry for the poor image quality, we'll fix this shortly!)
OK, the splitter's response looks
nice, but the S12 parameter degrades above 2.5 GHz. This may be
because the 50 ohm strips between the second and third stages of
the cascade don't have the same length (which also means that
the split ports won't be phase matched). This is an artifact
of of the compact design layout I chose, which I might fix in later
developments. But if you can live with it the eight-way combiner
stays a lot smaller.
There may be more going on
here that could explain the "extra" loss above 2.5 GHz.
Looking at the mismatch loss (S11, S22, S33, etc.) will give some
hints, it might be that the connectors are not grounded properly,
sometimes they are sensitive to not having via grounds underneath
the tangs that are soldered to the top of the board (but then again,
this is relatively low frequency for this problem to rear its ugly
head). Also, the close proximity of the paths after the second split
could cause some stray coupling. But all in all, we say job well
done, and wish Kjer all the best in his pursuit of microwave excellence
in the future!