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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, microwave cheapskates!
This is a good example of a microstrip, N-way, multi-section 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 at Microwaves101.com!)
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 deal.)
I found a good measured/modeled match over most of the frequency band, as you can see below:
Simulation in 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 some attention...)
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 for S25.
(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!