三路威尔金森功分器设计 3 way wilkinson

Three-way planar Wilkinsons

Updated November 13, 2011 Click here to go to our main page on Wilkinson splitters

Click here to go to our page on N-way splitters

Click here to go to our page on the Kouzoujian splitter, a great alternative to the conventional N-way Wilkinson

New for June 2010! This page will provide a basic analysis of planar, three-way Wilkinson splitters in 50 ohm system impedance. This is splitter is imperfect, because it is missing an isolation resistor between the two outer ports, however, this is what makes it easy to lay out. We divided the analysis into three "types" which are described below, and ranked according to bandwidth potential. Type 1 splitter

The Type 1 splitter is the simplest network possible. The three arms each employ a single quarter-wave impedance transformer. If you were to impedance match port 1 at center frequency, the transformers would all be 86.6 ohms (transforms each 50 ohm leg to 150 ohms, and three 150 ohms in parallel is 50 ohms). Sorry about the crummy schematic, you'd think by now Agilent would provide a means for graphic capture beyond the usual copy-and-past into Powerpoint, then shrink image with PaintShop...

The variables R1 and Z1 were allowed to optimize to provide the maximum "-15 dB bandwidth", in other words, it was required that reflection coefficients S11, S22 and S33 and isolation terms S23 and S24 were less than -15 dB. Note that by symmetry, it is not necessary to optimize (or monitor) S44, and S43.

The choice of -15 dB as the goal is arbitrary. However, in the planar three-way Wilkinson, you can't expect perfect isolation of the split ports, and without perfect isolation, you won't get perfect return losses for S22, S33 and S44.

The transmission line impedance values were restricted to no more than 100 ohms (in all three types), to make the circuit realizable in microstrip. It might be better to restrict to a lower value depending on what substrate is chosen, and yield considerations. The subject for another day!

For Type 1, Z1 was found to be 91.4 ohms and R1 was 83.6 ohms, resulting in -15 dB bandwidth of 39%.

Below is the transmission coefficient, showing the near-ideal value of 4.78 dB

[-10*log(1/3)]. All three transmission coefficients are equal in this simplified analysis, in practice the outer branches will behave slightly differently from the center branch.

Here are the return losses and isolation. Note that all parameters are somewhat compromised, as expected. This is the price that is paid for a planar design with only two isolation resistors.