Click here to go to our main page on Wilkinson power dividers
Click here to learn how to size Wilkinson isolation resistors in SSPAs
New for May 2019! We have an analysis of isolation resistor power handling in power combiners. This page is all about how to analyze dissipation in power dividers.
In an ideal case, when all ports see 50 ohms for a 50 ohm design, there will be no load-resistor dissipation. If the output ports see the same exact mismatch, there will also be no dissipation and reflectr power will be returned to the input. Dissipation occurs when the two output ports see different reflection coefficients. What if you don't know the angle of the two mismatches, but you know that they are specified to a certain VSWR? It is easy to find worst-case situations by sweeping the phaase angle of one of the ports while leaving the other fixed.
The Microwave Office schematic below shows a Wilkinson with output port impedances set to "ZT", an aribitrary impedance (25 ohms in the example, a 2:1 mismatch). Power and the input port (Port 1) is set to 30 dBm (one watt). Port 2 has an extra length of fifty ohm line, which we swept over a wide range of lengths. You will see that this has the effect of finding the worst-case situation. Always design for the worst case, even if your boss is yelling at you to get the 737 Max aircraft into production.
Resistor dissipation in milliwatts was plotted using harmonic balance. This is a convenient way of determining dissipations, voltages and currents in a simulation. For this problem it seems like overkill, your grandparents could have found the same answer using closed-form equations and a slide rule. Sweeping the line length on Port 2 varies the load dissipation considerably. The worst case is ~111 mW at center frequqney, we'll explain why that is later. The best case is 0 mW dissipation, which occurs when the loads are in phase.
For yucks we plotted the S-parameters during the sweep. The only parameter that changes much is S11. This is because the power has to go somewher... if it is inot dissipated in the isolationload, it comes back out the input port. The plot is in decibels, but we could just have easily plotted the reflected power in milliwatts using harmonic balance.
It's time for a Microwaves101 Rule of Thumb:
Microwaves101 Rule of Thumb #127
Considering two-way Wilkinson power dividers, worst-case dissipation in the isolation resistor can be easily calculated from the return losses seen by the two arms (harmonic balance is not needed). Assuming that the loads seen by both arms are 2:1 mismatch, 11% of the power will reflected back in, and in the worst-case situation it is all dissipated in the isolation resistor. You can figurethis out by noting that 2:1 VSWR is -9.54 dB return loss, and 10^(-9.54/10) is 11%. However, this only happens when the mismatches occur 180 degrees out of phase (if they are in-phase, reflected power will return to the Wilkinson input). Taken to the extreme, if the loads were 0 dB return loss and out of phase by 180 degrees (like an open and a short), the full incident power to the Wilkinson divider would dissipate in the isolation resistor (and the input of the Wilkinson would appear matched!)