Voltage or power added

[jousto]

Hi, I have a question about analyzing different coupler types. If you use a Wilkinson power combiner you add the power from the two input branches. That is clear so far.

For a directional coupler it is different. Let's name the branches as: port 1 is the one you input the signal on. Port 2 is the forward direction with just a small amount of attenuation (assume it is zero). Port 3 is the coupled port from port 1. If the coupling factor is C then P3=P1-C. (Note we talk in dB values here). Let port 4 be matched. If we have some missmatch at the port 2 (power reflection coefficient R2(dB)), we will get an extra signal to port 3 provided the directivity is not infinite. Contribution of the reflection from port 2 is P1-R2-C-D, where D is the directivity, defined as 10log(P3/P4) in matched case.

Now we have two signals at port 3. To calculate the POWER received in port 3 we need to add the VOLTAGES of the two signals rather than absolute powers.

I have some difficulties seeing this clearly. I suppose it has something to do with the physical coupling mechanism but I would be very happy to hear clarifying comments on this.

#jousto

 

[Higgler]

The confusion of voltage and powers in couplers is really common, so don't feel bad. Do the math making sure that all the power adds up to the same you put into a lossless passive device. If you do it one way, then another way, whichever one adds up with the same power is the correct answer.

Maybe a way to think of it physically is; you are really moving current/electrons on these metal surfaces in the coupler(which relates to voltage V=ri). Now if electrons from port 3 travel to port 4. If for example, 2 electrons from port 3 join 2 electrons from port 4, there is then 4 electrons, the voltage would double because your impedance didn't change instantly and the power would quadruple (V^2). If you think that the power only doubles, then some of your electrons would have to disappear magically and power would be lost since i^2*R would no longer apply.

That might apply in an antenna if it's radiating, but not in a coupler (although couplers do radiate and are a pain when trying to get low sidelobe antennas.)
kch