Hi Esakki,
Let me sketch out the way the power combiner works right now.
Assume we have a 2 port combiner with signals only at a single carrier frequency. Let E1(t) = A1(t)exp(jwt) and E2(t) = A2(t)exp(jwt). Where E1(t) is the input field in port 1, E2(t) is the input field in port 2. The carrier frequency is w. Thus the modulated amplitude is A1(t) for port 1 and A2(t) for port 2. The phase information is carried in A1(t) and A2(t) by allowing them to be complex numbers.
Now, if you require power to be conserved, the output port field cannot simply be Eout(t) = E1(t)+E2(t) = [A1(t)+A2(t)]exp(jwt) because (ignoring other factors) Pout = |A1(t)+A2(t)|^2 which will not equal Pin = |A1(t)|^2 + |A2(t)|^2. Therefore, for power conservation, the output field will have to be renormalized so that the output field is instead Eout(t) = N(t)[A1(t)+A2(t)]exp(jwt).
It turns out that there are actually physical reasons why the normalization factor N(t) exists and you can show (for example) for a symmetric waveguide Y-junction, N(t) = 1/sqrt(2). The problem here is that the power combiner is not a specific physical device, but an idealized model. In fact, one of our BPM and FDTD experts is at the moment looking at designing a physical-based power combiner device.
So the question then becomes, what are you going to use for the normalization factor? The way it works right now is we define
N(t) = sqrt(|A1(t)|^2 + |A2(t)|^2)/|A1(t)+A2(t)| (***of course with checks to make sure we are not dividing by zero***). From the argument above, you see that indeed power will be conserved when you use this as this is simply the factor by which the power is off by. However, as you quite rightly point out, the phase information is lost. Dividing by |A1(t)+A2(t)| essentially “normalizes out” any phase difference.
If you divided by ||A1(t)|+|A2(t)|| instead, you will retain phase information. That is, if both signals are in phase, Pout = Pin as above, but if the signals are 180 degrees out of phase, Pout = 0. I have tested this and it works. If you have some phase in between 0 and 180, you will have 0<Pout<Pin as you would expect. Now, is this a reasonable normalization? It works as you would expect for phase differences of 0 and 180 deg and gives you qualitatively what you’d expect for phases in between. It is also becomes the correct factor of 1/sqrt(2) in the perfectly symmetric case. Maybe its the best we can do?
I have tentatively modified the power combiner to have 3 options:
1. The old method: N(t) = sqrt(|A1(t)|^2 + |A2(t)|^2)/|A1(t)+A2(t)|. For users who want to enforce power conservation in all cases.
2. The phase-dependent method N(t) = sqrt(|A1(t)|^2 + |A2(t)|^2)/||A1(t)|+|A2(t)||. As discussed above, doesn’t always conserve power.
3. The symmetric device N(t) = 1/sqrt(2). Only conserves power when both input signals have identical amplitudes and phases. This is analogous to Wilkinson power divider/combiner.
I have also made similar modifications to the other combiners with more ports with the appropriate sums of amplitudes and powers over all ports. The symmetric device is now N(t) = 1/sqrt(n).
Sorry about writing all the equations inline, I didn’t want to attach a multitude of image files!
Thoughts?
.
