Click here to go to our main page on S-parameter measurements
Click here to go to our page on cold S-parameters
Click here to go to our page on balanced amplifiers
New for March 2014! One very good reason that engineers employ balanced amplifiers is that the reflection coefficients S11 and S22 ideally cancel out and the overall amplifier provides a good impedance match. However, there is a limit to how well this cancellation works in practice, especially if you try to stretch the bandwidth.
Sometimes an amplifier is turned off when its channel is not needed in order to save power. The VSWR of an amplifier turned off can be very poor, close to a short circuit. If off-state match is important, you are reading the best page of information on the topic. It stinks that MMIC suppliers don't post cold S-parameters (measured in off state, not in a refrigerator) for their products, which are needed for this type of analysis. If any readers have some cold data on a MMIC amp, we'll gladly analyze the reflection coefficient in balanced configuration, just This email address is being protected from spambots. You need JavaScript enabled to view it.
This is not going to be the most qualitative analysis ever, but maybe a reader could help us out some day and come up with equations that solve for exactly how well a quadrature coupler can reduce VSWR depending on coupling parameters.
Let's start the discussion by building a two-section branch line coupler using Microwave Office. We used the ideal values for Z1, Z2 and Z3 which can be found here.
Here is the "perfect" response. A signal incident to port 1 has exactly 3.01 dB power split to ports 2 and ports 3, with port 4 isolated.
One of the properties of a two section branch line is that the quadrature phase is flat over an appreciable bandwidth. Below are equations we used to plot the phase:
And here is the phase response. It has a flat spot that is maybe 4 GHz wide, if you allow a few degrees of error.
Now let's look at what it does to a massively mismatched amplifier, which we will simulate in the form of a pair of five ohm resistors (10:1 VSWR). We added a sweep variable to rotate the reflection coefficients of the "amplifiers" through 360 degrees of phase, so that you can visual the worst-case. In engineering, always examine the worst case, and try to plan for it, and you will do well. On the flip side, you also have to know when to quit analyzing and start building....
Here is the return loss, as the angle is swept. At center frequency, perfect match is achieved, for any reflection angle.
Now let's see what happens when we use an over-coupled coupler. We arrived at values of Z1=38 and Z3=62 ohms after we restricted Z2 to a 100 ohms, which still might not be practical. The amplitude response is what you would expect if you were designing for wide bandwidth. Three dB coupling occurs at two points (8.1 and 11.9 GHz) , in the band center it is over-coupled by 1.1 dB (the coupler arm receives 1.1 dB more power than the direct arm).
Below the phase response bandwidth actually improves, even though that was not part of the optimization procedure. Certainly the phases at 8.1 and 11.9 GHz are perfect or near perfect.
Below is the return loss looking into the over-coupled amplifier, with the 5 ohm amplifiers swept in phase. Notice that the VSWR dips quite low at the very same points where the coupler provided exactly 3 dB coupling and 90 degree phase. Not a coincidence! But at band center, the worst case match is 8.5 dB.
What happens is the termination on port 4 is not matched? We reanalyzed the network with 25 ohm termination. First thing to notice is that the relative coupling between the amplifiers is disturbed (now 2.1 dB over-coupled). But the 3 dB points are maintained.
Ninety degree phase is also maintained at the two 3 dB frequency points:
What about our amplifier? The reflection coefficient of the balanced amplifier does NOT change when the termination is mismatched. We'll take a short cut and plot the exact same image we used three plots above. If anyone disagrees, go ahead and prove us wrong; perhaps three our of four microwave engineers would get this wrong on a spot quiz. Why do you think they call that load port the "isolated port", kimo sabe?
What happens if you mismatch the reflection phases of the two amplifiers by 20 degrees? We can simulate this by adding 10 degrees transmission phase to the lower arm, as the signal passes through it twice when reflected. Note that we didn't forget to put Port 4 back to 50 ohms....
Mismatched phase certainly has a bad effect on overall amplifier VSWR, and should be minimized by picking amplifiers from the same wafer if you are combining MMICs.
Conclusions
In order to achieve perfect cancellation of identical poorly-matched amplifiers, there are two necessary and sufficient conditions:
- The coupler must provide perfect amplitude balance
- The coupler must provide perfect 90 degree coupling
Perhaps more interesting is this: the termination resistor VSWR does not matter when you are considering only the VSWR of the combined amplifier. However, if you don't use a 50 ohm resistor the coupling coefficients change, which could have an effect on the gain, power and efficiency response of a power-combined amplifier, especially if the input coupler has a different termination value from the output coupler. Certainly, you don't need to order a 1% tolerance when 10% or even 20% will do. Think of all the money that has been wasted laser-trimming thin film resistors for this purpose...
If you are expecting to perfectly match a pair of amplifiers that are turned off, it simply isn't going to happen over any appreciable bandwidth.