Test results

We ran some test using resistor values from the optimiser and got several frequency response charts from it.

This is the result through a single filter. The yellow is the input and the blue is the output. The size is expected because we use the summing amplifer to do most of the amplification. In addition we were expecting the output to grow at higher frequencies given the input to the optimizer.

This is the result through the pass-through filter. This as well is what we expected - simple reduction is amplitude so when it goes through the summing amplifier it is the correct magnitude.

This is where things get interesting. This is the final outpu from the summing amplifer. We would expect this to be a simple sum of the two magnitudes. However, unlike the first output, it is actually smaller at higher frequencies.

We currently think that the problem has to do with phase. If we look at the phase of the bandpass filters we are using: 

We can see that the phase is -90 degrees for most of the bandwidth and then gets worse as we near the peak. When two waves are 180 degress out of phase, they cancel perfectly. This is clearly a problem we did not anticipate and are not accounting for in the optimization. We are currently looking into solutions involving phase shift circuitry or different ways of optimizing the values.