JohnRoberts said:
You can force the combination to sum to one, if you ground the + input on the left most state variable opamp, and add a unity gain inverter stage between the BP integrator and the first opamp - input.
Then by definition the HP,BP,and LP sections will sum to unity, in the first stage opamp.
If you do that, you get the response I was talking about earlier, with 1.2dB hump for LP and HP and 0dB at center for the BP.
This will also bring the BP output into the same polarity as the HP and LP.
BP output is in quadrature with the LP and HP. Both polarities of BP produce the same amplitude output (phase is different) when recombined.
There are two issues there:
Unity summing, which, as we've just seen, can easily be achieved by tweaking some components or the topology.
Response under gain-reduction, which shows large interaction, because the HP and LP corner frequencies are the same (and same as the center freqiuency of the BP). The BP output is relatively narrow according to mathematical definition - about one octave, depending on the chosen allignment, but it spreads audibly over a spectrum of about 5 octaves. In contrast, the effect of applying GR to the BP creates a narrow notch that is almost insignificant.