The filter in question takes a mono signal of amplitude between 5 mVp and 200 mVp, and filters the signal based on the frequency. The potentiometer that leads into the inverting input of the op amp determines how this signal is ultimately affected. Depending on which extreme the potentiometer is dialed to, the circuit should amplify either low or high input frequencies, while attenuating the other end of the frequency extrema. When the potentiometer is dialed to the opposite extreme however, its behavior inverts; that is to say that if it amplified high frequencies by a voltage gain of A1 and attenuated low frequencies by A2, it should now amplify the low frequencies by A1 and attenuate the high frequencies by A2. When the potentiometer is set to exactly 50%, the gain should be -1, as no filtering is actually being done.
For this specific purpose, I need A1 to be 3 and A2 to be 1/3, i.e. A2 = 1/A1. I have values that I obtained somewhat coincidentally that achieve this behavior, which are shown in the circuit below. My question, finally arises from my lack of understanding of how to actually approach this circuit. It's almost like a band-pass filter, but not quite as one of the ends will amplify the voltage by the same amount it would have been attenuated. That's pretty much where my confusion lies. In this schematic, the circuit is designed to work towards the gains previously described, and is built to handle frequencies ranging from 20 Hz to 20 kHz.
I know that: C1 = C2 R1 = R7 R2 = R6 Due to the gain of the circuit being the impedance of the right hand divided by the impedance of the left, and at 50% of the potentiometer, this must equal 1. If the potentiometer is split 10k and 10k for both impedances, then in order for it to equal -1 the above relationships must hold true.
R3 is always a 20k potentiometer. However, as far as the other components go, they can vary so long as they fall in accordance with those relationships. My issue lies in that I'm not quite sure what to do next to get the answers I came up with. I think I maybe have to compare how the expression for gain changes at each extreme with the expression for a gain of -1, but I'm not sure. If anyone can walk me through this, as well as correct any incorrect assumptions I've made, it would be a great help.