## Sallen Key LPF Question

Hi,
I have a 4 pole active LPF.
I am seeing that the amplitude of Vs1 & Vs2 is higher than the amplitude of input signal.
I am not sure how.
In my calculation, I have taken the amplitude of the fundamental harmonic of the square wave (input) into consideration, reduce it by 6db and multiply by the gain. The amplitude results don't quite match up with what I see in simulation (JPEG of the circuit and waveform attached).
Also, I am assuming that the output of the 1st stage (Vs1) is a triangular wave, so that I am considering the fundamental harmonic of a triangular for the calculation of amplitude of the 2nd stage (Vs2).
The other thing that I don't understand is how come Vs1 and Vs2 are shifted up by some DC value. Does capacitor charging/discharging has got something to do with it?

Thanks.
Attached Thumbnails

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 You do have some gain because of R5, R6, R7 and R8. Those are for adjusting the "d" of the filter, but it also have a little bit of gain. Also, there is some sort of positive feedback from the output of the opamp back to the input area. You expect some sort of peak in the pass band and the amplitude goes up some also. The of R5 and R6, R7 and R8 are very sensitive. You change the kind of filter just by changing the ratio. You have to be particular careful when R5 and R6 come close to equal ( the op-amp has gain approach 2) it gets very touchy. Anything over that, it will burst into oscillation. Even when it get close to 2, it is very touchy. I just use this filter in my guitar electronics design two weeks ago, I got gain close to 2, every time I power up or power down, it gave me a "beep" sound. That is conditionally stable!!! regarding DC, it is a DC coupled circuit. If your square wave is not perfect 50% duty cycle, you are going to have an offset( DC shift). there is another thread on this that goes into detail analysis of this kind of filter, only difference is they concentrated on the op-amp being only a voltage follower. This is one of the very few circuit I am not interested in going into detail as the application is very straight forward but the analysis is quite long.