The picture below depicts a mixer driving a low pass filter. My question is what is the purpose of C1? I was told it is to add a high frequency pole to reject high frequency feedthrough. So, how is the pole formed? Is it just R1*C1 or R1*2*C1?
R1-C1 form a low pass filter (to first order approximation.) To get the exact relationships, draw the equivalent circuit diagram. The circuit is differential so you only need to draw half of it with the plane through the middle grounded. You will get a current source (gm of the transistor) shunted by R1 and 2 each C1 divided by two. Then the series R2 to a virtual ground.
So if I add capacitor from the differential line to Vdd (see above) that will also contribute to the pole frequency. Lets say I add cap Cx to each of the differential line to Vdd then the cutoff frequency is basically 1/(R1)*(C1+Cx), right? Also why would u use a T-netwok capacitor instead of a grounded capacitor?