How Do You Calculate Impedance in Filter Circuits?

[gh0st]

Homework Statement

Homework Equations

The Attempt at a Solution

Hi all, i have some doubts on how to find the impedances for active filter circuits.

Let's start with a simple low pass filter :

http://img85.imageshack.us/img85/6484/52244578oo4.th.jpg

The input impedance should be R + Xc; and the output impedance should be ZL || (RF+R1) once i short the input.

However, a same filter but at 2nd order configuration is confusing me. Assuming the circuit diagram is given as below :

http://img85.imageshack.us/img85/4529/lp2ia8.th.jpg

Will be output impedance be solely ZL || (RF+R1) if seen from port A-B ? Or will it have to include the feedback capacitor and the input side with the source short-circuited as well?

As for the input impedance, is this derivation method along the right line?

applying KCL at red node V1

Ii = I1 + I2
(Vi-V1)/R1 = (V1-Vo)/XC2 + (V1-0)/(R2+XC2)

where vo=KVx ; K is the DC voltage gain of the amplifier.

Vx = (V1*XC1)/(R2+XC1)

After that, from definition of Zi = Vi/Ii; try to arrange the equation to fit Vi/Ii?

 

[XiaominG]

can someone please help answer this?