How Do You Calculate Impedance in Filter Circuits?

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SUMMARY

This discussion focuses on calculating impedances in active filter circuits, specifically low-pass filters. The input impedance is defined as R + Xc, while the output impedance is ZL || (RF + R1) when the input is shorted. For a second-order low-pass filter, the output impedance from port A-B is questioned regarding whether it should include the feedback capacitor and the input side. The user attempts to derive the input impedance using Kirchhoff's Current Law (KCL) and seeks clarification on their approach.

PREREQUISITES
  • Understanding of basic circuit theory, including impedance concepts.
  • Familiarity with active filter design principles.
  • Knowledge of Kirchhoff's Current Law (KCL) and its application in circuit analysis.
  • Experience with complex impedance calculations involving resistors and capacitors.
NEXT STEPS
  • Study the derivation of input and output impedances in second-order filter circuits.
  • Learn about feedback mechanisms in active filters and their impact on impedance.
  • Explore the use of simulation tools like LTspice for analyzing filter circuits.
  • Investigate the role of capacitors in determining overall circuit impedance in active filters.
USEFUL FOR

Electrical engineers, students studying circuit design, and anyone involved in designing or analyzing active filter circuits will benefit from this discussion.

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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?
 
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