Filter circuit impedance?

In summary, The conversation is about finding impedances for active filter circuits. In a simple low pass filter, the input impedance is R + Xc and the output impedance is ZL || (RF+R1). In a 2nd order configuration, the output impedance may also include the feedback capacitor and the input side with the source short-circuited. The input impedance can be derived using KCL at the red node and rearranging the equation to fit Vi/Ii.
  • #1
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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 [Broken]

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 [Broken]

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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  • #2
can someone please help answer this?
 
  • #3


Any help is appreciated!

it is important to understand the impedance of a filter circuit in order to analyze and design its performance. Impedance is a measure of the opposition to the flow of an alternating current in a circuit. In the case of a filter circuit, it is important to consider both the input and output impedances.

The input impedance of a filter circuit is the measure of the opposition to the flow of current at the input terminal. In a low pass filter, the input impedance is the sum of the resistance and the reactance of the capacitor. This can be calculated using Ohm's law and the reactance formula for a capacitor, Xc = 1/(2πfC).

The output impedance of a filter circuit is the measure of the opposition to the flow of current at the output terminal. In a second order filter, the output impedance is a combination of the load impedance (ZL) and the impedance of the feedback network. This can be calculated using the formula Zout = ZL || (RF + R1), where || represents the parallel combination.

It is important to consider both the input and output impedances when analyzing and designing a filter circuit, as they can affect the overall performance and stability of the circuit. The derivation method mentioned in the post is a valid approach to calculate the input impedance, but it is important to also consider the impedance of the feedback network when calculating the output impedance. I hope this helps clarify any confusion.
 

What is filter circuit impedance?

Filter circuit impedance refers to the resistance that a filter circuit presents to an alternating current (AC) signal. It is measured in ohms and can affect the performance and efficiency of a filter circuit.

Why is filter circuit impedance important?

Filter circuit impedance is important because it determines the amount of current that can pass through a circuit, and therefore affects the filtering capability of the circuit. A higher impedance can result in a weaker filter, while a lower impedance can lead to excessive current flow and potential damage to the circuit.

How is filter circuit impedance calculated?

Filter circuit impedance can be calculated using Ohm's Law, which states that impedance equals voltage divided by current. In practical terms, it can also be calculated using the values of the resistors, capacitors, and inductors in the circuit using complex mathematical equations.

What factors affect filter circuit impedance?

There are several factors that can affect filter circuit impedance, including the values of the components used, the frequency of the AC signal, and the configuration of the circuit. Changes in any of these factors can alter the impedance and, consequently, the performance of the circuit.

How can filter circuit impedance be optimized?

Filter circuit impedance can be optimized by carefully selecting the values of the components in the circuit, such as resistors, capacitors, and inductors, to achieve the desired impedance. Additionally, using circuit simulation software can help in determining the optimal values for the components to achieve the desired impedance and filter performance.

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