Characteristic impedance and transfer function

In summary, the problem is to find the absolute value of the transfer function for a circuit with capacitors and inductors interchanged. The cross circuit has L in the upper and lower branch, and two C in the cross. Due to difficulties in forming the A-matrix, the characteristic impedance and transfer function cannot be determined. The suggested approach is to compute the input impedances and use the equation sqrt(Z0*Zs) to find the characteristic impedance. However, the desired method involves computing the A-matrix, which the speaker is unsure of how to do.
  • #1
ipmac
8
0
I have to find the absolute value of the transfer function for the circuit shown in the attachment. However, I have capacitors instead of inductors in my circuit and inductors instead of capacitors. So, the cross circuit will have L in the upper and lower branch and two C in the cross. I couldn't form the A-matrix of the two port circuit. Because of this the characteristic impedance couldn't be found and thus transfer function. Could you please enlighten me in this matter?
 

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  • #2
ipmac said:
I have to find the absolute value of the transfer function for the circuit shown in the attachment. However, I have capacitors instead of inductors in my circuit and inductors instead of capacitors. So, the cross circuit will have L in the upper and lower branch and two C in the cross. I couldn't form the A-matrix of the two port circuit. Because of this the characteristic impedance couldn't be found and thus transfer function. Could you please enlighten me in this matter?

What equations would you write to start to work toward an equation for Vout = f(Vin)?
 
  • #3
As far as my understanding, we first determine the characteristic impedance by computing the input impedances Zo(open) and Zs(short) in Laplace domain when terminating the other port with impedances infinity (open) and zero (short). The characteristic impedance follows squrt(Z0.Zs). This is one way to find the characteristic impedance but I am supposed to get with with the computation of A-matrix which I am quite not sure.
 

1. What is characteristic impedance?

Characteristic impedance is a measure of the opposition to the flow of electrical current in a transmission line. It is typically represented by the symbol Z0 and is calculated by dividing the voltage by the current at any point along the line.

2. How is characteristic impedance related to the transfer function?

The characteristic impedance is a key parameter in the calculation of the transfer function of a transmission line. It is used to determine the reflection and transmission coefficients, which are then used to calculate the transfer function.

3. Can the characteristic impedance change along a transmission line?

Yes, the characteristic impedance can change along a transmission line depending on factors such as the type of cable used, the length of the line, and the presence of impedance mismatches. However, it is typically assumed to be constant for simplification in most applications.

4. How does the characteristic impedance affect signal propagation?

The characteristic impedance plays a crucial role in the proper transmission of signals along a line. If the characteristic impedance of the line does not match the impedance of the source or load, it can cause reflections and distortions in the signal, leading to poor signal quality.

5. How do you calculate the characteristic impedance of a transmission line?

The characteristic impedance of a transmission line can be calculated by using its physical parameters such as the line's length, cross-sectional area, and material properties. It can also be measured experimentally using specialized equipment such as a network analyzer.

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