Impedance Transfer: Find Z_{input1}, Z_{transfer12}, Z_{transfer13}

  • Thread starter sandy.bridge
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In summary, the conversation is about finding the impedance in a circuit using mesh currents. The Z matrix for the circuit is a 3x3 matrix, with driving point impedances on the main diagonal and transfer impedances on the off diagonal. Zinput1 is the 1,1 element of the Z matrix and Ztransfer12 is the 1,2 element. The goal is to set up the Z matrix for the circuit.
  • #1
sandy.bridge
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Homework Statement


Hello,
I have encountered some sort of notation that I am not familiar with in regards to impedance. As an example, I have depicted a network here
hehe.jpg

The top loop is considered loop 1, the bottom-left loop is considered loop 2, while the bottom-right loop is loop 3.
[tex]R_2=5, R_3=10, R_1 2, C_1=C-2=-j4, L_1=j5, V=50e^{j0}[/tex]
Using mesh currents [tex]I_1, I_2, I_3[/tex] in clock-wise direction, find [tex]Z_{input1}, Z_{transfer12}, Z_{transfer13}[/tex]
I cannot seem to find anything in my notes regarding this... Any help is greatly appreciated. :)
 
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  • #2
I believe
[tex]Z_{input1}=\frac{50e^{j0}}{I_1}[/tex]
However, the "transfer12" and "transfer13" impedances are not making any sense to me.
 
  • #3
They want you to set up the impedance matrix (Z matrix) for the circuit. Since there are 3 loops, the matrix will be a 3x3 matrix.

The elements on the main diagonal, the Z(n,n) with n = 1 to 3, are the driving point impedances. The off diagonal elements are the transfer impedances.

Zinput1 will be the 1,1 element of the Z matrix. Ztransfer12 will be the 1,2 element, etc.
 

1. What is impedance transfer?

Impedance transfer is the process of calculating the input impedance of a circuit and the impedance transfer between components in a circuit. This can help determine how a circuit will behave and how to optimize its performance.

2. How do I find Z_{input1}?

To find Z_{input1}, you will need to use the formula Z_{input1} = V/I, where V is the voltage and I is the current. You will also need to know the resistance, capacitance, and inductance values of the circuit components.

3. What is Z_{transfer12}?

Z_{transfer12} is the impedance transfer between two components in a circuit, specifically between Z_{input1} and Z_{input2}. It is calculated using the formula Z_{transfer12} = Z_{input2}/Z_{input1}.

4. How can I calculate Z_{transfer13}?

Z_{transfer13} is the impedance transfer between Z_{input1} and Z_{input3}. To calculate it, you will need to use the formula Z_{transfer13} = Z_{input3}/Z_{input1}. This will give you the impedance transfer ratio between the two components.

5. Why is impedance transfer important in circuit analysis?

Impedance transfer is important in circuit analysis because it allows us to understand how a circuit will behave and how to optimize its performance. By calculating the input impedance and impedance transfer between components, we can determine the best values for our circuit components and ensure efficient and effective circuit operation.

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