2 Port Networks - Impedance Parameters

The summary of the conversation is that there is an error in the given equations and values for the variables. There are also some mistakes made by the quizmaster. Changes need to be made to the equations in order to get the correct solution.
  • #1
p75213
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0

Homework Statement


see attached


Homework Equations





The Attempt at a Solution


$$\eqalign{
& {V_1} = {Z_{11}}{I_1} + {Z_{12}}{I_2} \cr
& {V_2} = {Z_{22}}{I_2} + {Z_{21}}{I_1} \cr
& {\rm{ - - - - - - - - - - - - - - - - - - - - - - - - - - - }} \cr
& 2\angle 30 = 8{I_1} - j4{I_2} \cr
& 0 = - j4{I_1} + 8{I_2} & \to {I_1} = {{8{I_2}} \over {j4}} = - j2{I_2} \cr
& 2\angle 30 = - j16{I_2} - j4{I_2} \cr
& {{2\angle 30} \over {20\angle - 90}} = {I_2} \cr
& {I_2} = 0.1\angle 120{\rm{ A}} \cr} $$

As I2 is incorrect I haven't bothered with I1. Can somebody point out where the error is?
 

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  • #2
[strike]Z11 is 6 ohms. EDIT: Oops, I failed to notice you'd included the 2 ohms there.[/strike]

Where it says 2∠30°, change it to 20∠30°. :wink:
 
Last edited:
  • #3
Check the relation between I1 and I2. There's a sign error there!

Plus the magnitudes are wrong anyway unless you change the input to 20V or reduce the answers by a factor of 10 ...

Plus, the angle of I1 is off by 10 deg.

Not a good day for the quizmaster.
 
Last edited:
  • #4
Thanks guys.

I have learned a lot from this book in spite of the many errors.
 
  • #5


I would like to point out that the equations and calculations provided in the attempt at a solution are not completely accurate. The first two equations are correct, but the values used for Z11, Z12, Z21, and Z22 are not given in the problem and cannot be assumed. Additionally, the second to last line is incorrect as the division should be between 2∠30 and 20∠-90, not 2∠30 and 20∠90. This results in a different value for I2, which then affects the value of I1. Therefore, both I1 and I2 would need to be recalculated using the correct values for Z11, Z12, Z21, and Z22. It is important to carefully check all equations and values before proceeding with calculations to ensure accuracy.
 

1. What are 2-port networks and why are they important in electrical circuits?

2-port networks are a type of electrical circuit that contains two inputs and two outputs. They are important because they allow for the analysis and characterization of complex electrical networks in a simplified manner.

2. What are impedance parameters and how are they related to 2-port networks?

Impedance parameters, also known as Z-parameters, are a set of four parameters that describe the input and output impedance of a 2-port network. They are related to 2-port networks because they can be used to calculate the voltage and current at each port of the network.

3. How do you calculate the impedance parameters of a 2-port network?

The impedance parameters can be calculated by applying a test voltage or current at each port of the network and measuring the resulting voltage or current at the other port. These values can then be used to solve for the Z-parameters using a set of equations.

4. What is the difference between the impedance parameters and other network parameters like S-parameters or Y-parameters?

The main difference between impedance parameters and other network parameters is that impedance parameters are measured in terms of impedance, while S-parameters are measured in terms of reflection coefficients and transmission coefficients, and Y-parameters are measured in terms of admittance.

5. How are 2-port networks and impedance parameters used in practical applications?

2-port networks and impedance parameters are used in a variety of practical applications, including the design and analysis of electronic circuits, transmission line networks, and communication systems. They are also used in RF and microwave engineering for impedance matching and signal analysis.

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