What are the Y and Z parameters for a 2-port circuit and how do you derive them?

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Discussion Overview

The discussion revolves around the derivation of Y and Z parameters for a specific 2-port circuit. Participants are exploring the equations and methods used to calculate these parameters, addressing potential errors and uncertainties in their approaches.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents their calculations for Y parameters using current sources and arrives at Y = [3 -2/3; 0 8/3].
  • The same participant calculates Z parameters using KVL and finds Z = [1/3 1/6; 0 1/3], expressing uncertainty about the relationship between Y and Z.
  • Another participant suggests modifying the equations by replacing Ib and Ic with Ib - Ic = 2v1 to potentially correct the calculations.
  • A further reply indicates that after applying the suggested change, the participant recalculates Z parameters and finds Z = [1/3 1/9; 0 1/2], but notes discrepancies with the inverse of Z not matching the Y parameters.
  • Participants discuss the assumption regarding the voltage across the dependent source, suggesting that it should not be considered zero and that adjustments to the equations are necessary.
  • One participant confirms that their Y parameters are correct, while another expresses concern about the validity of their Y parameters before checking Z parameters.
  • A later reply acknowledges that algebraic errors were the source of confusion in deriving the Z parameters.

Areas of Agreement / Disagreement

There is no consensus on the correctness of the Y and Z parameters, as participants express uncertainty and propose different approaches to the calculations. Multiple competing views and methods remain present in the discussion.

Contextual Notes

Participants highlight potential errors in their calculations and assumptions, particularly regarding the treatment of dependent sources and the relationships between the variables. The discussion includes unresolved mathematical steps and varying interpretations of the circuit behavior.

Who May Find This Useful

Readers interested in circuit analysis, particularly in the context of deriving parameters for 2-port networks, may find the discussion relevant.

magnifik
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I am solving for the Y and Z parameters for the circuit below:
2vaauqt.png


For Y, I used the following equations by applying current sources at the terminals
va is the node at the 2v1 dependent source
(va-v1)/0.5 + (va-v2)/1 = -2v1
I1 = v1/1 + (v1-va)/0.5
I2 = v2/0.5 + (v2-va)/1
I got Y = [3 -2/3; 0 8/3]

For Z, I used KVL by applying voltage sources at the terminals
v1 = Ia - Ib
0 = Ib - Ia + 0.5Ib
0 = Ic + 0.5(Ic + Id)
v2 = 0.5(Ic + Id)
where Ia = I1, Ib = 2v1, Ic = -2v1, and Id = I2
I got Z = [1/3 1/6; 0 1/3]

I am not sure what I am doing incorrectly here. Y should be equal to Z-1, but I am not getting that. I'm not sure if my Y parameters are wrong, Z parameters, or both. :\
 
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magnifik said:
I am solving for the Y and Z parameters for the circuit below:
2vaauqt.png


For Y, I used the following equations by applying current sources at the terminals
va is the node at the 2v1 dependent source
(va-v1)/0.5 + (va-v2)/1 = -2v1
I1 = v1/1 + (v1-va)/0.5
I2 = v2/0.5 + (v2-va)/1
I got Y = [3 -2/3; 0 8/3]

For Z, I used KVL by applying voltage sources at the terminals
v1 = Ia - Ib
0 = Ib - Ia + 0.5Ib
0 = Ic + 0.5(Ic + Id)
v2 = 0.5(Ic + Id)
where Ia = I1, Ib = 2v1, Ic = -2v1, and Id = I2
I got Z = [1/3 1/6; 0 1/3]

I am not sure what I am doing incorrectly here. Y should be equal to Z-1, but I am not getting that. I'm not sure if my Y parameters are wrong, Z parameters, or both. :\

I think the major problem is where you have:

Ib = 2v1, Ic = -2v1

Replace those two items with Ib - Ic = 2v1

and see if you don't get better results.
 
when using Ib - Ic = 2v1

I got
v1 = Ia - Ib
= Ia- Ic - 2v1
= Ia + (1/3)Id - 2v1
====> v1/I1 = 1/3 and v1/I2 = 1/9
plugging in values to find the remaining parameters i got v2/I2 = 1/2 and v2/I1 = 0
so for Z parameters i got Z = [1/3 1/9; 0 1/2]

The inverse of this is [3 -2/3; 0 2] so there's still something off :\
 
You can't assume the voltage across the dependent source is zero; you have:

0 = Ib - Ia + 0.5Ib
0 = Ic + 0.5(Ic + Id)

You need to make those:

0 = -va + Ib - Ia + 0.5Ib
0 = va + Ic + 0.5(Ic + Id)

I'm not working out the complete solution using your method, so I may not see all the errors right away. I'm just pointing out what I see with a quick glance; you need to try to find errors also.

You might need to treat the middle two meshes together as a supermesh.
 
The Electrician said:
You can't assume the voltage across the dependent source is zero; you have:

0 = Ib - Ia + 0.5Ib
0 = Ic + 0.5(Ic + Id)

You need to make those:

0 = -va + Ib - Ia + 0.5Ib
0 = va + Ic + 0.5(Ic + Id)

I'm not working out the complete solution using your method, so I may not see all the errors right away. I'm just pointing out what I see with a quick glance; you need to try to find errors also.

You might need to treat the middle two meshes together as a supermesh.

are my Y parameters correct? just wondering because i don't want to be trying to use them to check if my Z parameters are correct if they aren't right in the first place..
 
Yes, they are correct. :smile:
 
Have you had any luck deriving the Z parameters?
 
The Electrician said:
Have you had any luck deriving the Z parameters?

yep, thanks. i just had a few algebraic errors that threw me off.
 

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