# Y and z 2-port parameters

• magnifik
In summary, the conversation revolved around solving for the Y and Z parameters for a circuit. The individual provided their method for calculating the parameters, but also mentioned difficulties with getting the expected results. They later discovered some algebraic errors and were able to successfully derive the Z parameters.

#### magnifik

I am solving for the Y and Z parameters for the circuit below:

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. :\

Last edited:
magnifik said:
I am solving for the Y and Z parameters for the circuit below:

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.

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.

## 1. What are Y and Z 2-port parameters?

Y and Z are two types of 2-port parameters used to describe the behavior of a linear network. These parameters are used to calculate the voltage and current at the input and output ports of a network.

## 2. What is the difference between Y and Z parameters?

The main difference between Y and Z parameters is the type of variables used. Y parameters use admittances (reciprocal of impedance) while Z parameters use impedances. Additionally, Y parameters are used for parallel networks while Z parameters are used for series networks.

## 3. How are Y and Z parameters related?

Y and Z parameters are related by a simple conversion formula. Y parameters can be converted to Z parameters using the following formula: Z = Y-1. Similarly, Z parameters can be converted to Y parameters using the formula: Y = Z-1.

## 4. What are the units of Y and Z parameters?

Y parameters have units of siemens (S) while Z parameters have units of ohms (Ω). These units represent the relationship between voltage and current in a network.

## 5. How are Y and Z parameters used in circuit analysis?

Y and Z parameters are used in circuit analysis to simplify the calculations for voltage and current in a network. They can be used to determine the input and output impedances of a network, as well as the voltage and current gain between the input and output ports.