Calculating y-parameters (admittance matrix)

[CoolDude420]

Homework Statement

Homework Equations

The Attempt at a Solution

I keep getting something over 0 for my Y_11. I'm not sure what I'm doing wrong. I thought the ideal transformer does not have an admittance or impedance matrix, which is why I should be getting something over 0 but the there is an answer that is provided to us.

 

[cnh1995]

Your first step should be transferring the secondary impedances on the primary side.

 

[CoolDude420]

Your first step should be transferring the secondary impedances on the primary side.

You mean transform the coupled indcutors to its own separate impedances?

 

[cnh1995]

You mean transform the coupled indcutors to its own separate impedances?

No. Have you studied impedance transformation in transformers? There are two circuits in your problem (primary and secondary). Using impedance transformation, you obtain a single equivalent circuit (referred either to the primary or the secondary) so that you can remove the transformer from the circuit.

 

[CoolDude420]

No. Have you studied impedance transformation in transformers? There are two circuits in your problem (primary and secondary). Using impedance transformation, you obtain a single equivalent circuit (referred either to the primary or the secondary) so that you can remove the transformer from the circuit.

Hmm.

The only thing I recall is that if an impedance Z_L is connected across one side of an idea transformer, it's impedance on the other side is just
V_1/I_1 = (n_1/n_2)^2Z_L

 

[cnh1995]

Hmm.

The only thing I recall is that if an impedance Z_L is connected across one side of an idea transformer, it's impedance on the other side is just
V_1/I_1 = (n_1/n_2)^2Z_L

Yes. Using that, convert the two-part circuit into a single circuit referred to the primary. Make sure you change the receiving end voltage also, by a factor of n.

 

[CoolDude420]

Yes. Using that, convert the two-part circuit into a single circuit referred to the primary. Make sure you change the receiving end voltage also, by a factor of n.

Ah. That's perfect. I got the right answer for y_11. What do you mean by changing the receiving end voltage?

 

[CoolDude420]

Okay, I'm kinda confused.
I have the following new circuit after replacing the transformer,

I'm trying to calculate y_21 = I_2/V_1 when V_2=0. But now, I_2 doesn't exist anymore since it was transformed?

 

[cnh1995]

What do you mean by changing the receiving end voltage?

V2 and I2 will change by a factor of n when you transfer them from one side to the other.

Here, you are transferring V2 to the primary side, so it will become V2*(1/n) and similarly I2 will become n*I2.

 

[Babadag]

I am not sure what are the known parameters. Let’s say you know R1,R2,C,n, V2 and I2.What you have to calculate is Y1=I1/V1.
You have to transfer the secondary parameters to primary as cnh1995 proposed.
However, at first you have to calculate E2 and I21 –the current flowing through the secondary winding.
E2 =SUM of all voltage drop [split I2 in I21 and I22 ] and you have I21[V2,I2] and E2[I2,V2]. And now E1=nE2 and I1=I21/n. So you have V1 and Y1=I1/V1.

 

[The Electrician]

CoolDude420, are you still working on this?

 

[Babadag]

 

[Babadag]

if E1/1=E2/n then:

Sorry.