Regarding with two port electrical network

[namal]

my problems comes from one of a book how to solve this one this is regarding with two port electrical network

 

[yungman]

For Z parameter

[tex]\left(\begin{array}{c}V_1\\V_2\end{array}\right)\;=\;\left(\begin{array}{cc}Z_{11} & Z_{12}\\Z_{21} & Z_{22}\end{array}\right)\;\left(\begin{array}{c}I_1\\I_2\end{array}\right)[/tex]

[tex] V_1=Z_{11}I_1+Z_{12}I_2[/tex]

[tex] V_2=Z_{21}I_1+Z_{22}I_2[/tex]

[tex]Z_{11}=\left(\frac{V_1}{I_1}\right)_{I_2=0}\;\;,\;\;Z_{12}=\left(\frac{V_1}{I_2}\right)_{I_1=0} \;\;,\;\;Z_{21}=\left(\frac{V_2}{I_1}\right)_{I_2=0}\;\;,\;\;Z_{22}=\left(\frac{V_2}{I_2}\right)_{I_1=0}[/tex]

For I=0 means open circuit.

For Y parameter just (I)=(Y)(V) and make one of the V=0 which is short circuit.

For transformer it is reciprocal circuit so Z12=Z21 and Y12=Y21.

I have not work out the detail, just use this on the transformer and it should work.

 

[namal]

thanks for your answer.but consider this
the circuit is reciprocal so that[y][/21]=[y][/12] , Am I right?

 

[The Electrician]

Have a look at this: http://www.daycounter.com/LabBook/Two-Port-Networks/Two-Port-Network-Topologies.phtml

and especially this: http://fourier.eng.hmc.edu/e84/lectures/ch2/node4.html

Since the Y matrix of a two port is the inverse of its Z matrix, then if Z12 = Z21 it follows that Y12 = Y21.