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Current I1 and I2 entering at 1 and port 2 respectively of two port network are given by following equation.
I1 =0.5V1 - 0.2V2
I2 = -0.2V1 +V2
Obtain T and Π(pi) representation.

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1.4kviews

Current I1 and I2 entering at 1 and port 2 respectively of two port network are given by following equation.
I1 =0.5V1 - 0.2V2
I2 = -0.2V1 +V2
Obtain T and Π(pi) representation.

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written 3.0 years ago by |

TT(pi) network

Applying KCL at node 1

$I_1=Y_1V_1+Y_2\left(V_1-V_2\right)=\left(Y_1+Y_2\right)V_1-Y_2V_2 $

Applying KCL at node 2

$I_2=Y_3V_2+Y_2\left(V_2-V_1\right)=\ -Y_2V_1+\left(Y_2+Y_3\right)V_2 $

Comparing the above equation with given equations

$Y_1+Y_2=0.5,\ \ \ Y_2+Y_3=1,\ \ \ Y_2=0.2\mho{} $

$\therefore{}Y_1=0.3\mho{},\ \ \ Y_3=0.8\mho{} $

For converting a TT N/W into equivalent T N/W we can use delta-star transformation technique

$Z_1=\dfrac{Z_AZ_C}{Z_A+Z_B+Z_C}$

$Z_2=\dfrac{Z_BZ_C}{Z_A+Z_B+Z_c} $

$Z_3=Z $

$Z_3=\dfrac{Z_AZ_B}{Z_A+Z_B+Z_C} $

$\therefore{}Z_1=\dfrac{16.5}{9.55}=1.72\Omega{};\ $

$Z_2=0.65\Omega{} $

$Z_3=0.65\Omega{} $

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