 GATE EC 2014 Electromagnetics Solution Q 6

# GATE EC 2014 Electromagnetics Solution Q 6

A two port network has scattering parameters given by

\left[S\right]=\begin{bmatrix}S_{11}&S_{12}\S_{21}&S_{22}\end{bmatrix}.

If the port-2 of the two -port is short circuited, the S11 parameter for the resultant one-port network is____.

a) \frac{S_{11}-S_{11}S_{22}+S_{12}S_{21}}{1+S_{22}}

b) \frac{s_{11}+s_{11}s_{22}-s_{12}s_{21}}{1+s_{22}}

c) \frac{s_{11}+s_{11}s_{22}+s_{12}s_{21}}{1-s_{22}}

d) \frac{s_{11}-s_{11}s_{22}+s_{12}s_{21}}{1-s_{22}}

Ans-(b)

Explanation

s=\begin{bmatrix}S_{11}&S_{12}\S_{21}&S_{22}\end{bmatrix} V_{01}=s_{11}V_{i1}+s_{12}V_{i2} V_{02}=s_{21}V_{i1}+s_{22}V_{i2}

When port-2 is short circuited, then V_{i2}=-V_{02}

\therefore\;V_{02}=s_{21}V_{i1}+s_{22}\left(-V_{02}\right)=\frac{s_{21}}{1+s_{22}}V_{i1} V_{01}=s_{11}V_{i1}+s_{12}\left(-V_{02}\right) V_{01}=s_{11}V_{i1}-s_{12}\frac{s_{21}}{1+s_{12}}V_{i1} =\left(s_{11}-\frac{s_{12}\times s_{21}}{1+s_{22}}\right)V_{i1} s_{11}^{'}=\frac{V_{01}}{V_{i1}}

Putting values, we can get the answer. Become PRO At Electromagnetics Basics With Our 4 Ultimate Visual FREE E-Books On Coordinate Systems & Transformations

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