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Transistor: Working

In the circui...

Question

In the circuit shown below, assume op-amp is ideal

The z-parameter matrix element $Z_{21}, Z_{22}$ are respectively

\frac{R_{2}}{R_{3}} a n d (R_{1} R_{2} + \frac{R_{4}}{R_{5}})

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R_{3} a n d (\frac{R_{2} R_{4}}{R_{3}} + R_{2})

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(R_{1} R_{2} + \frac{R_{4}}{R_{5}}) a n d \frac{R_{2}}{R_{3}}

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(R_{2} + \frac{R_{2} R_{4}}{R_{5}}) a n d R_{3}

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Solution

The correct option is D $(R_{2} + \frac{R_{2} R_{4}}{R_{5}}) a n d R_{3}$

$V_{f} = V_{0} [\frac{R_{5}}{R_{4} + R_{5}}]$

$V_{0} = \frac{V_{f}}{[\frac{R_{3}}{R_{4} + R_{3}}]}$

$V_{f} = I_{1} R_{2}$

$V_{0} = \frac{I_{1} R_{2}}{[\frac{R_{5}}{R_{4} + R_{5}}]}$

$V_{0} = [1 + \frac{R_{4}}{R_{5}}] \times R_{2} I_{1} . . . . (i)$

$I_{2} = \frac{V_{2} - V_{0}}{R_{3}}$

$V_{0} = V_{2} - I_{2} R_{3} . . . . (i i)$

By equating (i) and (ii),

$V_{2} - I_{2} R_{3} = [1 + \frac{R_{4}}{R_{5}}] \times R_{2} I_{1}$

$V_{2} = [(1 + \frac{R_{4}}{R_{5}}) \times R_{2}] I_{1} + R_{3} I_{2}$

$Z_{21} = (1 + \frac{R_{4}}{R_{5}}) R_{2} = [R_{2} + \frac{R_{2} R_{4}}{R_{5}}]$

$Z_{22} = R_{5}$

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