A two-port network is represented by ABCD parameters given by- V1- I1 - - - A B- C D - V2- -I2 -If port-2 is terminated by RL- the input impendance seen at port-1 is given by

V_1 = AV_2 BI_2 I_1 = CV_2 DI_2 V_2 = I_2R_L ∴ V_1I_1 = AV_2 BI_2CV_2 DI_2 = A.I_2R_L BI_2 C.I_2R_L DI_2 Input impendance = AR_L + BCR_L + D ...

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Circuit Theory

ABCD- parameters

A two-port ne...

Question

A two-port network is represented by ABCD parameters given by

$[\begin{matrix} V_{1} I_{1} \end{matrix}] = [\begin{matrix} A & B C & D \end{matrix}] [\begin{matrix} V_{2} - I_{2} \end{matrix}]$

If port-2 is terminated by $R_{L}$ , the input impendance seen at port-1 is given by

\frac{A + B R_{L}}{C + D R_{L}}

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\frac{A R_{L} + C}{B R_{L} + D}

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\frac{D R_{L} + A}{B R_{L} + C}

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\frac{B + A R_{L}}{D + C R_{L}}

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Solution

The correct option is D $\frac{B + A R_{L}}{D + C R_{L}}$

$V_{1} = A V_{2} - B I_{2}$

$I_{1} = C V_{2} - D I_{2}$

$V_{2} = - I_{2} R_{L}$

$∴$ $\frac{V_{1}}{I_{1}} = \frac{A V_{2} - B I_{2}}{C V_{2} - D I_{2}}$

$= \frac{- A . I_{2} R_{L} - B I_{2}}{- C . I_{2} R_{L} - D I_{2}}$

Input impendance $= \frac{A R_{L} + B}{C R_{L} + D}$

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Similar questions

The ABCD matrix for a two-port network is defined by
$[\begin{matrix} V_{1} I_{1} \end{matrix}] = [\begin{matrix} A & B C & D \end{matrix}] [\begin{matrix} V_{2} - I_{2} \end{matrix}]$

The parameter B for the given two-port network(in ohms, correct to two decimal places) is