Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1. Given V 1 = A 1 V 2 + B 1 I 2 I 1 = C 1 V 2 + D 1 I 2 V 2 = A 2 V 3 + B 2 I 3 I 2 = C 2 V 3 + D 2 I 3 A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , and D 2 are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source V T and an impedance Z T connected in series, then

Correct Answer is : VT=V1A1A2+B1C2,ZT=A1B2+B1D2A1A2+B1C2

V_{T} = {V_{1}}/{A_{1}A_{2}},Z_{T} = {A_{1}B_{2} + B_{1}D_{2}}/{A_{1}A_{2} + B_{1}C_{2}}

V_{T} = {V_{1}}/{A_{1}A_{2} + B_{1}C_{2}},Z_{T} = {A_{1}B_{2} + B_{1}D_{2}}/{A_{1}A_{2}}

V_{T} = {V_{1}}/{A_{1} + A_{2}},Z_{T} = {A_{1}B_{2} + B_{1}D_{2}}/{A_{1} + A_{2}}

V_{T} = {V_{1}}/{A_{1}A_{2} + B_{1}C_{2}},Z_{T} = {A_{1}B_{2} + B_{1}D_{2}}/{A_{1}A_{2} + B_{1}C_{2}}

GATE Electrical Engineering (EE) 2017 Shift 1 Solved Paper

Question : 39 of 65

Marks: +1, -0

Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1.

Given V₁ = A₁V₂ + B₁I₂
I₁ = C₁V₂ + D₁I₂
V₂ = A₂V₃ + B₂I₃
I₂ = C₂V₃ + D₂I₃
A₁, B₁, C₁, D₁, A₂, B₂, C₂, and D₂ are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source V_T and an impedance Z_T connected in series, then

$V_{T} = \;{V_{1}}/{A_{1}A_{2}},Z_{T} = \;{A_{1}B_{2}\;+\;B_{1}D_{2}}/{A_{1}A_{2} + B_{1}C_{2}}$
$V_{T} = \;{V_{1}}/{A_{1}A_{2} + B_{1}C_{2}},Z_{T} = \;{A_{1}B_{2}\;+\;B_{1}D_{2}}/{A_{1}A_{2}}$
$V_{T} = \;{V_{1}}/{A_{1} + A_{2}},Z_{T} = \;{A_{1}B_{2}\;+\;B_{1}D_{2}}/{A_{1} + A_{2}}$
$V_{T} = \;{V_{1}}/{A_{1}A_{2} + B_{1}C_{2}},Z_{T} = \;{A_{1}B_{2}\;+\;B_{1}D_{2}}/{A_{1}A_{2} + B_{1}C_{2}}$

Validate

Go to Question:

Prev Question

Next Question