GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 12 of 65

Marks: +1, -0

In the given circuit, the two-port network has the impedance matrix

[ {Z}]=[\table 40 , 60 ; 60 , 120] .

The value of

Z_{L}

for which maximum power is transferred to the load is

. . . . . . . Ω

Solution:

Old Parameters -

{V}_{1}=40 {i}_{1}+60 {i}_{2}

.......(i)

{V}_{2}=60 {i}_{1}+120 {i}_{2}

........(ii)

Z_{t h}

by testing method

KVL in mesh (i)

10 i_{1}+V_{1}=0

{V}_{1}=-10 {i}_{1}

\;\text " And "\; I_{2}=1 {A}

From eq. (i)

{V}_{1}=40 {i}_{1}+60 × 1

...........(iv)

-10 i_{1}=40 i_{1}+60

i_{1}=-6 / 5

{V}_{2}=60 ×(-\;{6}/{5})+120 × 1

=-72+120

=48 {V}

to deliver max. power to load

{z}_{L}

Z_{L}=R_{t h}

∴ z_{L}=\;{V_{2}}/{i_{2}}=\;{48}/{1}

=48 Ω

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