GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 25 of 65

Marks: +1, -0

The Bode magnitude plot for the transfer function

\;{V_{0}(s)}/{V_{i}(s)}

of the circuit is as shown. The value of

R

is _____________

Ω

. (Round off to 2 decimal places.)

Solution:

Given

{M}_{ {r}} {dB}=26 {dB}

20 \log {M}_{ {R}}=26

{M}_{ {r}}=20

M_{T}=\;{1}/{\sin 2 φ}=20

\sin φ=\;{1}/{\sin 2 φ}=20

2 φ=2.86,177.14

φ=88.57(>450^{∘})

{s}=\cos φ=0.025

Now, T.F. of RLC series circuit is

\;{V_{0}}/{V_{i}}=\;{1}/{s^{2} L C+s R C+1}=\;{1}/{s^{2}(10^{-3} × 250 × 10^{-6}) s(R × 250 × 10^{-6})+1}

=\;{4 × 10^{6}}/{s^{2}+1500 R s+4 × 10^{6}}

ω_{n}^{2}=4 × 10^{6}

ω_{n}=2 × 10^{3}

25 ω_{ {n}}=1000 {R}

2(0.25)(2 × 10^{3})=1000 {R}

{R}=0.1 Ω

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