In the circuit shown below, let

\mathrm { R } _ { 1 } = 1 \Omega , \mathrm { R } _ { 2 } = 2 \Omega , \mathrm { L } = 1 \mathrm { H } , \mathrm { C } = 0.1 \mathrm {~F} , \mathrm {~V} _ { \mathrm { b } } = \mathrm { V } _ { \mathrm { o } }

(a) Write a node equation at node 1 by summing the currents leaving node 1 .
(b) Write a node equation at node 2 by summing the currents leaving node

2 .

\mathrm { H } ( \omega ) = \mathrm { V } _ { \mathrm { o } } / \mathrm { V } _ { \text {in } }

.
(d) Plot the magnitude response

| H ( \omega ) |

and find the value of

| H ( \omega ) |

\omega = \infty

.
(e) What type (LPF, HPF, BPF, BSF) of filter is this?
$In the circuit shown below, let \mathrm { R } _ { 1 } = 1 \Omega , \mathrm { R } _ { 2 } = 2 \Omega , \mathrm { L } = 1 \mathrm { H } , \mathrm { C } = 0.1 \mathrm {~F} , \mathrm {~V} _ { \mathrm { b } } = \mathrm { V } _ { \mathrm { o } } (a) Write a node equation at node 1 by summing the currents leaving node 1 . (b) Write a node equation at node 2 by summing the currents leaving node 2 . (c) Find the transfer function \mathrm { H } ( \omega ) = \mathrm { V } _ { \mathrm { o } } / \mathrm { V } _ { \text {in } } . (d) Plot the magnitude response | H ( \omega ) | and find the value of | H ( \omega ) | at \omega = \infty . (e) What type (LPF, HPF, BPF, BSF) of filter is this?$

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