Exam 15: Circuits Analysis in the S-Domain

Plot the magnitude and phase Bode diagrams of the transfer function given by $H ( s ) = \frac { \left( s + 10 ^ { 4 } \right) ^ { 2 } } { 100 \left( s + 10 ^ { 3 } \right) ^ { 2 } }$

In the circuit shown below, let $\mathrm { R } _ { 1 } = 2 \Omega , \mathrm { R } _ { 2 } = 3 \Omega , \mathrm { C } = 1 \mathrm {~F} , \mathrm {~L} = 0.2 \mathrm { H } , \mathrm { v } \left( 0 ^ { - } \right) = 1 \mathrm {~V} , \mathrm { i } \left( 0 ^ { - } \right) = 2 \mathrm {~A} , \mathrm { i } _ { \mathrm { s } } ( \mathrm { t } ) = 3 \mathrm { u } ( \mathrm { t } )$ Draw the circuit in the s-domain and find the Norton equivalent current $\mathrm { I } _ { \mathrm { n } } ( \mathrm { s } )$ and the Norton equivalent impedance $Z _ { n } ( s )$ .

Plot the magnitude and phase Bode diagrams of the transfer function given by $H ( s ) = \frac { 10 ^ { 2 } ( s + 100 ) } { s ( s + 10000 ) }$

In the circuit shown below, let $\mathrm { R } = 3 \Omega , \mathrm { C } = 0.1 \mathrm {~F} , \mathrm {~L} = 2 \mathrm { H } , \mathrm { v } \left( 0 ^ { - } \right) = 2 \mathrm {~V} , \mathrm { i } \left( 0 ^ { - } \right) = 1 \mathrm {~A} , \mathrm { v } _ { \mathrm { s } } ( \mathrm { t } ) = 3 \mathrm { u } ( \mathrm { t } )$ Draw the circuit in the s-domain and find the Thévenin equivalent voltage $\mathrm { V } _ { \mathrm { th } } ( \mathrm { s } )$ and the Thévenin equivalent impedance $Z _ { t h } ( s )$ .

In the circuit shown below, let $\mathrm { R } _ { 1 } = 1 \Omega , \mathrm { R } _ { 2 } = 2 \Omega , \mathrm { C } = 0.2 \mathrm {~F} , \mathrm {~L} = 0.5 \mathrm { H } , \mathrm { v } \left( 0 ^ { - } \right) = 1 \mathrm {~V} , \mathrm { i } \left( 0 ^ { - } \right) = 2 \mathrm {~A} , \mathrm { vs } ( \mathrm { t } ) = 3 \mathrm { u } ( \mathrm { t } )$ $\text { Draw the circuit in the s-domain and find } V _ { 0 } ( s ) \text { and } v _ { 0 } ( t ) \text { for } t \geq 0 \text {. }$

In the circuit shown below, let $\mathrm { R } _ { 1 } = 2 \Omega , \mathrm { R } _ { 2 } = 1 \Omega , \mathrm { C } = 0.2 \mathrm {~F} , \mathrm {~L} = 2 \mathrm { H } , \mathrm { v } \left( 0 ^ { - } \right) = 1 \mathrm {~V} , \mathrm { i } \left( 0 ^ { - } \right) = 2 \mathrm {~A} , \mathrm { i } _ { \mathrm { s } } ( \mathrm { t } ) = 5 \mathrm { u } ( \mathrm { t } )$ Draw the circuit in the s-domain and find $V ( s )$ and $v ( t )$ for $t \geq 0$ .