Question

t (u)/Vin(a) for all ω·Vin(ω) is across the left (a) for all . Vin find the magnitude of Dou For the circuit below, ports, out () across the right ports R1 L1 C1

Answer 1

Parallel equivalent impedence of capacitor and inductor

$Z_1=\left [\left (\frac{1}{X_L}-\frac{1}{X_C} \right )i \right ]^{-1}=-\frac{X_CX_L}{X_C-X_L}i$

where

$X_L=L\omega,\ X_C=\frac{1}{C\omega}$

Series equivalent with resistor

$Z=Z_1+R=R-\frac{X_CX_L}{X_C-X_L}i$

Therefore, $V_{out}$ is

$V_{out}=\frac{V_{in}}{Z}Z_1$

$\frac{V_{out}}{V_{in}}=\frac{Z_1}{Z}$