Second Order Filters

a$.$ For Vout$($s$)=$V$\_($R$1)($s$)($resistor voltage$),$ R$=10\mathrm{.}1$kOmega,

a$.$ Determine the transfer function,

b$.$ Determine the attenuation constant, the resonant frequency and the damping ratio.

c$.$ Is the circuit overdamped, critically damped or underdamped

d$.$ Determine the poles and zeros of the transfer function.

e$.$ Sketch the Bode plots for the magnitude, including corrections.

b$.$ For Vout$($s$)=$V$\_($L$1)($s$)($inductor voltage$),$ R$=2$kOmega,

a$.$ Determine the transfer function,

b$.$ Determine the attenuation constant, the resonant frequency and the damping ratio.

c$.$ Is the circuit overdamped, critically damped or underdamped

d$.$ Determine the poles and zeros of the transfer function.

e$.$ Sketch the Bode plots for the magnitude, including corrections.

c$.$ For Vout$($s$)=$V$\_($L$1)($s$)($inductor voltage$),$ R$=1000$ Omega,

a$.$ Determine the transfer function,

b$.$ Determine the attenuation constant, the resonant frequency and the damping ratio.

c$.$ Is the circuit overdamped, critically damped or underdamped

d$.$ Determine the poles and zeros of the transfer function.

e$.$ Sketch the Bode plots for the magnitude, including corrections.

d$.$ For Vout$($s$)=$V$\_($C$1)($s$)($capacitor voltage$),$ R$=100$ Omega,

f$.$ Determine the transfer function,

g$.$ Determine the attenuation constant, the resonant frequency and the damping ratio.

h$.$ Is the circuit overdamped, critically damped or underdamped

i$.$ Determine the poles and zeros of the transfer function.

j$.$ Sketch the Bode plots for the magnitude, including corrections.