Ex:           Choose one R, one L, or one C to go in the box to make the circuit a high-pass filter with a cutoff frequency ωc = 105 r/s. Give the value of the element you chose.

    

         The voltage vg(t) changes instantly from −vo to vo at t = 0.

Ans:         L = 10 mH

 

Sol'n:      The output of the filter is given by the voltage divider formula, rearranged to express the transfer function H(ω):

H(jω)        where z is impedance in box

For high-pass, we want |H(jω)| = 0 for ω = 0. So we want z = 0 at ω = 0.

∴ Choose L so z = jωL and .

The resulting transfer function is

.

ωC is ω where denom R = ωL, i.e. Re[denom] = Im[denom].

∴