Find the poles and zeros of the transfer function Hs Hs s

Find the poles and zeros of the transfer function H(s). H(s) = (s - 2)(s - 4)/s(s - 3)(s - 7) zeros are: poles are: Given a series RLC circuit with R = 25 k Ohm, L = 10 mH, and C = 1.0 mu F, if the circuit is magnitude-sealed by K_m = 20 and frequency-scaled by K_f = 10^4, find the resulting sealed values of R, L, and C.

Solution

1a) H(S) = ((s-2)(s-4)) /(s(s-3)(s-7)) = N(s)/D(S)

to find the zeros N(s)=0

(s-2)(s-4)=0 from s=2 : s=4 are the zeros

to find poles D(s)=0

s(s-3)(s-7)=0 from this s=0 : s =3 :s =7 are the poles

zeros : 2 ,4

poles : 0,3,7

1b) R = 25 Kohms ;L=10 mH ; C = 1.0 uF

magnitude scaled by K_m =20

freequency scaled by K_f = 10⁴

scaling in magnitude and freequency results in

R^\' = K_mR =20 *25 Kohms =500 Kohms

L^\' = (K_mL)/K_f = 20*10mH / 10⁴ = 5 pF