Synthesis of LC and RC Input Impedances

By Que Luu

EE 175

Problem 1

a) What type of realization is the above circuit?

· This is a foster I realization

b) From the above circuit, design Z(s) and find the values of RC network

· To obtain RC network, we need to have

Therefore, I come up with an equation for Z(s) is:

Z(s) = (S+2) (S+5)

S(S+4)(S+6)

• To find the values for RC, I obtain the Foster I realization from (a)

- Expand Z(s) in partial fraction:

Z(s) = K₁ + K₂ + K₃

S S+4 S+6

K₁ = Z(s)|_S=0 = (S+2)(S+5) = 5

(S+4)(S+6) 12

K₂ = Z(s)|_S=-4 = (S+2)(S+5) = (-2)(1) = 1

S (S+6) (-4)(2) 4

K₃ = Z(s)|_S=-6 = (S+2)(S+5) = (-1)(-4) = 1

S (S+4) (-6)(-2) 3

Z(s) = (S+2) (S+5) = 5/12 + ¼ + 1/3

S(S+4)(S+6) S (S+4) (S+6)

C1 = 12/5, C2 = 4, R1 = 1/16, C3 = 3, R2 = 1/18

Problem 2

The reactance versus frequency is given:

a) Determine the corresponding impedance function Z(s)

Z(s) = (S² + 4) 4S

(S² + 1)

b) What is asymptotic component type value if S approaches zero?

Z(s)|_S--0 = 4/1 = 4

c) What is asymptotic if S approach ∞ ?

Z(s)|_S--∞ = ∞

d) Find network representing Z(s)

By using Cauer I: