Path P1 W(0 to ∞) M = 1/√42 + w2 √52 + w2 Φ = tan1(W/4) – tan1(W/5) W M Φ 0 1/20 00 1 0.047 25.350 ∞ 0 +1800 Path P3 will be the mirror image across the real axis. Path P2 :ϴ(π/2 to 0 to +π/2) S = Rejϴ G(S) = 1/(Rejϴ + 4)( Rejϴ + 5) R∞ = 1/ R2e2jϴ = 0.ej2ϴ = 0 
P1 W(∞ Ɛ) where Ɛ 0 P2 S = Ɛejϴ ϴ(+π/2 to 0 to π/2) P3 W = Ɛ to ∞ P4 S = Rejϴ, R ∞, ϴ = π/2 to 0 to +π/2 For P1 M = 1/w.w√102 + w2 = 1/w2√102 + w2 Φ = 1800 – tan1(w/10) W M Φ ∞ 0 3 π/2 Ɛ ∞ 1800 Path P3 will be mirror image of P1 about Real axis. G(Ɛ ejϴ) = 1/( Ɛ ejϴ)2(Ɛ ejϴ + 10) Ɛ 0, ϴ = π/2 to 0 to π/2 = 1/ Ɛ2 e2jϴ(Ɛ ejϴ + 10) = ∞. ej2ϴ [ 2ϴ = π to 0 to +π ] Path P2 will be formed by rotating through π to 0 to +π Path P4 S = Rejϴ R ∞ ϴ = π/2 to 0 to +π/2 G(Rejϴ) = 1/ (Rejϴ)2(10 + Rejϴ) = 0 N = Z – P No poles on right half of S plane so, P = 0 N = Z – 0 
TF = 1/1 + jw (2). Magnitude M = 1 + 0j / 1 + jw = 1/√1 + w2 (3). Phase φ = tan1(0)/ tan1w =  tan1w W M φ 0 1 00 1 0.707 450 ∞ 0 900 

(1). S = jw TF = 1/(1+jw)(2+jw) (2). M = 1/(1+jw)(2+jw) = 1/w2 + 3jw + 2 M = 1/√1 + w2√4 + w2 (3). Φ =  tan1 w  tan1(w/2) W M Φ 0 0.5 00 1 0.316 71.560 2 0.158 108.430 ∞ 0 1800
