0
985views
The voltage V(s) of network is given by v(s)=3s(s+2)(s2+2s+2) plot it's pole zero diagram and hence obtain v(t)
1 Answer
written 2.5 years ago by | • modified 2.5 years ago |
Solution:
Given V(s)=3s(s+2)(s2+2s+2)...(1)
zeros ⇒S=0
poles ⇒s=−2,S=−1+j1,S=−1−j1
By pole zero diagram, & eq −n (1) partial fraction expansion is:
V(s)=As+2+B(s+1−1j)+C(s+1+1j)...(2)
A=3(¯OP1)(P2ˉP1)(¯P3P1)=3(21180)(√2(−135)(√2⌊135)=3⌊180=−3
B=3(¯PP2)(ˉP1P2)(ˉP3P2)=3(√2⌊135)(√2⌊45)(2⌊90)B=32
C=3(¯OP3)(P1P3)(¯P2P3)=3(√2∣−135′)(√2⌊−45∘)(2⌊−90∘)C=32
Hence from (2)
V(s)=−3s+2+3/2(s+1−j1)+3/2(s+1+j1) Taking I.L.T. V(s)=−3⋅e−2t+32⋅e(−1+j)t+32e(−1−j)t=−3⋅e−2t+32⋅e−t[ejt+e−jt]=−3⋅e−2t+33e−t[ejt+e−jt2]V(s)=−3⋅e−2t+3⋅e−tcost