0
1.1kviews
A network and it's pole Zero diagram are shown in fig. Determine values of R, L, C. If Z(0)= 1.

Figure: Determine values of R, L, C. If Z(0)= 1.

enter image description here

1 Answer
0
139views

Solution:

From circuit diagram:

z(S)=(LS+R)(1CS)=(LS+R)(1/CS)LS+R+1/CSz(S)=LS+RLCS2+RCS+1....(1)

From pole, zero diagram,

zeros =3

zero factors, =(s+3)(s+3) \\

poles,

\Rightarrow-1.5+j \frac{\sqrt{111}}{2} ;-1.5-j \frac{\sqrt{111}}{2} \\

-1.5+j 5.267 \quad-1.5-j 5.267 \\

pole factors,

=(s+1.5-j 5.267)(s+1.5+j 5.267) \\

=(S+1.5)^2-(j 5.267)^2 \\

=s^2+3 s+2.25+27.741 \\

=s^2+3 s+30 \\

\therefore T \cdot F . Z(S)=\frac{H(z e r o \text { factors })}{\text { (pole factors) }} \\

z(s)=\frac{H(s+3)}{\left(s^2+3 s+30\right)}...(2) \\

To calculate,

H, given z(0)=1 \ z(0)=\frac{H(0+3)}{0+0+30}=\frac{3 H}{30} \\ 1=H / 10 \quad \therefore \quad H=10 \\ from (2) Z(s)=\frac{10 s+30}{s^2+3 s+30}....(3) \\ compairing (3) with (1) and rearranging (3) we get \begin{aligned} \\ &z(s)=\frac{10 s+30}{30\left(\frac{1}{30} s^2+\frac{3}{30} s+1\right)} \\ &z(s)=\frac{0.333 s+1}{0.0333 s^2+0.1 s+1} ....(4) \\ \end{aligned} \\ Now equating (1) and (4), we get \begin{array}{ll} \\ L=0.333 \mathrm{H} & R=1 \Omega \\ L C=0.0333 & R C=0.1 \\ C=\frac{0.0333}{0.333} & C=0.1 \mathrm{~F} \\ C=0.1 \mathrm{~F} & \\ \end{array} \\

Please log in to add an answer.