How to rearrange an equation in matlab to get the poles?

%Values

Vs = 1;

Z0 = 50;

R = 50;

C = 1e-9;

L = 0;

syms s

%Where s = j*w

%Impedance of the resistor

ZR = R;

%Impedance of the capacitor

ZC = 1/(s*C);

%Impedance of the inductor

ZI = s*L;

%Impednace of the load

ZL = ZR + ZC

%Transfer function

G = (2*ZL)/(ZL+Z0)

Currently I get:

G =

(2000000000/s + 100)/(1000000000/s + 100)

But I want to get:

Is there any way I can use matlab to rearrange the equation to get the poles?

Answer 1

[John D'Errico]

Vs = 1;
Z0 = 50;
R = 50;
C = 1e-9;
L = 0;
syms s
%Where s = j*w
%Impedance of the resistor
ZR = R;
%Impedance of the capacitor
ZC = 1/(s*C);
%Impedance of the inductor
ZI = s*L;
%Impednace of the load
ZL = ZR + ZC;
%Transfer function
G = simplify((2*ZL)/(ZL+Z0))

G = 

Easy enough now. simplify made it pretty clear. What does numden tell you?

[N,D] = numden(G)

N = 

D = 

The pole lives wherever D == 0.

solve(D==0)

ans = 

Answer 2

[Star Strider]

If the Control System Toolbox is available —

%Values
Vs = 1;
Z0 = 50;
R = 50;
C = 1e-9;
L = 0;
s = tf('s');
%Where s = j*w
%Impedance of the resistor
ZR = R;
%Impedance of the capacitor
ZC = 1/(s*C);
%Impedance of the inductor
ZI = s*L;
%Impednace of the load
ZL = ZR + ZC

ZL =
 
  5e-08 s + 1
  -----------
    1e-09 s
 
Continuous-time transfer function.

%Transfer function
G = (2*ZL)/(ZL+Z0)

G =
 
  1e-16 s^2 + 2e-09 s
  -------------------
  1e-16 s^2 + 1e-09 s
 
Continuous-time transfer function.

Ps = pole(G)

Ps = 2×1

0 -10000000

Zs = zero(G)

Zs = 2×1

0 -20000000

figure
pzplot(G)

Gmr = minreal(G)                                    % Remove Pole-Zero Cancellations

Gmr =
 
  s + 2e07
  --------
  s + 1e07
 
Continuous-time transfer function.

Psmr = pole(Gmr)

Psmr = -10000000

Zsmr = zero(Gmr)

Zsmr = -20000000

figure
pzplot(Gmr)

.