## Description

• Poles and Zeros

1. Solve the follow set of equations find if the system is stable or inestable. What

is the frequency at -3dB Use the plots of Bode and Nyquist and support your

response. Mathematical development is required, magic does not exist.

FL(s) = s(s + 10)

(s + 100)(s + 25)

F H(s) = 1 −

s

105

(1 + s

10000 )(1 + s

40000 )

2. Solve the follow circuits and interpret the result if those are stable o inestable

through Bode and Nyquist diagrams. Magic only exist in Hogwarts… and even

there you’ve to study…

In the follow circuit, the output voltage is referred to the inductor for a vg(t) =

10 sin(277t)

For the follow circuit, the output voltage is analyzed at resistor R2 = 4Ω. The

applied voltage is v0(t) = πt

2

. And yes, this is a variable source. So enjoy!!!.

1

3. For the next circuit, derive the expressions for V1/Vi

, V2/V1, V0/Vi

. Calculate the

poles and zeros, obtain the bode diagram and compare it with a simulation in

Spice, explain…, if (PLEASE: PAY ATTENTION HERE!!!!!!) R= 10 kΩ,

C1= 20 µF, R1= 10 kΩ, C2= 4.7 mF and Rf= 100 kΩ Vi = 100 cos(600t)

2