# exam2 review

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```					This is a nice figure that I found, I it should help.

As can be seen, the steady state value is 1 unit.

Source:

Test No. 2 Study items.

These are NOT test questions. The intent here is to provide some guidance to help you prepare for the
test.

A- Given a first or second order circuit , derive G(s) = Vo(s)/Vin(s)

First Order:

Vin                                                Vo

R1
C1

For Second order, as in the op-amp homework circuit.

B- Given a transfer function:

First analytically: Calculate         , determine if the system is overdamped, underdamped, critically
damped, or unstable. If unstable, then no need to do any calculations!

And:

1-      determine Vo(t) due to a unit step input.

2-      Plot the poles (roots of the characteristic polynomial) in the complex plane

3-      determine %overshoot, rise time, settling time

Examples of G(s)= Vo(s)/Vi(s)

a-

b-

c-

d-
4-     Refer to G(s) in case –a above, what would be the steady state value due to a unit step input if
the numerator is changed to 10?

C-      Second: Repeat problem B graphically. Draw clearly and understand.

D-      For the response shown, estimate the steady state value, the rise time, the settling time, the
damping frequency and the natural frequency. (Show clearly on the graph how you approached at
these estimates.)

Step Response
1.8

1.6

1.4

1.2

1
Amplitude

0.8

0.6

0.4

0.2

0
0   0.2   0.4   0.6   0.8   1   1.2   1.4   1.6          1.8      2   2.2   2.4   2.6   2.8   3   3.2   3.4 3.5
Time (sec)

E- Given the following transfer function:

Determine the values of A and B so that the system has an overshoot of 12% and a natural frequency of
400Hz.

F- with the op-amp circuit, be able to derive the equations, determine component values to meet
desired     and
G- Understand the plot of the poles moving on the half-circle I nthe complex plane as was done in class.

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