ECE 2100
Spring 2010
Homework assignment 5 Solution
Due April 23, 2010
Covered: Chapter 10:
Amplifiers and Opamps
1)
Prelab:
Consider the following differentiating Op Amp circuit.
a.
Derive a relationship between the input voltage and the output voltage.
Assume the Op Amp is ideal.
Iin=C·dV
in
/dt.
Vout=R
F
Iin = R
F
C·dV
in
/dt =
0.1ms·dV
in
/dt
b.
Assume the input voltage is a triangular wave. What is the output
waveform? Explain!
Output is a
square wave
: a triangle wave alternates slope between positive
and negative 2A/T, where A is the peaktopeak amplitude and T is the period.
Thus, the output will have an alternating sign every half cycle, with equal plus
and minus amplitudes.
c.
Find a relationship between the frequency and peaktopeak amplitude of
the triangular wave and the peaktopeak voltage of the output waveform.
Slope = +/2A/T, and frequency f=1/T, so the peaktopeak amplitude of Vout
will be
0.1ms·4Af
(4 instead of 2 because we want the output peaktopeak)
d.
Predict the output voltage peaktopeak value if the input is driven by a 1
volt peaktopeak, 200 Hz sine wave.
V
in
=0.5cos(400
π
t), Vout
=
0.1ms·dV
in
/dt=0.02
π
sin(400
π
t): peaktopeak:
0.1256V
2)
Consider the transformer plus fullwave rectifier shown, driven by a 120V (peak)
60Hz voltage (that is, V
1
=120V·cos(240
π
t)).
Assume that the diodes can be
modeled as ideal except with a turnon voltage of 0.7V.
Also assume that the
transformer is ideal.
a.
What will the peak voltage across the capacitor be?
V
Cmax
=V2
peak
2V
TO
.
V2=V1/6: V2
peak
= 120V/6=20V,
V
Cmax
=18.6V
10k
Ω
Vin

+
Vout
0.01
μ
F
D1
D2
D3
D4
+
V1

I
1
+
V2

1mF
6:1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Documentb.
If the capacitor is loaded with a 100
Ω
resistor, sketch the waveform of
Vout.
What, approximately, will be the difference between the minimum
and maximum voltage across the capacitor (that is, what will the ripple
be?)
25
20
15
10
5
0
5
10
15
20
25
0
5
10
15
20
25
30
time, ms
Voltage
V2
VC
V2
Droop rate is dV
C
/dt = V
C
/RC = 18.6V/100ms, T=16.7ms.
Can estimate ripple by assuming the capacitor voltage droops during the
entire half cycle of the input (actually it droops for slightly less time than that).
V
Cmin
~ V
Cmax
 V
Cmax
/RC·T/2 = 18.6V(18.33ms/100ms) = 17V: implies a
ripple of about
1.6V
(it will actually be less than this: more like 1.3V)
c.
Sketch the current waveform sourced by the voltage source V
1
.
What is
the maximum and minimum current, I
1
sourced?
(this is hard: its only for
bonus points)
0.4
0.2
0
0.2
0.4
0.6
0.8
0
5
10
15
20
25
30
time, ms
I1, A
I
1
= I
2
/6, I
2
will only be nonzero when the diodes are on, that is, when the
capacitor is recharging.
Recharging happens from when V2>Vc+2V
TO
until
V2 reaches its peak
.
This time starts (relative to the peak) when V21.4V =
V
Cmin
or about 17V (from above): if V2=20Vcos(
ω
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 KELLEY/SEYLER
 Amplifier, Operational Amplifier, Volt, Operational amplifier applications, Vout, Book problem

Click to edit the document details