3/2/12
1/5
University of Rochester
Department of Electrical & Computer Engineering
ECE113
Lab. #5
741 Operational Amplifier Applications
3-5-12
-----------------------------------------------------------------------------------------------------The write-ups for this lab are the week after Spring Break. Your lab TA must sign and date each
page of your notebook. These pages are to be handed in with your lab reports. Remember to
include an abstract on a separate page. Your grade will be based in part upon conciseness,
grammar, and spelling. Lat e wo rk wil l not be a ccept ed .
-----------------------------------------------------------------------------------------------------BRING SE V ER A L SH EET S O F 3×5 C YCL E LO G -LO G PAP E R TO THE LAB
-----------------------------------------------------------------------------------------------------O. Laboratory prepa ration
In this lab, you will assemble and test several basic op-amp circuits, a voltage
amplifier, an integrator, and a differentiator. To prepare for this exercise, study
the ideal voltage amplifier model for the op-amp. Also, re-derive the voltage
transfer function for the basic inverting amplifier configuration shown in Fig. 1.
Note that amplifier gain remains insensitive to A, the open-loop voltage gain, as
long as |A| >> 1. In your write-up, please explain the importance of avoiding
sensitivity to |A| in practical amplifier circuit designs.
The basic inverting amplifier circuit shown in Fig. 1 is used throughout this
exercise.
Z 2(s)
+
Vs
Fig. 1.
I.
Z1(s)
+
741
voltage gain:
+
-
Vo
H(s) =
Vo
Z (s)
!- 2
Vs
Z1(s)
Basic inverting amplifier configuration. Note that the expression for the voltage gain
H(s) remains correct for any generalized impedances Z1(s) and Z 2(s).
Some hints and reminde rs about OP-AMPS
To minimize problems, review the relevant lab assignments from ECE111.
Remember to leave the dc supply ground wire connected at all times.
Power up the circuit, i.e., turn on the dc supply only when you have
completed all necessary wiring and you are ready to make your
measurements, and only then turn on the ac input voltage signal vs(t).
To avoid the aggravation of blown chips and fuses, never change the
wiring or disconnect anything with the circuit powered.
For your convenience, the pin connection diagram for the in-line 741CN
op-amp IC is provided at the left of page 2.
-2-
II. Experimental procedure & lab questions
A.
Design and build a simple inverting amplifier with
NC
+Vcc output n u l l
a voltage gain |H| ≈10 by choosing appropriate
8
7
6
5
resistive values for Z1 and Z2. Do not choose
values that are either too high or too low; it is
LM
best to stay in the range of ~100 Ω to ~100
741CN
kΩ. Build your circuit and test it using
sinusoidal input. If your output signal appears
1
2
4
3
-Vcc
n
u
l
l
-in
+in
distorted (clipped), reduce the input amplitude.
741 pin connections
Suggestion: fix the input voltage at a
convenient value, say 0.1 v for the 20 dB gain amplifier, and then plot the
output multiplied by ten directly on log-log versus frequency f in Hz. At
each test frequency, measure phase with respect to the input and plot it
using a linear scale in degrees on the log paper. Cover the frequency range
from 10 Hz to 200 kHz, taking four points per decade. These points
should be roughly evenly spaced on the log scale. Find and record the
frequency at which the gain has "rolled off" by a factor of 0.707. In your
lab write-up, describe the performance of your amplifier and compare it to
the predictions of the ideal model.
Note: The 741 op-amp has a sle w rate of ~0.3 to 0.7 v/µs @ unity gain, meaning that a 20
dB amplifier probably will not perform well above ~10 kHz for an input voltage of ~2 v p-p. For
this reason, it is a good idea to limit the input to 0.1 v. You will know that you have
encountered the slew rate limit if the output starts to look like a triangle wave for a sinusoidal
(or any other periodic input) waveform.
B.
Repeat II.A for a second inverting amplifier having gain of |H| ≈ 100. Plot
this new data on the same graph . Determine the influence of the
higher gain on the bandwidth of the amplifier by finding the new value of
the roll-off frequency (that is, the freq. where the gain has dropped to
100/ 2 ≈ 70.7). From your results, estimate GB, the gain-bandwidth
product of the 741.
C.
Replace the 741 in the ckt for II.B with an LF411 op-amp. These devices
have higher gain-bandwidth and you will notice much improved frequency
response for |H| = 100 amplifier.
D.
Next, design and build an integrator by letting Z1(s) = R1 and using a
capacitor C in the feedback loop. Your circuit should look like Fig. 2. To
start the design process, set fc = 1.0 Hz, the frequency where the circuit
makes the transition from voltage amplifier to integrator performance.
-3-
Then, select the resistor and capacitor values to satisfy the following
design criteria:
(i) CR2 = 1/2πfc
Establishes lower operational freq. limit of integrator.
(ii) R3 = R1||R2
This compensation resistor provides a path for bias current to
the non-inverting input, thereby eliminating problems caused by
high-feedback impedance.
(iii) 100 Ω ≤ R1 ≤ 100 kΩ
(iv)
R2 ≈ 10R1
good practical limits for R1
DC drift problems ensue if C does not have means to discharge.
Z 2(s)
C
R2
R1
+
vs(t)
741
Vo
R3
Figure 2.
Practical (band-limited) integrator circuit with input
bias current compensation.
Wire up your design and test it with sinusoidal input to verify integrator
performance. Plot |Vo|/|Vs| and phase angle (in degrees) versus f using
3×5 log-log paper from 10 Hz to 100 kHz.
E.
Apply a square wave signal at several selected frequencies to verify the
integration function of the circuit. In your lab write-up, include input and
output voltage waveforms using the scope waveform capture feature of
the scope. Describe and explain deviations of the output from the
expected waveforms.
Hints:
Figure out what the integral of a square wave looks like before coming to the lab.
-4-
MAKE ALL HOOK-UP WIRES AND TEST LEADS AS SHORT AS POSSIBLE TO AVOID UNWANTED
OSCILLATIONS IN YOUR AMPLIFIERS. THIS PRECAUTION IS PARTICULARLY IMPORTANT FOR
HIGH-GAIN AMPLIFIERS. USE STAR GROUNDING. ALSO, LIMIT INPUT VOLTAGE TO AVOID
OUTPUT DISTORTION CAUSED BY CLIPPING OR SLEW RATE LIMITS.
F.
Design and build a differentiator using a coupling capacitor C in the input
section. One simple yet practical realization looks like Fig. 3. The resistor
R1 is needed to prevent undesirable amplification of the high-frequency line
noise inevitably present. The feedback capacitor Cf provides additional
protection against high-frequency noise and unwanted oscillations.
First, find an expression for the voltage transfer function H(s) of this
amplifier. Within what frequency range will the output voltage replicate
the derivative of the input voltage?
To design your circuit, start by choosing an upper frequency limit for
differentiator operation, say fc = 50 kHz. Then, select the resistor and
capacitor values in order to satisfy the following design criteria:
(i)
CR1 = 1/2πf c
Establishes upper frequency limit of the differentiator.
(ii)
R3 = R1||R2
compensation resistor for bias current to the non-inverting
input helps maintain op-amp in linear range of operation.
(iii)
100 Ω ≤ R1 ≤ 10 kΩ
(iv) R2 ≈ 10R1
(v)
good practical limits for R1
reasonable high-frequency gain value for f > fc.
C ≤ 0.1 µF & Cf ≤ 3 nF
good practical choices for capacitor values
In your design, do not neglect the limits imposed by the dominant pole of the 741 op-amp!
Your write-up should include a concise, but complete summary of the design
calculations you performed to select the component values.
-5-
Z 2(s)
Z 1(s)
Cf
R2
R1
-
C
+
vs(t)
741
Vo
R3
Figure 3.
Practical op-amp-based differentiator circuit with input bias
current compensation.
Wire up and then test your design using sinusoidal input to verify the
differentiator's performance. Plot gain |H| = |Vo|/|Vs| (log scale) and also
phase angle ∠H(jω) in degrees (linear scale) vs frequency f using 3×5 loglog paper from 10 Hz to 100 kHz. Pay close attention to the circuit
behavior at the higher frequencies, where performance is expected to
degrade.
G.
Apply triangular and ramp signals at various frequencies to verify that the
differentiation function of the circuit. In your lab write-up, provide
waveforms captured using the scope feature. Be sure to label all voltage
waveforms. Discuss explain any deviations of the circuit output from the
expected waveforms. Investigate the frequency limits of your
differentiator with these input waveforms.
Hint: Determine shape of derivatives for triangular & ramp functions first before doing part F.