# Slew-Rate Limit

```USC Electrical Engineering
ELCT 301
Project
Experimental Design to Measure some
Characteristics and Limitations of Op-Amps
Objective
The objective of this experiment is to investigate two of the limiting characteristics of the analog IC known
as an operational amplifier. The two characteristics you will investigate are the slew rate limit and the
gain-bandwidth product.
Background
Slew-Rate Limit
Large-signal applications of an op-amp often run into its slew-rate limit (SR), also related to the
maximum-power bandwidth, fp. The SR limit for an op-amp is the maximum rate of change of the
amplifier’s output voltage, due to a very fast-rising input voltage signal (ideally a step-function). It is a
non-linear effect of the amplifier and can cause distortion in the output if the input signal has too high a rate
of change of voltage. The SR is specified by the manufacturer and is based on a very specific amplifier
configuration and input signal. You will duplicate this circuit and measurement, and compare with the
manufacturer’s SR value. The SR limit is due to the fact that the internal compensation capacitor (see
discussion below), typically 10-20 pF, has a finite current that can charge or discharge it (hence the nonlinearity). This finite rate-of-rise of capacitor voltage transfers to the output as a finite rate-of-rise of output
voltage even though the input may have an extremely fast risetime. You can imagine that a near stepfunction on the input will be degraded at the output because of the SR limit. Changing the risetime of a
signal will change the harmonic content and thus introduce noise. A 741 op-amp has a SR specified as 0.5
V/s. A TL071 op-amp has a SR specified as 5 to 13 V/s.
The maximum power bandwidth, fp, is defined as the frequency at which a sine wave input, at rated
output voltage, begins to exhibit distortion. For example, if the output signal is
vo  V sin( 2f p t )
(1)
the rate of change of voltage is
dvo
 V 2f p cos( 2f p t )
dt
(2)
and the maximum slope occurs at t = 0:
dv
dt
max
 2f pV
(3)
If 2fpV &gt; SR, then the output response is distorted. fp is the frequency at which this distortion begins,
fp 
SR
2Vr
(4)
where Vr is the rated op-amp output voltage. Note that if the output voltage is lower than Vr, slew rate
distortion begins at a frequency higher than fp.
Gain-Bandwidth Product
Op-amps are internally compensated with a capacitor to create a dominant pole in the open-loop transfer
function of the amplifier. This dominant pole causes the phase characteristic (phase-shift of the output with
respect to input) of the op-amp to be well below 180o until the gain has dropped below unity. This
behavior increases the stability of the op-amp. The dominant pole causes the magnitude of the open-loop
gain to drop in frequency at the rate of about 20 dB/decade (as would be expected for a transfer function
with one pole).
 2008 by E. Santi
1
USC Electrical Engineering
ELCT 301
Project
Manufacturers of op-amps go to great lengths to achieve a dominant-pole open-loop frequency
response. The open-loop transfer function (voltage gain) is given as:
A( s ) 
Ao
1  s / o
(5)
where Ao is the dc open-loop voltage gain (typically 105 to 107), and o is the corner frequency (3 db or cutoff frequency). A Bode plot of the frequency response for a transfer function with one pole (a dominant
pole) is shown below in Figure 1. Note that the gain-bandwidth (GB) product is the frequency at which the
magnitude of the voltage gain is unity. For an open-loop op-amp, the GB from (5) (typical value is 3 MHz
= 18.85x106 rad/s) is given as:
GB    Ao2  1  o  Aoo
(6)
As a closed-loop amplifier is designed, the voltage gain is modified by the external components, such as in
a typical inverting amplifier. The closed-loop voltage gain for an inverting amplifier that includes the
frequency-dependent open-loop gain function is given as:
Av ,closedloop 
 A( s ) R f
[ A( s )  1]R1  R f
(7)
Note that the assumption for an ideal op-amp, that the open-loop gain, A(s), is infinite, causes (7) to reduce
to the form usually discussed in your first electronics class.
Figure 1. Frequency response of an amplifier with one pole (dominant-pole opamp). The different values
of Av are for closed-loop operation of the amplifier.
Prelab
All the prelab work should be done in your lab notebook. You are to design experiments such that the GB
product and SR of a typical op-amp can be measured directly or inferred (extrapolated) from data you
obtain in your experiments. A short report detailing the test circuits and the measurements to be made will
be presented prior to the lab. Derive equation (6) from equation (5) remembering that the gain bandwidth
product is equal to the frequency at which the open-loop op-amp gain becomes unity. Derive also equation
(7) using equation (5) for an inverting amplifier circuit. Draw a circuit model of the closed-loop inverting
amplifier including (5) as a voltage-controlled voltage source representing the op-amp. For a dc gain of
about –10, and the feedback resistor , Rf, of 10 k, plot the frequency response of the amplifier (magnitude
and phase). Run a Spice simulation of the same circuit (you may use the LM324 or the UA741 opamp
model available in the eval.lib library in Spice) and plot the frequency response (magnitude and phase).
Examine the printed circuit board and figure out how the +VCC pin is connected to pin 7 of the LM741
OPAMP. Describe in your lab notebook.
Solve the opamp exercise below in your lab notebook.
 2008 by E. Santi
2
USC Electrical Engineering
ELCT 301
Project
Opamp Exercise
Consider the opamp circuit shown below with R1 = 1kΩ, R2 = 10kΩ and C = 10nF.
1. Write the transfer function
G (s) 
2.
3.
4.
5.
6.
V0 ( s )
Vi ( s )
What are the poles and zeros?
What is the DC gain?
What is the high frequency gain?
Sketch the asymptotic magnitude and phase Bode plots for the case of an ideal OPAMP.
Sketch the asymptotic magnitude and phase Bode plots for the case of an OPAMP with a gainbandwidth product of 1MHz.
R2
R1
Vi
C
+
V0
Lab Project
Experimentally determine the GB and SR for a typical op-amp. Compare to the manufacturer’s ratings.
Discuss any differences. Make a Spice simulation of the experiments you used to determine GB product
and slew rate and compare with your experimental results.
Final Instructions
The report of your experimental design (pre-lab requirement) is due at the time you start your lab session.
The lab report will be due at the following lab time.
NOTE: Study of a manufacturer’s data sheet is highly recommended. Failure to deliver an experimental
design by lab time will result in a grade of 0 being recorded for this lab experiment. DON’T PUT THIS
OFF!!!!! START NOW!!!
 2008 by E. Santi
3
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