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PHY3802L: INTERMEDIATE LAB
Iel.1 Summing (inverting) amplifier
1. Purpose: Learn about operational amplifiers.
2. Apparatus: power supply (+/- 15V)
function generator
oscilloscope
breadboard
electronic components (resistors, op.amp. chip, ..)
DMM
3. Background information:
3.1 About operational amplifiers:
An operational amplifier is a differential amplifier with very high gain ("open-loop gain" A0),
very high input impedance (Zin), and very low output impedance (Z out).
V+
v+
v-
8
1
+
_
vout
V-
Fig. 1
2
_
7
3
+
6
5
4
Fig.2
In normal operation, it needs to be supplied by symmetric voltages V+ and V- (V- = -V+ ).
Its behavior is described by vout = A0 (v+ - v- ). In amplifier applications it is usually used
with "negative feedback", i.e. part of the output signal is fed back to the negative input (i.e.
effectively subtracted from the input signal). The behavior of such circuits can be
calculated using the "golden opamp rules":
1. the input currents are 0: i+ = i- = 0
2. the input voltage difference is 0: v+ - v- = 0
(These rules are strictly speaking only valid for a circuit with an ideal opamp, but are a
reasonable approximation also for circuits with real opamps).
The opamp chip that we are using in this lab is the 741A opamp. It comes in an 8-pin dualinline package (DIP) (see fig. 2). The connections for the pins are as follows: pins 2 and 3
are for input signals v- and v+ , pin 4 is for negative supply voltage, pin 7 for positive
supply voltage, and pin 6 is for the output.
3.2 Negative feedback
In amplifiers, opamps are used in circuits with "negative feedback", i.e. a circuit in which a
fraction of the output voltage is subtracted from the input.
The effective input voltage v' is therefore
v' = vin - B ∙ vout
,
where B = "feedback factor" (feedback fraction) is determined by details of the
feedback circuit.
The amplification with feedback, Af (called "closed-loop gain"), is defined as
vout
vin
From the property of the opamp, it follows that
and therefore
A0
Af 
1 A0 B
Af 
vout
= A0 v' = A0 (vin - B vout ),
Note:
 The “closed loop gain” is smaller than the open loop gain: Af < A0
If A0 B >> 1, then Af ≈ 1/B , i.e. the gain of the amplifier depends only on the
feedback fraction B, not on the open-loop gain A0 of the opamp; so, variation of A0
does not matter!
4. Procedure:
Fig. 3: Summing amplifier
(1) Construct the summing amplifier shown in fig. 3, using resistor values Rf  10k, R1 
2k and R2  1k. (Measure the resistances of the resistors that you actually use in
the circuit, record them and use these values in calculating the expected gain). Use
±12 V as supply voltage, unless instructed otherwise.
(2) Apply a 1kHz sinusoidal signal of about 200mV amplitude (from the function
generator) to each input separately with the other grounded and measure the sign
and magnitude of the amplification factor.
(3) Then connect the same signal to both inputs (i.e. make va = vb = vin) and measure
the output magnitude. Compare with predicted values (do they agree within errors?
Estimate how precisely you measure the voltages and thus the gain, and how
precisely you measure resistances and thus how precisely you can predict the gain).
(4) Apply a 1kHz sinusoidal signal to both inputs (i.e. make va = vb = vin); vary the
amplitude vin of the input signal from 100mV to 1.2V (in 100mV steps) and measure
the output voltage amplitude vout and determine the gain (i.e. vout / vin , the ratio of
amplitude of the output signal and amplitude of input signal). Plot the output
amplitude as a function of the nominal output signal amplitude (i.e. the output signal
amplitude expected from the formula given in fig.3). Estimate uncertainties on
measured and expected signal size and gain. Describe your observations, and try to
explain what you observe.
(5) Change the supply voltage to ±10V, and repeat the measurements of (4)
for the same set of input signal amplitudes (from 100mV to 1.2V).
(6) Restore the supply voltage to ±12V. For a fixed input amplitude (abut 0.5V), measure
the gain (vout / vin) as a function of frequency of the sinusoidal input signal, from
about 100Hz to the maximum frequency available on the function generator (
2MHz). Take data for 3 frequency values per decade (e.g. 100, 200, 500, 1000,
2000,…). Discuss the frequency dependence of the gain, and establish a relation
between it and the observations of steps (7) and (8) (Consult appropriate sources –
textbooks, websites,..to learn about this).
(7) Instead of a sinusoidal signal, use a triangular wave and a square wave as input, and
observe the output waveforms for three frequencies (lowest, highest, and a value in
the middle of your range). Draw the waveforms and comment on your observations.
(8) Set the frequency of the function generator to about 1kHz, keeping the amplitude at
0.5V. Measure the rise time of the square wave signal (both input to and output from
the amplifier). Determine the slew rate from your measurement. Compare the slew
rate determined from the observed rise times to the typical value expected for this
chip (see data sheet). Relate your measurement of the slew rate of the opamp to the
frequency dependence of the gain. Given the slew rate, can you estimate at what
frequency you would expect the gain to start decreasing? (Consult appropriate
sources – textbooks, websites,..to learn about this).
5. Notes:
Things to note:
 determine measurement uncertainty of input/output signal amplitude, as well
as uncertainty of measured and expected gain (understand your measuring
instruments to estimate uncertainties on voltages and resistances);
 compare measurement with expectation -- agreement within measurement
uncertainties?
 about gain vs. input amplitude:
- think about the fact that the output signal size saturates at some value
-- no matter what the input is, the output does not exceed a certain
value;
- the saturation value is lower for supply voltage of 10 V than for 12 V
supply voltage -- any explanation for this?
- what is the difference between supply voltage and saturation value of
the output? -- Do you see a pattern there?
- do you think it would be possible to build an opamp chip which does
not have this limitation?
 add a graph of output amplitude (or gain) vs. frequency (plot frequency on log
scale -- i.e. plot gain or amplitude vs. log of frequency)
 From the measured rise time and size of the square wave output you can
determine the slew rate of the opamp.
 Slew rate = dVout/dt = speed at which opamp output voltage can
follow an input voltage step (input with zero rise time);
 observed rise time of output signal has two contributions: one from
input rise time and one from slew rate.
 Note that “rise time” is the time it takes for signal to rise from
fraction 0.1 to 0.9 of its maximal (peak-to-peak) size.
6. Bibliography:
There are many books on electronics; examples of more useful ones are:
(1) Robert E. Simpson: Introductory Electronics for Scientists and Engineers,
Allyn and Bacon, Newton, Mass. 1987
(2) William L. Faissler: An Introduction to Modern Electronics
John Wiley & Sons, New York 1991
(3) Paul Horowitz and Winfield Hill: The Art of Electronics,
Cambridge University Press, Cambridge 1989
(4) D.V. Bugg: Electronics Circuits, Amplifiers and Gates, Institute of Physics
Publishing,
Bristol 1991
(5) Mark N. Horenstein: Microelectronic Circuits and Devices, 2nd ed., Prentice Hall,
1995
(6) A. de Sa: Electronics for Scientists, Prentice Hall, 1997