ECE 3144: Circuit Analysis I
Experiment 8
Title:
IDEAL OPERATIONAL AMPLIFIER
OBJECTIVE: Assess the basic inverting and non-inverting configurations of the ideal operational amplifier as represented by
the 741C opamp.
DISCUSSION: The naked opamp has the following characteristics:
Rin
(a) Input resistance (= Rin) = large (typical 2MΩ)
(b) Output resistance (= Rout) = small (typical 50Ω
vI
(c) Transfer gain (= Av = vO/vI) = large (typical 105)
vO
Rout
Figure 8-1: Opamp circuit symbol
The circuit symbol (arrowhead) indicates that the ideal opamp is unidirectional in its action and usage.
Exceedingly large gain is of no practical value in itself, since the output produced would be severely distorted (clipped) by the
limits on the output voltage swing as defined by the upper and lower voltage rails. In fact the large gain is only of value when
the opamp is connected in a negative feedback mode as shown by figure 8-2.
vO
R2
vF
R1
v F = ------------------- v O
R1 + R2
R1
Figure 8-2: Negative feedback via simple voltage divider.
As represented by this figure, a fraction of the output vO is fed back to the negative (inverting) input. This construct, for which
vO is compelled to be linked to a finite vF , keeps the output finite.
But then the nearly infinite gain, Av forces the differential input (between the + and - nodes) vin to be “virtually” zero, i.e.
v in = v O ⁄ A V ≅ 0
And because vin is ‘virtually’ zero, and because the input current is also ‘virtually’ zero (due to the high input resistance), the
opamp is sometimes called a nullator/norator, since its inputs operate at (virtually) null levels and its output is (ideally) able to
drive a load without constraint, (since Rout is virtually zero). This behavior is a little magical, and puts the opamp in the realm
of ideal. And so at first exposure Mr. opamp is often treated as an ideal component.
But an opamp is also an integrated circuit, and so it also may be treated more as an electronics circuit rather than an ideal component, depending on the textbook. You will probably revisit the opamp when you visit the realm of electronics.
The real opamp has a few more terminals, as represented by figure 8-3a and 8-3b. The package and pin-out for the opamp that
will be used for this experiment, the 741C opamp, are represented by figures 8-3a and 8-3b. You should have one or more
741C opamps in your parts kit.
non-inverting input
+VS
+VS
Vo
V-
V+
V+
Vo
V-
-VS
inverting input
Figure 8-3a: Operational amplifier symbol
-VS
Figure 8-3b: 741C Opamp: 8-pin DIP
When the opamp is connected as an item in a feedback loop, the amplitude ratio of output signal to input signal vo/vI is the
inverse of the feedback ratio = β. The smaller the feedback sample to the input, the larger the output signal.
The symbol for the opamp is represented by figure 8.3a. The package and pin-out for the opamp that will be used for this
experiment, the 741C opamp, is represented by figure 8.3b. For the first run of this experiment two741C opamps will be in a
ziploc bag in the parts/wires drawer of your workstation, one for usage and one for backup. Otherwise they will exist in your
parts kit manifest.
If Mr. opamp expires in the line of duty, curl up his little legs and put him aside. You may infer that any opamp or other such
insectoid with curled legs is a ‘dead bug’.
PROCEDURE:
A-1: Non-inverting configuration: This configuration is one for which the input is applied to the (+) input, and a fraction
vF of the output signal vO is fed back to the (-) input as represented by figure 8-2. This inverse of the sampling fraction
= β = vF/vO is the gain. The basic configuration is shown by figure 8A-1.
vI
vo
vF
R2
R1
R1
v F = ------------------- v O = βv O
R2 + R1
R2 + R1
vo
1
----- = --- = -----------------β
R1
vI
(ideal opamp)
Figure 8A-1: Basic non-inverting configuration
A-2: Construct the non-inverting configuration on your prototyping motherboard. Suggestions about wiring layout are
indicated by figure 8A-2.
A-3: Note that the opamp requires three voltage rails: +VS, -VS, and GND. Connect these power rails first, but do not
turn on the power until the inputs and feedback network are connected. Power rails should be +VS = +12, and -VS = -12. Set
signal input vS to 4 kHz signal at peak-peak amplitude 100mV.
A-4: For the first set of tests let R1 = 1.0kΩ and R2 = Rbox (Rx) = 10kΩ. Connect input to CH1 and output to CH2, (see
figure 8A-2) for purpose of measurement of transfer gain vo/vI. If your circuit is hooked up correctly, the output signal amplitude should be approximately 1.0V peak-peak. Measure and record transfer gain vo/vI as reflected by the peak-peak amplitudes observed on CH1 and CH2, respectively. Make use of the fiducial marks on your O-scope screen and the cursors to
obtain accurate measurements.
A-5: Reduce input to 20mV, peak=peak. Set the Rbox to 31,623Ω, 100kΩ, 316,227Ω, 1MΩ, respectively, measuring
and recording transfer gain vo/vI in each case.
(To Oscilloscope)
(CH 1)
BNC
SWITCH
FREQUEBCY
(To function generator)
OUTPUT INDICATORS
10KΩ
MULTIPLIER
(To Oscilloscope)
WAVEFORM
(CH 2)
VOLTAGE
+VS
+12V
5V
R1
-12V
AMPLITUDE
GND
-VS
(To R box)
DC OFFSET
1KΩ
POWER
CLOCK
PULSE
MFJ
Figure 8A-2: Recommendations for set-up of opamp circuits.
LOGIC SWITCHS
A-6: Replace the Rbox with a 100kΩ resistance (defined as R2) and R1 with the Rbox. Set the Rbox to 100kΩ and measure and record the transfer gain vO/vI. Set the Rbox to 31,623Ω, 10kΩ, 3,162Ω, 1kΩ, 316Ω, 100Ω, respectively, measuring
and recording transfer gain vO/vI in each case.
B-1: Reconfigure the opamp network so that it is almost back to figure 8A-2, with R1 = 10kΩ and R2 = Rbox. Now
move connections so that it is of the form of figure 8B-1a, b. Note that in this case the input is changed so that it is applied
through R1 to the (-) input of the opamp. The (+) input is connected to GND, as shown.
This configuration is called the simple inverting configuration for the opamp. with gain as indicated by figure 8B-1.
R2
vO
R1
R2
vF
vI
vO
R1
v F = ------------------- v O
R2 + R1
vO
R
----- = – -----2vI
R1
R1
(ideal opamp)
vI
Figure 8B-1a: Basic inverting config
Figure 8B-1b: Same topology, simplified
B-2: Measure transfer gain vo/vI in similar manner as was done by parts A-4 thru A-6. Signal generator should be set to
10mV peak-peak at 4kHz for best results.
ANALYSIS:
1. Complete a data table that show vo/vI and a column for calculated gain for the non-inverting configurations. Make a loglog plot overlaying measurements and the calculated (ideal) response. Comment on the comparisons between the measurements and the calculations, if any. Notice that you have cleverly chosen values of R2 for which the resistance values and the
gain are in terms of half-powers of 10, for which the values will show up as evenly spaced numbers on a logarithmic scale.
Therefore the log-log plot can be readily constructed using an ordinary quadrille scale, such as engineering paper.
2. In similar manner, complete a data table and a log-log plot that shows vO/vI and the calculated gain for the inverting configurations. Comment on the comparisons between the measurements and the calculations.
REPORT: This is an informal report, completed by checkoff from your instructor