Subsections
We have built voltage and current amplifiers using
transistors. Circuits of this kind with nice properties (high gain and
high input impedance, for example), packaged as integrated circuits
(ICs), are called operational amplifiers or op amps. They
are called ``operational'' amplifiers, because they can be used to
perform arithmetic operations (addition, subtraction, multiplication)
with signals. In fact, op amps can also be used to integrate
(calculate the areas under) and differentiate (calculate the slopes
of) signals.
Figure 22:
A circuit model of an operational
amplifier (op amp) with gain and input and output resistances
and .

A circuit model of an operational amplifier is shown in
Figure 22. The output voltage of the op amp is
linearly proportional to the voltage difference between the input
terminals by a factor of the gain . However, the output
voltage is limited to the range
, where
is the supply voltage specified by the designer of the op
amp. The range
is often called the
linear region of the amplifier, and when the output swings to
or , the op amp is said to be saturated.
The output ranges of the amplifiers we built as part of
Lab 3 were similarly limited by the supply voltage.
An ideal op amp has infinite gain (), infinite input
resistance (
), and zero output resistance (). You should use these two assumptions to analyze the op amp
circuits covered in the assignments below. A consequence of the
assumption of infinite gain is that, if the output voltage is within
the finite linear region, we must have . A real op amp has
a gain on the range  (depending on the type), and hence
actually maintains a very small difference in input terminal voltages
when operating in its linear region. For most applications, we can get
away with assuming
.
Figure 23:
(a) Schematic symbol for an op amp. (b)
Connection diagram for the LM741 and LF411 8 pin dual inline packages
(DIPs). We will not make use of the null (LM741) / balance (LF411)
pins. Pins labeled NC are not connected to the integrated circuit.

We will use two operational amplifiers in our laboratory exercises,
the LM741, a general purpose bipolar junction transistor (BJT) based
amplifier with a typical input resistance of 2 M, and the LF411,
with field effect transistors (FETs) at the inputs giving a much
larger input resistance (
). Detailed data sheets for
these devices are available for dowload at the National Semicondictor
web site
(www.national.com
).
Of the two, the LF411 comes closest to satisfying our two assumptions
associated with ideal op amp behavior. It costs more than the LM741 (a
whopping $0.61 vs. $0.23 as of spring 2001). The schematic symbol for
an op amp and the connection diagram for the chips, called dual inline
packages (DIPs), we will be using are shown in
Figure 23.
The inverting amplifier (4.1) and Schmitt trigger
(4.8) are mandatory for everyone. Of the remaining
circuits, choose at least 4. Whether you use a LM741 or LF411 op amp
is up to you, but in at least one circuit, compare the two. For all
circuits and both kinds of op amp, V.
Inverting Amplifier
Figure 24:
Inverting amplifier circuit.

An inverting amplifier circuit is shown in
Figure 24.
 Show that the gain of the amplifier is

(18) 
 Build the circuit, and check your prediction experimentally for
gains of 10 and 100.
 Measure the bandwidth (the difference between the upper and
lower 3 dB points) of the amplifier for each gain. The product
of the gain and bandwidth should be constant. Is it?
 Check the linearity of the amplifier for each gain over its
useful frequency range.
 Measure the input impedance of the amplifier by placing various
resistors in series with the source. Explain your result.
Noninverting Amplifier
Figure 25:
Noninverting amplifier circuit.

A noninverting amplifier circuit is shown in
Figure 25.
 Show that the gain of the amplifier is

(19) 
 Build the circuit, and check your prediction experimentally for
gains of 10 and 100.
 What is the input impedance of the amplifier?
Voltage Follower
Figure 26:
Voltage follower circuit.

A voltage follower circuit is shown in
Figure 26.
 What's the point?
 What is the input impedance of the amplifier?
 Build the circuit, and use it to improve the input impedance of
an inverting amp.
Differential Amplifier
Figure 27:
Differential amplifier circuit.

A differential amplifier circuit is shown in
Figure 27.
 Show that the output signal of the amplifier is

(20) 
 Build the circuit, and check your prediction experimentally for
a gain of 10.
 Measure the input impedance of the amplifier by placing various
resistors in series with the source. To measure the impedance of one
terminal, drive it with a small signal through a resistor and ground
the other. Explain your result.
Summing Amplifier
Figure 28:
Summing amplifier circuit.

A summing amplifier circuit is shown in
Figure 28.
 Show that the output signal of the amplifier is

(21) 
 Build the circuit, and check your prediction experimentally for
a gain of 10.
 Measure the input impedance of the amplifier by placing various
resistors in series with the source. To measure the impedance of one
terminal, drive it with a small signal through a resistor and ground
the other. Explain your result.
Integrator
Figure 29:
Integrator circuit.

An integrator circuit is shown in
Figure 29.
 Show that the output signal of the amplifier is

(22) 
 Build the circuit with k, F and
use square and sinusoidal wave forms to test the predicted
behavior. Also place a M resistor in parallel with the
capacitor. This resistor drains charge to avoid saturation due to very
low frequency or DC signals.
Differentiator
Figure 30:
Differentiator circuit.

A differentiator circuit is shown in
Figure 30.
 Show that the output signal of the amplifier is

(23) 
 Build the circuit with k, F and
use triangle and sinusoidal wave forms to test the predicted
behavior.
Schmitt Trigger
Figure 31:
Schmitt trigger circuit. and
are relative to ground, or some reference between
and .

A Schmitt trigger circuit is shown in Figure 31. The
analysis is not difficult. It is, however, tedious. The ,
voltage divider sets the rough neighborhood of the trigger
thresholds. controls the hysteresis of the switch (the
difference between the ``turn on'' and ``turn off'' thresholds). The
feedback resistor should be a factor 10100 larger than the
voltage divider resistors. Otherwise, it drags the thresholds apart.
 Predict the ``turn on'' and ``turn off'' thresholds for k, k, k, and k. Rather than finding a general expression, it's fine
to consider this particular case. For the analysis, assume a maximal
output voltage swing of V. This actually varies with each op
amp, but should not be far from the truth.
 Build the circuit, using the resistance values given
above. Measure the input thresholds of the trigger and compare with
your predictions.
Copyright © 20012004, Lewis A. Riley

Updated Mon Jan 19 13:29:10 2004

This work is licensed under a Creative Commons License.