#### August 1967 Electronics World
[Table
of Contents] People old and young enjoy waxing nostalgic about
and learning some of the history of early electronics. Electronics World
was published from May 1959 through December 1971. All copyrights are hereby acknowledged.
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*Electronics World* articles. |

There is no such thing as too many introductory articles on
operational amplifiers (opamps). Of course, when this story
was written for Electronics World back in 1967, opamp were relatively
new to the scene. Prior to the advent of opamps, circuit design
for controllers, filter, comparators, isolators, and just plain
old amplification was much more involved. Opamps suddenly allowed
designers to not worry as much about biasing, variations in
power supply voltages, and other annoyances, and instead focus
on function. Even from the very beginning with the μa741 operational
amplifier, the parameters came close to those of an ideal device:
infinite input impedance, zero output impedance, perfect isolation
between ports, and infinite bandwidth. OK, the bandwidth spec
was more constrained compared to the other three, but still,
with frequencies being what they were compared to today, it
was close enough. Opamps allowed engineers to design with the
simplicity of LaPlace equations.

## The Operational Amplifier

Circuits & Applications

By Donald E. Lancaster

These highly versatile controllable-gain modular or integrated-circuit
packages have been used in computer and military circuits. New
price and size reductions have opened commercial and consumer
markets. Here are complete details on what is available and
how the devices are used.

Typical modular package and TO-5 style IC
operational amplifiers.

Once exclusively the mainstay of the analog-computer field,
operational amplifiers are now finding diverse uses throughout
the rest of the electronics industry. An operational amplifier
is basically a high-gain, d.c.-coupled bipolar amplifier, usually
featuring a high input impedance and a low output impedance.
Its inherent utility lies in its ability to have its gain and
response precisely controlled by external resistors and capacitors.

Since resistors and capacitors are passive elements, there
is very little problem keeping the gain and circuit response
stable and independent of temperature, supply variations, or
changes in gain of the op amp itself. Just how these resistors
and capacitors are arranged determines exactly what the operational
amplifier will do. In essence, an op amp provides "instant gain"
that may be used for practically any circuit from a.c., d.c.,
and r.f. amplifiers, to precision waveform generators, to high-
"Q" inductorless filters, to mathematical problem solvers.

Op amps used to be quite expensive, but many of today's integrated
circuit versions now range from $6 to $20 each and less in quantity.
Due to price breaks that have occurred very recently, the same
benefits now available to the analog computer, industrial, and
military markets are now extended to commercial and consumer
circuits. One obvious application will be in hi-fi preamps where
a single integrated circuit can replace the bulk of the low-level
transistor circuitry normally used.

Fig. 1A shows the op-amp symbol. An op amp has two high-impedance
inputs, the inverting input and the non-inverting input, as
indicated by a "-" or a "+" on the input side of the amplifier.
The inverting input is out-of-phase with the output, while the
non-inverting input is in-phase with the output. The amplifier
has an open-loop gain A, which may range from several thousand
to several million.

On closer inspection, we see three distinct parts to any
operational amplifier's internal circuitry, as shown in Fig.
1B. A high-input-impedance differential amplifier forms the
first stage, with the inverting input going to one side and
the non-inverting input the other. The purpose of this stage
is to allow the inputs to differentially drive the circuit and
also to provide a high input impedance.

Fig. 1. (A) Op-amp symbol. (B) Block diagram
of typical op amp.

There are several possibilities for this input stage. If
an ordinary matched pair of transistors (or the integrated circuit
equivalent) is used, an input impedance from 10,000 to 100,000
ohms will result, combined with low drift, low cost, and wide
bandwidth. By using four transistors in a differential Darlington
configuration, the input impedance may be nearly one megohm.
Drift and circuit cost are traded for this benefit.

Fig. 2. Characteristics of the Fairchild
μA702C. Price: $9.00.

Field-effect transistors are sometimes used, yielding input
impedances of 100 megohms, but often with limited bandwidths.
FET integrated-circuit operational amplifiers are not yet available,
limiting this technique to the modular-style package at present.
One or two novel techniques allow extreme input impedances,
but presently at very high cost. One approach is to use MOS
transistors with their 10^{13}-ohm input impedance;
a second is to use a varactor diode parametric amplifier arrangement
on the input.

Fig. 3. Characteristics of Motorola's MC1430.
Price: $12.00.

The input differential amplifier is followed by ordinary
voltage-gain stages, designed to bring the total voltage gain
up to a very high value. Terminals are usually brought out of
the voltage-gain stage to allow the frequency and phase response
of the op amp to be tailored for special applications. This
is usually done by adding external resistors and capacitors
to these terminals.

Since an operational amplifier is bipolar, the output can
swing either positive or negative with respect to ground. A
dual power-supply system, one negative and one positive, is
required.

Fig. 4. The RCA CA3030 operational amplifier.
Unlabeled terminals are used for frequency-compensation. Price:
$7.50. Note that the prices given here and above are for single-unit
quantities and these prices are subject to change.

The final op-amp stage is a low-impedance power-output stage,
which may take the form of a single emitter-follower, a push-pull
emitter-follower, or a class-B power stage. This final circuit
serves to make the output loading and the over-all gain and
frequency response independent. It also provides a useful level
of output power.

THE MATH BEHIND THE OP AMP

The gain of an operational-amplifier circuit is always chosen
be much less than the open-loop gain of the amplifier itself.
This allows the circuit response to be precisely determined
by the external feedback and input network impedances. Feedback
is almost ways applied to the inverting (-) input. This is negative
feedback for any change in output tries to produce an opposing
change in the input.

The feedback and input network impedances are normally chosen
such that they are much larger than the op amp's output impedance,
much smaller than the op amp's input impedance, and such that
the gain they require for proper operation is much less than
the amp's gain.

If these assumptions are met, the ratio of input to output
voltage (the gain of the circuit) will be given by:

Circuit Gain =

For instance, the op-amp circuit of Fig. 5B has an input
impedance of 1000 ohms and a feedback impedance of 10,000 ohms
Its gain will be - 10k/1k = - 10. Any of the op amps of Figs.
2, 3, or 4 may be used for this circuit.

Some circuit analysis will show that the inverting input
is always very near ground potential, and this point is then
called a virtual ground insofar as the input signals and output
feedback are concerned. Thus the input impedance to the circuit
will exactly equal the input network impedance.

When capacitors are used in the networks, the phase relationships
between current and voltage must be taken into account. These
differences in phase allow such operations as differentiation,
integration, and active network synthesis.

But isn't an op amp a d.c. amplifier and don't d.c. amplifiers
drift and have to be chopper-stabilized or otherwise compensated?
This certainly used to be true of all amplifiers, but today
such techniques are reserved for extremely critical circuits.
The reasons for this lie in the input differential stage. It
is now very easy to get an integrated circuit differential amplifier
stage to track within a millivolt or so over a wide temperature
range. This is due to the identical geometry, composition, and
temperature of the input transistors.

Matched pairs of ordinary transistors can track within a
few millivolts with careful selection. FET's offer still drift
performance, as one bias point may be selected that is drift-free
with respect to temperature over a very wide range. Thus, chopper-stabilized
systems are rarely considered today for most op-amp applications.

There are three basic op-amp packages available today. The
first type consists of specialized units used only for precision
analog computation and critical instrumentation circuits. These
are priced into the hundreds and even thousands of dollars for
each category, and are not considered here. The second type
is the modular package, and usually consists of a black plug-in
epoxy shell an inch or two on a side. Special sockets are available
to accommodate the many pins that protrude out the case bottom.
The third package style uses the integrated circuit. Here the
entire op amp is housed in a flat pack, in-line epoxy, or TO-5
style package. (See lead photograph.)

Generally speaking, the modular units are being replaced
in some cases by the integrateds, but at present, each package
style offers some clear-cut advantages. Table 1 compares the
two packages. The IC versions offer low cost, small size, and
very low drift, while the modular versions offer higher input
impedances, higher gain, and higher output power capability.

Table 1. Comparison between integrated operational
amplifiers and modular-type operational amplifiers.

Three low-cost readily available IC op amps appear in Figs.
2, 3, and 4. Here, their schematics and major performance characteristics
are compared. Devices similar to these at even lower cost may
soon be available.

A directory of op amp makers is given in Tables 2 and 3.

Table 2. Listing of modular-type operational-amp
manufacturers.

Table 3. Listing of integrated-circuit op-amp
manufacturers. Industrial Op-Amp Applications

We can split the op-amp applications into roughly three categories:
the industrial circuits, the computer circuits, and the active
network synthesis circuits. The industrial circuits are "ordinary"
ones, which will carryover into the consumer and commercial
fields with little change.

The boxed copy (facing page) sums up the mathematics. An
operational amplifier is often used in conjunction with two
passive networks, an input network, and a feedback network,
both of which are normally connected to the inverting input.
The gain of the over-all circuit at any frequency is given by
the equation shown. It is simply the ratio of the feedback impedance
to the input impedance at that frequency. For the circuits shown,
a low impedance path to ground must exist for all input sources
to allow a return path for base current in the two input transistors.

Fig. 5A shows an inverting gain-of-100 amplifier useful from
d.c. to several hundred kHz. The basic equation tells us the
gain will be -10,000/100 = -100. The 100-ohm resistor on the
"+" input provides base current for the "+" transistor and does
not directly enter into the gain equation. It may be adjusted
to obtain a desired drift or offset characteristic.

The higher the gain of the op amp, the closer the circuit
performance will be to the calculated performance. In the -of-100
amplifier, if the op amp gain is 1000, the gain error will be
roughly 1 %. The exact value of the gain also depends upon the
precision to which the input and feedback components are selected.

Choosing different ratios of input and feedback impedances
gives us different gains. Fig. 5B shows a gain-of-10 amplifier
with a d.c. to 2 MHz frequency response and a 1000-ohm input
impedance.

We might ask at this point what we gain by using an op amp
in this circuit instead of an ordinary single transistor circuit.
There are several important answers. The first is that the input
and output are both referenced to ground. Put in zero volts
and you get out zero volts. Put in -400 millivolts and you get
out +4 volts. Put in 400 millivolts you get out -4 volts. Secondly,
the output impedance is very low and the gain will not change
if you change the load the op amp is driving, as long as the
loading is light compared to the op amp's output impedance.
Finally, the gain is precisely 10, to the accuracy you can select
the input and feedback resistors, independent of temperature
and power-supply variations. It is this precision and ease of
control that makes the operational amplifier configuration far
superior to simpler circuitry.

If the output is connected to the "-" input and an input
directly drives the "+" input, the unity-gain voltage follower
of Fig. 5C results. This configuration is useful for following
precision voltage references or other voltage sources that may
not be heavily loaded. The circuit is superior to an ordinary
emitter-follower in that the offset is only a millivolt or so
instead of the temperature-dependent 0.6-volt drop normally
encountered, and the gain is truly unity and not dependent upon
the alpha of the transistor used.

Fig. 5. Industrial op-amp circuits. (A) Gainof-100
inverting amplifier. (B) Gain-of-10 inverting amplifier. (C)
Unity-gain high input Z amplifier. (D) Band-stop amplifier.
(E) Band-pass amplifier. (F) Precision ramp or linear saw-tooth
generator. (G) Detector with low offset. (H) Logarithmic amplifier.
(I) Voltage comparator. (J) Sine-wave oscillator.

By making the gain of the op amp frequency-dependent, various
filter configurations are realized. For instance, Fig. 5D shows
a band-stop amplifier. For very low and very high frequencies,
the series RLC circuit in the feedback network will be a very
high impedance and the gain will be -10,000/1000 = -10. At resonance,
the series RLC impedance will be 100 ohms and the gain will
be -100/1000 = -0.1. The gain drops by a factor of 100:1 or
40 deci\bels at the resonant frequency. The selection of the
LC ratio will determine bandwidth, while the LC product will
determine the resonant frequency.

Fig. 5E does the opposite, producing a response peak at resonance
100 times higher than the response at very high or very low
frequencies, owing to the very high impedance at resonance of
a parallel LC circuit. More complex filter structures may be
used to obtain any reasonable filter function or response curve.
Audio equalization curves are readily realized using similar
techniques.

Turning to some different applications, Fig. SF shows a precision
ramp generator. Operation is based upon the current source formed
by the reference voltage and 1000-ohm resistor on the input.
In any op-amp circuit, the current that is fed back to the input
must equal the input current, for otherwise the"-" input will
have a voltage on it, which would immediately be amplified,
making the input and feedback currents equal.

A constant current to a capacitor linearly charges that capacitor,
producing a linear voltage ramp. The slope of the ramp will
be determined by the current and the capacitance, while the
linearity will be determined by the gain of the op amp. A sweep
of 0.1-percent linearity is easily achieved. The output ramp
is reset to zero by the switch and the 10-ohm current-limiting
resistor. For synchronization, S may be replaced by a gating
transistor. A negative input current produces a positive voltage
ramp at the output. Note that the sweep linearity and amplitude
is independent of the output loading as long as the load impedance
is higher than the output impedance of the op amp. Ramps like
this are often used in CRT sweep waveform generation, analog-to-digital
converters, and similar circuitry.

Silicon diodes normally have a 0.6-volt offset that makes
them unattractive for detecting very low signal levels. If a
diode is included in the feedback path of an operational amplifier,
this offset may be reduced by the gain of the circuit, allowing
low-level detection. Fig. 5G is typical. Here the gain to negative
input signals is equal to unity, while the gain to positive
input signals is equal to 100. The diode threshold will be reduced
to 0.6 volt/100 = 6 millivolts.

Another diode op-amp circuit is that of Fig. 5H. Here the
logarithmic voltage-current relation present in a diode makes
the feedback impedance decrease with increasing input signals,
reducing the circuit gain as the input current increases. The
net result is an output voltage that is proportional to the
logarithm of the input, and the circuit is a logarithmic amplifier.
This configuration only works on negative-going inputs and is
useful in compressing signals measuring decibels, and in electronic
multiplier circuits where the logarithms of two input signals
are added together to perform multiplication.

An operational amplifier is rarely run "wide open", but Fig.
51 is one exception. Here the op amp serves as a voltage comparator.
If the voltage on the "-" input exceeds the "+" input voltage,
the op amp output will swing as negative as the supply will
let it, and vice versa. A difference of only a few millivolts
between inputs will shift the output from one supply limit to
the other. Feedback may be added to increase speed and produce
a snap action. One input is often returned to a reference voltage,
producing alarm or a limit detector.

Op amps may also be used in groups. One example is the low-distortion
sine-wave oscillator of Fig. 5J, in which three op amps generate
a precision sine wave. Both sine an cosine outputs, differing
in phase by 90° are produced. An external amplitude stabilization
circuit is required, but not shown. Output frequency is determined
solely by resistor and capacitor values and their stability.

Computer Circuits

The analog computer industry was the birthplace and once
the only home of the operational amplifier. In fact the name
comes from the use of op amps to perform mathematical operations.
Many of these circuits are of industry-wide interest and use.

Perhaps the simplest op-amp circuit is the inverter. This
is an op amp with identical input and feedback resistors Whatever
signal gets fed in, minus that signal appears the output, thus
performing the sign-changing operation.

Addition is performed by the circuit of Fig. 6A. Here the
currents from inputs E1, E2, and E3 are summed and the negative
of their sum appears at the output. Since the negative input
is always very near ground because of feedback, there is no
interaction among the three sources Resistor R is adjusted to
obtain the desired drift performance.

By shifting the resistor values around, the basic summing
circuit may also perform scaling and weighting operations. For
instance, a 30,000-ohm feedback resistor would produce an output
equal to minus three times the sum of the inputs; a smaller
feedback resistor would have the opposite effect. By changing
only one input resistor without changing the other, one input
may be weighted more heavily than the other. Thus, by a suitable
choice of resistors, the basic summing circuit could perform
such operations as E_{OUT}= -0.5 (E1 + 3E2 + 0.6E3).
Subtraction is performed by inverting one input signal and then
adding.

Two very important mathematical operations are integration
and differentiation. Integration is simply finding the area
under a curve, while differentiation involves finding the slope
of a curve at a given point. The op-amp integration circuit
is shown in Fig. 6B, while the differentiation circuit is shown
in Fig. 6C. The integrator also serves as a low-pass filter,
while the differentiator also serves as a high-pass filter,
both with 6 dB/octave slopes.

The differentiator circuit's gain increases indefinitely
with frequency, which obviously brings about high-frequency
noise problems. The circuit cannot be used as shown. Fig. 6D
shows a practical form of differentiator in which a gainlimiting
resistor and some high-frequency compensation have been added
to limit the high-frequency noise, yet still provide a good
approximation to the derivative of the lower frequency inputs.

These two circuits are very important in solving advanced
problems, particularly mathematics involving differential equations.
Since most of the laws of physics, electronics, thermodynamics,
aerodynamics, and chemical reactions can be expressed in differential-equation
form, the use of operation amplifiers for equation solution
can be a very valuable and powerful analysis tool.

Active Network Synthesis

Fig. 7. Operational amplifiers in active network synthesis.
(A) One form of active filter. (B) A twin-T network is identical
to an LC parallel resonant circuit except for the "Q". (C) Circuit
to realize "Q" of 14 without using an inductor. Perhaps the
newest area in which operational amplifiers are beginning to
find wide use is in active network synthesis. There is increasing
pressure in industry to minimize the use of inductors. Inductors
are big, heavy, expensive, and never obtained without some external
field, significant resistance, and distributed capacitance.
Worst of all, no one has yet found any practical way to stuff
them into an integrated-circuit package. If we can find some
circuit that obeys all the electrical laws of inductance without
the necessity of a big coil of wire and a core, we have accomplished
our purpose. Operational amplifiers are extensively used for
this purpose.

One basic scheme is shown in Fig. 7 A. If two networks are
connected around an op amp as shown, the gain will equal the
ratio of the transfer impedances of the two networks. Since
we are using three-terminal networks, and since the op amp is
capable of adding energy to the circuit, we can do many things
with this circuit that are impossible with two-terminal passive
resistors and capacitors.

Fig. 7. Operational amplifiers in active
network synthesis. (A) One form of active filter. (B) A twin-T
network is identical to an LC parallel resonant circuit except
for the "Q". (C) Circuit to realize "Q" of 14 without using
an inductor.

Fig. 7B shows an interesting three-terminal network called
a twin-T circuit. It exhibits resonance in the same manner as
an ordinary LC circuit does. It has one limitation - its maximum
"Q" is only 1/4. If we combine an op amp with a parallel twin-
T network, we can multiply the "Q" electronically to any reasonable
level. A gain of 40 would bring the "Q" up to 10. We then have
a resonant "RLC" circuit of controllable center frequency and
bandwidth with no large, bulky inductors required even for low-frequency
operation.

One example is shown in Fig. 7C where an operational amplifier
is used to realize a resonant effect and a "Q" of 14 at a frequency
of 1400 Hz. As the desired "Q" increases, the tolerances on
the components and the gain become more and more severe. From
a practical standpoint, value of "Q" greater than 25 are very
difficult to realize at the present time. Note that the entire
circuit shown can be placed in a space much smaller than that
occupied by the single inductor it replaces.

Fig. 6. Computer operational-amplifier circuits.
(A) Addition. (B) Integration. (C) Differentiation. (D) Practical
operational-amplifier differentiator.

Posted 9/6/2011