Operational Amplifier Basics
May 1968 Radio-Electronics

May 1968 Radio-Electronics [Table of Contents] Wax nostalgic about and learn from the history of early electronics. See articles from Radio-Electronics, published 1930-1988. All copyrights hereby acknowledged.

It seems like just last week that I was sitting in my first circuits class at the University of Vermont, learning about the Fairchild Electronics-designed μA741 operational amplifier. That was 1987, a mere two decades after the 741 was first released commercially. The professor told us that if we remembered the basic characteristics of the ideal opamp that we could easily derive equations for the circuit which controlled it. Those characteristics are: Infinite input impedance, zero output impedance, infinite bandwidth, infinite open-loop gain, zero noise, infinite slew rate, and a virtual short between the "+" and "-" inputs (did I miss any?). I'm guessing that still holds true of today's classrooms. The virtual short between the inputs, while not necessarily intuitive, is the most important point for making analysis easier. There were actually vacuum tube versions of opamps (hybrids) before ICs came along, the most notable of which was the Philbrick K2-W (c1950).

Operational Amplifier Basics - Progress - from computers to household devices

By Thomas H. Lynch*

The operational amplifier (OP amp) has recently become one of the most versatile tools in electronics. It had its expensive beginnings in analog computers, but inexpensive semiconductors have brought the cost of op amps down considerably. Now they can be used wherever analog (time-varying) signals are processed - for example, in audio amplifiers, oscillators, voltmeters and power supplies. They can easily take the place of a large assortment of individual transistors, resistors and capacitors in many applications,

Probably the op amps' primary advantage is the simplicity with which circuit performance may be predicted. The passive components used to connect the operational amplifier almost entirely determine circuit performance.

Basic characteristics

The versatility of an op amp arises from its unusual set of specifications:

1. It amplifies dc as well as ac signals.

2. Its gain (A) at dc is ideally infinite.

3. Its input impedance (Z_in) is ideally infinite.

The reasons for these specifications will become clear as we proceed.

An operational amplifier is basically a very-high-gain direct-coupled amplifier that uses external feedback for control of response characteristics. It was originally designed as a device to perform mathematical functions - integration, differentiation, addition and subtraction. Since its inception, however, the op amp has found wide usage in such things as signal amplification and wave shaping, servo and process controls, analog instrument and system design and impedance transformation.

Op amps are versatile and useful because external negative feedback controls response characteristics. If an op-amp circuit provides enough gain, the closed-loop amplifier characteristics become a function of only the feedback components. Hence the circuit designer's ingenuity in choosing and using feedback parts is the only limiting factor.

A common arrangement for op amps is a direct-coupled cascade of two balanced differential-amplifier stages, with the second stage driven push-pull by the first.

In most cases the op amp has two inputs, one inverting and one non-inverting (Fig. 1). This characteristic means that if a positive signal is applied to the ( - ) input, the output will swing negative. Similarly, with a positive input connected only to the (+) input, the output will swing positive. We can further see that if the same signal voltage is applied at the same time to the ( + ) and ( - ) inputs, the output will not change - it will stay zero (Fig. 2). This is because (ideally):

e_in( -A) + e_in(A) = e_out = 0 This rule will (ideally) held for any value of e_in, (+) or (-). (A measure of this specification is called common mode rejection - a ratio of the change in the output for a given common change in the input.)

Thus far, we can see that the approximate output of the op amp is given by:

e_out = A(e₁ - e₂)

where:

A is the gain, typically very large,

e₁ signal voltage at the ( +) input,

e₂ signal voltage at the ( - ) input.

At this point you might notice that if gain (A) is large - say 10,000 - the output voltage will be rather large for very small input voltage differences. For example, if (e₁ - e₂) was as small as +0.005 volt the output would be +50 volts. Since all amplifiers are capable only of a certain maximum output (say ±10 volts in this case), clearly for input differences in excess of 1 mV the output voltage will not in-crease beyond 10 volts (Fig. 3).

What practical use is there for an amplifier that saturates with only a 1-mV input signal? If we connect an op amp as shown in Fig. 4, what will the output voltage be?

First note that the amplifier gain is very large, and R_f is connected from the ( - ) input to the output. Negative feedback results, forcing e to be a very small value, regardless of the output voltage. For example, if e_out = 5 volts, e would only be e_out/A = 5/100,000 = 0.00005 volt.

Second, remember that the input impedance is large (Z_in = 1 megohm). This means that very little current will go into the ( - ) input:

i (-) = 0.05 mV/1 megohm for a 5-volt output

= 0.05 nA (nanoampere)

The negative input terminal is thus a "virtual ground" - i.e., the voltage drop is approximately zero (as a ground point) but little current flows into it (as an insulator).

Since e_in is much greater than e, a current will flow through R_in equal to 1 volt/10,000 ohms, or 0.1 mA (see Fig. 5). Kirchhoff's laws state that currents flowing into a circuit point must equal the currents flowing out of that node point. Thus, if (ideally) no current flows from the node into the ( - ) input of the op amp, the 0.1 = mA current must flow out of the node through the 50,000-ohm resistor R_f. If a current of 0.1 mA flows through 50,000 ohms, it must have a voltage drop of E = (0.1 mA) X (50,000 ohms) = 5 volts. Since E = e_out, e_out must clearly be equal to -5 volts. (Fig. 6).

This then is a simple amplifier with gain equal to:

A_v = R_f/R₁ = -5

An important conclusion is that the gain is essentially dependent only on the external feedback resistors.

Put It to Work

To begin with, Figs. 7 through 10 shows several basic amplifier connections. There are a few considerations to make when using the inverting amplifier of Fig. 7.

First, source impedance R_s of signal source e_in must be added to the amplifier's nominal input impedance to get the actual value of R_i; this value is needed to determine amplifier gain accurately. Because of this, the inverting amplifier usually is used only with a low signal impedance, such as the output of an amplifier like this one.

Second, since the output of this amplifier must drive both the load and R_f in parallel, their combined impedance should be greater than the minimum value for the particular amplifier being used - usually 2,000 ohms or greater. R is added to make the resistances seen by both the ( + ) and ( - ) inputs identical. This improves the temperature-drift characteristics of the amplifier. If R_in is small (10,000 ohms or less) R can usually be eliminated.

A non inverting follower is shown in Fig. 8. Since all the output is fed directly back to the input, the gain will be +1. Also, the input impedance will be very high (usually 50 megohms or greater). This is useful when the previous stage must not be loaded down-as in a tuned circuit, a voltmeter input, or a ceramic microphone.

The gain follower (Fig. 9) has feedback to the ( - ) input reduced so that the amplifier has a positive gain. The input impedance will be very high also:

When the loop gain is high, this can be 50 megohms or more. It is significant to note that the overall closed-loop gain does not depend upon the source impedance.

The previous circuit can be modified for ac applications, as shown in Fig. 10. When the closed-loop gain is 100 or more, the input impedance will be 10 megohms or greater. At the signal frequencies, X_ci is so small it may be neglected. The circuit then looks similar to Fig. 9, except that R has been added. This resistor is "boot-strapped" since the voltages at both ends are almost identical. This means that a signal voltage at the input (the top of R) will cause a similar in-phase voltage at the bottom of R because of the feedback divider R₁/(R_i + R_f). Almost no signal current flows through R, and therefore its value is effectively increased to 10 megohms or more.

The other applications on page 58 are a small sample of the wide variety of circuit functions that can be easily accomplished with an op amp. Because of the frequency response of most op amps, these applications are usually limited to frequencies less than a few hundred kilohertz. More applications along with discussions of problem areas can be found in the reference material.

Tables I and II list a wide selection of integrated and discrete operational amplifiers priced at $20 or less in single quantities. For the sake of brevity, only the more important parameters are listed.

The integrated circuits are packaged in multi-pin TO-5 cans or flat packs. The package type has some effect on price, the TO-5 usually being cheaper by a couple of dollars. Many other factors are included in the final price and each particular amplifier has its virtue. (For example, the NSC type LM201 provides the highest gain for its moderate cost.)

More information on each type can be obtained directly from the manufacturer, who will provide a list of distributors. Manufacturers' addresses are listed at the end of this article.

Discrete op amps are easier to use, as they have been frequency-compensated for a 20 dB/decade roll off (which insures unconditional stability). Most of these discrete op amps are generally more rugged electrically than the integrated ones - a point to consider for experimentation. This is because of the larger transistors and resistors used in construction. The output of most of these op amps will supply a standard 2.2 mA at ±1 0 volts.

The most common size is 1 1/8" square and 5/8" high with the input/output and power pins on the bottom. This is a common industry-accepted size. An exception is Fairchild's ADO-49C; it is a μA709C with frequency-compensation components in a small, round epoxy package. The manufacturers of these op amps should likewise be consulted for further information.

Where to Get More Information

A listing of useful material on op amps is included under "References" on page 84. Much of this can be obtained at little or no cost by writing to the manufacturers (see page 85 for addresses). References marked (*) are especially useful. Also included is a glossary of op-amp terminology. R-E

* Bunker-Ramo Corp.