Some years ago, I was traveling on a seminar trip with Analog Devices, when our luggage was lost between Stockholm and Milan. Attired in new Italian clothes, I awkwardly faced the rather large, paying audience without slides. Assuring them that things would be fine after lunch, I decided to just talk about op amps, having some ideas about their inherent limitations, and an inclination to make these better-known than my experience with users suggested they were. Someone was able to find a few blank view-foils and a solitary black marker pen, and off we went into uncharted waters.

I began by asking, "Who in the audience uses op amps?". I think everybody raised a hand, many with a wry smile and a murmur of confident chuckles. Then I asked, "Why?", and the auditorium became very hushed, as the smiles turned to looks of apprehension. After a few seconds, somebody ventured, "Well, there are lots of them to choose from!", which I acknowledged is certainly true. Someone else observed, "They're cheap!", also true, and tacitly implying that they provide good value in solving contemporary problems. Eventually, some brave soul said, "They have very high gain!", which was the lead comment I'd been waiting for, because that is manifestly not true, in almost all op amp applications. It is, in fact, one of several op amp myths. "Let's talk about that", I said.

The "operational amplifier" has become the quintessential icon of analog electronics. This ubiquitous element has a long history, stemming from the times of analog computers. The name is so commonplace that we rarely stop to think about its original meaning, far less worry about whether is has a counterpart called a "non-operational amplifier." Of course, it has, apart from the trivial meaning of an amplifier which doesn't operate. There are probably as many amplifiers that are not based on the "op amp paradigm" as those that are, starting with one-transistor cells, which often out-perform an op amp in a specialized domain, such as an LNA for RF applications, and including variants of the basic theme such as current-feedback and active-feedback forms. This column asks the question, "Why are op amps so popular?", and examines some little-known problems they can cause, in spite of their ubiquity, if not well understood. Future articles will explore the outlook for what might replace this singularly popular workhorse in the years ahead, including current-feedback types and a rather new alternative to precise low-distortion, wideband, voltage-mode amplification.

Choices and Ideals

Today, the system designer can choose from numerous different kinds of what can be called "traditional" monolithic op amps -- you know, the sort that has a differential high-impedance input accepting a small voltage, V_IN, and a single-sided (or so it seems) low-impedance output at which V_OUT = AV_IN appears, where the amplification factor A is usually reckoned to be extremely large. We'll call this sort of amplifier an OPA; other types, the TZA and the AFA, will be described in later columns.

Every OPA has its special qualities, such as those providing mere femtoamps of bias current (usually called electrometer-grade op amps); or ultra-low offset voltage (so-called "instrumentation-grade op amps", not to be confused with "instrumentation amplifiers", a term generally reserved for a fixed-gain differential-input amplifier); or, having very low noise, including the erratic and troublesome low-frequency noise known as 1/f; or, wide bandwidth, usefully (though not necessarily) accompanied by high slew rates; or, micro-power operation, sometimes from very low supply voltages; or, those able to drive large powers into a load; and so on. Each OPA embodies a strong set of optimization criteria and, of course, no single design can ever be universal.

Why is the OPA so widely used? Could some of its popularity be attributed to a Madison Avenue style of promotion? Are its unique benefits -- its near-panacea-like properties -- just a myth? Clearly not; yet it enjoys a reputation for accuracy that is not always deserved. If one opens most text books about operational amplifiers, the discussion invariably begins with a list of so-called "ideal properties" that begins something like this:

• Infinite Gain,
• Infinite Bandwidth,
• No Time Delay.

I frankly don't know how one could use such an amplifier, even in traditional applications, since quite simply stated it would never be stable -- even if there were absolutely no gain and phase errors in the OPA proper, indeed, precisely because of that fact. Consider a simple feedback circuit realizing a unity-gain inverting-mode amplifier. In a practical embodiment the physical resistor from the output to the inverting terminal has distributed resistance and capacitance, and a rather complicated gain/phase behavior. Though the characteristic time-constants are very small, usually picoseconds, they would nevertheless guarantee instability, and continuous oscillation, if the amplifier really had flat gain out to a frequency beyond a critical limit. A quick simulation will demonstrate this likelihood. But the issue is academic, of course. Real op amps are notoriously well-behaved in most applications, and it is this very predictable, benign behavior that has allowed them to become such a pervasive part of modern analog design. How is this achieved?

The inherent "inertia" in the elements in a practical OPA each contributes phase lag, which add up to significant proportions at high frequencies, leading to large phase angles. Most of this comes from the transistors, but the capacitance of monolithic resistors can also contribute phase lag. If the gain magnitude is too high, the closed-loop response will be unstable. This situation is specifically addressed by the "HF compensation" means included in most contemporary op amps. The criteria for stability are well-known, and given full consideration in a reliable text book. (One of the best to have been written on this topic is Operational Amplifiers by Jim Roberge of MIT). By far the most common stabilization technique is the use of a "dominant pole," which guarantees a closed-loop response that is unconditionally stable (at least, down to unity closed-loop gain and with a load that is not very reactive), and although quite inefficient in certain ways, it considerably simplifies the utilization of an op amp. It is this very technique, however, that results in abysmally low ac gains in so many real-world applications.

An OPA is characterized, in its data sheet, by many numbers having to do with its dc behavior. One of these is the open-loop dc voltage gain, A_O. An op amp with an A_O of under 100 dB (that is, less than x100,000) is often regarded as barely coming up to snuff in a modern competitive world. So, there has been a lot of effort put into making this parameter as high as possible -- a million being fairly routine, and ten million not being uncommon. I have no idea why anyone would ever need such a high gain. Even in such applications as a strain-gauge interface, a multi-million dc gain is barely justified.

For example, suppose we wish to achieve a closed-loop gain of x10,000, in order to raise a 100 mV signal to a useable 1 V. To contribute a -1% error the finite A_O certainly must be a million. But the resistors used in the feedback network, used to define the gain, may not match any better than 1%; the uncertainty in the gauge factor will often cause even larger scaling errors. To the extent that individual calibration of a strain-gauge channel is usually mandatory, it is easily possible to provide quite adequate performance with a much lower A_O, particularly if this parameter is stable with temperature and supply voltage, as is generally true in a well-designed modern product.

An Erstwhile Enigma

Occasionally, it is noted that a very high electrical dc gain may be thwarted by certain subtle -- and at one time puzzling -- limitations arising in the physics of integrated circuits. These effects used to be quite a problem, in the early days of monolithic op amps, when the peculiarities of the silicon reality were less well understood than by a skilled contemporary designer. Indeed, when the problem first appeared it was quite enigmatic. Not only was the gain lower -- often much more -- than expected, but it could even reverse sign: that is, the nominally negative feedback supplied by the external network became positive at very low frequencies, yet the closed-loop response remained stable! How could this be?

It was soon realized that the culprit was thermal feedback from the output stage, which may run quite hot, back to the differential pair invariably used as the input stage. The resulting thermal gradient could generate a V_BE between these devices. The effect is a strong one: for bipolar transistors a temperature difference of only 1/100^th of a degree Celsius generates an offset voltage of some 20 µV at room temperature (more, if the general chip temperature is higher). Suppose this difference results from a power change caused by a 1-V output; then the "thermal gain" is simply 1 V divided by 20 µV, or a mere 50,000. Clearly, the sign of the thermal feedback will depend on the precise details of the layout; if it should be positive, it will operate in opposition to the electrical feedback. But the ac response remains stable, because it is determined by the behavior at much higher frequencies. In fact, the ac response dominates in almost all practical applications of op amps.

The problem of thermal feedback rarely appears in modern op amps, in which various kinds of common-centroid layout techniques are used. One of the earliest uses of such can be attributed to Mitch Madique of Analog Devices, and involves the use of a "cross-quad" of transistors: instead of a single pair, two sets of transistors were placed in a square formation and connected in such a way that their thermally-induced offsets cancel. But this is not the only possible layout to achieve the required nulling of gradient effects. A sometimes more convenient scheme is what I call a "poor man's cross-quad", namely a linear A-B-B-A arrangement. Common-centroid methods are now routine; they minimize many sources of dc errors at the input of an amplifier, such as those caused by doping gradients across the chip -- and the effects of mechanical strain -- and are useful in numerous other areas of monolithic design, such as in current mirrors.

Integrator Inside

Op amp data sheets also specify the "unity-gain" frequency, which we'll call f₁. Using the dominant-pole method, the gain-magnitude will increase at lower signal frequencies, f_s, and there is no mystery about its value: it is simply f_s/f₁. Thus, if we have an op amp with a unity-gain frequency f₁ = 10MHz, the gain at 100kHz is precisely 100 -- a far cry from infinite! After making this point, at the seminar, I asked the audience, "Suppose you have a 100-MHz unity-gain op amp, what is its open-loop gain to a 30MHz signal?" The response was quite interesting: clearly, a lot of people had done the calculation in their head and had concluded the gain was 3.3. But "everyone knows" that op amps have extremely high gain, causing them to have grave doubts about the correctness of their math. The show of hands was sparse!

This is not any exaggeration to make a dramatic point. It is a simple fact. Op amps of the OPA persuasion do not have high open-loop gain at most signal frequencies -- by design. If we return to that strain-gauge interface and ask, "What is the open-loop gain at a signal frequency (f_s) of only 100 Hz (not at all unusual in vibration instrumentation) for an amplifier having a dc gain of ten million and a unity-gain frequency (f₁) of 1 MHz?" Well, it is just 10,000, that is, a thousand times lower than the dc open-loop gain, which is clearly quite irrelevant to the dynamic response.

Let's take a closer look at the response of a classic op amp stabilized by means of a dominant pole (which is, to this day, the dominant technique!) We've seen that the gain below f1 increases in simple inverse proportion to frequency, right down to a very low corner frequency, whose value would be 1 MHz divided by 10 million in the above example, or 0.1 Hz, though as noted this number is all but meaningless. It also decreases with frequency, in a roughly linear way, for an fS above f1, at least for a while. So, what is the name we give to a function of this sort? It's an integrator, an element whose ac gain is described by the Laplace form A(s) = 1/sT₁, where T1 is a characteristic time-constant, and related to f1 by the equation f₁ = 1/2pT₁. Thus, we can say that the most important parameter of an op amp, as far as accuracy at frequency is concerned, is its unity-gain frequency, f₁, equivalently, its characteristic time-constant T₁. With apologies to Intel, we could say that the icon for an op amp is Integrator Inside!

This is a different view of the OPA to the text-book ideal noted above. And while, in its own way, it is also an ideal, it fits the reality much more closely. Further, it matches exactly the text-book claim of infinite dc gain, since 1/sT₁ becomes infinite at s = 0 (that is, f = 0). If an op amp is to be benign and predictable in practical applications, the 1/sT₁ behavior is often necessary (though not essential: advanced high-speed amplifiers use a modified stabilization paradigm.)

The "integrator view" of an OPA is really quite valuable. Unfettered gain up to GHz frequencies, the ideal implied by most textbooks and widely taught in university classrooms, is only a useful idea in the most na•ve vision of the applications domain. Indeed, one might go so far as to assert (I will!) that it is the singularly simple integrator aspect of the traditional op amp that has commended it in countless applications, leading to trouble-free operation without the need for excessive care on the part of the user. On the other hand, one might argue that this free-and-easy adoption of op amps for every application is regrettable, since it leads to a certain sort of laziness, and often a serious ignorance about the alternatives which may better serve the problem at hand.

Active-R Filters. Huh?

As perhaps an example of this "universal" notion, there was, many years ago, a flurry of misguided academic papers about a seriously-flawed utilization of op amps, in an application for which they were terribly unsuited. It was well-known that filter design (of the Sallen-and-Key kind then popular) was badly impacted at high frequencies by what was being called the "excess phase due to the op amp". Of course, applying the integrator view, we can see that it is in no sense an "excess!" The op amp is delivering precisely what it was designed to provide: a gain magnitude that falls at 20 dB per decade, with a constant phase of -90 degrees. The term "excess phase" is more properly used either in referring to the way the magnitude of the phase angle increases rather rapidly above the unity-gain frequency, or to additional phase incurred by a simple time delay. But neither of these were the cause of the troublesome Q-enhancement so often noticed in filters.

Then, one day, some bright spark said, "I know -- let's use that op amp pole to make the filter time-constant!" A good idea, and quite literally the birth of what we nowadays call the "gm/C" style of filter design. But it was badly flawed by several practical considerations. It was also over-hyped by the use of the name "Active-R" which is all but meaningless. Any pure-analog filter fundamentally must employ energy-storage devices -- capacitors in most monolithic low-frequency filters -- and therefore must always be "Active-CR". And sure enough, the capacitor was there, embedded in the op amp, as the dominant-pole generating element. I suppose the academics knew that much, but they were singularly unwarranted in pretending that it could be dismissed from further consideration by a change of name.

Concerned about the practice, I wrote a piece for Electronics Letters entitled, "Use of the Operational Amplifier Pole: A Caution," in which I pointed out that the unity-gain frequency f₁ of commercial op amps is not precise, and its tolerance never specified: it merely has to guarantee stability, usually with a generous margin. As an aside, this raises an interesting point. In view of the importance of f₁ in almost all applications -- it completely determines the open-loop gain over the several decades below it -- the absence of op amps with a calibrated f₁ is quite surprising and is in no small measure, I suspect, a reflection of the still-limited awareness of how basic this parameter is to the use of op amps. Now, a CR product (the thing determining the T₁ in A(s) = 1/sT₁) can only be controlled in production to about ±35%, but could easily be trimmed to 1% using modern product equipment, and held very close to its room-temperature value by careful design.

As well as the poor absolute control of f₁ (and consequentially, the terrible scattering of the pole locations in a multi-pole filter, using randomly-selected amplifiers) and the often poor temperature-stability of this parameter in most commercial op amps, there were other serious limitations to the badly-named "Active-R" technique, which happily has died a natural death. One of these is the very limited signal capacity of a typical bipolar input stage, leading to massive odd-order distortion at levels that would not be attractive in many practical filters. The HD3 of a simple bipolar pair is 1% (-40 dBc) for a base-to-base drive level of only ±20 mV at T = 27 °C.

Having thus scolded the academic community for their indiscretion, I was surprised to later receive a letter from a professor starting, "Dear Dr. Gilbert: With regard to your criticisms of our 'Active-R' filter research, I assure you that these are fully practical. Indeed, one of my students, etc. . . . Sometimes, it's hard to make a very simple, factual point.

"Virtual Ground" Virtually Groundless

Books about op amps delight in extolling the virtues of the "virtual ground" that arises at the input of an OPA having negative feedback to its inverting input, and a (usually) grounded non-inverting input. (This node may be only ac-grounded, or even used for other signal-related purposes.) The inverting input is also called a "summing node", because it used to be common in analog-computer applications to sum several voltages by converting each of them to a current through an individual resistor, relying on the summing-node to act as a so-called "virtual ground". It is virtual, because it isn't really connected to ground through a wire, but (we're told) the whole system (OPA and resistors) acts pretty much as if it were, except that all the summed current flowing toward it must proceed to flow through the feedback resistor, and generate an output voltage.

Because the gain is so very, very high, the text-books explain, there is never any significant voltage change at this magical summing-node/virtual ground, so the input voltages are accurate converted to proportional currents, and the output, being referred to 'ground, via the OPA', is likewise accurate. It's an alluring notion, but never completely correct. The bit about "all the summed current" is okay, because OPAs usually have negligible input current, even at frequencies quite close to f₁; what little there is can be attributed to the input capacitance. And even a moderate shunting input resistance -- say 1 Mohms -- is not very troublesome.

So what's the problem? Simply that the finite ac open-loop gain requires a certain finite voltage to be present at the input, meaning that the "virtual ground" is nothing more than a node at which a moderate and possibly troublesome voltage must be present whenever there is any change in the input. To understand how far from the ideal this can get, consider an OPA used to convert the output current from a DAC to a voltage, that is, the classical transresistance function. Let the feedback resistor that scales this function be RF. Now model the op amp as an integrator -- which you really must -- and consider the voltage swing at that "virtual ground" in response to a current step. To begin with, the output from the op amp doesn't move at all; its initial response is ramp-like, as the amplifier performs the operation V_OUT = -V_IN/sT₁. But what is V_IN in this case? Well, it is simply the DAC output current step, call it IDAC, times the feedback resistor RF. For a typical case of I_DAC = 2 mA, R_F = 5 kohms (for a final output of 10 V) the input step is also 10 V!

As the OPA output integrates this "error voltage" of the full final value at its input, the error declines exponentially at a rate fully-determined by the unity-gain frequency, that is, on a time-constant of T₁. During all this time the inverting node is far from being a "virtual ground!" Rather, the voltage rises to the full output value of 10 V in this case, and only later falls back to close to zero. In practice, the actual voltage would be less than this, because the input transistors will invariably go into emitter-base breakdown. (The DAC, too, will often limit the voltage swing during slewing).

Sometimes, the OPA may include a "box of diodes" at the input to provide protection against such large inputs. Occasionally, Schottky diodes are added on the board, with the idea of "speeding things up". Do such diodes help the situation? Well, they certainly prevent the degradation of beta that will be caused in the input transistors by long-term exposure to reverse bias (whether transient or continuous) but they certainly do not speed up the settling of the op amp, for a very simple reason: now, instead of integrating a large error voltage, V_IN is constrained to only some few hundred millivolts, and the dV/dt at the output drops in proportion, to about 1/20^th of the original rate!

Where's the Output Ground?

Few users of op amps seemed concerned about the loose definition of where the output ground is located. Most don't have a specific pin called "OUTPUT GROUND". So where is it? Using the method of Sherlock Holmes we find by a process of elimination that it's got to be one of the supply pins, or maybe both of them! And this is in fact the case.

The classic OPA consists of a gm stage, followed by a current-mirror, whose (single-sided) current is integrated in an on-chip capacitor, C_c, generally called the "HF Compensation Cap". The characteristic time-constant T₁ is formed by the quotient C_c/gm (just as in modern filters built in this fashion) and f₁ = gm/2pC_c. Now, many OPAs use what is called a Miller Integrator topology, in which this important capacitor is connected between what is essentially one of the supply lines (often V_NEG, in an npn embodiment) and the output. Thus, the ac output reference for the amplifier is literally this supply line. If it is noisy, or rattling around for any reason, all of this voltage appears at the output. Worse things can happen but we can afford to put off these worries until a future column.

Barrie Gilbert (IEEE Member 1962, Fellow, 1984), b. 1937, in Bournemouth, England, pursued an early interest in solid- state devices at Mullard Ltd, working on first-generation planar ICs. Emigrating to the US in 1964, he joined Tektronix, in Beaverton, OR, where he developed the first electronic knob-readout system, and other advances in instrumentation. Between 1970-1972 he was Group Leader at Plessey Research Laboratories. He later joined Analog Devices Inc. and was appointed ADI Fellow in 1979. He manages the development of high-performance analog ICs at the NW Labs in Beaverton.

For work on merged logic he received the IEEE "Outstanding Achievement Award" (1970) and the IEEE Solid-State Circuits Council "Outstanding Development Award" (1986). He was Oregon Researcher of the Year in 1990, and received the Solid-State Circuits Award (1992) for "Contributions to Nonlinear Signal Processing". He has written extensively about analog design and has five times received ISSCC Outstanding Paper Award. He has been issued over 40 patents and holds an Honorary Doctorate from Oregon State University.