Control Engineering

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What is a differential amplifier?
June 11, 2007

A differential amplifier has two independent inputs and puts out a signal proportional to the difference between them. Operational amplifiers (op-amps) are a special case of differential amplifiers with extremely high gain (typically >10,000) that were originally invented to give engineers a basic building block for designing analog computers.

Today, analog computers are largely obsolete, but differential amplifiers based on op-amp technology are among the most versatile of analog circuits. I’ve used them to build home stereo sets, highly stable oscillators, extremely low frequency (ELF) radio receivers, astronomical photometers, a device for reading astronomy photographic plates directly in stellar magnitudes, and a slew of data acquisition signal conditioners.

A differential amplifier has two inputs and one output. The output equals the gain times the difference between the inputs.

Figure 1 shows the basic differential amplifier connections. The inverting (-) and non-inverting (+) inputs give the device its name: the output equals the voltage difference between them times the amplifier gain. The little tail on the right marked “V0” is the output terminal. Finally, there are power-supply terminals V+ and V-. It is important to remember that neither of these is a ground reference terminal. In fact, the device has no ground reference terminal!

The only one of these terminals that needs a reference at all is the output, and it is implicitly referenced to the midpoint between V+ and V-. For example, a 741 op-amp (which is a monolithic semiconductor device with a gain in the hundreds of thousands) is rated for a maximum ±15 V dc. That means a total of 30 V dc between the supply terminals. The minimum voltage is ±5 V dc, for a total of 10 V dc between the supply terminals.

A differential amplifier with a gain of, say, 500,000 is pretty useless. To (mis)quote a line from a movie: “The wind blows and [it] goes bat $#@&!” With a maximum peak output voltage of +15 V, any input greater than 3 ìV will slam the output to the rail. Anything from a nearby toaster to a passing cat will induce that much voltage on an unconnected input.

Now, that’s fine if what you really want is a comparator that will give +15 V if the non-inverting input is as much as 3ìV above the inverting input, and -15 V if it’s as much as 3ìV below. There are lots of applications where that’s exactly what you want, and lots and lots of op-amps go into just those applications. But it’s pretty useless for an amplifier.

Practical differential amplifiers can be made by wrapping an operational amplifier in a feedback network that controls the overall gain, as this diagram from National Semiconductor shows.

Figure 2 shows a practical differential amplifier circuit. The four feedback resistors knock down and stabilize the gain to a moderate value equal to your design target, instead of whatever happens to come out of the box. Since op-amp manufacturers assume that these parts will be subject to loads of feedback, they can afford to be pretty cavalier about the gain of a particular unit. Who cares, after all, whether the thing’s open-loop gain is 500,000X or 1,000,000X!

Note that in this circuit, the non-inverting input connects to a ground reference. Be very, very careful of your ground reference here. Don’t blithely power the thing with two batteries in series and trust the common point between them to provide a good reference. That only works when the amplifier gain is well below 100X, because the common mode voltage will wander erratically as one battery ages faster than the other. I like to use a 10-turn potentiometer placed across the power supply rails to create a fairly stable and easily adjustable ground reference. If I need more than 100X, I use additional stages.

Cascading multiple differential amplifier stages provides high gain with stability.

Figure 3 shows such a two-stage amplifier. Note that the non-inverting input of the first stage op-amp is referenced to the wiper of a potentiometer. This point provides the low input for the second-stage as well. A similar potentiometer provides the reference for the second-stage op-amp’s non-inverting input. The gain for each stage is a modest 100X, but when they are combined, they provide a pretty spectacular 10,000X.

To set the potentiometers, short the inputs to the second stage (Vt) with a jumper to ensure zero input. Most commercially available op-amps can stand this treatment for a reasonable time without damage. With the second-stage inputs shorted, adjust second-stage potentiometer for zero output. Then, move the jumper from the second-stage input to the first stage input (Vo) and adjust the first stage potentiometer for zero output (Vo). Since the sensitivity is now amplified by the second-stage gain, it will be about 100X more ticklish than the previous adjustment. If you want more gain, simply add more stages, but remember that the adjustment for each stage will get more difficult.

Posted by on June 11, 2007 | Comments (0)