The bipolar junction transistor (BJT)-pair emitter-coupled differential-amplifier circuit is a familiar amplifier stage in the repertoire of analog designers, but has an interesting complication. This article examines the emitter-circuit current source, *I*_{0}, of BJT diff-amps and the effects on amplifier gain of different implementations for it.

The widespread belief that a BJT current source can temperature-compensate the BJT-pair diff-amp is true, but the conditions for it do not appear to be widely known. The typical circuit is shown below.

This is a differential-input, differential-output voltage amplifier. With both input and output quantities differential, the incremental voltage gain of the circuit is

The condition for differential amplification is that *A*_{
ν
1} = *A*_{
ν
2}. The circuit is made symmetrical whenever

Then the voltage gain becomes

where *r*_{M} is the *transresistance*, the resistance across which the input voltage develops the (pre-*α*) output current.

A goal of good design is to make *A*_{ν} a fixed value. The choice of resistors with a low temperature coefficient (TC) and sufficiently tight accuracy is one factor. This is usually easy to achieve, though for high-precision design, the change in resistance caused by a change in ambient temperature is a factor to be considered. Even more so are "thermals", dynamic, waveform-related changes in resistance caused by changes in power dissipation with *ν*_{i}. For very precise design, the change in resistance with applied voltage must be considered too.

Other transistor parameters than the two (*r*_{e} and *β*) of the BJT T model used here - namely, *r*_{o} - also need to be included for precision design. We will assume that the BJTs have a sufficiently high Early voltage that *r*_{o} need not come into our list of considerations - at least not here. In practice, this assumption is often valid.

BJTs are typically the least ideal elements of the circuit. From the gain formula, it is evident that two BJT parameters affect gain, the incremental emitter resistance, *r*_{e}, and
*β*
. For high
*β*
- that is, for
*β*
>> 1 - the gain factor,

approaches 1. For a typical
*β*
value of 200, then *α* = 0.995, contributing a gain error of 0.5 %. If that is too much error, *α* -compensation techniques are required. Usually, this error can be compensated by including it in the gain formula, as we have done. What is more important is how much it drifts with temperature. Typical

Then for large *β*, *α* has a TC of around 50 ppm; *α* is usually not much of a problem.

The r_{M} transresistance expression of Av - the denominator - is the resistance across which the input voltage develops the (emitter) current that is common to input and output loops. The output current is modified by *α*, which accounts for loss along the way from the emitter circuit. This transresistance, *r*_{M}, also includes *β* in the *R*_{B} term. If *R*_{B} is kept small, and the inputs are driven by voltage sources, then this *β* is of no concern. If the sources are high in resistance, then the *R*_{B} term will affect gain by *β* variation with temperature. Its 1 %/^{o}C variation is scaled down by the extent to which *R*_{B}/(*β* + 1) is not dominant in *r*_{M}. Keeping *R*_{B} small is another design factor.

The most troublesome term in *r*_{M} is *r*_{e}, for it varies with temperature and emitter current, *I*_{E}, according to

With *I*_{E} constant, *r*_{e} varies with the thermal voltage, *V*_{T}, which varies in proportion with absolute temperature;

At 300 K (about 80^{o}F), this is 1/300 K or about 0.33 %/K = 0.33 %/^{o}C. For laboratory-quality instrument design, let us suppose, the temperature range over which the equipment ought to be able to operate within its specifications is over 25^{o}C +/- 15^{o}C which is 10^{o}C to 40^{o}C. Over a 15^{o}C maximum change from ambient, *V*_{T} changes about 5 % - far too much for most precision designs. Therefore, *V*_{T} variation in gain needs to be compensated.

The simplest compensation for *r*_{e} is to make it a negligible term (along with the *R*_{B} term) in *r*_{M}. This is accomplished by making *R*_{E} dominant. For *R*_{E} >> *r*_{e}, the drift in *r*_{e} affects gain far less than 5 %. In many cases, dominant external emitter resistance solves the drift problem, but at the expense of gain and power dissipation. By increasing *I*_{0}, then *r*_{e} is reduced proportionally, though circuit power increases. This is not only undesirable for power-limited equipment but it also exacerbates thermals by increasing Δ*P*_{D}(*ν*_{i}) in the BJTs.

In some cases, *r*_{e} cannot be made negligible, and some compensation for it is desired. One of the most common schemes is to make I0 track *r*_{e} and cancel its effect, at least approximately. To make *I*_{0} have the TC of *V*_{T}, the simplest scheme is to use a BJT current source implementation of *I*_{0}. The *b-e* junction voltage of the current-source BJT then decreases with temperature, *I*_{0} increases, and decreases *r*_{e}.