Why are only 3 of 6 single-transistor amplifier configurations useful?

Question

Almost any analog design book or course I have ever seen starts by introducing the three basic single-transistor stages. For example, in a bipolar technology these are the common-emitter, common-base, and common-collector configurations.

For instance, Gray and Hurst's classic book says

Bipolar and MOS transistors are capable of providing useful amplification in three different configurations.

Why is this? Given that there are three readily accessible terminals in each transistor and 3 possible functions to be performed (ac ground, input, output), it follows that there are 6 conceivable configurations. Why are we uninterested in the other 3? Is the answer as simple as "experience has shown that they're not useful" or is this something that should be obvious to me a priori?

Answer 1

We are interested in them, but not as amplifiers.

You've noted the three permutations of common terminal, so that leaves the two permutations (each) of input and output.

So your question reduces to: what happens when we swap input and output?

But I think you can begin to see why this isn't a very interesting question...

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In RF circuit analysis, we express a simple amplifier as a general ("black box") network consisting of two ports. All the waves entering/exiting each port are measured, and the relative amounts of each (incident and reflected, ports 1 and 2) are compiled into a matrix. When this is normalized to a given system impedance (e.g. 50Ω), we call it the s-parameter matrix. There are other equivalent* expressions, but this one is probably the most common in RF work.

*Not quite equivalent, as -- as mentioned, s-params are normalized to a system impedance, but the rest are general and equivalent, expressing some relation of voltage and current, impedance and conductance, or input to output; or the inverses thereof.

The s-parameters can be described thus:

• s11: Ratio of received power from port 1, to power incident upon port 1 (input reflection)
• s21: Ratio of received power from port 2, to power incident upon port 1 (forward amplification)
• s12: Ratio of received power from port 1, to power incident upon port 2 (reverse amplification/transfer, feedback, or isolation)
• s22: Ratio of received power from port 2, to power incident upon port 2 (output reflection)

Swapping input and output of the transistor, and adjusting biasing networks accordingly, simply swaps s11 for s22, and s12 for s21. We have reverse amplification, and forward isolation. If we simply swap the ports around, we end up with the identity transformation -- we get the circuit we started with.

Note: this is an AC equivalent point. Things are different at DC, where the directions of current flow and polarities of voltage matter, independently of (AC) signal level and magnitude,

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is this something that should be obvious to me a priori?

Probably? Maybe? I'm not sure how far you are in your curriculum (or how thorough the material has been -- or how effective the instructors), but it might also be an insight that you simply haven't put together yet.

The combination of factors, for me, are the following; and, approximately where in a normal (as of when I took it) EE curriculum the student might be exposed to it:

• AC steady-state analysis (first year). Basic biasing theory; DC vs. AC circuits, set capacitors to open and inductors to short for DC, vice versa for AC (high-frequency limit).
• Introductory transistors (2nd year I think?). Basic operation. Common building blocks (amplifiers, current sources, etc.). Apply biasing principles to transistors. → Choosing biasing appropriate for the pin(s) after swapping should be a fair move in the above analysis; we chose favorable conditions for every other configuration after all.
• Transmission line theory, E&M (3rd or 4th year?). Hardly any of it, but more just to be aware that we can reduce the voltages and currents in a circuit, to a pair of waves travelling in opposite directions, of given impedance and amplitude. This gives rise to the incident/reflected analysis used in...
• RF network theory (graduate level, or elective?). I choose this route, more just to formalize the expression -- we can measure these things in a less general way of course, and indeed the h-parameters that undergrad students use to model BJTs are in fact a general two-port matrix method, it's just not usually taught that way (or at least, I wasn't, that I recall). Presumably to avoid overloading students who might not've even taken linear algebra at that point yet, or to avoid pinning it as a prerequisite or concurrent course. But, in fact, h-params are one of several general cases of the two-port, which lead directly into general network analysis.

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Didactic semi-aside:

Maybe I'm hitting a nail with a jackhammer here, or maybe I'm showing off my depth/breadth of knowledge for subconscious bragging rights more than giving the simple, well-grounded explanation I imagine it to be. (Take your pick, I suppose; it could be both or neither!) But if nothing else, this is the web of facts which link together in my mind, and when I pluck the strings of this question, I follow them onward into these topics, and find the reasoning quite sound. The question remains, whether you (readers, in general) find this as well motivating.

I could just as well make the point without invoking network theory, and just softball it with perhaps h-params alone -- first defining the h-matrix, showing what transistor parameters correspond (occasionally h-params are given directly, though h_re can be a rare sight), and how it changes under the given permutations.

(Maybe it suffices just to make the permutation point, and not need to justify it with matrices at all!)

I think doing it with h-params would be less convincing, simply because -- sure, whatever, you're packing a bunch of numbers in a matrix, and you swap around some numbers, but so what, of course you did, you swapped numbers to swap numbers -- you know? Well, maybe I'm imagining it would be worse than it is; describing the parameters, what they do, how they relate to real device parameters and characteristics, does a similar thing to the above explanation.

But equally so, the abstractness of network theory likely loses a lot of readers. Perhaps more.

What appeals to me about this explanation, is that: by raising the problem to the absolute highest level of abstraction, we don't need to concern ourselves with resistors, capacitors, transistors, currents, voltages; it's the mathematical perfection of a triangle, and you can rotate and flex that triangle in your fingers and see exactly how it works, all its angles and symmetries. So too, the triviality of the point here, which, I think is just a tiny example of the many beautiful symmetries in EE theory. But just as well, it's hard to ask a student (or the more casual readers) to understand things at such depth, just to make a relatively trivial point, and it becomes more a case of -- take it for granted that this mumbo-jumbo actually makes sense. Which is, again, not a very satisfying proof.

I would at least propose it as a point of encouragement -- there is an abstract beauty to be found here, as well as practical working knowledge to make complex problems tractable; you might not understand it now, you might not understand it several years from now -- but perhaps with the mountain peak revealed occasionally from behind the clouds, you have something to look forward to, as you find your path up along this deep subject.

Answer 2

As you say, in a bipolar technology there are the common-emitter, common-base and common-collector configurations.

Those are the only circuit configurations in which the BJT can be a current amplifier, which is its major application in manufactured circuits.

You say that each BJT terminal can be one of (AC ground, input, output) - but they can't.

Each terminal on a BJT is almost always used as unidirectional for current flow, not as bidirectional. These current flow directions differ for PNP and NPN. They are:

   BJT terminal    PNP   NPN
   Base            out   in
   Emitter         in    out
   Collector       out   in

This leads to the three configurations you keep finding. By volume of BJTs used in circuits, these three current amplifying configurations are used in the vast majority of those circuits, nearly all of them. There were used a lot of amplifiers, radios, control units etc. at very high manufacturing volumes for many decades.

There are uses for BJTs that don't used those terminals for those directions of current but they are in the minority and more obscure. Hence why your books go straight into those three typical configurations, for amplifying current.

Answer 3

As far as amplifiers are concerned, we have three main configurations because the transistor has three nodes (one of the three can be used as a common node for input and output signals).

Besides these basic amplifier applications there are many other useful applications (if I remember well, the late B. Gilbert has listed more than 20).

Answer 4

Why are we uninterested in the other 3? Is the answer as simple as "experience has shown that they're not useful" or is this something that should be obvious to me a priori?

Depending on your education level, maybe this one is on you.

Leaving avalanche mode conditions aside for now . . .

At its heart, a transistor is two diodes. Diodes are semi conductors. In each of the three "basic" configurations, the base-emitter junction is forward biased, and the base-emitter junction forward current makes the magic happen.

In "the other three" configurations, either the base-emitter junction or the collector-emitter path is reverse-biased and cutoff.

Try this. Sketch up a generic circuit for each of the three basic configurations, using a 9 V battery, an NPN transistor, and 3 or 4 resistors for each one. Next, leave the resistors unchanged and try the other transistor connection options in each circuit, write in the node voltages, and see if the current directions allow operation.

I assume that "the other three" configurations you mention do not include diode connections such as tying together the base and collector. The fact that you can tie the base to either the collector or emitter and the part will act as a diode should give some insight.

Answer 5

Transistors (BJT) are voltage-controlled "resistors" (indeed, non-linear but still resistors). Their input (port) is the base-emitter junction and their output (port) is the collector-emitter "junction". So regardless of how the input voltage is applied (to the base, the emitter, or both), there is ultimately only one "true" input voltage applied in parallel to the base-emitter junction. In the output, there is only one "real" quantity - the current, that is controlled by the collector-emitter part connected in series with a resistor acting as a current-to-voltage converter.

From this "amplifier point of view" only the three configurations make sense because they are the only ones where the input voltage is applied to and the output current is taken from the right place.

Answer 6

Because in the 3 other configurations, assuming proper DC biasing and small signal, there is no amplification and we can obtain the same effect with passive components.

I'm coming late with this explanation, there's already that answer.

Answer 7

You don't appear to have allowed for the directional nature of the junctions in a transistor. Three of the function/pin combinations give combinations which are either non-viable or of very limited use.

For instance a NPN transistor with a grounded collector, and positively biased emitter and base is not a generally useful amplifying topology.

Answer 8

The bipolar junction transistor works in the other three configurations too. These are obtained by reversing the roles of the collector and emitter in the three classic configurations.

It works, just not very well.

The geometry and the doping are generally optimized for the emitter to inject carriers into the base, most of which make it through and arrive at the collector. In modern transistors, the emitter is usually small and heavily doped, while the collector is the largest region (usually the substrate), and doped much less. If you use it the other way, the base-collector junction is larger and less sharply defined, with a wide region of spatial charge. If injected from the large, fuzzy collector, much more carriers recombine in the base before they reach the emitter. This simply means much lower amplification (1-2 orders of magnitude). In AC, amification is further reduced by the high cacacity of the base-emitter junction (optimized for a narrow, sharply defined region of spatial charge).

I would like to point out that it's counter-productive to think of the transistor as two diodes back-to-back. It is precisely the failure of the base-emitter junction to work as a diode that gives rise to the transistor effect, because the thin base fails to catch and recombine the vast majority of the charge carriers that enter it. Only one of the two junctions is optimized for this "non-diodey" operation.

MOSFETs are four-terminal devices, and they're bidirectional: the source and drain are usually identical, and interchangeable. The difference comes from the fact that, in three-terminal devices, the source is connected internally to the substrate, so there's no way to bias it usefully if reversed. Power MOSFETs often include a reverse diode between drain and source, so they're even less reversible. But the general MOSFET with a separate substrate terminal is, indeed, reversible.

JFETs are generally bidirectional.