Fun Question - Most gain from a single Transistor?

[Bill Mountain]

What single transistor gain stage would have the most possible gain at 9V?

My thoughts are a Darlington can get pretty loud but so can MOSFET.  I'm not talking about clean gain.  Just which circuit has the capability to produce the most.

[R.G.]

Do you mean the correct sense of "gain" as in the setup with the highest output multiple of the input appearing at its output, or the incorrect but widely used "gain" meaning most distortion?

One technical problem with your question is that the setups with the highest gain (in the technical sense) require quite large collector or drain resistors and effectively no load on the output. Any loading on the output appears in parallel with the collector/drain resistor and lowers any voltage gain the transistor does. The input source impedance and output load impedance are always part of the circuit, but most beginners don't know this yet.

[Gargaman]

I'm a begginer and the language barriers are toruble. 'Load', 'drives the load', makes me cry!

..setups with the highest gain (in the technical sense) require quite large collector or drain resistors and effectively no load on the output. Any loading on the output appears in parallel with the collector/drain resistor and lowers any voltage gain the transistor does...

Do you mean circuit parts after the transistor and before output cap?

[Bill Mountain]

As with most of my threads the first post usually doesn't make much sense.

I meant true gain with the highest output.  I understand every circuit is a series of compromises.  Just wondering what some people have come up with that produced a lot of volume.  Clean or otherwise.  No particular project in mind just hoping for a theoretical discussion.

If a circuit needs specific accommodations to work to its fullest then please just assume low source impedance and high load impedance.

Thanks!

Do you mean the correct sense of "gain" as in the setup with the highest output multiple of the input appearing at its output, or the incorrect but widely used "gain" meaning most distortion?

One technical problem with your question is that the setups with the highest gain (in the technical sense) require quite large collector or drain resistors and effectively no load on the output. Any loading on the output appears in parallel with the collector/drain resistor and lowers any voltage gain the transistor does. The input source impedance and output load impedance are always part of the circuit, but most beginners don't know this yet.

[antonis]

I meant true gain with the highest output.

Maybe I don't understand the term "true gain" but if you mean the highest undistorted signal for a given power supply and ignoring in & out losses, then the answer is ANYONE...

[midwayfair]

[EDIT: I know there are a couple places where I conflate current gain and voltage gain in this post, so see RG's a few below to see how to deal with the current amplification of individual transistors.]

GAIN or GAIN FACTOR? These are actually two different ways to answer this question.

A transistor's hFE is the upper limit of its current gain factor.

The supply voltage is the upper limit of the output signal size, peak to peak, in volts. More voltage gain is also more gain.

The collector (or drain, but who are we kidding -- a BJT has more gain than a MOSFET and certainly more than a FET) bias determines the center point of the output wave swing, so assuming maximum gain is both sides of the wave, then ~ half supply is the correct bias.

The input signal needs to have as little loading as possible, so let's go with a 100M base bias resistor tied to a Vb point, so we can adjust the base voltage. We can use another 100M for the output.

As gain goes up, our input resistance drops. So our instrument matters. Hotter pickups will produce more output signal, but we're only concerned about GAIN, which the pickups can't provide. So let's go with low output pickups, as low as we can get. (Possibly lipstick pickups from an old Dano?) We could cheat and use a low-impedance source, like an acoustic guitar with a built-in preamp, and assume a trivial impedance, but I feel like that definitely uses another transistor. We could bypass the restriction of "transistor" with a transformer DI box, maybe ...

Anyway, the most gain will be from a transistor with

Extremely high HFE
Running on the highest voltage you can run it on
Its emitter grounded
A nearly-perfectly high-impedance receiver
As low as possible source impedance

"Extremely high HFE" could mean about 1,500 from something like an MPSA18 if you test a whole bunch of them and get lucky. An MPSA14, off the top of my head, is something like up to 20,000 hFE ... but a Darlington is two transistors, so if we're being super pedantic, we can't use a Darlington. I'm not aware of any single transistor that's higher gain than the MPSA18.

But its maximum collector-emitter voltage is 45. Very very high to be sure, but there are transistors that go much higher. Power transistors can handle over a hundred ... sometimes a couple hundred volts! But you'll find as you go up the voltage capability of transistors that their hFE is lower. I don't know the reason for that.

So this leaves you with a new way to evaluate it:

The transistor with the highest possible operating voltage that still has enough hFE to amplify the source signal's peak voltage to its supply voltage. A transistor that can run on a 200V supply with only 50hFE won't get your 1V guitar signal to 200V. A transistor running on 100V with 100hFE can.

Why do I think I just overthought this?

You're probably building a guitar pedal running on 9V. The answer is an MPSA18 with a grounded emitter, a 100K or so collector resistor, a big base-collector resistor, a big volume pot value, and the base bias adjusted to get 4.5V at the collector. You probably will not notice any difference with any other transistor above a couple hundred hFE in that same set-up.

[R.G.]

I'm a begginer and the language barriers are toruble. 'Load', 'drives the load', makes me cry!
[...]
Do you mean circuit parts after the transistor and before output cap?

I very much respect your efforts to do something technical in a language that's not your native language.

"Load" is used as a technical word, and it has a very specific meaning in electronics. It means some circuit or component outside the circuit being described. The electronic load "eats" some of the signal produced by the circuit, making the circuit work harder or maybe changing how the circuit works.

For example, imagine that *you* are the circuit, and your "output signal" is how fast you walk or run. You can do this at some speed, whatever you're able to do. But if we "load" you with a rope attached to a large rock, your walking and running speed is reduced by this loading.

If we take an electric guitar as a circuit, then the load that is attached to the guitar is the combination of the connecting cord, and the input of the amplifier or effect connected to the chord. If the load is too great (that is, it eats the signal current from the guitar), the guitar's internal inductive nature causes more loss of treble frequencies than bass frequencies. This happens with loads of a resistance smaller than about 1M, so we are careful to keep effects input loading at roughly 1M or higher in most cases to avoid losing this treble signal.

For what I was describing, I meant "load" to be anything attached to the output of the transistor *after* the output cap. And my comment was that there is always an output load if the signal is used in any way. No matter how you use the signal, it loads down the transistor.

For simple transistor circuits, the higher the collector or drain resistor, the higher the electrical voltage gain. So adding an external load after the output cap will lower the gain that the circuit has otherwise.

[midwayfair]

For example, imagine that *you* are the circuit, and your "output signal" is how fast you walk or run. You can do this at some speed, whatever you're able to do. But if we "load" you with a rope attached to a large rock, your walking and running speed is reduced by this loading.

[antonis]

Nice decal for a buffer pedal, Jon...!!

[Gargaman]

Yep, that's me, Jon

[R.G.]

I meant true gain with the highest output.  I understand every circuit is a series of compromises.  Just wondering what some people have come up with that produced a lot of volume.  Clean or otherwise.  No particular project in mind just hoping for a theoretical discussion.
If a circuit needs specific accommodations to work to its fullest then please just assume low source impedance and high load impedance.

True gain in the technical sense, is the output voltage swing divided by the input voltage swing. So if you want the highest output, this translates to an output that is closest to the full power supply of 9V. And this in turn means that the output amplitude is fixed at 9V minus whatever saturation losses happen in the transistor and any emitter or source resistors.

True gain goes *down* when the input gets bigger than the amount needed to just start distorting at the output; If you get a lot of distortion from the output being near the power rails, then the input is providing a bigger signal than needed to drive the output that big, and so the effective gain is lower than it would have been with a smaller input.

Volume and/or signal size is not really connected to gain at all. The size of output signal that can be made by one transistor is limited by how big the power supply voltage is and how close to the power (and ground) voltages the transistor output can go. For a single transistor, the output can go fully to the 9V power supply, pulled up to there by the collector (/drain) resistor when the transistor shuts off all current flow. How low the collector (/drain) can go depends on how big the collector (/drain) resistor is, and whether the transistor can pull down the current allowed by the full power supply voltage through that collector/drain resistor, and what voltage exists across the transistor at that current.

As an example, assume we have a 2N3904 transistor with a 10K collector resistor to +9V, with its emitter grounded. When the transistor is shut off entirely, the collector sits at +9V.  If we imagine that the transistor is a metal-contact switch, then when the switch is closed, a current no bigger than 9V/10K = 900uA can flow. We know the transistor cannot go to 0V from collector to emitter no matter how hard we drive it, so the actual current is somewhat less than 900uA, and the voltage across the transistor never goes to 0.

Fairchild's data sheet for the 2N3904 shows that a typical device of that part number can pull 1ma down to about 55mV. So for a 9V power supply and a 10K load resistor, a 2N3904 cannot produce an output swing bigger than 9V -55mV = 8.945V peak to peak no matter what else happens.

A "higher gain" transistor like the MPSA13 darlington illustrates this issue another way. Darlingtons have much higher current gain than non-darlingtons, but they cannot saturate to as low a voltage. The MPSA13 data sheet shows that it really can't go much lower than about 400mV between collector and emitter (this is largely a result of the two-transistor internal structure), so while it has a much higher current gain, it produces *less* output swing.

So the bottom line here is that output "volume" and gain are not necessarily even coupled together. They mean very different things.  Did you want the biggest output swing from a single transistor, or the highest gain?

[Bill Mountain]

Once again I am humbled by everyone's knowledge and willingness to help out.  Thanks for all of the detail.  This is a great discussion.

I guess I was just looking for people's preferences in transistor designs with high output swing (both clean and dirty).  Could we call it is high Voltage Gain or is that not the same thing either?  Maybe there were some biasing tricks I didn't know or maybe one device is much better suited than others.

Like I said, I have no particular circuit in mind but since this is DIYstompboxes then obviously I was looking for ideas that would work in a pedal application.

[GibsonGM]

Just to put this out there - the other answers are very comprehensive! - but when 'cranking up the gain', one also wants to keep in mind the possibility of introducing instability into the design...I have heard (HAM radio handbooks?) that <20 to 25dB is really what one wants to stick to for a single gain stage.   Over that, you increase your risk of oscillation due to parasitics and them feeding back, being amplified and there ya go.

So, it's not always the best thing to try to wring every last dB from a stage...sometimes, a 2nd stage is the way to go!  Plus - to get the extra bump from one stage that would be difficult can be so easily done, in spades, by adding another with the benefit of additional tone shaping and stability issues....

This might work better by suggesting some real world voltage values, Bill?  It's a good question, everyone can learn something from this discussion, I bet!   Many designs already give us the 'best' gain output, depending on what you want to do with it...

[antonis]

As R.G. said, we have to make clear if we are talking about max output swing or max gain...

IMHO, in no case we can have more gain than 45dB (practically less than 40dB) from a signle stage transistor amp powered at 9V...
(depending also on signal frequency, of course..)

But, as Sir Mike suggested, it should be quite intertesting to deal with some actual values...

[R.G.]

Good comment, Mike. That was in fact one of the items of advice from my circuits course - shoot for a gain of about 10 max if you want to have the stage gain be reliable and have the bias point and other characteristics be stable and independent of device properties.

The course had a few big lessons. One was that device properties are variable as bought from the manufacturer, and on top of that, the properties drift. Another was that you use feedback to trade "excess" gain for stability and predictability.

I've been avoiding answering the OP's original question. The real answer is that you can usually get infinite gain from a single transistor - that it, it produces an output from zero input by oscillating. Sometimes you want that, but not often. You can get gains of 2000-3000 from a "normal" NPN if you set it up just right, but "just right" usually involves current source loading and wide variation with temperature and other environmental conditions, so it's more of a party stunt than a useful design technique. Also, Bill seemed more interested in bigger output than actual gain, which is orthogonal to the question of gain.

[PRR]

> the most possible gain

Voltage gain or Current gain?

Why "one transistor"? Are they costing you $17 each?? (I remember when they did.)

Since we usually look-at Voltage, your Darlington is pointless. Who needs current gain when you have set NO limit to source impedance? I recall early amplifiers with hFE around 5 (for $17) giving pretty good voltage gain but the input was not far from a short-circuit.

> at 9V?

Is that limit even relevant?

For RESISTOR-loaded stages, yes. The maximum voltage gain is not-quite Vcc/30mV, around 300. However at this bias the maximum clean output is about zero. Say 1/10th of Vcc, or 1V. So max clean input is 3mV.

Which means "ANY" stage-audio level will be past-clean and distorted.

If biased for max output level, the gain is about half, 150, "clean" output may approach 3V, the max "clean" input is about 20mV. However "clean" is just no gross clipping; the THD will exceed 20%.

BTW: for resistor-loaded devices in this universe, that is about the limit. Shockley has details, but voltage influences current just-so-much, and modern clean Silicon BJTs hew very close to the fundamental limit.

Still not enough? Study '741 and similar chip-amps. The middle stage is "one" transistor, plus a current-source load (another transistor), a buffer on the output (often 2 more transistors), and generally a buffer at the input (guess what?) to ease the strain on the first stage. This gives voltage gain of about Mu/2, where Mu is analogous to the Mu Amplification Factor of a vacuum tube. But where a tube has Mu of 2 to 100 (800 for some pentodes), any modern clean BJT has Mu over 1,000, and often in the range of 5,000. Yes, gain >1,000 in "one stage", but the stage is 4 or more transistors.

Voltage gain is NOT the problem in audio. Just add a few tubes (whatever), you can have too-much gain before you know it. Using Mike's Gv=17 stages, just four stages is voltage gain of 83,000; five stages is 1,400,000; 24,000,000. Even if universal hiss were as low as 0.1uV, that's over 2V of hiss at the output.

Radio-astronomers get that far down in the hiss (a little more hiss here than there gives clues about cosmic structure). In Audio we are allergic to hiss, and don't want anywhere NEAR that level.

Radio is different, but in Audio we often want *controls*. And we rarely want gain of more than 10 or 100 between controls. So jonesing for obscene gain in one stage is just wrong.

If you WANT distortion... You probably do not want to raise universal hiss to the level of your clipped signal. In guitar work that suggests gain less than 1,000 (1mV input hiss makes 1V output hiss, which is probably too much). And there's more flavor in multi-stage distortion chains. Gain of 20*20 (400) with some tone and gain tweak between stages is more likely more musical.