Transistor gain vs noise

[John Lyons]

How does noise relate to hfe?
For example: If I have a 2n5089 as an emitter follower/buffer with a gain of 700 hfe.
Will the same name model transistor with a gain of 200 be quieter or noisier theoretically?

And if what about amplifications stages? Assuming the circuit is not sensitive to hfe
(big muff etc) does the extra gain just add noise?

[merlinb]

For a given collector current, higher hfe results in lower current noise, because you have less base current. In general, current noise is the important thing for guitar circuits, so anything you can do to reduce base current is a good thing.

Yes, extra gain adds noise. Well, sort of. Most of the noise comes from the input stage so the extra stages don't really add noise per se, they just amplify whatever noise is already coming from the input stage. But usually they also clip the signal, making it smaller relative to the noise, so you get worse SNR.

[R.G.]

I started to do a reply to this last night, realized I was too foggy to make sense.

Yep, higher hfe makes for lower noise, but it's complicated. There are two components in most noise models for any active device - the current noise and the voltage noise. Current noise in the base is made lower by lower base currents, hence higher hfe is lower noise for that component.

But that's not the whole story. Noise has several mechanisms, and current noise is only one of them. There is also voltage noise from thermal resistances, and in the case of the base region, the base spreading resistance responds this way, as do the base and emitter ohmic resistances. There is excess noise if any, and avalanche/leakage noise which manifests as shot noise. At the low end you run into flicker (1/f) noise. And there is recombination noise from majority/minority charge carriers in the base region. For *well made* transistors, most of these are pushed out of the mid audio band. Early transistors had contamination and problems with packaging and passivation, which led to issues with excess noise; germaniums are an example.

The noise picture is complicated by impedance. Noise depends on source impedance feeding the transistor input, and the bandwidth which you let in and out. In feedback amplifiers, you have to evaluate all of the noise inputs from components around the active device, as well as the device, and then sum them to an input noise as amplified by the stage.

In general, yep, any additional gain amplifies any noise sources at the input and increases noise. Cascaded stages all amplify the input noise of the first stage by the combined cascaded gain, so the input noise of the first stage will nearly always dominate.

[John Lyons]

Thanks guys!
So in general a high gain for Emitter follower = good
and the input stage is the place to watch for excess noise,
got it. 

[SISKO]

Current noise in the base is made lower by lower base currents, hence higher hfe is lower noise for that component.

But isnt it a circular problem? I mean, if you need lower base current, then you would need higher input impedance ( higher resistance in DC). Or is the resistor/impedance noise smaller than the base current noise?

[PRR]

As Merlin and R.G. say: it aint that simple.

> If I have ...an emitter follower/buffer

Noise voltage will "usually" be similar to that of the _next_ stage, because a follower has unity voltage gain, and you'd usually use similar parts. Therefore total noise could be 3db higher.

There are marginal cases where follower can reduce total noise.

And in most guitar work, any sanitary design will give quite low noise.

And often the real advantages of a buffer are worth it.

More important than high hFE is appropriate device current for the source resistance, and then not-low hFE. hFE=20 is low, device current is picky. (And on modern devices, hFE=20 suggests problems in the device, dirty or too-darn-big.) hFE over 100 gives a broad range of near-optimum source resistance.

> 700 hfe.. a gain of 200 be quieter or noisier theoretically?

Tend to be noisier. In practice the diff is slim to none.

[boogietone]

Can't add much to the technical discussion above. But, keep in mind that for practical purposes we are interested in two things: 1) absolute noise floor, which is added to by each component in one way or another,  and 2) signal to noise ratio. Each of these are more or less important at each gain and compression stage.

It would seem that a simple model would say that noise coming from the base and around the base junctions would be multiplied by the gain of transistor while noise due to collector-emitter current would simply be added to the post gain noise floor. Gain though would effect the latter of these since the current is a function of gain and assuming noise is a function of current. The question becomes then which dominates and does that change depending on the "quality" of the transistor and the circuit in which it finds itself.

[PRR]

John, do you know the intrinsic emitter resistance Hie?

For Silicon, using round numbers, 30 ohms at 1mA, inverse to current (300 ohms at 0.1mA, 3 ohms at 10mA,etc).

That's (simplified) the resistance which causes the noise voltage. We want it to be much less than the source resistance. It acts in series with the base-emitter junction.

There is also an equivalent shunt resistance, Rie time hFE. It acts in parallel with the base-emitter junction. We want this to be much greater than the source resistance.

Therefore for 1mA and hFE=400, we want source resistance much greater than 30 ohms and much less than 12,000 ohms.

In most real problems we can't control the source resistance. Guitar pickups evolved for vacuum tubes, where "Hie" is over 1K and "hFE" is "infinite". Optimum source resistance is very-high. Practical issues of winding and cable give 5K at bass/mid and up to 150K in the highs.

An additional factor is the on-board volume pot. If we really cared about noise, we would NOT have this. Yet we always do, which maybe says something about guitar noise tolerance.

With 250K pot the "source resistance" seen by the first amplifier in the upper audio range with pot from half to full is around 100K.

To find an optimum device current, we must first assume an hFE. Say 400. Take square-root, 20. We set Hie (or series noise resistance) at 100K/20= 5K. Since hFE is assumed 400, the shunt noise resistance is 5K*400 or 2,000K.

Adding 5K series to 100K, or 2000K shunt to 100K, or both, gives hardly any increase of noise, half a db.

To get Hie of 5K we set emitter current at (30/5K)mA or 0.006mA or 6uA.

Does anybody do that? Look at Uni-Vibe:
click for more

The biasing is tricky, but Q2 Base must be at low voltage so that Q2 collector is at the 1/4 to 1/3 point that Q3 needs to work split-load. Assume Q2 base at 2V and 16V supply. 14V across 1.2M+100K is 11uA, essentially the same as the 7uA that I derived above (allowing for different assumptions about guitar resistance and device hFE).

(BUT: note that the actual plan has 22K and 47K resistors out front. Considerable level is lost, S/N is well below what-it-could-be. Showing again that a very-lowest-noise result is NOT essential in guitar work.)

10uA is a very small current to drive additional loads. As seen it works near 1Meg in the collector side, so any load must be OTOO 1Meg. UniVibe buffers this with Q2 to get 47K, then Q3 to get (split) 10K output(s).

That's a lot of circuitry, and as R.G. observes, three stages together may be stable on the matchbook simplification but unstable in real implementation with "minor" parasitics. Such 3-stage inputs are rare in guitar. 2-stage or 1-stage inputs will generally want to run the first device at some higher current.

Running at 0.1mA, hIE is 300, and that adds "no" hiss to 100K source. However the shunt resistance is 400*300= 120K, which adds 2.9db hiss to our 100K source.

Assuming we can get hFE=900 is only a slight help. At 0.1mA, 300*900= 180K shunt noise resistance.

Darlington is an obvious thing to try, but Darlington noise is not simple.