Designing circuits for a given range of gain or for maximum stability?

[Thecomedian]

In most instances, the decision that is made is to make the circuit so it works fine as long as the transistor's gain is just high enough.

I guess that in some ways the answer is that it is more difficult to design circuits around a specific transistor, but that idea misses the point of design philosophy. Good design is to make circuits not be picky or need lots of tweaking to work.

I'm think there's a reason that there's different values of hFE for different species of transistors, from power transistors to small signal, and for families of resistors within each species, such as 2n2222 variants and such, right?

Is the intention to design with specific voltages and currents in mind, and then use the highest gain transistor within a family of transistors that have the general volt/current/frequency behaviors you want?

if you build a circuit for a specific function, do you want the resistors in the circuit to be of much higher values than the internal resistance of the transistor, or do you want the transistor to be of near equal resistance, as long as the volt/current limits are observed? I would imagine the latter makes the circuit more "sensitive" to individual transistors while the former makes the circuit less sensitive. Is that correct?

A maximum stability circuit would allow any gain of transistor, but the gains themselves would be probably pretty low because you'd design the circuit so that it doesn't have a lot of oomph, which would keep the circuit from being unstable given variations in gain across individual transistors (I have managed to build one such circuit in spice), while a more 'efficient' circuit might be designed to push as much gain as possible given a range of gains in a transistor family?

[Digital Larry]

Not sure what you mean by "unstable".  To me that means that the circuit oscillates.

The way I learned transistor circuit design is the way you state it.  You circuit has some needs for current, voltage and frequency limits.  That's what you use to start your device selection.  If you're designing a medium gain circuit you pick a high gain transistor and then the voltage gain is determined by the resistors, which you can specify with 1% tolerance if you think that's what you need.  This type of engineering starts off by deriving an exact, but complicated, equation for the voltage gain. Then they say, "well, 1/99 is pretty close to 1/100, so let's just call it 1/100". 

After awhile you tend to forget that these things are approximations.  I spent lots of time analyzing multi-stage transistor amplifiers with vast amounts of open-loop gain that was all tossed out when you applied lots of negative feedback.  Gain came down but frequency response flattened out and in general the circuit behaved itself and didn't swear in church.  A wide variety of transistors would have been fine in that application.

I'm glad that somebody questioned this, either on purpose or by accident, because the end result (amplifiers with specific intentional distortion characteristics) are SO MUCH MORE INTERESTING!!!!  At least for guitar.

Audio is a pretty non-challenging application for transistors from almost all points of view (we'll ignore power amps for now).  I was always surprised there were so many type of transistors!  2N2222 or 2N3904 probably cover 95% of possible needs for low level signal amplification and switching.

Now when you're talking FUZZ, it's a whole different story.  The devices were not specifically designed to sound that way, but somebody discovered that they did, and over time this came to be desirable.  This part of the story, where physics, psychoacoustics, and psychology intersect, is quite fascinating to me.  But I digress.

When you connect your transistor's emitter directly to ground (e.g. many fuzz designs), you maximize the impact of that transistor's particular parameters on the behavior of the circuit.  There's no negative feedback helping to keep things under control.   It's funny that the first stage of a grounded emitter fuzz is chosen for a relatively small beta, even though the circuit configuration maximizes gain.  So, high gain is not really the goal of the fuzz first stage.  Rather, it is to maximize the effect that "going around the corner" of the Vbe-Ic curve has on your guitar signal's SHAPE.  If that curve had a sharp corner on it you would probably not like the result!  But it's nice and smooth and it causes distortion even at low signal levels.

With a normally biased common emitter amplifier, the operating point is well away from that curve which gives high gain and low distortion.  Sounds clean unless you slam it into the rails by overloading it.

Regarding the ratio of circuit resistors to transistors, you want (e.g.) the current going through the base-bias resistors to be quite a bit larger than the base current, so that fluctuations in the base current don't change the operating point.

I probably didn't exactly answer all your questions, sorry!

[PRR]

> I'm think there's a reason that there's different values of hFE

Price/Profit.

You bake a tray of cookies. Some come out crispier than others.

You bake a tray of transistors. Some come out hFE=20, others hFE=1000 (and possibly unusably low breakdown voltage).

Designers prefer not to have to cover a w-i-d-e range of hFE.

But they usually like "a lot".

So the hFE=20-50 get sold for a penny, hFE=50-100 for 2 cents, hFE=100-200 for a dime, hFE=200-400 for 13 cents. Maybe under a series of related JEDEC numbers, but there's also a large spec-contract (or "private number") market.

Note (I think I said this before?) that two low-gain stages gives more gain than one high-gain stage. Any time you can't meet your goal by throwing darts at one transistor, you should be thinking pairs/triples.

[Thecomedian]

Okay, so could be considered down to "personal preference"?

I think what I mean by unstable is that if you pick a hFE that is much  too low, the circuit wouldn't behave as intended, and vice versa with hFE too high, such as clipping with too much hFE or other unwanted complications.

I'm trying to come up with a simple one sentence explanation for how to build a circuit that is not dependent on hFE of the transistor to function, but you make a good point about Fuzz Q1 = low hFE sounds better, although from that perspective, it's about achieving a very specific distortion/clip function, and the more "hFE independent" Fuzz face would probably have some forms of negative biasing or other resistor/caps placed on Q1 to "stabilize" a wide range of hFE to make the circuit "sound correct" with a decent range of transistor differences as long as they all came from within the same family.

I think I'm starting to understand that gain/mA is an important factor. It seems like there's an important required voltage for vCE to Current at the Collector in order to maximize the effectiveness of specific transistors, and this maximum effectiveness changes per different type of transistor, even when the transistor itself doesn't vary that much from other families with similar maximum voltage/current ratings.

This is just what I'm going by off data sheets, so a 2n3904 has 100-300 gain if Ic = 10mA and Vce = 1, while getting 100-300 gain out of the 2n4401 transistor requires Ic = 150mA and Vce = 1. Both of these "appear similar" with their gains, and with their maximum VcbO's and VceO's, yet from the data sheet it looks as though one will only "shine" in a much higher current application.

Can anyone else confirm that this is a sound theory?

[Digital Larry]

I think what I mean by unstable is that if you pick a hFE that is much  too low, the circuit wouldn't behave as intended, and vice versa with hFE too high, such as clipping with too much hFE or other unwanted complications.

I'm trying to come up with a simple one sentence explanation for how to build a circuit that is not dependent on hFE of the transistor to function, but you make a good point about Fuzz Q1 = low hFE sounds better, although from that perspective, it's about achieving a very specific distortion/clip function, and the more "hFE independent" Fuzz face would probably have some forms of negative biasing or other resistor/caps placed on Q1 to "stabilize" a wide range of hFE to make the circuit "sound correct" with a decent range of transistor differences as long as they all came from within the same family.

Sorry, I'm not someone "else"   but I may be later. There!

Transistors should always behave as "intended" - that is, as intended by "God" or whoever it is you presume to be in charge of the laws of physics.  It's just that the complexity of the circuit model decreases when you have high gain and negative feedback.  The approximation (where you can ignore the contribution of base current to emitter current) is less valid with lower gain but you can still calculate and predict it.

Using negative feedback (as in a resistor emitter in stage 1 of a fuzz face) will certainly give you more predictable gain, at the expense of compressing the range over which the exponential curve https://coefs.uncc.edu/dlsharer/files/2012/04/C4.pdf is active.  For a fuzz, you probably WANT to ride that curve, not suppress it.

[amptramp]

Not sure what you mean by "unstable".  To me that means that the circuit oscillates.

Transistor characteristics are notoriously dependent on temperature and stability here may mean constant characteristics over temperature.  If you build a circuit with no emitter resistor for feedback and tune it using various biasing resistors for room temperature, you would have to vary the bias to get the same effect over temperature and transistors themselves have different gains at different temperatures (usually higher at higher temperatures).  Many fuzzes operate in a portion of their gain curve where thermal effects are pronounced because the fuzz effect requires the transistor to be operating at a specific portion of a bias / gain setting and this is sensitive to temperature.

[Digital Larry]

Many fuzzes operate in a portion of their gain curve where thermal effects are pronounced because the fuzz effect requires the transistor to be operating at a specific portion of a bias / gain setting and this is sensitive to temperature.

Fair enough!

[PRR]

> a 2n3904 has 100-300 gain if Ic = 10mA and Vce = 1, while getting 100-300 gain out of the 2n4401 transistor requires Ic = 150mA and Vce = 1

2N4401 is an "interesting" choice for a small-signal high impedance first-stage. '4401 is a big device, maybe 10 times the die-area of a '3904. Like using a 3/4" breaker-wrench to tighten a jack-nut (maybe not THAT extreme). And in some ideal world, '4401 could cost 10 times as much as '3904. (In this world, package is 90% of the cost and the same both ways; in DIY quantity the overhead and picking costs are as much as the actual part cost, so '4401 and '3904 cost the same.)

And interesting because '4401 _is_ used in preamp first-stages: in microphone preamps which need near-theoretical hiss from 200 ohm sources.

Interesting also that you used Vce=1V. Yes, that's what most of the '4401 specs show; and yes, that's about where a FuzzFace's Q1 lives. Usually you'd run at least a few volts. Depending on transistor, hFE falls when Vce is very low.

> while getting 100-300 gain out of the 2n4401 transistor requires Ic = 150mA and Vce = 1

The 0.1mA-10mA numbers on the '4401 sheet are, as said, Minimums. Actually more like "reject" numbers. I doubt you could ever find a quality-made (no eBay deals) '4401 with such low hFE at low current.

Look on this '4401 sheet, page 6, Fig 15, hFE curves. There's not a lot of fall-off from 150mA to 1mA. And I think, with modern processes, this old spec is pessimistic. hFE falls-off due to leakage defects, modern processes don't fall off much over several decades of current.

In the FuzzFace, Q1 current is *stable*, being nearly 9V divided by Q1 collector resistor. Where Q1 hFE matters is in the drop in Q1 Base resistor, which adds to the voltage forced at Q2 Emitter resistor. A low-hFE part has high base resistor drop, high Q2 emitter voltage, large Q2 current, and may slam Q2's Collector as low as it can go.

[Thecomedian]

oh, well 2n3904 are .02$ and 2n4401 are .05$ from tayda, so I thought I'd get some. I didn't know they had such a big size difference for the die, because they both come in a TO-92.