voltage gain of a transistor

[lowell]

I know ohm's law Jon. Condescending posts really irk me. You still did not explain how JM came up w/ 2ua BEFORE deciding on a resistance to ground. Maybe it's the way in which he explained it, but it seems that he DERIVED his resistance from knowing Vb (1.7v) and current base to ground. I get the rest of your explanation. It's really this 2ua from base to ground that I'm stuck on.

[Merlinb]

Jon,
That's the thousandth time that I've read that explanation of how transistors work. Obviously I still don't quite get it. As JM has been saying, most explanations of transistors are bad ones. It IS TRUE though that the base/emitter junction (diode) needs to be forward biased to turn the damn things on... so no it's not ONLY current.

You are correct, transistor are voltage controlled devices. The collector current is given by gm*Vbe.
However, for simple audio applications it is often convenient to think of them as current controlled since the actual change in base voltage has to be really tiny (between 0.6-0.7V) to cause the collector current to change fully between zero and saturation. This gives the familiar formula of Ic = Ib*hfe
This is a reasonable approach within the limited range of circuits you get in audio. Nevertheless, hfe is highly variable with temperature and other things, so for critical applications you will find the more accurate voltage controlled model used.
You might like this explanation:
Small Signal Audio Design - Google Books

[lowell]

Thanks Merlin. It's making more and more sense now. I have a question about the Ebers-Moll equation.

Ic=Ies(Vbe/e^vt-1)

vt=thermal voltage=~26mv @ room temperature (25°C)

What is e?

[R.G.]

Base of natural logarithms, 2.718281828...

[lowell]

aaaaahaaaaa...

[lowell]

The BC547C datasheet says Hfe is 420-800. Why is 500 the number you decided upon JM? Finally if I was to try and use a different transistor (just as an exercise) how would I go about deciding on Hfe when all the datasheets seem to give a "range" of Hfe, not an exact #.

[J M Fahey]

Dear Lowell, the key lies in:

I already said that Ib=2uA, so I choose to "waste" another 2uA through the Base to ground resistor.

I'm *designing* to achieve something, not refrying some old vintage circuit and afraid of not using 100K as a plate resistor or 1k5 on the cathode (or 2k7, or 820r, the other "magic" values) and making the Leo or Jim Gods angry.
Now, the question might be: "why did I choose that?" , also: why did I choose B+=24V, Ic=1mA, gain 10x, a BC547C , an Fb of around 50Hz and so on?
Well, what am I trying to achieve?
I'll explain some of these but be certain that there is nothing cast in bronze, there are 1000 ways of doing certain things, all valid. (There's life beyond the 5E3)
1) 24V? :
Most small signal, reasonable low noise transistors stand 25V, a few stand 30 or 40/45V, the 60V and over ones trade heavily beta or noise to achieve that.
Using less, such as 12 (or 9 or 5 V) is reasonable if I only have that available, otherwise I'm losing headroom for nothing.
2) Ic 1mA?:
It lets me use a 10K collector resistor, a nice midrange impedance, neither so low that it eats too much current not too high which rises output impedance too much, making it harder driving the next stage.
3) Gain 10x?= just what you asked for.
I have a possible over 300x on tap, but it's often too much for a single stage, would lower input impedance too much, etc.
Dallas Rangemasters use max. gain, and tame it with a very small input capacitor to turn them into Treble Boosters.
It works, sort of, but it's a poor and noisy solution.
It was used by Clapton,Brian, Richie and Jimi among others, so Mojo sure beats most defects. Oh well.
It's difficult to argue Religion.
4) BC547C?:
I live in Argentina, an "European" area, we follow DIN standards; Siemens, Philips, Telefunken, ST, are revered names, and 90% of what you find in shops, so ....
Besides, it's an *excellent* transistor, cheap and plentiful.
I'm certain that although it's easily available in the US, others may be easier though.
I think Enzo has already posted which his favorite general purpose ones are. (and some "japanese" ones too)
The beast's ON Semiconductor datasheet (there are many others):
http://www.datasheetcatalog.org/data.../128424_DS.pdf
Incidentally, Fig 8, labelled "On voltage), shows that:
COLLECTOR CURRENT IS VOLTAGE CONTROLLED , as in :you apply "x" volts (Base to emitter), and you get "y" milliamps flowing through that collector.
To be more precise: Vbe is NOT "fixed" at 0.6 or 0.65 or 0.7V AT ALL.
That's just a simplification, which works many times, but as all simplifications, starts falling apart if you really dig into it.
One of the most misleading simplifications is the "hydraulic" explanation (electrons in wires = water in tubes), by the way.
Back to Fig. 8 and Vbe, you can easily see that collector current goes from 0.2mA to 200mA when Vbe goes all the way from 0.55V to 0.84V.
Notice that the curve is not horizontal in any point.
For *any* Vbe voltage applied we have a matching unique Ic.
Mmmmhhhh !!! .... I think Tubes behave in a similar way.
Of course, if that varying, voltage controlled current passes through a load resistor, we have a varying voltage, a.k.a. audio signal (in this case).
Being much higher, yet proportional to voltage input, we can talk about voltage gain.
Fig 8's curve is not quite linear?
A typical tube's neither.
EDIT: I chose Hfe(beta)=500 because it's a nice round number within the range and very close to what I actually measure now and then.

[lowell]

"There's life beyond the 5E3" - JM

Haha! ... seriously though, no there isn't.



Again thanks JM. So really to answer my last question regarding how you came up with wasting 2ua is that you knew AHEAD OF TIME that this was going to be the outcome and that it's so small as to be neglected. You were more likely concerned with input impedance thus chose the 820k base-ground resistor. That's how I make sense of it anyway. In any case I think I can actually design a transistor audio amplifier stage with a good amount of confidence and use datasheets to do so. Thanks!