Amplification factor for common emitter amplifier

And there are some real, ohmic resistances too, wire bonds and contact/spreading resistances in the silicon of a real transistor.

All that reduces the gain a bit from the theory.

Already posted the fix. Also > Here are two circuits with identical operating points. Your formula sets

Legg is right.

Vg = Zc / Ze

You have to include the impedance in the emitter.

Your formula is useless and misleading. You normally never run a transistor with the emitter grounded. You need some way to stabilize the bias. Also, there is usually some load on the collector, which you ignore. You could also have transformer coupling or a resonant circuit in the collector, which would produce a low dc resistance and consequently low voltage drop. This would produce low gain in your formula.

Legg's formula includes the impedance on both the collector and emitter, and includes loading due to the following stage and bypassing on the emitter.

Legg's formula can also consider the DC case by omitting the load impedance and emitter bypass. So you can get both the DC gain and high frequency gain.

Your equation is only for DC gain, and ignores the resistance in the emitter. It does not include the load impedance on the collector or degeneration in the emitter. It is useless for real-world circuits.

That's infinite with no emitter resistor, right?

That's trivial. If you assume that the active emitter resistance is only the resistor that you add external to the transistor, that's wrong. The emitter diode has a dynamic resistance that matters, and limits the gain to below infinite.

Merely correct. I can't help what people want to believe.

You normally never run a transistor

Why not? It's done all the time.

Lots of ways to do that. For example, bypass the emitter as you did in your sim.

Also,

Also trivial. Any real signal source drops when you load it. Do that after you calculate the unloaded gain.

You could

There a million ways a smart person can wreck the gain of an amplifier. Actually, a dumb person can do that too.

Dead wrong. It is an estimate of the small-signal (that means AC) gain.

The "resistance in the emitter" is the dynamic impedance of the b-e junction. That's fundamental to understanding transistors.

It does not include the load impedance on the collector or

It's an algebraic result of the actual transistor behavior in one simple stated case. It's merely right.

base

Sure. If you apply that to the bias divider fine, it will further stabilise the stage but will lower input Z. It may even clip off the top of the outp ut if you really want the stability. The lower the Z of the bias the better Re works. I could put you together a stage that has near infinite voltage gain, but has one ohm input Z and 32 megohn output Z. Pretty much useless. (PRETTY MUCH, THERE ARE TIMES...)

In anything near that you don't have much real gain. (if any) It can be use ful but if you get anywhere near that then you want to use a common base st age. In fact a real old time cascode stage would really do it. How much rea l gain does a cascode have ? It has voltage gain coming out of the cracks i n the sky, but real gain is a whole different thing.

Conversely take the typical audio amp. At the output stages with just the d rivers and outputs of course there is gain. But it is current gain, in fact it inherently has negative voltage gain. But there is a stage before that which does the voltage amplification and the output stage which is only cur rent amplification serves to allow the voltage amplifier stage to run into a lighter (higher Z) load.

I know I responded to you and you probably know all about this, but I think you forgot to mention a thing or two. Most of this is for the OP. What I s aid about what you said is to find out if you agree and perhaps start a muc h better argument. (there is an idea I aim to contact you with, but I gotta write it)

Already posted the fix. Also > Here are two circuits with identical operating points. Your formula sets

Legg is right.

Vg = Zc / Ze

You have to include the impedance in the emitter.

Ahmmm....

Sure, the bias needs stabalised...many designs use an emitter resister bypassed with a big cap....taking the resister out of the game.

Some designs use a grounded emitter with a potential divider from collector to base and ground, fixing the output voltage referred to as a Vbe multiplier

Sure... What's your point?

It's a very well known, useful approximation for the maximum gain with a resistive load. That is, the actual gain will always be less.

One can easily add in the effect of emitter resistance by computing Re' = re

• Re,, re=1/(40.IC)

One can also include the effect of base resistance by adding rbb'/hafe to Re'

With a current source load it becomes Va/vt as the maximum voltage, where Va is the early voltage.

I have a tutorial on this here:

Pretty much all hand calculations are of limited value in the real world.

However, today, Spice is the only realistic way to design reliable multi transistor circuits, well for asics anyway...

I'm designing fairly complex analog asics with 10k transistor system level blocks, and I would say out of millions of simulations, I do hand calculations as often as number as the fingers on that hand.

Its just not worth the agro to piss about when there are computers.

Even a diode resister circuit requires some effort to solve...

Id = Vt/R.W(is.R/vt.exp(Vs/Vt).... Where W is the Lambert W function...

-- Kevin Aylward

True. Why don't you try to convince him?

Absolutely nothing. I proposed a circuit that reduces the temperature drift. In the following ASC file, the temperature changes from 25C to 80C. The drift is 50mV vs 854mV, an improvement of a factor of 17.08. Version 4 SHEET 1 1288 680 WIRE 560 -208 288 -208 WIRE 1104 -208 560 -208 WIRE 288 -192 288 -208 WIRE 560 -144 560 -208 WIRE 1104 -144 1104 -208 WIRE 288 -96 288 -112 WIRE 560 -48 560 -64 WIRE 608 -48 560 -48 WIRE 656 -48 608 -48 WIRE 1104 -48 1104 -64 WIRE 1152 -48 1104 -48 WIRE 1200 -48 1152 -48 WIRE 560 -32 560 -48 WIRE 1104 -32 1104 -48 WIRE 320 16 288 16 WIRE 496 16 320 16 WIRE 1008 16 992 16 WIRE 1040 16 1008 16 WIRE 288 32 288 16 WIRE 560 96 560 64 WIRE 624 96 560 96 WIRE 656 96 624 96 WIRE 1104 96 1104 64 WIRE 1168 96 1104 96 WIRE 1248 96 1168 96 WIRE 560 112 560 96 WIRE 1104 112 1104 96 WIRE 1248 112 1248 96 WIRE 288 128 288 112 WIRE 1248 192 1248 176 WIRE 560 224 560 192 WIRE 560 224 288 224 WIRE 1104 224 1104 192 WIRE 1104 224 560 224 WIRE 288 240 288 224 WIRE 288 336 288 320 FLAG 320 16 Vin FLAG 288 128 0 FLAG 608 -48 Q1C FLAG 624 96 Q1E FLAG 288 -96 0 FLAG 288 336 0 FLAG 1152 -48 Q2C FLAG 1168 96 Q2E FLAG 1008 16 Vin FLAG 1248 192 0 SYMBOL npn 496 -32 R0 SYMATTR InstName Q1 SYMATTR Value 2N3904 SYMBOL voltage 288 16 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value SINE(0 0.005 1k) SYMBOL res 544 -160 R0 SYMATTR InstName R1 SYMATTR Value 1k SYMBOL res 544 96 R0 SYMATTR InstName R2 SYMATTR Value 1.856k SYMBOL voltage 288 -208 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V2 SYMATTR Value 10 SYMBOL voltage 288 224 R0 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V3 SYMATTR Value -10 SYMBOL npn 1040 -32 R0 SYMATTR InstName Q2 SYMATTR Value 2N3904 SYMBOL res 1088 -160 R0 SYMATTR InstName R3 SYMATTR Value 1k SYMBOL res 1088 96 R0 SYMATTR InstName R4 SYMATTR Value 1.856k SYMBOL cap 1232 112 R0 SYMATTR InstName C1 SYMATTR Value 1 TEXT 720 -352 Left 2 !.tran 0 10m 0 1u TEXT 720 -384 Left 2 ;'Voltage Gain TEXT 464 288 Left 2 ;Vg = 5.35e-3 / 10e-3 = 0.535 TEXT 1016 288 Left 2 ;Vg = 1.767/ 10e-3 = 176.7 TEXT 552 256 Left 2 ;A TEXT 1096 248 Left 2 ;B

Can you do that with one transistor?

Why not if the hfe can handle it. Low current, small signal, possibly a tra nsistor meant for RF amplification at the front end. High hfe and low Icmax .

So you got say a 33 meg collector resistor and say a 100 meg from collector to base to bias it. No Re at all. The 100 meg is going to clip your top en d you know, but it can work. And don't come crying to me when it is thermal ly unstable. You either find another transistor or heat sink it. Now imagin e putting a heat sink on one that has a maximum Pd of 30mW. But then there are instruments that actually do put certain components in an oven, I shit you not. Like the crystal that controls the frequency of a TV or radio stat ion. They need that by law and it is not cheap.

Yes, you can have a million voltage gain with one transistor and two well c hosen resistors. Stability is a different story.

Now remember you can't just feed this to anything. Lower input Z in subsequ ent stages will just short it out. I you want all that gain, feed it to an FET, infinite input impedance.

You have the first stage as described, a kagillion gain. Then the FET is en ough of a current amplifier, that is with current gain but no voltage gain (but you supplied that) to drive a transistor base, and then subsequently m ore current gain stages to where you can burn the house down by coughing.

se the stage but will lower input Z. It may even clip off the top of the ou tput if you really want the stability. The lower the Z of the bias the bett er Re works. I could put you together a stage that has near infinite voltag e gain, but has one ohm input Z and 32 megohn output Z. Pretty much useless . (PRETTY MUCH, THERE ARE TIMES...)

Can you post the circuit? In LTspice?

Thanks

ransistor meant for RF amplification at the front end. High hfe and low Icm ax.

or to base to bias it. No Re at all. The 100 meg is going to clip your top end you know, but it can work. And don't come crying to me when it is therm ally unstable. You either find another transistor or heat sink it. Now imag ine putting a heat sink on one that has a maximum Pd of 30mW. But then ther e are instruments that actually do put certain components in an oven, I shi t you not. Like the crystal that controls the frequency of a TV or radio st ation. They need that by law and it is not cheap.

chosen resistors. Stability is a different story.

quent stages will just short it out. I you want all that gain, feed it to a n FET, infinite input impedance.

enough of a current amplifier, that is with current gain but no voltage gai n (but you supplied that) to drive a transistor base, and then subsequently more current gain stages to where you can burn the house down by coughing.

When you're done add resonance & pfb for lots more gain.

NT

I don't think so.

That's cute, but the the Gm spec of the LM13700 covers about a 2:1 range. The bias mirror alone may be better.

Once you are willing to buy an opamp, you can make an arbitrarily accurate current mirror.

OK, I have done zero math on this and this is all off it is off the top of my head. It will probably work but with certain transistors and maybe some tweaking... If you want math send a sixpack. But this should give you a bit of an idea of what kind of circuit values you might need.

Version 4 SHEET 1 880 680 WIRE 224 128 144 128 WIRE 384 128 224 128 WIRE 64 144 64 128 WIRE 64 144 0 144 WIRE 64 176 64 144 WIRE 160 176 144 176 WIRE 224 272 224 224 FLAG 224 272 0 FLAG 224 32 0 SYMBOL npn 160 128 R0 SYMATTR InstName Q1 SYMBOL res 208 32 R0 SYMATTR InstName R1 SYMATTR Value 470 meg SYMBOL res 160 112 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R2 SYMATTR Value 4,700 meg SYMBOL res 160 160 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R3 SYMATTR Value 820 meg TEXT -24 144 Left 2 !IN TEXT 384 128 Left 2 !OUT TEXT 208 8 Left 2 ;Vcc

Should work, maybe. It should have a ton of voltage gainbut due to the curr ent loss its power gain is not high, in fact might be less than unity.

And you know you need a really low impedance to feed the thing, and a well buffed high impedance thing to drive with it or it just shorts out the outp ut, it really should feed an FET stage.

Bottom line is that voltage gin does not equal gain. No actually if the inp ut and output Zs are the same then it is. Comes to power gain, which is rea l gain, if the output Z is half the input Z then power gain is twice that o f the voltage gain. If the output Z is twice the input Z then power gain is half the voltage gain.

You cannot ignore Z in a circuit. Tubes came close, they gave you a hell of alot of leeway. In solid state, impedance is almost more important than vo ltage.

Then if you get into frequencies, impedance is now the vector sum of resist ance and reactance. It gets fun, but the math isn't all that hard, really.

Sure, put a high Q tank on it and bias it class C and god will knock on the door trying to buy your sine wave.

I thought we were talking about a stage that can amplify pretty much any old frequency.

Sometimes used in CMOS design, where one has a not bad npn, but no decent pnp but you need a low noise top side current source. The opamp can loop around a pmos with the noise of the npn.

-- Kevin Aylward

One fun circuit uses the V+ supply pin of the opamp as the current output, so it has one amp and two resistors. There is a little Iq error. That circuit can be cascoded too.

Two of those can make the perfect class B signal splitter.