How to calculate gain on an EHX LPB-1 Circuit (Common Emitter Amplifier, no cap)

[bushidov]

Hi All,

Thanks again for the explanations for the input impedance calculations for the LPB-1. (https://www.diystompboxes.com/smfforum/index.php?topic=123934.0) This is really helping me understand single transistor audio applications. I have one more question of understanding: the calculation for voltage gain.

Using the same reference schematic:


I know some sites that simply say, "oh, just use collector resistor over emitter resistor" which would just be R4 / R3 or:
10,000 / 390 = 25.64

Making a voltage gain of 25.64, or 28-ish dB. This sound about right, but when I look at ElectroSmash's explanation of the Range Master, which is a similar circuit (but uses a Germanium PNP transistor) it states voltage gain is:
Voltage Gain = gm (transconductance) x Resistance of Collector
Also stating the emitter resistor is excluded because of the bypassing capacitor, which the LPB-1 lacks.

I guess this leads to my next couple of questions.
1. In an un-bypassed Common Emitter Amplifier like the LBP-1, voltage gain is just Collector Resistance over Emitter Resistance?
2. If number 1 is true, what happens when the emitter is just straight shunted to ground, because that would be collector resistance divided by 0, which I wouldn't think one can do?
3. In a circuit similar to an LPB-1, why do we not use a 2N3904? I know it doesn't have as much "gain" as a 2N5088, but if the voltage gain is determined by the collector and emitter resistors, I don't see how changing out the transistor would matter much in this particular application. I have a feeling I am missing something crucial here.

Help me oh guru's of the DIYStompBoxes forum!

[swamphorn]

You can say that

A_V = R_C * g_m

and

A_V = - R_C / R_E

are approximately equivalent because g_m (the ratio between input voltage and output current) for a common emitter amplifier is close to -1 / R_E. It is actually slightly smaller because of the additional equivalent small-signal resistance of the base emitter junction r_π which is usually in the tens of ohms, but depends on the current across the junction.

• That is approximately correct. In reality this gain depends on β and r_π but it is good enough for most purposes.
• When the emitter is shunted to ground the gain is limited by r_π.
• The input impedance of a common-emitter amplifier (ignoring biasing network) is approximately equal to β * R_E. A transistor with higher gain will have higher input impedance.

[bushidov]

Thanks for answering. This is helping me out a lot.

That is approximately correct. In reality this gain depends on β and rπ but it is good enough for most purposes.

How is the voltage gain dependent on the β? And where on the datasheet of the transistor is the correct β to pull from? I've usually been told to pull the minimum value for β to be safe. Also, what is "rπ"?

Sorry for sounding like a noob (probably because in a lot of ways, I am).

[PRR]

> what happens when the emitter is just straight shunted to ground, because that would be collector resistance divided by 0, which I wouldn't think one can do?

There is no such thing as "ZERO" resistance. There is always some resistance. (Superconductors are different and not convenient for stage use.)

The emitter resistance of a BJT transistor is 26 Ohms at 1mA, 260 Ohms at 0.1mA, etc.

If you really have "grounded emitter", the Input Resistance is likely to be very very low for pedal chains. This is where hFE may matter. At 1mA, re is 26r, times hFE of 100 is 2.6k, which is real low compared to typical 10k-200k guitar impedance.

[Rob Strand]

You need to read some stuff about small-signal models of transistors.   It's hard to get all the details from fragments in posts.

How is the voltage gain dependent on the β?

How to interpret that only gets into confusing details.   If you keep the collector current IC constant then the gain stays constant.   However, if you keep IE constant then the gain is proportional to  alpha = β/(β+1).
[EDIT: I you keep the circuit the same and vary only β then the collector current will change
and that will change re, gm, and rpi and change the gain.]

And where on the datasheet of the transistor is the correct β to pull from?

β is essentially the same as hFE.   In the old thread I mentioned how to get hFE from the tabulated data and the graphs.

I've usually been told to pull the minimum value for β to be safe.

That's not really good thing to follow blindly.

In reality there is a range of  hFE values that causes a corresponding:
- range of bias currents
- range of gains
- range of input impedances.

Condensing the ranges to single numbers by only looking at the minimum hFE isn't always helpful.   It is likely to give you the case with least current IC, highest collector voltage,  lowest gain, lowest input impedance.    For the input impedance you are normally concerned with the lowest input impedance.

When designing a circuit you don't design *at* the minimum hFE, you design it so with the range of hFE's the input impedance, gain, collector voltage all sit around the "middle" as tightly as possible.     The minimum hFE case will be driving factor behind choosing the resistors for the DC divider to the base.

A design without an RE  will generally show a wider variability in gain, input impedance and collector DC voltage.  RE helps make things constant by watering down the effect of varying hFE.

Also, what is "rπ"?

rpi is the input impedance looking into the base of a transistor *when the emitter is grounded*.
rpi is related to re from rpi =  (β+1)*re

rpi comes form the Hybrid-pi model
https://en.wikipedia.org/wiki/Hybrid-pi_model

re comes from the T-model.    There's many models, they are all equivalent just some are more convenient than others.  In fact the h from hFE  comes from the h-parameter model!!!

Another thing that comes in the small details is 'ro'  it's a resistance that appears across C and E and is caused by the Early effect.

https://en.wikipedia.org/wiki/Early_effect


If you want to keep all the fine-details in transistor calculation is can get laborious with only small improvements in accuracy.   For example we often treat alpha = 1, IC = IE,   rpi  = beta * re as rough approximations, knowing fully well they are not 100% correct.     You only pull out the real stuff when you know it matters.

[swamphorn]

And really, when it comes down to it, β or h_fe isn't a parameter that exists in any ideal sense except in the small signal model. Transistors aren't really current-controlled current sources, but rather voltage-controlled voltage sources scaling with the exponential of the V_BE. A transistor without an emitter resistor is highly nonlinear and the only reason we have the - R_C / R_E abstraction is because the emitter resistor linearizes transistor through feedback (in the same way that op amps have a voltage gain in the hundreds of thousands and feedback linearizes them).

[bushidov]

There is no such thing as "ZERO" resistance. There is always some resistance. (Superconductors are different and not convenient for stage use.)

Yeah, I am aware that there isn't such a thing as 0 resistance. I just didn't know where the new calculation of that value would come from, but I see the emitter resistance values now. Thanks!

Also, thanks Rob and Swamphorn for again setting me straight. I probably should have went to school for this, or at least hooked up with a dude that I could bounce questions to, on the regular. But it's just a hobby for me, so that unfortunately never happened.

You need to read some stuff about small-signal models of transistors.

What would be some good reads for this, Rob? Also, how often would this apply to guitar pedal circuits? Any good examples?

[swamphorn]

...
I probably should have went to school for this ... What would be some good reads for this[?]
...

I didn't--I just read a lot and do a lot of experimentation in circuit simulators. An excellent book on electronics in general is The Art of Electronics¹.

¹ https://www.pearl-hifi.com/06_Lit_Archive/14_Books_Tech_Papers/Horowitz-Hill/The_Art_of_Electronics.pdf

[Rob Strand]

What would be some good reads for this, Rob? Also, how often would this apply to guitar pedal circuits? Any good examples?

It all boils down to what problem you want to solve.   When a problem comes up you need the right hammer to hit it and without the background in a field it's hard to find that hammer in the noise of the internet.

This is a general problem with electronics.    Unless you are really keen to study this stuff you would be best digging into problems when they come up but being aware that might need more digging than you expected.

For example in this thread you wanted to know the input impedance of a transistor circuit.  From that you needed to be able to read the datasheet into, calculate DC bias point, then do calculations based on small signal models.   So that seemed to be a simple question bring up a whole lot of background junk you need to understand.    Also there's the rough answer and the accurate answer to the question.

It's always good to have a few books for reference even if you don't read them.   The internet can be good but honestly the information can be very fragmented, that's OK if you know what you are looking for, but it's a real pain when you want to learn something new.  Books tend to have a story which holds the ideas together in one place.  Use the internet to fill in the blanks or to help you understand specific points.

So I'd recommend Sedra & Smith "Microelectronic circuits" for transistor stuff and  Horowitz & Hill "The Art of Electronics" for general electronics.

As for on-line books on transistors, this book is OK but it is fairly formal,

https://archive.org/details/TransistorCircuitAnalysis/page/n55/mode/2up

There's a few more books in this old post as well,
https://www.diystompboxes.com/smfforum/index.php?topic=119315.msg1112782

The GE Transistor Manual has some good stuff in it without being too theoretical.

[antonis]

Lust a quick reference, Erik..



P.S.
All the above Gain formulas are considered for unloaded outputs..
In any case of load value comparable with Rc, the last should be replaced by Rc//Rload..

Also, for a mind-trouble free approximation of Output impedance, just consider the value of Rc..
(Collector resistance V_Early/I_Collector could be safely ignored..)

[bushidov]

To Rob Strand and Swamphorn, checking out those books. My background is IT and network engineering, but am also aware that schooling is nice, but years of actual experience works out better. I have only been plinking with pedal electronics for 3 or so years, but before that was doing more microcontroller and macrocontroller stuffs in C. Again, no degree there, but a bit of coding experience. Analog electronics is more of a new world for me, so I do still need some good jumping on points. Thanks again for this.

As of Antonia, holy crap, that's what I was looking for. Thanks for that.

[antonis]

As of Antonia,

You're the third one who calls me with my feminine name in a month or so..
(may it's time to alter my habbits..)

P.S.
Finding what you were looking shouldn't make you lazier, should it..?? 

[Rob Strand]

You're the third one who calls me with my feminine name

You can blame the querty keyboard.  At least in Italian the 'o' and 'a' are far apart.