Voltage Feedback biasing in a Fuzz Face

[object88]

Can someone help me understand Voltage Feedback biasing, as used in the Fuzz Face?  I read RG's "The Technology Of The Fuzz Face", and I thought I understood it, until I realized that I didn't get how the input was being biased.  I think what I really don't understand is the whole Thevian equivilant, and what happens when you're in a feedback loop.

So I get how biasing works in a simple emitter follower or common emitter (ala Art Of Electronics pgs. ~70-71).  I sorta kinda understand bootstrapping, maybe, which this seems to resemble in that there's feedback into the base / bias, but really, I don't get it.

If the base of Q2 is specified by the collector on Q1, and the base of Q1 is specified by the emittor on Q2, well, how do we come to an actual value?  How is the 1/2V bias calculated?

Thanks for any help!

[onboard]

Over my head, but I Googled "voltage feedback biasing" out of curiosity. Wouldn'tcha know it - the result at the top of the list is a GEO article.

Go figure :wink:

[Rodolfo]

I was serching for the subject on the forum and i ran into your post. I have your same problem. I already post the same question and got two answers, later Joe Davison deleted his reply, becouse it contained some errors (¿?).
Have you solved the thing?
I searched in the entire web and found "voltage feedback" on op-amps and so on, not a single word about this feedback with two transistors, aside the articles you already know.
I have done a lot of thinking (with my no-particulary-powerfull-brain-left) and come to this:

As the "technology of the fuzz face" states, when there is a signal passing trough the Q1 base, current flow trough Q1 collector-emitter, causing a voltage drop en the base of Q2. So there is less current flowing through Q2 emitter. This causes a voltage drop on Q1 base, reducing the amount of current collector-emitter on the Q1. AND SO WE ARE INTO A DAMM LOOP.

Well, this is wath i think: the circuit with no signal must have a steady state where the currents divide between Q1 Collector-Emitter and Q2 Base-Emitter in a certain proportion, similarly as wolud happen on a current divider made of resistors.

That´s all i can tell you. I wish i could help more.

If you find the answqer, please let me know. You can search for my post, where you have an answer to the same problem. I´m still trying to figure it out.

May Kirchoff be with you!

[R.G.]

I ran into a description of how the thing biases in a very old text book.

The problem with doing a straightforward equations-from-first-principles approach to this thing is that there are no parts in it to make it independent of transistor characteristics, so the equations will be incredibly messy and there will be no way to just drop out the messy terms as being irrelevant compared to things caused by the parts put in to make them irrelevant like many more modern circuits.

Which should not surprise us much - we already know from experience that the thing usually needs trimpots to diddle with whatever the transistors give us.

I'll see if I can find the text. May take a while, all the old texts are still in boxes.

I will admire you a lot if you can do a clean from-first-principles set of equations on this. I burned a lot of time trying to do that.

[brett]

Hi.
Straight off the top of my head....

When you turn a FF on, the base of Q2 is way high, turning Q2 on, and pulling the emitter up from zero to a couple of volts.
Ha! The base of Q1 is now on, which pulls the collector of Q1 (and base of Q2) down.

This will happen until the increasing degree of "off-ness" of Q2 has balanced the degree of "on-ness" of Q1.

Maybe you all knew this before ( :oops: ), but it helped me to think it through. (And please excuse my technical gobbledegook)

To solve this mathematically, at a guess I'd think you'd solve for the limit of 2 differentials descibing the balance of on-ness and off-ness.  But I'm a biologist, not an engineer.

cheers

[petemoore]

There must be thousands of texted entries about FF biasing...that I've read...do I know everything about a FF...not exactly, but after reading every FF entry I saw for years, everything from Piggybacking, Tech of FF, J Davissons calculator to building probably more than 10 of them [and that means about every permutation of FF] certain things matter alot and others matter 'less'.
 The identifier' resistor, the 100k fb resistor, can be larger or smaller [47k to 150k works good and different], the caps should be tuned to taste[s, the transistors should be gain matched [tho throwing in high gain tranny's makes for mongo Fuzz, but less variable'], the Q2R should be adjustable [unless you know what your'e doing], And the 33k works good at 33k-47k, but I've been following the Davisson Calculator for these values depending on Si, Ge, and gains.
 That leaves...the 9v battery...and the gain pot. I tune the gainpot value using a pot in parallel with the gain pot turned all the way up...at a 'certain' oversaturation level, I pull the 'tuning' pot, measure and replace with a fixed resistor.  
 Maybe there's a more scientific way to deduce the FF internal activities and tune accordingly, I haven't heard of it and rely on links and memory to apply known FF tunings.
 Oh ... the 470 ohm or 1k...I used a 1k, then clipped a 1k parallel to it...just to 'see' the difference, I just use 470, FF output is a plenty..

[brett]

As far as general fuzzface stuff goes, I think that the need for a capacitor to bypass the 330/470/1k resistor is as important as anything else (Edit: where Si transistors are used).

[Rodolfo]

Well, i´m a little bit surprised. I thoght the "Voltage Feedback Bias" mathematical aproach wouldn´t be so elusive.

R.G: I´m sorry but i don´t quite understand what means "from-first-principles". I know the words, but i don´t get the expression. I´m from Argentina, you know. What it means?

Bret: Limit and differentials are bad news for me. I guess i must get some math book off the library. Oh well...

Petemoore: Your post its pretty usefull, i´m printing it right away. Still I´m interested in the mathematical aproach. I know maybe i could learn faster skipping this for some time but i just can´t help my intellectual curiosity.

[petemoore]

As far as general fuzzface stuff goes, I think that the need for a capacitor to bypass the 330/470/1k resistor is as important as anything else (Edit: where Si transistors are used).

I would have to agree, I think...the Axis Face Si Phillip Bryant, very nice FF, that's a great place to add a cap, though I find a very small [2n2 or a little bigger] at the input is nice, rolloff here and there in the circuit seems to work well...Q2 B/C is another good place to put a small cap.
 Another thing I use on a FF is high end rolloff knob [in fact in place of a gain knob on the box], because I often like to boost into FF, which increeases high end content or sizzle, I find being able to reduce that is quite useful.
 FF is a good thing because it's sound is extremely variable, and 'tone' is very subjective.

[Transmogrifox]

I, like RG, have burned much time trying to break down and simplify the FF feedback bias circuit mathematically.

I often end up with a logarithm/exponent problem where the best method we have for solving this is the "trial and error" approach where you guess values for variables and compute the other side of the equation, then pick another and keep iterating this process until you reach a reasonable level of precision in your answer.

When all this is said and done, the information is not useful because a different transistor changes the outcome in the circuit so you have to do some tests on the tranny or run a curve tracer on it to determine the constants necessary in the equation--by the time you do that, you were just as well off using a trimpot to adjust it.

You can use a Taylor series to approximate the exponential terms, but using enough terms in the series to get acceptable accuracy in results makes the equations more messy than without.

I somehow think this circuit was designed in close conjunction with the laboratory testing such that the designer could depend on acceptable parameters to mass produce these things with relatively consistent results:  high gain and lots of fuzz.

This is not to discourage you from trying, but it looks simple from the outside looking in.  When you really try to break it down and analyze it at that level, you're in for a real legitimate math problem.

This does not, however, require any differential equations--that is, unless you want to do a transient analysis on the effect of the emitter capacitor when you turn on the power supply :wink:   It is just algebra and logarithms--and the logs are what make it so difficult to resolve into a simplified, yet effective mathematical format.

[Steben]

As far as general fuzzface stuff goes, I think that the need for a capacitor to bypass the 330/470/1k resistor is as important as anything else (Edit: where Si transistors are used).

I would have to agree, I think...the Axis Face Si Phillip Bryant, very nice FF, that's a great place to add a cap, though I find a very small [2n2 or a little bigger] at the input is nice, rolloff here and there in the circuit seems to work well...Q2 B/C is another good place to put a small cap.
 Another thing I use on a FF is high end rolloff knob [in fact in place of a gain knob on the box], because I often like to boost into FF, which increeases high end content or sizzle, I find being able to reduce that is quite useful.
 FF is a good thing because it's sound is extremely variable, and 'tone' is very subjective.

Yet I allways had tone sucking with my non-buffered FF's (even with non-DIY RM classic rockets). Low input impedance... There has never been clean high end (when backing off volume).

[davebungo]

The DC biasing of the circuit is one thing, and usually that is arranged in most circuits so it will be roughly correct for any given transistor of a particular type although some trimming may be needed.  Given the characteristics of the transistors you should be able to come up with an equation which takes these into account including any leakage, temperature and other effects, however I'm not saying it would be easy (as others have also pointed out).

The small signal behaviour is another subject though, and this can be used to understand the feedback mechanism in use but it only analyses the circuit in a linear way so it can't really be used to describe what happens when your signal swing in any part of the circuit is so large that it can no longer be assumed to be linear i.e. once you start to hit the end-stops.  Nevertheless, it is a worth-while exercise - you just have to accept that once the circuit is driven harder it will distort (as you would expect).  You should use small signal transistor models to do this - if I can I will try to work this out but it may take a week or so as I'm no expert.

Any decent electronics book should have a section on small signal transistor models (low frequency and possibly high frequency).  Microelectronics by Grabel and Millman is one to look out for.  If you need the ISBN let me know and I'll post it (I haven't got it with me at work).

[gaussmarkov]

I'm not sure this helps to "understand" voltage feedback biasing
in the Fuzz Face.  I'd appreciate "feedback" anyone has to offer.
Basically what I describe below is some information that comes out
of applying SPICE simulations.  It does inform some of the previous
discussion I've read.  I'm sorry this post is so long.

Following Transmogrifox's suggestion, I tried using SPICE to
model the DC circuit of the Fuzz Face.  I cannot find any
SPICE models for the germanium BJTs that are usually mentioned,
so I had to go with a Si Fuzz Face for this round.  That also
allows me to compare the output of the model with actual measurements
made by Marcelo Tripodi,
the site of calculations mentioned by Joe Davisson.  I am
using Marcelo's abbreviated circuit, without input or output, and
combining two resistors into the single R2 shown there.

First, here's a comparison of the measurements Marcelo made on his
Si Fuzz Face Clone and the output of the SPICE model, which has
two identical PN2222A transistors.  The SPICE model for the PN2222A
comes from SPICE MODELS PAGE. I used 5SPICE for the calculations.

Marcelo's Measurements .... Spice Model Calculations        
Q1PN2222A .. hfe1=122 ..... 130.82
Q2PN2222A .. hfe2=124 ..... 149.91
R1 .......... 23.581K ..... taken as given        
R2 ......... 4.948K ...... taken as given        
R3 ......... 0.981K ...... taken as given        
R4 ......... 99.601K ..... taken as given        
Vcc ......... 8.980V ...... taken as given        
Vc2 ......... 4.490V ...... 4.678V  
Vc1 ......... 1.537V ...... 1.501V  
Vbe1 ........ 0.618V ...... 0.619V  
Vbe2 ........ 0.644V ...... 0.645V  
Ve2 ......... 0.898V ...... 0.856V  
i1 .......... 0.315mA ..... 0.317mA  
i3 .......... 0.915mA ..... 0.873mA  
ib1 ......... 2.560uA ..... 2.380uA

I leave it to others to judge how good this is.  I haven't got the
expertise to judge.  It's interesting to note how Q2, which has the
identical Hfe actually performs at a higher observed Hfe in the
SPICE simulation.  I believe Marcelo rated his transistors before
putting them into the circuit.  I've seen recommendations to put the
higher Hfe in the Q2 slot.  Does this increase the difference in
operating Hfe's?

Also note that the potential difference from base to emitter is
predicted pretty well for the two transistors, and this is for
two different values.  Coincidence?

Second, I explored the relationship between R1 and Vc2 using the
SPICE simulation.  This is what Joe Davisson said was a key feature
for biasing.  I am interested in what sort of functional form would
fit this relationship, given that it's hard to solve for a closed
form relationship.  If anyone wants the raw data, I'll send it to
them (just send me a pm).  The relationship for resistance from 11K
to 49K closely follows

     Vc2 = log(-49.4844 + 8.193833 R1 - 0.05613 R1^2)

where log is the natural logarithm.  The first two digits after the
decimal always agree in a comparison of Vc2 and the predicted value.
For the other components I rounded R2 to 5K, R3 to 1K, and R4 to 100K
(holding them fixed at these values).  Even though this is not the
analytical solution, this shows that a simple functional form can give
excellent results and it suggests what kind of approximations will
work well in an approximate analytical solution.

So, does anyone have SPICE models for an AC128 or an NKT275?  I have
some for other silicon devices, the BC108A/C and BC109B/C, mentioned
by RG in The Technology of the Fuzz Face.

What other components (besides R1) would it be nice to vary in trying
to understand the best approximation for predicting Vc2?

Edit:Because the log-quadratic functional form works so well
for the initial values of Rc2, Re2, and Rbias, maybe a useful next
step would be to see whether one can track the changes in the coefficients
as these initial values change?

[Arno van der Heijden]

That also allows me to compare the output of the model with actual measurements made by Marcelo Tripodi,
the site of calculations mentioned by Joe Davisson.  

Very interesting site!!

[gaussmarkov]

Having worked on this some more, I have a few suggestions/questions.  When it comes to understanding the DC analysis of the fuzz face, I guess I don't know what that means.     Even if the equations were linear, or nonlinear but solvable, so what?  Having worked through it, I agree with Transmogrifox that if you want to experiment then breadboard and/or SPICE the circuit.  Breadboarding has the additional value of letting you hear what is happening, too.  

For back-of-the-envelope calculations, I wonder if the SPICE simulations that I have done offer some simple refinements to the approximations already suggested by Transmogrifox, Joe Davisson, and Marcelo Tripodi.  I have not worked out how important these are to the calc's.  Maybe the approximation error swamps the refinements.

For Si BJT's setting Vbe1 and Vbe2 about 0.03V apart (Vbe1<Vbe2) seems reliable.  Vbe1 is usually around 0.62.  I have run simulations for the 2N2222A, BC109C, and 2N3904 (all NPN).

Prespecifying Hfe seems like the weakest link because it's not constant.  Also Hfe may be hard to know in advance.  Transmogrifox suggested 170 for the 2N3904 while a SPICE simulation says Hfe1 is 112 and Hfe2 is 134 (Rc1=25K, Rc2=5K, Re2=1K, Rbias=100K, Vc2=4.53V).  It's probably better to go with Transmogrifox's value.  However, given a value for Hfe, note that there is a pretty consistent difference of about 20 between Hfe1 and Hfe2.  So why not add that in?  Try Hfe1=150 and Hfe2=170 for the 2N3904.

Why not include a voltage for Vc1 as well?  In addition to setting Vc2 at 4.5V, is it helpful to set Vc1 at 1.5V=Vcc/6?  That's the usual outcome for the resistor values above.  This reduces the prespecified resistors by one.  It seems pretty widespread to keep Rbias at 100K and Re2 at 1K, germanium or silicon.  If we also prespecify Vc1 then we can compute both Rc1 and Rc2.[/list:u]
As always, comments are welcome.  I learn a lot from them.  Cheers!

[Joe Davisson]

In the Blackfire, the non-linearity of one transistor counteracts the other, as long as Q1's current drive is low. This works because the 2nd transistor "inverses" the non-linearity of the 1st, cancelling it out to a degree.

By this logic, some of the non-linearity in the Fuzz-Face would be also be negated, although to a lesser degree. So a source-follower coupled to a voltage amplifier helps to make an amplifier more linear. In the Fuzz-Face, there isn't really a source-follower, but it's a similar effect since the bias comes from Q2's non-inverted end.

Just some thoughts...