Impedance question between a Big Muff stage

[midwayfair]

Let's say I needed to eliminate R12 because I absolutely can't fit it on a layout that I've already made ...

If I double R18 (and change R21 to re-bias), does the feedback loop in Q2 "care" or is everything essentially the same? The impedance is the same, right?

[mgigrigi013]

When you re-bias be care to the feedback in Q3 you are changing!

[midwayfair]

When you re-bias be care to the feedback in Q3 you are changing!

How much does R21 affect the feedback loop though when we're keeping the gain essentially the same after rebiasing and the change in resistance is fairly small?

[snap]

Ehx would have eliminated R12 and others decades ago, if it just were a matter of recalculating a few other values?

[Gus]

You need to find a way to fit it.  Feedback at Q3 lowering it's output resistance and Q2 is an inverting gain stage R15 and R12 set the gain and input resistance to the third stage

[midwayfair]

Feedback at Q3 lowering it's output resistance

? Are you saying that R12 LOWERS the output resistance of Q3? That doesn't make any sense to me.

R15 and R12 set the gain and input resistance to the third stage

And R18 is the output impedance of Q3, which ought to be added to R12 and also divides against R15. This still doesn't explain how adding 10K to R12 is any different than  adding 10K to R18 and adjusting the bias elsewhere unless my understanding of transistors is completely wrong in this instance.

[PRR]

> Are you saying that R12 LOWERS the output resistance of Q3?

No. R17 "at Q3" reduces the impedance at that node.

Use an axial cap, one leg down in the board, the other up in the sky. Stick R12 in the other hole. Twist the C and R sky-leads together, solder, trim.

[midwayfair]

I'm sorry to be stupid, but I honestly cannot understand what is happening here. Gus was talking about R15, which is the negative feedback of Q2, and now PRR is talking about R17, which is the negative feedback of Q3. How does R17 reduce the impedance of Q3's collector? And what is special about R12 that makes it affect the impedance in a way that the collector resistor CAN'T? I just don't see what that R12 is doing except forming a voltage divider with the base resistors.

Also, I did manage to fit it onto the PCB layout. I just really want to know what the heck it's doing still.

[Rob Strand]

How does R17 reduce the impedance of Q3's collector? A

For a "normal" common emitter amplifier the output impedance is (more or less) the value of the collector resistor.  However, in the circuit topology like the Big Muff, the resistor between the Collector and the Base of the stage (for example) R17 provides negative feedback around the stage.   The presence of the negative feedback lowers the output impedance of the stage considerably ie. it is no longer equal to the collectors resistance.  It is not uncommon for the output impedance to be hundreds of ohms on a stage with collector resistors in 10's of kohms.

However ...  if your closed-loop gain (roughly the ratio of R17/R15) is high the feedback doesn't lower the impedance as much as is could (As a side issue, in this example, the presence of the sustain pot adds to the value of R15, which will help keep the output impedance of Q3 low).

This behaviour isn't commonly known to DIY's.


To get back to the main problem why not just stuff R12 in series with C13.   Other alternatives are to mount a through-hole R12 on the back of the PCB.  If that's too tight maybe an SMD resistor on the back of the board.

[typo fix]

[midwayfair]

Thanks, Rob. I understand now, at least somewhat.

EDIT: Is there something you can think of that talks about the collector impedance dropping with collector-feedback biasing? It's not mentioned here and this is pretty thorough:
http://www.allaboutcircuits.com/textbook/semiconductors/chpt-4/biasing-calculations/

[Rob Strand]

No problem.

FYI the 560pF caps actually make the situation more complex.   The output impedance is lower at high frequencies as the caps provide more feedback.

Hfe = 800, Rc = 15k,  Rf = 470k, Rb = 100k, Cf = 560pF, Cin = 100nF

Re=150, Rin = 10k
Zout    6k ohm @ 300Hz, 800 ohm @ 10kHz

Re=150, Rin = 39k
Zout    3.4k ohm @ 300Hz, 360ohm at 10kHz

Varying Re from 100R to 220R causes +/- 20% or so variation is the output impedance .
Lower Re = lower output impedance.

[Rob Strand]

If you have to toss out a resistor, shorting R10 would be fairly benign.
Perhaps change R12 to 11k compensate.

[Gus]

To add some more. 

R17 at the second stage is the feedback/part of the bias for that stage

You need to think about what R12 and R15 do. The gain of the third stage is partly set by R15/R12.  R15 is trying to set the input at the base at 0 ohms it can't because the openloop gain and current available from the  transistor, however it does lower the input resistance at the base

Now if you adjust R12 value down the gain will go up at the third stage and the input of the 3rd stage will load the output of the 2nd more
combine this with a lower output resistance from the 2nd stage and take it to the extreme of removing R12 and what happens?

[PRR]

"If it turns out it's like an onion with millions of layers... then that's the way it is." — Richard Feynman

What it is. Many layers.

The upper limit is R18 10K. But R17 R19 470K:10K NFB action reduces this. But the R19 10K leg also includes the Sustain and Q4 impedances. And the nominal 47:1 ratio is very similar to Q3's forward voltage gain, so the NFB action is not-large. Just this far, Zout may be 1/2 to 1/4 of R18 10K.

But! C12 increases the NFB above 600Hz, to very-large NFB at the top of the audio band. Zout may be a hundred ohms up there.

There is additional low-frequency effect from C5, tho this may be small for our uses.

All that assumes it is "linear". It will be, for very small signals. However the MAIN domain of a Big Muff Pi is OVER-LOADED. Non-linear!

First D3 D4 conduct. This increases NFB substantially. Zout falls to a very low value. (This is why R12 is probably critical for a Muff's sound-- to mask the abrupt change of Q3 Zout.)

I don't know if a Muff's 2nd stage will get there, but at some very BIG signal Q3 is smacked from hard-on to hard-off. When on the Zout will fall to a few hundred ohms. When off there is no NFB action and Zout is almost 10K.

Layers within layers, Bendreth.

With R12, Q2 "sees" 10K to 20K. With-out R12, Q2 sees 100r-10K. Upping R18 from 10K to 20K might give 200r-20K; the low-side is still way lower than the Matthews-approved design. And since Q3's Zout is a large factor in Q2's gain and frequency response, result with R12 omitted (jumped) will probably not give the expected sound.

Dubious argument: if R12 is not needed, why was Matthews spending the extra penny? Any good design, especially high-production in a cash-strapped market, includes a final study "what can we leave out?" All audio companies (except Harman and Bose) go broke; penny-pinching delays that, sometimes for decades. True, the cost of one R12 at E-H's production volume probably won't make a difference; it may be more important to get new products to market before copy-cats than to sweat every resistor. But it hints that R12 may do something more than what a change in R18 would do.

[midwayfair]

Thanks for the thorough explanation -- I'll bookmark this in case the question ever comes up again. And I have a new appreciation for how resilient the original design is to variations.

It also occurs to me that this is why the source Z in the Big Muff schematic in Duncan's Tone Stack calculator is 1K.

I soldered in some resistors on the old layout ... sounds much more like a Muff and isn't just insanity levels of gain. I certainly won't argue with results!

[amz-fx]

It also occurs to me that this is why the source Z in the Big Muff schematic in Duncan's Tone Stack calculator is 1K.

Nope.   It's 1k because when I was persuading him to add it to the tone stack calculator, I sent a graph from Pspice that just happened to have a 1k source and we left it like that.   

Best regards, Jack

[PRR]

> source Z in the Big Muff schematic in Duncan's Tone Stack calculator is 1K.

I eye-ball it as 7K mids down to below 1K in highs "clean", 15K-150r slammed.

DTS was not intended to model overload. That would be incredibly complicated to compute and display. It would be quicker to build and play the darn thing.

As the network is 22K and higher, "1K" is as good a number as any.