Calculating voltage drop

[rhdwave]

Hey all.  I've begun to actually try and learn some basic electricity theory.  A friend of mine who is an electrician gave me a textbook and i've been reading it...My question refers to the axis fuzz schematic:

http://www.diystompboxes.com/pedals/axisfuzz.gif

I've been having some strange readings on the voltages of the transistors.  I originally built one of these for myself and all the readings are correct, the thing is i actually like the way the new one sounds better, the distortion is not as harsh.  So, i'm trying to figure a couple of things out...
First: Why are the values off for the new pedal
Second: What is making the sound of the new pedal more pleasing to my ears

I have checked the voltages where the battery enters the board and have begun to trace through the schematic testing the voltages along the way.  After the 180k resistor near the battery i've noticed a major voltage difference between the two pedals.  Also, there is a voltage difference in what is getting to the base of Q1.  So, i'm assuming the problem or solution resides somewhere in this area. 

My question is that i would like to calculate what the voltage drop should be across the 180k reisistor.  Is it possible to do this without having to figure the total resistance for the entire circuit and the current as well.  The examples in the book i am reading all deal with obviously simpler circuits and how to approach this baffles me.  I am not sure how to deal with the transistors in terms of the calculations and also, as part of the circuit goes to the output, this was confusing me as well. 

So, if anyone can steer me in the right direction, i would be very grateful!

Thanks!!!

[R.G.]

To calculate the voltage across a resistor, you have to know the resistance and the current through it.

Let's see if we can get close to the right answer. First, all capacitors are intended not to conduct DC at all. So we can mentally erase all the caps. That leaves a path from +9V to the 180K, through the 820K to the base of the 2N3906 and from there through the 680K to ground.

We can ignore other things connected across 9V and ground because they cannot (in principle at least) affect the current through this path. This would reduce to one of the simple resistors-in-series problems if it wasn't for that pesky transistor base. If the 2N3906 was not connected at all, then the current in the 180K/820K/680K chain would be 9V/(180K+820K+680K) = 5.35uA.  That makes the voltage across the 180K be 180K*5.35uA = 0.963V. Since this is measured down from 9V, the voltages on the two ends of the 180K are 9V and 8.039.

The key here is to remember that transistors have current gain. That transistor's emitter is in series with a 220 ohm and a 47K to the collector of the second transistor, and from there through a 10K and a 22K to +9V. If the second transistor was completely off (and it won't be) then the first transistor could only pull emitter current through a total of 79K to +9V. The most that could EVER be is 9V/79K = 114uA. In fact, it's a reasonable guess that it would be less than that, maybe half. Then the current into the base of the transistor is less by the gain of the transistor, perhaps 100. So let's say that the base of the transistor is conducting 1/2 uA.

So the base of the transistor is contributing about 0.5uA to the 680K resistor. That would increase the voltage across the 680K by V=680k*0.5uA = 0.34V over what it would otherwise be. So the first suggestion is - ignore it.

Even if you can't ignore it, the effect of that estimated 0.34V is reduced by the 820K, and would only change the voltage at the end of the 180K by the ratio of the resistances - a factor of 180/(180+820) = 0.18 or 0.18*0.34 = 0.0612V. So it looks like it may be a good idea to ignore it. It won't change much.

If you have problems with one of the circuits, look for (a) solder problems, opens and shorts (b) capacitors put in the wrong way for the polarized capacitors and (c) pinout errors on the transistor.

[rhdwave]

RG, Thanks so much for the detailed reply!

It makes things much clearer.  I did a lot of searching online for ways to calculate this w/ the transistors, but could never find anything.  I have checked the entire circuit for continuity, and it's all good.  The thing is that the pedal works and sounds good.  It's just different then the original in terms of the sound.  It doesn't have quite as much gain, but i feel it actually has a more pleasing distortion.  I did an experiment and desoldered the 680K resistor just before the base of Q1.  At first, i just wanted to check to make sure the resistor was good and measured it w/ the DMM.  It was right on, but before replacing it, i tried out the pedal.  It sounded really good i thought.  It really brought the pedal some more life, more gain still not as much as the original pedal, but i could live with it (or my friend can i guess).  At this point i'm really just trying to understand what's creating the difference in the sound. 

So, if you could bear with my beginner electronic mind for a moment...Is the general purpose in this circuit of these resistors to simply regulate the amount of current that is going into the two transistors? Is this what biasing is all about?

Thanks again RG and anyone else that would care to respond!!!

[R.G.]

Is the general purpose in this circuit of these resistors to simply regulate the amount of current that is going into the two transistors?

In a sense, yes. Current and voltage are two sides of the same coin. Most people would think of it as setting the voltage on the base of the first transistor, which then causes the currents that set the operating condition of the second transistor. But it's also correct to think of it as setting the current going into the first transistor, and that causing the same chain of events.

Is this what biasing is all about?

Pretty much - it's about setting up the correct (that is, correct for what you're trying to do, which varies) set of internal conditions for the devices. In a bipolar transistor, it's setting up the right voltage/current for the base. In FETs, it's getting the right gate voltage because FET gates can't eat current, only voltage.

Once you get the voltage on the base/gate/grid correct, you then have to worry about how much signal the biasing network eats as a side effect. In many cases, the biasing network is almost all of the input impedance of the circuit. Lower value resistors make the biasing more rock solid, but also eat more signal and load down the signal source more. It's a balancing act.

[rhdwave]

Thanks again RG! And since i've got your ear here for a moment, lol...Now obviously i didn't design this circuit, so i'm trying to get the voltages going into the base of Q1 to be 'correct' based on what they 'should be' according to the designer (in this case Roger Mayer).  If i was designing my own circuit, what factors would change how much voltage i would want going into that first base.  In other words, how would the sound change with differnt voltages going into that first base?
Also, If one was to simply leave off the second transistor circuit entirely...would this act as a simple booste? With just the gain of the first transistor or would it do something else entirely?

I really appreciate the responses, i feel like i'm gaining a lot of insight finally into how all of this acually works.  So again, any responses are greatly appreciated!!!   Thanks again.

[R.G.]

I wish I had a better answer for you on this one.

This particular circuit is a DC coupled feedback circuit. In the sendup I wrote up for you I only put a limit on the base current of the first transistor rather than calculating it. I ducked the deeper issue because it's a more complicated question.

I'm very rusty on my two transistor compounds, but let me wade through it a bit. I'm going to do the hand-waving explanation rather than the equations.

The base of the 3906 is held at about 3.5V by the input bias network. This forces the emitter to be about 0.6V higher if the transistor is conducting. The collector of the second transistor must be a bit higher than that to get current to flow to the emitter of the first transistor. How much higher?

The current through the 3906 must supply the base current of the 3904, but also it must supply current to the 100K to ground at its collector. A 100K resistor is equal to 10uA per volt across it. We know the 3906 must not be saturated completely, so the collector of the 3906 must be a bit lower than the base of the 3906. How much lower???

Well, it must also be the same amount lower as the base of the 3904, since they're connected. And in turn the 3904 must not be saturated, or it would not pass audio. So the collector of the 3904 must be a bit higher than the emitter of the 3904 to pass audio. Ooops, we're getting circular. We just traversed the internal DC conditions loop.

But we can make some approximations and get closer. Let's guess an operating condition and see if we come close. Let's say that the collector of the 3904 is at 6V. That means that there is 9-6=3V across the 10K and 22K, or a current of 3V/(10K+22K) = 94uA. That same 94 uA (approximately) flows in the 39K emitter resistor, so the emitter sits at 94uA*39K =3.66V. And the base of the 3904 must then be 3.660+0.5V = 4.16V.

That means that 41.6uA flows through the 100K and hence through the 3906. That means that the 47K drops 1.95V, and the collector of the 3904 must be 1.95V higher than the emitter of the 3906, or 3.5V(from the input bias voltage) + 0.6V (Vbe on the 3906) + 1.95 = 6.05V

Honest, I didn't precalculate all this - we just got really close by guessing. I'm a little surprised that my first guess would be within 50mV, too. By starting with some knowns (bias voltage, voltage across a base-emitter, knowledge that a transistor must not be saturated or open for audio) and a guess at how much voltage is across the second transistor, we came very close. If I had guessed 5V for the collector on the NPN first, we'd have found that working back around the loop we'd have been off, and could make a better second guess.

Notice that an important point in how this came out was the Vbe guesses. An unseen factor was ignoring the base currents of the transistors and the unspoken guess that the gain of the transistors was so high as to make the base currents tiny. And I think that along with resistor value tolerances, the variation in transistor gain and Vbe value is what causes the variation in otherwise working versions of this.

So how do the voltages affect the sound?

First of all, this thing has an output that can only swing by a couple of volts peak. The 3904 NPN is heavily constrained by the big emitter resistor for DC conditions, so it bangs into saturation easily. Moving the bias voltage for the 3906 around will affect this a lot. You will get very different sound depending on whether the 3904 bangs into saturation or cutoff first, as these two clipping points sound different. The tone will also change because the sheer size of the output will change. Our ears interpret bigger or smaller sounds as having different tones, whether they really do or not. Lastly, the actual instead of theoretical gain of the two transistors is what makes the AC gain as separate from the DC gain. The AC gain of this thing is huge, but highly dependent on the specific transistors.

That was a long wandering way of saying (a) learn and live by Ohm's law (b) learn what junction voltage drops do (c) make good guesses.

There is a long roundabout simultaneous-equations version of this with a closed form, but it also will include estimates for Vbe and hfe in it to write the equations. I always like the reason-it-out approach better than the equations versions.

[rhdwave]

Again RG, thank you! I have just finished reading the reply and i actually understood a good deal of it.  Some things i need to go back and make sense of in my head.  Anyway you should write a book or something.  I would gladly pay for in depth descriptions and examples of how some of these circuits and components interact and why or in what way changes in their values influence the sound of the effect.  This is invaluable information for people who are new to this or just trying to make sense of the basics.

Thanks again!