Let's talk about the Jordan Bosstone. An odd one...

[Groovenut]

Imma throw some gasoline on the fire and say Q2 is a DC connected buffer (emitter follower) using Q1s collector voltage for bias.

[Rob Strand]

Imma throw some gasoline on the fire and say Q2 is a DC connected buffer (emitter follower) using Q1s collector voltage for bias.

It's kind of that.   That view would make the effective collector resistance of Q1 (hfe+1) * RE.

However,  the resistor RB between the Base and Emitter of Q2 takes some of the gain away so you end-up with the impedance looking into the RB +Q2 as, 

      Zin = (hfe + 1)  RE RB / (RB + Rpi)

which is less than (hfe+1) * RE.

Rpi is Q2's hybrid-pi resistance.   We can simplify a bit by realizing Rpi depends on the Q2's collector bias current.  The collector current is set by the bias point voltage across RE , ie. I_RE = (9-VE)/RE.   The collector current is about 84% of I_RE because the bias current through RB (=VBE/RB) steals some of the RE current.   If you crunch the numbers you end up with Rpi  approximately 1.8 * RE.

So that means,

            Zin  = (hfe + 1) RE RB / (RB + 1.8 RE)

If we now choose RB = RE as per the circuit (the 18k's)

          Zin = (hfe + 1) RE / 2.8

So the presence of RB  reduces the gain by a factor of 1/2.8 from the straight DC connected buffer view.

Here's an AC coupled version,  (R2 on this schematic has no equivalent on the Boss Tone)
http://www.nutsvolts.com/uploads/wygwam/NV_0903_Marston_FIG19.jpg
From,
http://www.nutsvolts.com/magazine/article/bipolar_transistor_cookbook_part_3
(bit more here http://www.nutsvolts.com/magazine/article/bipolar_transistor_cookbook_part_2)

[PRR]

> The common form is like this

That also is CE-CE. Q2's input is just Vr4, B to E.

> the collector of Q1 shows *all* of the gain.

Because it bootstraps from Q2. But the input to Q2 is just the ~~20mV at Q2's B-E port.

[Rob Strand]

That also is CE-CE. Q2's input is just Vr4, B to E.

Sure, all transistors, independent of the circuit configuration, are transconductance devices.  So they all have an input between B and E.

transconductance  doesn't mean CE.   CE and CC are special cases.

When you use the term CE amplifier  the inputs *and* outputs of the circuit must use the "E" as the common ground reference; that's why it's called *Common* Emitter.   The concept of gain only means something with that constraint.  Where there are external input and output connections these have a pre-defined ground node.  You are not free to choose a different ground node if you want to call the connection a CE amplifier.   If you have two CE amplifiers the emitters must share the same "Common" ground (the power rail obviously being treated as ground for ac signals as well.).     Only then can you multiple the gains of each stage to get the overall gain.  If they don't share a common ground then one or none of those stages is allowed to be called a CE amplifier and the gains don't multiply.  Sure, they are still a connection of transconductance amplfiers but they are not a cascade of two CE amplifiers.

For the case of a one transistor Colpitts oscillator there are no external connections so  we are free to move the ground node to E.

I can give two examples where the problem is clear.

1) A CC amplifier ie a buffer.    The gain is 1 (well just under).  We can measure the input and output voltages referenced to ground, which is the collector.  The reason we call this CC is *because* C is the common ground connection.

Suppose we have a 9V rail and a RE=10k and the output is biased to 4.5V  then the transistor's small signal re is approximately 60 ohms.   If we take the view that this is a CE amplifier, with the ground at E, the gain ~ 10k/60 ~170 from the input between B & E and the output between C and E.   *BUT* because the external connections have their grounds referenced to C and the input to output gain is 1 not 170.

2) Now consider the case of connecting two CC amplifier in series.    Here the gain is still 1.  If we view one of these as a CE amplifier we would choose one of the E's as the ground node.   The first issue is the E is not the ground node for the input and output signals but say we ignore that.  The E of the first stage is different from the second stage.  There's no way we can draw the circuit  to look like two CE amplifier in cascade and so we don't see a gain of 170*170 = 28900.    If we chose the E of the other stage as ground we still get the same problem.   Each individual amplifier might have a gain of 170 from BE to CE but it is not correct to conclude that the overall gain from the input signal to output signal perspective is the product of these the individual CE gains.   

If there we no external connections, like in an oscillator, we are only allowed to redefine one of the E's to be ground.   We cannot choose one E then the other E as the ground as separate cases and compute the product of the gains.

3) I could give a third example of a CE amplifier follow by a buffer but the argument is the same as (2).

[antonis]

When you use the term CE amplifier  the inputs *and* outputs of the circuit must use the "E" as the common ground reference; that's why it's called *Common* Emitter.   The concept of gain only means something with that constraint.  Where there are external input and output connections these have a pre-defined ground node.  You are not free to choose a different ground node if you want to call the connection a CE amplifier.

Correct me if I'm wrong, Rob but that only stands for grounded Emitter CE amp..
(i.e. not in case of Emitter degenerated amp w/o Emitter by-pass cap..)

Unless you refer to "ground" as the point standing to the greatest extend from Vcc (something like orientation of JFET's Source pin ..) but in such a case it should be possible to exist some "different" value GNDs..

[Rob Strand]

Correct me if I'm wrong, Rob but that only stands for grounded Emitter CE amp..
(i.e. not in case of Emitter degenerated amp w/o Emitter by-pass cap..)

Yes you are correct.    I was yacking about the high gain case.  It makes the main point easier to get through.   The degenerated case is the same idea (since RE just adds onto re and reduces the transconductance) but then you have to keep saying "or the ground side of the emitter resistor".

[antonis]

OK, now...
(gasoline jerrycan holder seeking for matchbook owner..)

Despite its designation, does Q2 "add" gain or not..?? 

[rutabaga bob]

Being more of a nuts-and-bolts guy, let me sneak in here to ask if adding the 68pF B to C of Q1 is the cure for the noise issue(s)?  I put together a layout for this recently, and am glad to have run across this thread.  Larry

[Fancy Lime]

Being more of a nuts-and-bolts guy, let me sneak in here to ask if adding the 68pF B to C of Q1 is the cure for the noise issue(s)?  I put together a layout for this recently, and am glad to have run across this thread.  Larry

Almost. If you look at the last schematic I posted on this thread you can see a 3n9 cap (C6) across the diodes. This C6 is necessary at minimum settings of the Tone control to stop some bizarre low-frequency oscillations at high Gain / high Impact settings, which may or may not be a breadboard-specific problem due to parasitic capacitances and crosstalk between neighboring tracks. But even without a tone control, a small cap across clipping diodes is often a good idea to keep the clipping musical and not overly harsh and it also helps keep high-frequency noise down. That aside, the 68p cap across B-C of Q1 kills all oscillation tendencies in my breadboard unit (which for this beast may or may not mean that it will do the same for your build but it's a starting point). 68p is a bit on the large side and actually cuts of at about 4.2kHz. I could not here a difference through the fuzz even at minimum gain settings without the clipping diodes with a bass. If you intend to feed a Tele into this, 47p (6kHz) or 33p (8.6kHz) may be more suitable, I just did not have mica caps with those values and I have not jet tried ceramics. Ceramics are probably fine, I was just going for a "lowest possible noise" version and ceramic caps are supposedly "noisy" and microphonic. Supposedly. Or allegedly, which seems to be the Word of 2017.

Cheers,
Andy

[rutabaga bob]

Thanks!  I was planning to do a 'regular' version to start.  Cheers!

[Fancy Lime]

Hi Larry,

the original version is awesome as it is but I would most certainly encourage you to breadboard this thing and try some of the extra bells and whistles. Makes this by far the most versatile fuzz pedal I know of and is just soooooo much fun to play around with. There are settings that sound like a pretty convincing tube amp emulator. Thats not the point of this pedal at all, just goes to show how insanely versatile it is for such a simple circuit.

Have fun,
Andy

[Rob Strand]

Despite its designation, does Q2 "add" gain or not..??

No it's just a buffer (so gain = 0.9xxx ~ 1.0) .   The signal at the base pretty much identical to the signal at the emitter.

Putting the finer arguments aside, here's my summary of the key points,
- Q2 acts a buffer.   The signal at the Q2's base is roughly equal to that at the Q2's emitter.
- The collector load for Q1, which determines the gain of Q1, is roughly RE (the emitter resistor of Q2) times the gain of Q2; as Groovenut mentioned.  However it's actually less than that due to the presence of RB (the base-emitter resistor of Q2), roughly half;  see my response to Groovenut.
- RB sets the bias current of Q1 to a sensible value.   IC of Q1 = VBE of Q2  / RB.   If RB wasn't there the collector current of Q1 would be very small.
- The bias voltage at the output is set by the 2x560k's and the 150k.
==================================
We can take things one step further.  The re of Q1 is determined by IC of Q1,

         re1   =   VT  / (VBE / RB)     = RB * (VT/VBE) ;    where VT = 26mV and VBE ~ 0.65V

The gain of Q1 is then (CE amplifier gain)

      gain = collector load of Q1  /   re1

The collector load of Q1 is the "Zin" I gave before

       Zin = (hfe + 1) RE RB / (RB + 1.8 RE)             ; hfe = gain of Q2

So
       gain = (hfe + 1) (VBE/VT)  RE / (RB + 1.8 RE)

If RE = RB then

       gain = (hfe + 1) (VBE/VT)  ( 1/2.8 )

              =  (0.65/0.026) * ( 1/2.8 ) * (hfe + 1)

              =  8.9 * (hfe + 1)

So when RE = RB, the gain is roughly 9 times the hfe of Q2.   
Which is 60dB to 70dB.

The actual gain is a bit less because input impedance of Q1 loads the pickup.

The gain of a CE amp running at a 4.5V collector voltage is  CE_gain = (4.5/VT)  = (4.5 / 0.026) = 170 or 45dB.
If we had a straight buffer after it the gain would still be 45dB. 

So the tricky connection of the Boss Tone gives you an extra 20dB gain.

[sergiomr706]

Exactly Andy, i was playing with mine, modified as per jimi photon, and with a epi sheraton and 5watt epi, i was getting some electric mud alike tones, not that i play that good, but sound was there. Impressive

[PRR]

> For the case of a one transistor Colpitts oscillator there are no external connections so  we are free to move the ground node to E.

It is not about "ground". Transistor does not know ground from a hole in the dirt.

It is about what is "common" to the input and output *loops*.

First-- we may simply be whipping both sides of the same dead horse, and denying the other's whippage.

Second-- that drawing is all bent up. Let's draw it out clearer.


Nothing is changed topologically. It may be mildly clearer that Q1's output appears only as a floating voltage source (my)R127. Q1's intrinsic collector impedance is infinite (about 2Meg), so both ends of R127 can float to any voltage. This is constrained by the top of R127 being tied to Q2 E. R127's voltage appears directly across Q2 B-E.

Q2 is also perverse in that the usual sequence of battery and resistor has the battery and resistor swapped. I think Broskie refers to "chain of pearls"(?), that you can slide these things around and the *loop* still works the same.

I marked-up where Q2's In and Out loops come together. The "common" is the Emitter.

For self-gratification I plotted the gain vs. frequency curves, for Q1 B-E, Q2 B-E, and Q2's load resistor. Oddly the 50pFd has about no effect. While the CE-CE is prone to oscillate at unity-gain, here we are far from unity gain. Also the two transistors are at very different currents, and their working fTs are about a decade apart (Q1 6MHz, Q2 60MHz). The 50p may be "a good idea" which is not needed.


The gain of Q1 is about 10, which we would have expected from Shockley. The gain of Q2 is near 80, again validating Shockley. Total gain is near 750.

For comparison, I fotochopped-in the connection to make Q2 work as a follower, while keeping DC currents the same. Gain of Q1 rises to 170, Q2 now works unity gain, total 170. However you account this, the BossTone has about 4X the gain that we would expect from Q2 being unity gain.

I do not know why it bumps at ~400Hz; I assume the two poles through the DC feedback network. I threw-in a source impedance (there are no infinitely strong audio sources) and get significant fall-off above 3KHz, much of this right at Q1 Base. There is no real sign of a 10MHz bump, the usual trouble with a Sziklai (which this is, except no overall NFB).

Coming around to your side of the horse: yes, this can be studied as a bootstrap. And wow, it comes to the same answers (math is funny like that). I feel the CE-CE analysis is more direct and insightful. I know you are a very sharp thinker and if you still disagree, oh well.

[Fancy Lime]

As the saying goes: "The only major difference between magic and science/engineering is understanding how it works." I start to understand why the Bosstone in particular is surrounded by a misty aura of magic. I wonder how this thing was first designed. Seems hard to imagine that the designer came up with this on a piece of paper, thinking it was an obvious solution and then no-one ever again though the same way. Or did they just accidentally stick an PNP where an NPN should have gone and found it worked and went on refining from there? The California version is a whole lot more conventional, and when you take that, replace the NPN Q2 with a PNP, ditch the cap between the stages and the n-feedback resistor of Q2, you arrive at a topology very similar to the Nashville version.

But apart from historical musings: It makes sense to me that "commonality of loops" should be the decisive factor for terminology. Although the way I had it explained to me was: The terminal, which is not the input and not the output is "common" to both. Therefore, if the input is the Base and the output is taken off the Emitter, it is a Common Collector. Which also seems to make sense. I also learned that (simplified and always assuming B is the input) the Emitter output gives us current gain (at ~voltage unity) and the Collector gives us voltage gain. Making a CC a buffer and a CE a voltage gain stage after the above mentioned naming scheme. Can someone clarify? Also, if the loops are the decisive factor, what makes and what breaks a loop? Working backwards from Paul's last post it seems that rails and active elements break a loop, correct or not?

Thanks,
Andy

[antonis]

The gain of a CE amp running at a 4.5V collector voltage is  CE_gain = (4.5/VT)  = (4.5 / 0.026) = 170 or 45dB.

Or 180 (half a db higher), if we take VT=25mV (which, IMHO, is closer to reality 'cause 26mV are considered for 20^oC working temperarure..) confirming the rule-of-thumb for maximum Gain of a CE(grounded & unloaded) amp, biased at V_CC/2, being 20 times V_CC.. 

P.S.
Part of my previous post had to do with putting on fire with gasoline (which, I think, worked well..  ) and part of it for checking if Q2 arrangement is set to play some "active load" role..

But, different circuit analysis points of view don't have to be identical to be both correct.. 

[rutabaga bob]

Andy...
  Doesn't that .0039uF cap across the output cut an awful lot of high end?  That's 3900pF...the stuff I've seen before is in the 150 - 220pF range.  Just asking...

[Fancy Lime]

Hi Larry,

I wouldn't say it cuts an awful lot of high end, just a bit of awful high end Kidding aside, a cap in this position is not really part of a "proper" R-C circuit and therefore does not form a normal low pass unless you put a resistor before it because the only resistance before it is the output impedance of Q2, which seems to be rather small (but at this point in the thread I hardly know what's what anymore when it comes to them dang transistors). That is why the Stupidly Wonderful Tone Control works really well in this circuit. When the 47n cap C7 is shifted all the way to the input of the Tone pot, it cuts almost no treble, shifted to the output, it forms an R-C circuit with the (at first parts of and then the full) 5k resistance of the pot. The 3n9 cap is mostly there for killing oscillations, I cannot really hear a difference when I take it out or put it back in (in the settings where it does not oscillate anyway). That being said, try smaller values if you like, it will probably work. 3n9 was simply the first thing I happened to stick in there and it worked exactly as I hoped so I did not fiddle with it. But I'm pretty sure this is not a critical value.

Cheers,
Andy

[Rob Strand]

First-- we may simply be whipping both sides of the same dead horse, and denying the other's whippage.

Thanks for putting the response together.
What you have done there is a little different  to what I thought you meant before.
I understand what you have done here 100%.  I've no disagreement.
In fact I've used that idea many times before.

For your analysis (case A) the output of the first stage, and the input of the second stage is
defined as vb2-ve2.

         gain1A    =  (vb2 - ve2) / vin    = 10    ; first stage
         gain2A    =   vout / (vb2 - ve2) =  80   ; second stage
         gainA        = gain1A * gain2A    =  vout/vin

When we calculate the overall gain the internal voltage (vb2 - ve2) cancels out.

For my analysis (case B)  the output of the first stage, and the input of the second stage is
defined as vb2 (referenced to ground).

         gain1B    =  vb2 / vin     = 800     ; first stage    (I actually got  about 900 but 800 is OK for the argument)
         gain2B    =   vout / vb2  = 1.0     ; second stage
         gainB        = gain1B * gain2B    =  vout/vin

When we calculate the overall gain the internal voltage vb2 cancels out.

Obviously the overall gain agrees gainA  = gainB.

However if we want to ask the questions: What is the gain of the first stage? and what is the gain of the second stage?  We end-up with a dilemma  because your first stage gain is small and my first stage gain is large.
The dilemma obviously arises because of the different definitions of what the output voltage of the first stage is.

Suppose we try to answer these questions by measurement.  We take a CRO and measure the input voltage, the collector voltage of Q1 and the output voltage, then calculate the gains of the first and second stages.

The numbers would match my case B values.   That doesn't mean the case A values are wrong.  It's just that the definition of the case A  gains don't match how we *normally* consider gain to be defined.   

If I chose to measure the voltage  (vb2 - ve2) and compute the gains from that then we would end-up with the case A gains.   The thing is we don't normally consider the gains measured like that.   (There are cases where you *have* to measure gains like that as it has no other meaning.)

We can ask the circuit what it thinks the gain of Q1 is by adding a capacitor, say Cf = 33pF, between the collector and base of Q1.    We then look at the input capacitance of Q1 and see what it is, alternative we could add 10k series resistance and measure the -3dB point and deduce the input capacitance.   The Miller effect will multiply this capacitance by the gain of the first stage (Q1),  so

      Cin   = (gain1-1)  * Cf

From Cin and Cf we can find what the circuit sees as gain1.

If we do this what we find is Cin corresponds to the large gain of gain1B  not the smaller gain of gain1A.

The analysis of case A can be used to derive gain1B.   We simply divide the total gain gainA by 1, the gain of the output buffer, and use that value for gain1.   Which is in fact identical to gain1B!

Coming around to your side of the horse: yes, this can be studied as a bootstrap. And wow, it comes to the same answers (math is funny like that). I feel the CE-CE analysis is more direct and insightful. I know you are a very sharp thinker and if you still disagree, oh well.

There's nothing wrong with your analysis.  I have no disagreement.    I even agree that the method is often easier for calculations.  I use different methods depending of what I want to know.   The *only* disagreement, and it's not even a disagreement, is the definitions of gains in each case is different and in your case it's not what we normally use when we measure the gain of a stage.  For analysis we don't care what internal variables are, they are just an ends to means.

[Rob Strand]

Or 180 (half a db higher), if we take VT=25mV (which, IMHO, is closer to reality 'cause 26mV are considered for 20oC working temperarure..) confirming the rule-of-thumb for maximum Gain of a CE(grounded & unloaded) amp, biased at VCC/2, being 20 times VCC.. 

For an office I think it's 25.5mV, I often use 26mV because it's between that and the 300K value PSPICE defaults to.

There's more fine grain problems with that circuit the 'ro' value of the transistor Q1 has an effect on the gain, maybe 10%.  If you look at Ic1/vbe1  it doesn't agree with the gm value based on the Q1's collector current as some output current is lost through ro.

But, different circuit analysis points of view don't have to be identical to be both correct..

Indeed!