Maintaining a Vbe Multiplier's bias value

[Jon Kirwan]

I think this fits in sci.electronics.design, not .basics.

I'd like to consider the Vbe multiplier often used in audio
amplifiers to maintain a bias voltage for the output stage.
The purpose is to better mitigate against ripple in the
unregulated power supply rails and against the the VAS
voltage output resulting from amplified signal voltages.

(The only active device under consideration is a BJT, though.
No JFETs or MOSFETS or opamps or other ICs.)

The basic starting form for a Vbe multiplier is shown in Fig.
1 and the bias voltage output is indicated there. Assume Q1
is thermally coupled in some magic way, for now, in just the
right way so that if the current through the Vbe multiplier
were perfectly stable, that the bias voltage would track just
as needed (The 'Eg' of Q1 is exactly what's needed for the
output stage's temperature tracking in some nice way and the
values of R1 and R2 are set correctly and the thermal
coupling and location is somehow where it needs to be.) The
focus is on the Vbe multiplier's variation of bias in the
face of changes in sourcing current at the top of Fig. 1.

: +V
: |
: resistor or
: current source
: |
: ,---+---,
: | |
: \ |
: / R2 |
: \ +-----> upper quadrant
: / | ^
: | | |
: | |/c Q1 BIAS
: +-----| VOLTAGE
: | |>e |
: \ | |
: / R1 | v
: \ +-----> lower quadrant
: / |
: | |
: '---+---'
: |
: VAS ---'
:
: FIGURE 1

If I use a resistor as the load for the VAS, it's obvious to
me that the Vbe multiplier will need to cope with varying
currents. But even if I use a BJT (or two) to make a current
source sitting above the Vbe multiplier, it's still not going
to hold entirely still with +V ripple and with varying VAS
drive voltages. That variation will ultimately manifest
itself in a varying Vbe bias voltage. That will change the
operating point for the output stage.

If it is class-A, I suppose it doesn't matter that much. But
I don't want to be forced into class-A operation. Nor do I
want to be forced into regulated rails. So it becomes a
little more important, I think, to get this nailed down
better.

There's the problem, anyway.

To quantify how bad all this really is, I tried my hand at
figuring out the small signal analysis of the Vbe multiplier.
If I got a first approximation about right, it is based
squarely upon the small-re of the BJT. The very familiar
value for (kT/q)/Ic.

There is also the value of R2 shown in Fig. 1, but since its
effect is only affected by the change in base current, I
believe it's contribution is divided by Q1's beta. So the
actual equation is something like:

R_ac = (1/Ic)*(kT/q)*(1+R2/R1) + R2/beta

For a 2X multiplier where R2 is about R1, this is:

R_ac = (2/Ic)*(kT/q) + R2/beta

The Vbe multipler value is:

V_bias = Vbe*(1+(R2/R1)) + R2*Ic/beta

(The latter term being a correction for base current.)

Ignoring base current for now and assuming I had Ic set
around 5mA and placed R1=R2=1k for the 2X factor, this R_ac
value works out to about 15.4 ohms.

A variation of half an mA in Ic yields about 7.7mV change in
the bias point.

I decided to see if the Early effect made much of a
difference. The adjustment appears to be something like
this:

R_early = dV/dI = -Ic/VA*R^2

If I'm interpreting it right, it really does show as negative
resistance added to R_ac. The fuller equation, then,
including the Early effect, would be:

R_ac = (2/Ic)*(kT/q) + R2/beta - Ic/VA*R^2

(Which requires a quadratic solution to solve for R.)

If R_ac is 15.4 ohms and Ic is around 5mA, a VA of 100V would
suggest about R_early=-10mOhms. Which is roughly a factor of
1500 less than 15.4 Ohms. Since it now appears to be on the
order of 0.1% or so for typical Ic, VA, and, R_ac values, I
think I can ignore it for these considerations.

So drop it, I will.

I had scouted around a few weeks back (not for this reason)
and found what is shown in Fig. 2. I remembered it, but
didn't understand it then.

: +V
: |
: resistor or
: current source
: |
: ,---+---, <-- node A
: | |
: | \
: | / R3
: \ \
: / R2 /
: \ |
: / +-----> upper quadrant
: | | ^
: | |/c Q1 |
: +-----| BIAS
: | |>e VOLTAGE
: \ | |
: / R1 | v
: \ +-----> lower quadrant
: / |
: | |
: '---+---'
: |
: VAS ---'
:
: FIGURE 2

I think I now understand why R3 was there. Changes in Ic
create changes in Q1's collector voltage, per Ic*R3. The
result is that dV=dI*R3. If R3 is on the order of the above
computed R_ac, then variations at node A caused by changing
currents through the Vbe multipler (most of which are seen as
Ic changes) will be neatly compensated for the change in the
voltage drop caused by R3.

However, that can only be set for some assumed Ic. Nearby
changes will work pretty well. But further deviations will
start to show problems again. Also, the Fig. 2 version will
use a slightly higher multiplier value to get node A up high
enough for the R3 drop to hit the right place required to
bias the output stage. That higher multiplier means that
while, let's say, the two (or four, if that's it) output
BJT's Vbe values vary over temp and the thermally coupled Q1
above also varies it's own Vbe value, the multiplier other
than 2 (or 4) will mean the variation of the bias will match
at only one place -- if it ever did more than one spot. How
important that is, I've not considered yet.

I'm wondering about additional topology changes to improve
the performance still more. Obviously, if they are crazy and
wild, I'm probably going to live with the above and be done
with it. But I think there's got to be something still
better. Another BJT as a bypass route across Q1 and R3?

Getting this nailed down should help mitigate against both
unreg supply ripple (on one side, anyway) putting hum into
the output and also against large scale changes in the VAS
amplified signal voltage (which means distortion.)

Jon

 

[Jamie]

Hang a big capacitor across it.

John

actually, I was going to suggest a diode in the base circuit to VAS to
help with thermo issues with that type of circuit..

oh well.

 

[Jon Kirwan]

Hang a big capacitor across it.

Nice try.

Jon

 

[Jon Kirwan]

What's a "VAS"?

Sorry. I read it somewhere regarding audio amplifiers and
the term stuck in my mind, I suppose. It's short-hand for
Voltage Amplifier Stage. It's almost so simple that no one
would bother creating a term for it, except that it seems as
though someone did and folks have used it in places where
I've been reading.

By the way, if you look at the semi-conceptual schematic at
the top of this page:

http://en.wikipedia.org/wiki/Electronic_amplifier

You will see Q3 acting as the VAS. Together with R6 it
converts the beta multiplied current into drive voltage.

(The Vbe/Ic transfer nasties this up, but I think it may be
survivable. Everything is important, but I'm leaving
worrying about this till later.)

That schematic isn't entirely realistic, either. R3/R4 are
better replaced with a mirror, regular, Wilson, or otherwise.
R5 is often itself a current source or sink (depending on
which way you flip the schematic polarities) and may be a BJT
and diodes or two BJTs, etc.

What exactly are you trying to do?

If you look again at the schematic mentioned above, note the
function of D1 and D2. They stack to create a bias voltage.
That's used to set the point of operation for the output
stage (two-quadrant emitter follower -- which may be just two
BJTs as in that picture, or more.) Often, this is replaced
with an adjustable BJT configured as a Vbe multiplier. That's
what I'm trying to do. Except that I'd like to have the +V
and -V supply rails (ground is also present in the system) be
unregulated.

Part of the function of the Vbe multiplier is to also track
the Vbe requirements for the output stage as it heats up and
cools down. The variation of Vbe is quite large, as you
know, where the controlling Eg term in the Is(T) equation
overwhelms the otherwise oppositely-signed dV/dT of the
Shockley equation. Above -2mV/K. And with the exponential
dependance of Ic on Vbe... well, it serves that function as
well. So the Vbe value needs to track temperature in just
such a way that it maintains the design operating point for
the output stage, over temperature, while also ignoring
variations in the current that sources through it.

I'm trying to keep my options open, regarding the amplifier's
class. If it were operating class-A all the time, my limited
understanding suggests that some variation across the Vbe
multiplier isn't nearly as important as it clearly would be
for, say, class-B operation. I'm not exactly sure where I
want to wind up biasing things.

So I am slowly learning this stuff and, assuming the Vbe
multiplier has some part within it thermally coupled as
appropriate to some well-chosen part of the output stage,
trying to gather how I'd: (1) stabilize the voltage at some
fixed temperature T against variations in the current flowing
through it, and (2) calibrate it's Vbe multiplication factor
in just the right way so that it tracks well with the
effective Eg found in the Is(T) function of the output stage
needed to hold the operating point steady vs temperature.

My question here was regarding (1), not (2). I'm not far
enough along on that one to even begin on that one, yet. To
be honest, I just started learning about audio amplifier
design, including terms like VAS, starting around the 26th
last month. So I may be far off the mark in a few places.

I'm finding it a very interesting education, though, and I'm
glad I started down the road a small bit. But "being exact"
about what I want remains part of the learning process,
itself. So what you see here is as far as I've gotten to.

My nickname, as a kid engineer at Motorola (48 years ago), was "Vbe"
Thompson, because I could pull so much magic with Vbe compensation
methods ;-)

Well, I can believe it. And I mean that as a sincere
compliment. If you can suggest something still better than
what I've already posted, I'd like to look at it.

(Vbe multipliers generally are used just to create a smaller dead-band
that is temperature stable.

In this case, I want it to track the output stage so I'm
going to have to couple it thermally in some useful way. What
I'm considering, right now, is how to make it immune to
unregulated supply variations and VAS output voltage swings.

Class AB bias is an art form of which I
am expert, but cannot divulge publicly at this time

Well, I want to examine class-AB at some point. It may be
where I want to settle, though class-B would be quite fine
for my needs.

If you can't help with class-AB, then you can't. I will have
to struggle along. However, anywhere else you can send me a
clue I'd certainly appreciate it.

There is no interest other than personal. Certainly nothing
commercial in mind. I'm just a hobbyist trying to learn.

Jon

 

[Jon Kirwan]

No, seriously, that solves a bunch of problems.

John

Which problems does a slew-dependent, C*dV/dt bypass current
solve?

Jon

 

[Tim Williams]

Part of the function of the Vbe multiplier is to also track
the Vbe requirements for the output stage as it heats up and
cools down.

The general idea is to put the Vbe transistor on the same heatsink as the
outputs, if not glued to a transistor directly.

Unfortunately, for widely mismatched current densities, this doesn't work.
http://webpages.charter.net/dawill/Images/Ampere.gif
In this boringly typical circuit, the 2N3904 Vbe mult. doesn't have enough
tempco to compensate the far beefier (= lower current density??) output
darlingtons.

I was thinking of adding another CCS so a constant voltage drop appears on
the Vbe's base divider resistor. Algebraically subtracting a fairly stable
voltage results in the effective tempco (percentwise) increasing. The base
divider ratio has to be changed to compensate.

In this case, I want it to track the output stage so I'm
going to have to couple it thermally in some useful way. What
I'm considering, right now, is how to make it immune to
unregulated supply variations and VAS output voltage swings.

Don't worry about stability -- as John said, bypass and forget about it.
Most of the dynamic VAS/CCS current flows into the output stage, since
that's what it's there for anyway. The capacitor helps turn on the N side /
turn off the P side for rising edges and vice versa.

As for PSRR, the CCS's and gobs of feedback keep that in check. Of course,
in principle you need something to start the CCS's. ICs do this with a JFET
(i.e. current regulating diode) or bandgap reference (e.g., TL431), or
sometimes both, to set a master current, from which everything else is
mirrored. Most discrete circuits just use a resistor, which is "0%" PSRR,
but it's not all that bad because the currents are balanced (*on average*,
which means you'll see IMD products when it's moving).

Tim

 

[Jon Kirwan]

This topology, thermally coupled Vbe multiplier, was mediocre 50 years
ago. And still is.

A trek of a thousand miles starts with but the first step.

Jon

 

[Ban]

I think this fits in sci.electronics.design, not .basics.

I'd like to consider the Vbe multiplier often used in audio
amplifiers to maintain a bias voltage for the output stage.
The purpose is to better mitigate against ripple in the
unregulated power supply rails and against the the VAS
voltage output resulting from amplified signal voltages.

No this is not the purpose of this stage. It is used as an adjustable Zener
and is used to create and temperature compensate the bias voltage of the
output stage. A pur DC function. Since the power Transistors draw quite a
bit of quiescent current the ripple of the power supply will be higher then
without. The supply ripple is reduced mainly by negative feedback from
output to the input stage.

snip>

If I use a resistor as the load for the VAS, it's obvious to
me that the Vbe multiplier will need to cope with varying
currents. But even if I use a BJT (or two) to make a current
source sitting above the Vbe multiplier, it's still not going
to hold entirely still with +V ripple and with varying VAS
drive voltages. That variation will ultimately manifest
itself in a varying Vbe bias voltage. That will change the
operating point for the output stage.

If it is class-A, I suppose it doesn't matter that much. But
I don't want to be forced into class-A operation. Nor do I
want to be forced into regulated rails. So it becomes a
little more important, I think, to get this nailed down
better.

In class A you do not use this kind of bias generator

snip

I think you should understand before calculating. It is not much of a use to
view this stage in isolation without the output stage and the associated NFB
paths.

ciao Ban

 

[Jon Kirwan]

Have you read Randy Slone's power amplifier book? This stuff really
isn't rocket science. Nor is AB. ;-)

I haven't. It's not rocket science. But it is interesting
at my level.

<http://www.amazon.com/High-Power-Audio-Amplifier-Construction-Manual/
dp/0071599258/ref=dp_ob_title_bk>

I'll look, but the title appears more on the contruction
side. I am using this to educate myself a little better.

The black art is all in assembly, protection circuitry, and making
sure it starts up cleanly. [Most engineers never look at start up, so
you get designs that thump when you power them. I have lots of gear
with power-on thumps.]

I recall reading of a recommendation suggesting that all
electronic devices use less than 1W when on, but not
performing their intended application. This would also seem
to require a little added effort to achieve, as well. But I
take your point.

I'd pick one of his MOS designs. Bipolar designs often have good
intentions, but ring like a bell. MOS is mushy, but predictably mushy.

I'm still learning about BJTs. In fact, that's what this is
about for me. MOS later. ICs later. BJTs now.

Jon

 

[Jon Kirwan]

<snip>
Have you considered making R2 and/or R3 constant current devices
(depletion FETs are good here)?

I've not. Could you be more specific?

Jon

 

[Jon Kirwan]

No this is not the purpose of this stage. It is used as an adjustable Zener
and is used to create and temperature compensate the bias voltage of the
output stage. A pur DC function. Since the power Transistors draw quite a
bit of quiescent current the ripple of the power supply will be higher then
without. The supply ripple is reduced mainly by negative feedback from
output to the input stage.

I think your perspective is more comprehensive than mine,
obviously. And I am still building up bits, piecewise. It's
how I have to approach this.

That said, and I may yet be getting this wrong, but it seems
to me that I've seen some serious attention in amplifier
schematics; not only looking at global NFB to solve such
problems -- though that seems central, of course.

But I need to take things one at a time, right now. This is
education for me, after all. Not constructing an amplifier
to solve some problem I have. I've no problem focusing upon
this, a bit, until I subsume it, and then not wind up using
all the options I looked at. Learning doesn't only come from
taking all the right steps, but also from taking many others
that aren't entirely in the right direction. I could only
hope to be so perfect as to never choose wrongly. And if so,
I probably wouldn't be learning.

Anyway, the understanding I wrote can certainly be wrong.
However, your later comment seems to say it is wrong because
it's "better" to do it using the NFB from output to the diff
amp. Yet I still wonder if doing some of this locally is
appropriate. In any case, it seems certain that temp comp is
one of its functions. Unless I've somehow completely missed
things altogether.

snip>

In class A you do not use this kind of bias generator

If I set it "wide enough" it seems to operate that way.
Perhaps I've got that wrong, too?

snip

I think you should understand before calculating. It is not much of a use to
view this stage in isolation without the output stage and the associated NFB
paths.

I think it is useful for me to learn by studying the small
building blocks, right now, and considering some thoughts
(but not necessarily all the right ones) about larger issues
these may need to cope with. I'm in no way ready for the
"larger view" you are talking about. Not yet. And only a
rare few can start there. I'm not such. For me, it goes
from small to large, then back to small, then back out again,
and so on until it "gels."

I think I will take this structure just a little further in
thinking... perhaps a 3rd BJT, I'm thinking. But not more
than that. Diminishing returns. I was just wondering if
there was more I hadn't come across. Perhaps not.

Thanks,
Jon

 

[Jon Kirwan]

A big cap across the biasing gadget keeps the voltage drop across it
fairly constant, of course. That nukes some of the problems you
referred to. More peak current is available to the output bases, for
example.

What size cap would help with power supply ripple? Seems the
dV/dt is so small that a fair sized cap would be required to
make any difference. Similarly for low frequency amplified
signal out of the VAS. When you say "big," maybe you mean
it.

Ban is suggesting global NFB from output back to input.
You've said as much when you say to apply "lots of NFB." I
don't doubt the sincerity of either of you and I'm certain it
will do a lot. But right now I'm interested in seeing what
can be done right on this local subcircuit and at LF as well
as higher frequencies. Unless someone wants to walk me
through the thinking towards the larger concepts. I'm good
either way, as it's the learning that takes place I'm looking
for. But without such guidance, I need to move along at the
pace I can handle while guiding myself.

Jon

 

[Jon Kirwan]

"I'm wondering about additional topology changes to improve
the performance still more."

Hi Jon, I've been 'sorta' following your thread on s.e.basics. I
wonder if you abandoned class A operation too early? Why not keep
things linear evreywhere and avoid the ‘dead band’? So what if you
need a bigger heat sink. It’s certainly a lot simpler.

George H.

Well, George... No, I've not abandoned it. Actually, it's my
hope to wind up building the amplifier and then operating it
(by hopefully choosing a design where that is possible) in
different modes for the learning experience of it. I hope
that is in the cards. I really do.

But to make a sharp point on it, although it's probably just
an extreme case, I remember reading about a 10W amplifier,
single channel, dissipating 120W! Creeps me out. So I
definitely _want_ to consider other classes of operation. And
cripes, I want to learn, anyway. So why not keep my options
open?

Jon

 

[Jon Kirwan]

<snip>
Less words and real schematics would get you more readers. [The only
thing worse than ascii equations are ascii schematics.]

ASCII is what I'll post. It's the only way to get them
archived or properly posted to a text newsgroup. I no longer
have access to the binary for schematics, sadly. If I lose
some people because they cannot manage fixed-spaced fonts, I
guess I lose them. I could place links up on my domain, I
suppose. But in this case, the schematics are really very
basic and not overly burdensome in ASCII. Besides, Win Hill
posted some really nice examples here, before. Folks seemed
to live with that. Not sure why you are picking on me, here.

In any event, just google improved vbe multiplier. I've seen all sorts
of circuits published to get lower impedance at the nodes.

Okay. I'll do that if folks here aren't interested at all in
talking about it.

Jon

 

[Jon Kirwan]

The general idea is to put the Vbe transistor on the same heatsink as the
outputs, if not glued to a transistor directly.

Unfortunately, for widely mismatched current densities, this doesn't work.
http://webpages.charter.net/dawill/Images/Ampere.gif
In this boringly typical circuit, the 2N3904 Vbe mult. doesn't have enough
tempco to compensate the far beefier (= lower current density??) output
darlingtons.

Which makes sense to me. I think I already understood this,
generally, if not in intimate detail. One of the reasons I
included in the opening salvo, talking about Eg matching.

I was thinking of adding another CCS so a constant voltage drop appears on
the Vbe's base divider resistor. Algebraically subtracting a fairly stable
voltage results in the effective tempco (percentwise) increasing. The base
divider ratio has to be changed to compensate.

I need to think about this, more. As you write above,
several alternatives appear in my mind and if you wouldn't
mind including a short example, I'd appreciate it.

Don't worry about stability -- as John said, bypass and forget about it.

I can't agree, yet. Slow changes, without a crazy-sized cap
there, will have the same effective R_ac I'd mentioned
before. The cap's Z just won't change it. And I'm not ready
to chalk everything up and pile it all onto the global NFB,
either -- not because I disagree with you or John, because I
can't... I just don't know enough either way. But because
this whole post is about _learning_ something.

In particular, I was very specific about what I'd like to
study right now. Vbe multipliers and various incarnations
that may help to deal with current ripple (from 20Hz to
20kHz, I suppose.) I'm wanting to make sure my analysis so
far isn't grossly wrongly made, accepting corrections as they
arrive, and I'd like to consider interesting ideas, too.

Hopefully, my question here on this narrow subject won't be
taken as "Well, what does he know about the field of audio
amplifier design?" If that's the question to be asked, the
answer is easy. "Not much."

Cripes, I just started looking at the whole idea about two
weeks ago. If I knew enough to ask all the right questions
on this topic in barely more than 10 days, I'd likely be
headed into being the next Bobby Fischer of audio amps!

I'm just a hobbyist, for gosh sake. I found a few circuits
on the web that included a collector resistor in the Vbe
multiplier and, at first, had no idea why it was there. I
asked in .basics and no one else seemed firm about knowing,
either. I grew more curious about it and sat down and lo,
and behold, the scales fell from my eyes and I could _see_! I
could actually see why it was there. Not only why, but how
to estimate quantitative values for it and what to expect as
a result. It's that sense of discovery that sometimes pushes
one further.

So I want to understand a little better how one might do even
more about compensating vs current variations? In this
focus, I don't even need to care about amplifier design, at
all. It is purely about the Vbe multiplier right now and
nothing else. Sure, audio amplifier design questions caused
me to look more closely at this structure. That was my
inspiration to set down this short path, right now.

But is it wrong to want to explore this area a little more
before moving on?

Most of the dynamic VAS/CCS current flows into the output stage, since
that's what it's there for anyway.

I think I see that, though I'll see it a lot better later on.
Hopefully where I'll be able to put quantities to it.

The capacitor helps turn on the N side /
turn off the P side for rising edges and vice versa.

I think I gather that much. It's got very low impedance when
the dV/dt is there.

As for PSRR, the CCS's and gobs of feedback keep that in check.

Yes, and yes. John L. mentioned this, too, a week ago and
more. No question I've got the point, there. The CCS's
aren't perfect and where they don't do so well, it gets all
nicely lumped into the global NFB and left for it to deal
with. I don't mind, though, investigating things just a
little more. And I will very soon start taking on the CCS's
themselves. I know a few and I know there are a lot more
than I'm not even remotely aware of, too. So that is going
to be fun. But I'm not one to just borrow and run. I need
to _understand_ the mathematics and try my hand at deriving
certain features in quantitative ways, not just qualitative
ones. I expect to analyze at least four or five different
CCS structures before I move on, in what quantitative detail
I can manage at the time.

Of course,
in principle you need something to start the CCS's. ICs do this with a JFET
(i.e. current regulating diode) or bandgap reference (e.g., TL431), or
sometimes both, to set a master current, from which everything else is
mirrored.

I've seen that done time and time again in ICs. I can
remember tracing my fingers from one to another to another as
I spent time understanding them better.

Last July, in fact, here in this very group, I posted this
about the LM334:

: By the way, I just looked at the general schematic for the LM334 on
: National's datasheet and with a quick sweep of my arms came up with a
: design Iset/Ibias of 8, not 16 as they show on page 5. I'm off by a
: factor of two.
:
: My logic went like this. 1/2 of the I from V+ flows via Q6 to the R
: rail. 1/4 via Q4 and 1/4 via Q5. Q5's 1/4*I flows via Q1 to the R
: rail, too. So now up to 3/4*I into the R rail. Q4's 1/4*I passes
: through two paths. The Ic(Q2)=Ic(Q1)/2... but Ic(Q1)=1/4*I, so that
: is 1/8*I, leaving the other 1/8*I for Q3's Vbe conduction, which also
: flows to the R rail. So the R rail gets 7/8*I and the V- picks up
: 1/8*I. Multiplying through by 8 to get rid of the divisor, I see a
: factor of 8 for Iset/Ibias... not 16.
:
: Can someone do a quick description about how to arrive at something
: more like 16? I'm missing a clue (or two.)

No one here _did_ fully answer my question, Tim. There it
is, and I did try to follow it.

I'm aware of the frequent practice, at least.

Most discrete circuits just use a resistor, which is "0%" PSRR,
but it's not all that bad because the currents are balanced (*on average*,
which means you'll see IMD products when it's moving).

Tim

Intermodulation distortion?? I never saw the term IMD
before, but that seems as though it must be what you just
said. Fits, anyway. Which brings me back to the MC1495,
again. And yes, I think I see why you bring it up.

Jon

 

[Jon Kirwan]

Hey Jon, I found a derivation of the input impedance of the two-resistor
/transistor Vbe multiplier you might be interested in looking at:

http://paginas.fe.up.pt/~fff/eBook/MDA/Mult_Vbe.html

That one takes an approach that I'm not familiar with and
didn't take. I'll have to consider the approach more.
However, I did take a look at the end of it. It says:

R = (R1+(R2||re)) / (1+(1/R1+gm)*(R2||re))

If I understand the value gm, and I may not, it's just 1/re
or else re=1/gm. Basically, just the (kT/q)/Ic I'd mentioned
when I wrote. If that is the case, I used these to see how
that page predicts:

ic=.005
vt=k*300/q
gm=ic/vt
re=1/gm
r1=1000
r2=1000
r2p=r2*re/(r2+re)

and then computed:

(r1+r2p)/(1+(1/r1+gm)*r2p)

and got:

502.5719049 Ohms.

This is so far from my own calculations of about 15.4 Ohms
that I just _had_ to put this into LTspice and test it. To
do that, I simply set up the basic circuit with the two
resistors and BJT and then hooked up a variable current
source to the topside. I set it up as an AC source of 5mA
with peaks of 500uA, and then ran a .TRAN on it and plotted
the upper rail of the structure's voltage. I used a 2N2222
BJT, as well. Convenient, and I have them laying about.

Anyway, so I ran the sims and got 17.44mV, peak to peak.
Divided by the peak to peak current variation of 1mA gives an
apparent R of 17.44 Ohms. My calculations arrived at 15.4
Ohms, or so.

All this could be operator error. I may be operating the web
page you suggested incorrectly, so that the 503 Ohms I get is
because I didn't know what I was plugging in and where. I
may be operating LTspice incorrectly, so that it's results
aren't usable and it's just luck that the numbers worked out
in my favor.

But there it is.

Here is the LTspice file:

Version 4
SHEET 1 880 680
WIRE 128 0 16 0
WIRE 224 0 128 0
WIRE 288 0 224 0
WIRE 128 32 128 0
WIRE 16 112 16 0
WIRE 224 112 224 0
WIRE 128 160 128 112
WIRE 160 160 128 160
WIRE 128 208 128 160
WIRE 16 224 16 192
WIRE 128 320 128 288
WIRE 224 320 224 208
WIRE 224 320 128 320
WIRE 128 336 128 320
FLAG 128 336 0
FLAG 288 0 V_rail
FLAG 16 224 0
SYMBOL npn2 160 112 R0
SYMATTR InstName Q1
SYMATTR Value 2N2222
SYMBOL res 112 192 R0
SYMATTR InstName R1
SYMATTR Value 1k
SYMBOL res 112 16 R0
SYMATTR InstName R2
SYMATTR Value 1k
SYMBOL current 16 192 R180
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName I1
SYMATTR Value SINE(5m 500u 50)
TEXT -76 296 Left 0 !.tran 1

For bypassing purposes the rule of thumb I've always heard is to make
the impedance of the capacitor 1/10th the value of the impedance looking
in to the circuit at the lowest audio frequency.

Well, let's assume that I got lucky and LTspice and I agree
on the figure of about 16 Ohms. With a signal at 20Hz, we
are talking:

C = 1/(2 PI f (R_ac/10)) = 5000uF

Yikes. John L. wasn't kidding when he wrote "big." Luckily,
in steady state it could be a low voltage cap!

Jon

 

[Jon Kirwan]

A trek of 23,000 miles starts with but the first step in the wrong
direction.

There is no wrong direction at the start. It's all good.

Jon

 

[Jon Kirwan]

(1) Split R1, bypass that junction to ground
Understood.

(2) Make R5 and R6 into mirrors, resistor feed from VDD, but split and
bypassed.

I had been thinking more like this structure:

: to input to voltage
: stage mirror amp stage
: | ,---, |
: | | | |
: | | | |
: | gnd | |
: | \ |
: | / R4 |
: | \ |
: | / |
: | | |
: | ,------+ |
: | | | |
: | --- C1 | |
: | --- | |
: | | \ |
: | | / R3 |
: | | \ |
: | | / |
: | Vdd | |
: Q2 c\| | R5 |/c Q3
: |-----------+----/\/\-----|
: e<| | |>e
: | | |
: | R1 |/c Q1 |
: +---/\/\----| |
: | |>e \
: | | / R6
: | | \
: \ | /
: / R2 | |
: \ | |
: / | |
: | | |
: Vdd Vdd Vdd

However, I take your point.

(3) As you said, replace R4:R3 with a mirror, I don't think a compound
device mirror, such as Wilson, is necessary.

Understood. Although I'm not able to make my own decisions
on this, yet, I've read repeatedly that the distortions to
deal with are not at the input stage. The input stage can be
made better, the improvements are small in comparison to what
remains in the rest of a well-designed system. Point taken.

Study this if you want more info....

http://analog-innovations.com/SED/EnhancedCurrentMirrors.pdf

Thanks, I will!

(4) Since you're on a learning curve, just replace D1/D2 with 1.5*Vbe,
losing about 1/5 of the Q3 quiescent current in the resistors.

Thanks for taking a moment to confirm the "1/5th" division.
I'd already figured that was commonly done and had some ideas
of my own about why that makes sense. (I could talk about
that, but I'm sure you already know and I think I know, too.)

Bypassing base-to-base (of Q4-Q5) will help at all but very low
frequencies.

Okay. That's how I see it, too.

(5) Long haul as you "oomph" the power:
Q3 goes to Darlington, as do Q4 and Q5; D1/D2 becomes more
complicated (Darlington extension of Vbe multiplier).

This is what I'd like to explore, right now. Extensions.
It's because it is where my mind is at, right now. And I
want to explore this more fully before walking away from it
and moving on.

Start simple, then grow it, that way you learn before you flame it ;-)

hehe. Good advice, of course. As I'm still struggling to
make sure I understand each piece, right now, I'm just not
yet ready to put it all together -- not even in a low power
system. I might be able to vaguely grasp what I would be
doing, but I prefer taking each part and thoroughly looking
at its function before moving on. Then, when I look once
again at the whole, I can better "read" what I see and that
helps a lot in terms of gaining a global view. I'm still in
the trenches, right now, and not allowing myself to raise my
head much above that until I get some of the details nailed
down.

Speaking of that, can you confirm (or correct) the equation I
developed for the simple Vbe multiplier's small signal R? Or
the relative scale and _sign_ of the Early effect correction
to it, which I peg near -1 part per thousand in the case I
cited?

All this is good for me to go through.

Thanks,
Jon

 

[Jon Kirwan]

<snip>
Useless nonsense....

Are you talking about my comments, those of others here, or
the link you posted below?

http://home.comcast.net/~mercerd/MobileStudioProject/Activity_6_zero_gain_amp.pdf

I'll take a look, today.

Thanks,
Jon

 

[Jon Kirwan]

" I remember reading about a 10W amplifier,

It might have been here,
http://www.passdiy.com/default.html
I got to reading about amplifiers on the above site... Do in part to
your interest.

George H.

Egads. Loads of PDF files. Now I have to create a
directory, download them one by one, and then call them up
with my slow machine to look. Any particular page or file
where you saw it? (No, that isn't where I saw the comment.)

But thanks for the link. I'll add it to those I read, also.

Jon