Wilson Current Mirror - some confusion

[M. Hamed]

As I was doing some of the experiments in the AoE student manual
(highly recommended for beginners, if you have access to a lab), I've
reached the section about current mirrors, specifically Wilson current
mirror. And in trying to understand some temperature dependent
behavior and how the current tends to increase when the output
transistor gets hot, even though its current and voltage parameters
are pretty much fixed. In trying to understand that, I came up with a
more fundamental question...

How can the transistor that is directly connected to the load, how can
it tolerate its VBE and IC being fixed, even though its VCE can vary
considerably depending on the load.

For example, in the mirror of the first figure in
http://en.wikipedia.org/wiki/Wilson_current_source and assuming VCC is
large, IC1 is fixed, and from Ebers Moll that fixes VBE for Q1, which
also fixes VBE for Q2, which in turn fixes the emitter of Q3 and hence
VBE for Q3.

Since VBE for Q2 is fixed, IC2 is fixed (Ebers-Moll), and that causes
IE3, IC3 to be fixed (neglecting base currents).

Now the anomaly is Q3. Here we have a transistor with VBE fixed by the
two other transistors, yet it can maintain a current that really
doesn't depend on its own VBE (where is Ebers-Moll here?). Not just
that. For varying loads at its collector, VCE can change considerably,
yet it still can pass the same current (where is Early effect here?).

In summary, how can the transistor equations and curves not hold for
Q3 in that case?

Anybody got an answer?

Thank you!

 

[Jon Kirwan]

On Mon, 18 May 2009 20:45:15 -0700 (PDT), "M. Hamed"
<mhelshou@hotmail.com> wrote:

As I was doing some of the experiments in the AoE student manual
(highly recommended for beginners, if you have access to a lab), I've
reached the section about current mirrors, specifically Wilson current
mirror. And in trying to understand some temperature dependent
behavior and how the current tends to increase when the output
transistor gets hot, even though its current and voltage parameters
are pretty much fixed. In trying to understand that, I came up with a
more fundamental question...

How can the transistor that is directly connected to the load, how can
it tolerate its VBE and IC being fixed, even though its VCE can vary
considerably depending on the load.

For example, in the mirror of the first figure in
http://en.wikipedia.org/wiki/Wilson_current_source and assuming VCC is
large, IC1 is fixed, and from Ebers Moll that fixes VBE for Q1, which
also fixes VBE for Q2, which in turn fixes the emitter of Q3 and hence
VBE for Q3.

Since VBE for Q2 is fixed, IC2 is fixed (Ebers-Moll), and that causes
IE3, IC3 to be fixed (neglecting base currents).

Now the anomaly is Q3. Here we have a transistor with VBE fixed by the
two other transistors, doesn't depend on its own VBE (where is Ebers-
Moll here?).

Not just
that. For varying loads at its collector, VCE can change considerably,
yet it still can pass the same current (where is Early effect here?).

In this case, a significant point in the extra transistor is to remove
its impact.

In summary, how can the transistor equations and curves not hold for
Q3 in that case?

Anybody got an answer?

A schematic would be helpful.

: Vcc Vcc
: | |
: \ \
: / R1 / RL
: \ \
: / /
: | | <--- V3
: | |
: | |/c Q3
: V2 +---------|
: | |>e
: | |
: | ,-----+
: | | |
: Q1 c\| | |/c Q2
: |---+---|
: e<| V1 |>e
: | |
: gnd gnd

In the above diagram, I labeled three nodes. V1, V2, and V3. V1 is
the joint Vbe of Q1 and Q2. V2 is Q1's Vce, which is also equal to V1
plus Q3's Vbe, whatever that is.

Assume for a moment that all the transistors are operating in their
normal quadrant and forget about the base drive currents, for now.

I'm going to use a function f() that accepts a collector current and
computes a Vbe for the BJT. The function g() will reverse that,
accepting a Vbe and giving an Ic. a=g(f(a)) and b=f(g(b)). Keep in
mind that for a 10-fold change in the collector current, the Vbe will
go up or down only about 60mV. Walk through the circuit in a loop,
starting with I(RL):

I = I(RL) = (Vcc-V3)/RL
V3 = Vcc - I*RL
Ic(Q3) = I
V2-V1 = f(Ic(Q3)) = f(I)
Ie(Q3) = Ic(Q3) = I
Ic(Q2) = Ie(Q3) = I
V1 = f(Ic(Q2)) = f(I)
Ic(Q1) = g(V1) = g(f(I)) = I
V2 = Vcc - I*R1 = V1+f(I) = 2*f(I)

But,

I = (Vcc-V2)/R1 = (Vcc-2*f(I))/R1

Note that I doesn't depend on RL. Just R1.

What happens if RL starts pulling more current? This change would
imemdiately be reflected in a higher Ic in Q1. The higher Ic there
would force I*R1 to drop V2 downwards, pinching it against the rising
V1 (rising because the load current increased and changed the Ic at
Q2.) That pinching effect, even small voltage changes, would have
very large impact on forcing Q3 to reduce its collector current to
counteract the effect.

Think about even a slight change at V2 that changes it only by +26mV.
Just that little change would mean a doubling of Ic at Q3. But this
would also mean a doubling of Ic at Q1, too. (Walk the loop.) And a
doubling of Q1's Ic would be twice the voltage drop on R1, which is
already 'large' by definition. That means V2 gets pushed back down by
far, far more than it tried to rise. V2 would never get close to that
large of a change. The swings in currents would make that impossible.

Even a tiny change from the operating point would be immediately
countered. So V2 basically is held stable by Q3 no matter what RL
does. And since V1 is shared by both Q1 and Q2, Q3's Vce must be
flexible and adjust itself in order to accomodate this. So long as
the Vce of Q3 doesn't go into saturation, anyway.

f(I) will depend on the BJT, of course. And the exact magnitude of V2
(which is 2*f(I)) that everything will settle on will depend. But
even gross errors on your part in assumption about that will quickly
remedy themselves. If you assumed 0.66V in your design, but the
reality should have been 0.60V then of course more current would be
conducted than you expected to be. But how much more?? Well, let's
assume Vcc=30V. You'd compute R1=(30-2*0.66)/I_design. If I_design
is 10mA, then R1=28.68/10mA=2868 ohms. However, reality would have
been V2=1.2V for 10mA, not 1.32V. So what happens? Well, V2 rises
from the 1.2V upwards. As it does, though, so does I. And I goes by
a factor of 10 for each 60mV of V2-V1 or factor of 2 for each 26mV. As
you can see, the voltage may go up a little, but not very much from
where the transistors would have been at the design current. You
don't really care where it settles. You just know that it will settle
pretty close to the design current. At least, if Vcc is large.

What about the Early effect in Q3? Not an issue. The collectors of
Q1 and Q2 are going to be very close to each other (a Vbe different,
is all.) Because their Vce's are close to each other and regardless
of the rest, their Vbe as a function of their Ic currents will be
independent, because Q3 isolates them. So the Early effect doesn't
matter with those two, whose only function is to transcribe over the
currents faithfully. Q3's Early effect is part of the loop. If the
Q3 Ic varies with larger Vce for the same Vbe, that will get
transcribed over and force a drop in Vbe to compensate and force Q3
back in line.

I think. I'm just a hobbyist, though. Which if nothing else means I
spent way too long explaining something that could be explained better
with much less.

Jon

 

[whit3rd]

On May 18, 8:45 pm, "M. Hamed" <mhels...@hotmail.com> wrote:

Now the anomaly is Q3. Here we have a transistor with VBE fixed by the
two other transistors, yet it can maintain a current that really
doesn't depend on its own VBE (where is Ebers-Moll here?). Not just
that. For varying loads at its collector, VCE can change considerably,
yet it still can pass the same current (where is Early effect here?).

In summary, how can the transistor equations and curves not hold for
Q3 in that case?

Yep, this is confusing, all right.
Firstly, Q3 has fixed emitter current, THAT'S what makes the
collector current controlled, not the Vbe; that Q3 doesn't need to be
similar to the other transistors to do its job. It doesn't, strictly
speaking, need to be a bipolar transistor - you could put a MOSFET
there. Ratio of Ic to Ie (usually called alpha) is the important
characteristic here!

"Early voltage" refers to curves with fixed Vbe which, as we just
heard,
isn't held constant on Q3. So, there's no reason to involve Q3 in
the Early effect, only Q2 (and Q2 feeds Q3's emitter, which is low
impedance, so the Early effect is slight).

The various transistor curves all apply as usual. The
approximations, and equations are all approximate, have to be applied
according to the circuit requirement, and this circuit is a good
test of that principle.

 

On May 19, 11:51 am, whit3rd <whit...@gmail.com> wrote:

On May 18, 8:45 pm, "M. Hamed" <mhels...@hotmail.com> wrote:

Now the anomaly is Q3. Here we have a transistor with VBE fixed by the
two other transistors, yet it can maintain a current that really
doesn't depend on its own VBE (where is Ebers-Moll here?). Not just
that. For varying loads at its collector, VCE can change considerably,
yet it still can pass the same current (where is Early effect here?).

In summary, how can the transistor equations and curves not hold for
Q3 in that case?

Yep, this is confusing, all right.
Firstly, Q3 has fixed emitter current, THAT'S what makes the
collector current controlled, not the Vbe; that Q3 doesn't need to be
similar to the other transistors to do its job.  It doesn't, strictly
speaking, need to be a bipolar transistor - you could put a MOSFET
there.   Ratio of Ic to Ie (usually called alpha) is the important
characteristic here!

"Early voltage" refers to curves with fixed Vbe which, as we just
heard,
isn't held constant on Q3.  So, there's no reason to involve Q3 in
the Early effect, only Q2 (and Q2 feeds Q3's emitter, which is low
impedance, so the Early effect is slight).

The various transistor curves all apply as usual.  The
approximations, and equations are all approximate, have to be applied
according to the circuit requirement, and this circuit is a good
test of that principle.

Jon, thanks for the detailed explanation, and whit3rd for your
insight.

So, I think the conclusion here would be something along the line of
"Q3 Vbe is not fixed, it changes with the early effect, but those
changes are too small to cause any effect on Q1's current. Does that
sound correct? I tried simulating the circuit in LTSpice but the
voltage seems fixed. I'm guessing the standard LTSpice NPN doesn't
model early effect.

 

[Jon Kirwan]

On Tue, 19 May 2009 15:50:16 -0700 (PDT), mhelshou@hotmail.com wrote:

On May 19, 11:51 am, whit3rd <whit...@gmail.com> wrote:
On May 18, 8:45 pm, "M. Hamed" <mhels...@hotmail.com> wrote:

Now the anomaly is Q3. Here we have a transistor with VBE fixed by the
two other transistors, yet it can maintain a current that really
doesn't depend on its own VBE (where is Ebers-Moll here?). Not just
that. For varying loads at its collector, VCE can change considerably,
yet it still can pass the same current (where is Early effect here?).

In summary, how can the transistor equations and curves not hold for
Q3 in that case?

Yep, this is confusing, all right.
Firstly, Q3 has fixed emitter current, THAT'S what makes the
collector current controlled, not the Vbe; that Q3 doesn't need to be
similar to the other transistors to do its job.  It doesn't, strictly
speaking, need to be a bipolar transistor - you could put a MOSFET
there.   Ratio of Ic to Ie (usually called alpha) is the important
characteristic here!

"Early voltage" refers to curves with fixed Vbe which, as we just
heard,
isn't held constant on Q3.  So, there's no reason to involve Q3 in
the Early effect, only Q2 (and Q2 feeds Q3's emitter, which is low
impedance, so the Early effect is slight).

The various transistor curves all apply as usual.  The
approximations, and equations are all approximate, have to be applied
according to the circuit requirement, and this circuit is a good
test of that principle.

Jon, thanks for the detailed explanation,

I'm not sure it was good enough. But maybe.

and whit3rd for your insight.

So, I think the conclusion here would be something along the line of
"Q3 Vbe is not fixed, it changes with the early effect, but those
changes are too small to cause any effect on Q1's current. Does that
sound correct? I tried simulating the circuit in LTSpice but the
voltage seems fixed. I'm guessing the standard LTSpice NPN doesn't
model early effect.

LTSpice will plop down an "NPN" that doesn't show the Early effect,
unless and until you use something 'real,' I think. I just dropped
one up and looked and it is very "flat" in behavior (infinite VAF.)

Take what you've got and use a real BJT or else add this:

.model MYNPN NPN VAF=100

You can do that by hitting the 'S' character on your keyboard and
adding that line into the dialog box and then placing it on the
schematic. Then right click on the word "NPN" near your BJT and
replace it with MYNPN, instead. This will force a VAF to be added to
the standard NPN type. Be careful about the right click. If you
mouse over the NPN BJT and right click when there is a pointed hand,
you'll get a list of real BJT types to select from. But if you move
the mouse over the NPN designation near the BJT, but not on it, the
mouse cursor will look like a text-vertical-bar thing and that's what
you want to right click. Then it just lets you type in any text at
all. And if it matches what's on that .model, then you are okay.

The Vbe of Q3 will remain very solid, though. Probably within 1 or 2
mV over a wide range of load values (so long as the programmed current
times the load resistance doesn't exceed the compliance range.) There
has to be a little change, but not very much. Do you follow why?

Jon

 

On May 19, 9:57 pm, Jon Kirwan <j...@infinitefactors.org> wrote:
<-- snip -->

Thanks for the tips. They were pretty helpful. I wonder if you know a
way to select all NPN transistors at once and change their models.

The Vbe of Q3 will remain very solid, though.  Probably within 1 or 2
mV over a wide range of load values (so long as the programmed current
times the load resistance doesn't exceed the compliance range.)  There
has to be a little change, but not very much.  Do you follow why?

Jon

My understanding is that the small change in Ic due to the early
effect would cause Vbe to change to maintain it constant but since
these changes are very small, Vbe changes are logarithmically smaller.
If the programming current times the load resistance is big enough to
put the transistor into saturation, then base currents cannot be
neglected anymore, and the currents of the two transistors in series
don't have to be equal.

 

[Jon Kirwan]

On Wed, 20 May 2009 20:36:57 -0700 (PDT), mhelshou@hotmail.com wrote:

On May 19, 9:57 pm, Jon Kirwan <j...@infinitefactors.org> wrote:
-- snip --

Thanks for the tips. They were pretty helpful. I wonder if you know a
way to select all NPN transistors at once and change their models.

I guess you'd use that .MODEL technique. Just change the .MODEL
itself and all the references to it will also change. I think.

The Vbe of Q3 will remain very solid, though.  Probably within 1 or 2
mV over a wide range of load values (so long as the programmed current
times the load resistance doesn't exceed the compliance range.)  There
has to be a little change, but not very much.  Do you follow why?

Jon

My understanding is that the small change in Ic due to the early
effect would cause Vbe to change to maintain it constant but since
these changes are very small, Vbe changes are logarithmically smaller.

If I gather your thinking, then that's about it.

If the programming current times the load resistance is big enough to
put the transistor into saturation, then base currents cannot be
neglected anymore, and the currents of the two transistors in series
don't have to be equal.

It goes to hell in a handbasket, in other words. Yes.

Jon