[Eeyore]

I was trying to explain in another (audio) group the details of why Class AB
output stages always have *some* crossover distortion even when there's a decent
quiescent current.

What happens is that the output device variation in transconductance with output
current does not sum as a constant figure, no matter how much quiescent current
you add, there's always some non-linearity.

I'd like to show a thorough mathematical analysis. Now, I'm familiar with the
classic 38mA/V per mA of Ic figure for silicon bipolar devices that applies at
currents say up to ~ 3mA but I'd like to know if there's a similar generalised
equation that's useful for currents up to say one amp. I was under the
impression that device bulk resistances play a significant role in practice, but
even so a theoretical model would be nice.


Graham

 

[John Popelish]

I was trying to explain in another (audio) group the details of why Class AB
output stages always have *some* crossover distortion even when there's a decent
quiescent current.

What happens is that the output device variation in transconductance with output
current does not sum as a constant figure, no matter how much quiescent current
you add, there's always some non-linearity.

I'd like to show a thorough mathematical analysis. Now, I'm familiar with the
classic 38mA/V per mA of Ic figure for silicon bipolar devices that applies at
currents say up to ~ 3mA but I'd like to know if there's a similar generalised
equation that's useful for currents up to say one amp. I was under the
impression that device bulk resistances play a significant role in practice, but
even so a theoretical model would be nice.

Douglas self gets pretty deep into the analysis at:
http://www.dself.dsl.pipex.com/ampins/dipa/dipa.htm

 

[Eeyore]

I think it gets all transcendental and isn't very much amenable to
analytical solution, unless you're a lot better at maths than me.

LOL !

I know how to use Mathcad (at some intermediate but non-total-expert level) if
that's what you mean. I've used it to do some cute stuff for sure though.

Empirically (in simulation) you can get the third-order intermodulation down
quite a lot if the emitter degeneration resistance (including any that is
inside the transistor) is made to drop 0.75 times kT/q (0.75*26mV or so) at
the quiescent current, and this is useful in RF amplifiers etc where you
can't use global negative feedback.

You mean there's a specific value of external emitter resistor that's optimal ?

Graham

 

[Chris Jones]

I was trying to explain in another (audio) group the details of why Class
AB output stages always have *some* crossover distortion even when there's
a decent quiescent current.

What happens is that the output device variation in transconductance with
output current does not sum as a constant figure, no matter how much
quiescent current you add, there's always some non-linearity.

I'd like to show a thorough mathematical analysis. Now, I'm familiar with
the classic 38mA/V per mA of Ic figure for silicon bipolar devices that
applies at currents say up to ~ 3mA but I'd like to know if there's a
similar generalised equation that's useful for currents up to say one amp.
I was under the impression that device bulk resistances play a significant
role in practice, but even so a theoretical model would be nice.


Graham

I think it gets all transcendental and isn't very much amenable to
analytical solution, unless you're a lot better at maths than me.

Empirically (in simulation) you can get the third-order intermodulation down
quite a lot if the emitter degeneration resistance (including any that is
inside the transistor) is made to drop 0.75 times kT/q (0.75*26mV or so) at
the quiescent current, and this is useful in RF amplifiers etc where you
can't use global negative feedback.

Chris

 

[Rich Grise]

I was trying to explain in another (audio) group the details of why Class
AB output stages always have *some* crossover distortion even when there's
a decent quiescent current.

What happens is that the output device variation in transconductance with
output current does not sum as a constant figure, no matter how much
quiescent current you add, there's always some non-linearity.

I'd like to show a thorough mathematical analysis. Now, I'm familiar with
the classic 38mA/V per mA of Ic figure for silicon bipolar devices that
applies at currents say up to ~ 3mA but I'd like to know if there's a
similar generalised equation that's useful for currents up to say one amp.
I was under the impression that device bulk resistances play a significant
role in practice, but even so a theoretical model would be nice.

OK, so I'm an ignoramus - do bipolars even _have_ "transconductance"?
Isn't the equivalent usually called "beta"? ;-)

Notwithstanding that, some guy showed me a circuit many, many years ago,
where he bootstrapped out the crossover distortion. I don't remember
the exact circuit, but it had complementary compound transisors - i.e.,
on the positive half of the circuit, there was an NPN driving the base
of a mongo PNP, mirrored on both sides (i.e., a PNP to an mongo NPN on
the negative half-cycle side), but he strapped the gain down by feeding
the output (from where the mongo collectors joined) back to the emitters
of the drivers. According to the guy who showed me the circuit, it's
limited by "second breakdown", which, as a mere tech, I've never
understood, but other than that, it looked like a rather kewl circuit.
(I'm guessing it might have to do with the dearth of short-circuit
protection, and that sort of thing.) But, there is equipment available
Off-The-Shelf that satisfies even the most discriminating ear, but of
course, as everyone knows, the perceived sound quality generally is
proportional to the price of the equipment. ;-)

Cheers!
Rich

 

[Tam/WB2TT]

OK, so I'm an ignoramus - do bipolars even _have_ "transconductance"?
Isn't the equivalent usually called "beta"? ;-)

Transconductance has units of Amps/Volt, or 1/Ohms, whereas beta is
Amps/Amp, or unitless.

Tam

 

[John Larkin]

OK, so I'm an ignoramus - do bipolars even _have_ "transconductance"?
Isn't the equivalent usually called "beta"? ;-)

Gm is the ratio of collector current over base voltage, as the
incremental value d(Ic) / d(Vbe). Its value in Siemens (mhos) is
roughly 40 * Ie, where Ie is the DC emitter current.

Beta is Ic/Ib.

Notwithstanding that, some guy showed me a circuit many, many years ago,
where he bootstrapped out the crossover distortion. I don't remember
the exact circuit, but it had complementary compound transisors - i.e.,
on the positive half of the circuit, there was an NPN driving the base
of a mongo PNP, mirrored on both sides (i.e., a PNP to an mongo NPN on
the negative half-cycle side), but he strapped the gain down by feeding
the output (from where the mongo collectors joined) back to the emitters
of the drivers. According to the guy who showed me the circuit, it's
limited by "second breakdown", which, as a mere tech, I've never
understood, but other than that, it looked like a rather kewl circuit.
(I'm guessing it might have to do with the dearth of short-circuit
protection, and that sort of thing.) But, there is equipment available
Off-The-Shelf that satisfies even the most discriminating ear, but of
course, as everyone knows, the perceived sound quality generally is
proportional to the price of the equipment. ;-)

Negative feedback fixes soft crossover distortion.

John

 

[Eeyore]

OK, so I'm an ignoramus - do bipolars even _have_ "transconductance"?

Yes absolutely.

Isn't the equivalent usually called "beta"? ;-)

Different thing.

Notwithstanding that, some guy showed me a circuit many, many years ago,
where he bootstrapped out the crossover distortion. I don't remember
the exact circuit, but it had complementary compound transisors - i.e.,
on the positive half of the circuit, there was an NPN driving the base
of a mongo PNP, mirrored on both sides (i.e., a PNP to an mongo NPN on
the negative half-cycle side), but he strapped the gain down by feeding
the output (from where the mongo collectors joined) back to the emitters
of the drivers.

Yes I've used an arrangement like that. It does linearise the transfer
characteristic somewhat but still not enough.

According to the guy who showed me the circuit, it's
limited by "second breakdown", which, as a mere tech, I've never
understood, but other than that, it looked like a rather kewl circuit.

Well *all* output stages using bipolars are limited by secondary breakdown to
some degree. Unless they never see more than say 30 - 50V !

Primary breakdown is simple over-dissipation / temperature rise. Secondary
breakdown takes account of the fact that in bipolar power devices as Vce
increases, the current tends to 'focus' in several places on the die which
results in differential heating and a breakdown dissipation that's less than the
primary figure.

(I'm guessing it might have to do with the dearth of short-circuit
protection, and that sort of thing.) But, there is equipment available
Off-The-Shelf that satisfies even the most discriminating ear, but of
course, as everyone knows, the perceived sound quality generally is
proportional to the price of the equipment. ;-)

Perception is a whole different matter.

Graham

 

[Eeyore]

Gm is the ratio of collector current over base voltage, as the
incremental value d(Ic) / d(Vbe). Its value in Siemens (mhos) is
roughly 40 * Ie, where Ie is the DC emitter current.

Well, that approximation certainly works well at low currents.

Maybe it holds true generally including at large currents, I honestly don't know
about that (that's why I'm asking), but of course as the value of gm gets higher,
real device bulk resistances will raise their ugly heads, enter the equation and
change that relationship.

Beta is Ic/Ib.


Negative feedback fixes soft crossover distortion.

It reduces it proportionally by the numerical value of the feedback factor.

It never eliminates it. Indeed NFB can never *eliminate* distortion, that's why
for purists, designing circuits that are initially as linear as possible *before*
applying feedback is so important.

Graham

 

[Robert Baer]

I was trying to explain in another (audio) group the details of why Class AB
output stages always have *some* crossover distortion even when there's a decent
quiescent current.

What happens is that the output device variation in transconductance with output
current does not sum as a constant figure, no matter how much quiescent current
you add, there's always some non-linearity.

I'd like to show a thorough mathematical analysis. Now, I'm familiar with the
classic 38mA/V per mA of Ic figure for silicon bipolar devices that applies at
currents say up to ~ 3mA but I'd like to know if there's a similar generalised
equation that's useful for currents up to say one amp. I was under the
impression that device bulk resistances play a significant role in practice, but
even so a theoretical model would be nice.


Graham

What you do, is take the "perfect" model and add a resistor in the
base (Rbb prime, if i remember corretly), and one in the emitter (Rsat
if i remember correctly).
This works for noise figure in the very low power, audio and RF
regions, and high current useage as well.

 

[Phil Hobbs]

What you do, is take the "perfect" model and add a resistor in the
base (Rbb prime, if i remember corretly), and one in the emitter (Rsat
if i remember correctly).
This works for noise figure in the very low power, audio and RF
regions, and high current useage as well.

One of the many nice things about small-signal BJTs is that they really
obey their noise models--Rbb' and Re are real physical resistances.
Power transistors are a bit different, because there are significant
gradients in voltage and temperature across the die in normal use.

To the device experts: Why do power BJTs have such big saturation
voltages compared with small-signal devices? Seems like it wouldn't be
too hard to make a die with, say, 100 integrated 2N3904s wired in
parallel. You could do that sort of litho with a crayon.

Cheers,

Phil Hobbs

 

[Eeyore]

To the device experts: Why do power BJTs have such big saturation
voltages compared with small-signal devices? Seems like it wouldn't be
too hard to make a die with, say, 100 integrated 2N3904s wired in
parallel. You could do that sort of litho with a crayon.

Funny you should say that.

The Japanese always seemed to have superior devices (higher fT - larger SOA) to
US semi outfits like RCA and Motorola. From what I can gather, a large part of
that was indeed due to the use of finer feature widths. Toshiba also made/makes
a big thing about their 'perfect crystal technology'.

Graham

 

[Chris Jones]

LOL !

I know how to use Mathcad (at some intermediate but non-total-expert
level) if that's what you mean. I've used it to do some cute stuff for
sure though.



You mean there's a specific value of external emitter resistor that's
optimal ?

For a given quiescent current, yes. Conversely, for a given degeneration
resistor, there is an optimum quiescent current. I've mostly seen this in
npn-only push-pull RF amplifiers with a transformer coupled output. The
thermal stability can get interesting too.

Chris

 

[John Larkin]

One of the many nice things about small-signal BJTs is that they really
obey their noise models--Rbb' and Re are real physical resistances.
Power transistors are a bit different, because there are significant
gradients in voltage and temperature across the die in normal use.

To the device experts: Why do power BJTs have such big saturation
voltages compared with small-signal devices? Seems like it wouldn't be
too hard to make a die with, say, 100 integrated 2N3904s wired in
parallel. You could do that sort of litho with a crayon.

100 emitter wire bonds?

John

 

[joseph2k]

OK, so I'm an ignoramus - do bipolars even _have_ "transconductance"?
Isn't the equivalent usually called "beta"? ;-)

Yes they do, but it is part of the device physics model and generally masked
in real world application.

Beta is a small signal device model property and is not so directly
aapplicable at large signal.

Small signal means that you do not vary too far around the quiescent (bias)
point. Large signal includes swings into the non-linear regions of cutoff
and saturation.

 

[joseph2k]

Well, that approximation certainly works well at low currents.

Maybe it holds true generally including at large currents, I honestly
don't know about that (that's why I'm asking), but of course as the value
of gm gets higher, real device bulk resistances will raise their ugly
heads, enter the equation and change that relationship.



It reduces it proportionally by the numerical value of the feedback
factor.

It never eliminates it. Indeed NFB can never *eliminate* distortion,
that's why for purists, designing circuits that are initially as linear as
possible *before* applying feedback is so important.

Graham

For a nice change you are correct on this one. Moreover it becomes even
more useful in broadband and some VHF, UHF, and SHF amplifiers.

 

[joseph2k]

One of the many nice things about small-signal BJTs is that they really
obey their noise models--Rbb' and Re are real physical resistances.
Power transistors are a bit different, because there are significant
gradients in voltage and temperature across the die in normal use.

To the device experts: Why do power BJTs have such big saturation
voltages compared with small-signal devices? Seems like it wouldn't be
too hard to make a die with, say, 100 integrated 2N3904s wired in
parallel. You could do that sort of litho with a crayon.

Cheers,

Phil Hobbs

Early on, when real HF and VHF power bipolar transistors were new they did
just that. They may still, but MOS power parts into UHF has eclipsed them.

 

[Rich Grise]

Yes they do, but it is part of the device physics model and generally
masked in real world application.

Beta is a small signal device model property and is not so directly
aapplicable at large signal.

Small signal means that you do not vary too far around the quiescent
(bias) point. Large signal includes swings into the non-linear regions of
cutoff and saturation.

Well, lessee if I can wrap my headbone around this: base current is
related to base voltage by that exponential curve with temperature in it,
and beta is either the collector current divided by the base current, or
the emitter current divided by the base current; so multiplying those
together would give you collector current/base volts, which is
transconductance, right?

So it's a pretty big number, and temperature-dependent?

Thanks,
Rich

 

[Rich Grise]

One of the many nice things about small-signal BJTs is that they really
obey their noise models--Rbb' and Re are real physical resistances. Power
transistors are a bit different, because there are significant gradients
in voltage and temperature across the die in normal use.

To the device experts: Why do power BJTs have such big saturation
voltages compared with small-signal devices? Seems like it wouldn't be
too hard to make a die with, say, 100 integrated 2N3904s wired in
parallel. You could do that sort of litho with a crayon.

100 emitter wire bonds?
[/QUOTE]
300-ball BGA. ;-)

Cheers!
Rich

 

[Eeyore]

Well, lessee if I can wrap my headbone around this: base current is
related to base voltage by that exponential curve with temperature in it,
and beta is either the collector current divided by the base current, or
the emitter current divided by the base current; so multiplying those
together would give you collector current/base volts, which is
transconductance, right?

So it's a pretty big number, and temperature-dependent?

It's a large-ish number at high currents for sure.

Graham