mikep

identifying sources of 3rd harmonic in discrete circuits
« on: March 01, 2006, 08:47:59 PM »
This is something that I have been thinking about.  I am recently out of work and looking for a job.  Im using the free time to dig into the books and trying to fill some of the bigger holes in my EE knowledge. (ive got some DIY stuff to catch up on too!) Mostly Im trying to get better at working with discrete transistor circuits (I've already got a pretty good grasp on opamp theory).  I wonder if someone could shed some light on the common mechanisms that cause distortion.  I'm aware of some of the basic stuff regarding distortion as a whole, but don't have much understanding about how to design a circuit with a specific characteristic.   right now im just concentrating on even versus odd.  right now I just design something for low overall distortion then simulate it and tweak.  in low distortion circuits reducing odd products seems difficult.   Can anyone give me some pointers?
 
thanks a bunch,
mike p


hagtech

identifying sources of 3rd harmonic in discrete circuits
« Reply #1 on: March 01, 2006, 11:44:12 PM »
Odd harmonics come from differential circuits - as they tend to cancel out the even ones.  Also feedback will multiply any harmonics into non-integer fractions, which are musically the most nasty.

Warm, pleasant sounds generally have even order harmonics.  But sound can get congested and confused rather quickly, depending on the complexity of the song.  Orchestras can turn to mush.  Solo vocals and jazz will sound great.

First lesson is to reduce the forward open loop distortion.  Do not depend on feedback.  Clipping, of course, is the ultimate source of odd harmonics.

jh
Jim Hagerman
Hagerman Technology LLC - making audio fun again

mikep

identifying sources of 3rd harmonic in discrete circuits
« Reply #2 on: March 02, 2006, 12:34:47 PM »
Quote from: "hagtech"

First lesson is to reduce the forward open loop distortion.  


Maybe I should have clarified, this is what I am doing.  Im trying to get a handle on the sources of *open loop* distortion.

Quote from: "hagtech"

Odd harmonics come from differential circuits - as they tend to cancel out the even ones.
 


And this is the primary reason I am interested in locating sources of odd harmonics.  Is it possible to design a differential circuit that does not have predominantly 3rd harmonic?  Seems like the only way to do that would be to locate the mechanisms that are causing the distortion in the first place.

mike p

bcarso

identifying sources of 3rd harmonic in discrete circuits
« Reply #3 on: March 02, 2006, 01:16:05 PM »
Quote from: "mikep"
Quote from: "hagtech"

First lesson is to reduce the forward open loop distortion.  


Maybe I should have clarified, this is what I am doing.  Im trying to get a handle on the sources of *open loop* distortion.

Quote from: "hagtech"

Odd harmonics come from differential circuits - as they tend to cancel out the even ones.
 


And this is the primary reason I am interested in locating sources of odd harmonics.  Is it possible to design a differential circuit that does not have predominantly 3rd harmonic?  Seems like the only way to do that would be to locate the mechanisms that are causing the distortion in the first place.

mike p


There is a good discussion of distortion in Dennis Feucht's  Handbook of Analog Circuit Design.  Since it is virtually unobtainable, PM me here with an email addy and I could be persuaded to copy an excerpt, or if you can spring for the coin find his website and get the CD ROM that is the revised version of the book.

Even-order mechanisms are basically due to asymmetry around the quiescent operating point  of an instantaneous gain curve.  If my volts out for a given volts in curve looks like the right-hand half of a parabola (or more likely the upper of lower half of a y^2 = x parabola), I will see second harmonic in the output of an input sinusoid, along with a d.c. shift.  That is, in this situation my instantaneous (i.e., no memory effects, phase lags, etc.) gain is progressively higher on one side of my operating point on the parabolic segment than on the other.

If, instead, my gain curve looks like an S curve and my operating point is at the center of the inflection, my gain is falling off symmetrically either side of the operating point, and I will get at least 3rd harmonic distortion.  Jim's comment is correct in that balanced and/or differential arrangements of things with second-order will tend to cancel the second if the sections are matched, and you are right that it is tougher to cancel odd-order.

Some ways besides feedback involve predistortion of the signal well-matched to the nonlinearities of the amplifying devices.  An example: Barrie Gilbert's current gain cells using bipolars.

You also might want to check out the thread I started in the Drawing Room discussing a paper by Boyk and Sussman: http://www.groupdiy.com/index.php?topic=13703

By the way, good for you to use your temporary spare time to study this stuff!

EDIT: for typo and grammar

Larrchild

identifying sources of 3rd harmonic in discrete circuits
« Reply #4 on: March 02, 2006, 01:51:41 PM »
"We distort...You Decide"

mssrs bcarso and larrchild

Good for you!

(In next week's episode, we crash a 2SK364 into a 20 foot tall 2-tone signal!)

mikep

identifying sources of 3rd harmonic in discrete circuits
« Reply #5 on: March 02, 2006, 02:34:16 PM »
Quote from: "bcarso"

There is a good discussion of distortion in Dennis Feucht's  Handbook of Analog Circuit Design.  


I just checked and they have this at the university library where my girlfriend is currently enrolled.  She is going to check it out for me tomorrow!  Thanks for the suggestion.:guinness:

I looked up gilbert and his gain cells... it is a bit over my head but seems pretty nifty.  highly linear current multipliers? could something like that be used to make a current-input opamp?  I havent found the predistortion stuff yet, ill keep looking.

thanks,
mike p

bcarso

identifying sources of 3rd harmonic in discrete circuits
« Reply #6 on: March 02, 2006, 02:49:46 PM »
Quote from: "mikep"
Quote from: "bcarso"

There is a good discussion of distortion in Dennis Feucht's  Handbook of Analog Circuit Design.  


I just checked and they have this at the university library where my girlfriend is currently enrolled.  She is going to check it out for me tomorrow!  Thanks for the suggestion.:guinness:

I looked up gilbert and his gain cells... it is a bit over my head but seems pretty nifty.  highly linear current multipliers? could something like that be used to make a current-input opamp?  I havent found the predistortion stuff yet, ill keep looking.

thanks,
mike p


Excellent!  Copies are scarce, probably because after a limited print run anyone who got one holds on to it.

The Gilbert predistortion gambit (it may not be described as such, so don't look too hard) can be, and is used for current mirrors and at the inputs of a class of ~op amps that were heavily promoted for a while (so-called Norton op amps---example: the LM3900).  And the technique is at the heart of the typical transconductance multipliers and, with a slight stretch, the log-antilog variable-gain cells like David Blackmer's.

PRR

identifying sources of 3rd harmonic in discrete circuits
« Reply #7 on: March 02, 2006, 11:59:04 PM »
> Is it possible to design a differential circuit that does not have predominantly 3rd harmonic?

For decades I wudda said: Doubt it!

But see this thread.

You can quibble about what "differential" really means. Have fun.

cuelist

identifying sources of 3rd harmonic in discrete circuits
« Reply #8 on: March 03, 2006, 04:08:05 AM »
In Doug Selfs book "Self on Audio" there is a lengthy and detailed piece on distorsion mechanisms in amplifiers. It focuses on power amplifiers but it also holds true for small signal amplifiers as well.


http://www.audioxpress.com/bksprods/books/bkb87.htm
Mr K

mikep

identifying sources of 3rd harmonic in discrete circuits
« Reply #9 on: March 03, 2006, 11:56:24 AM »
So far Ive only spent about 2 hours with the Feucht book, ive got alot more to read -- but I already found some good insights.  

In his analysis of the two BJT transistor diff-amp he mentions the S-shape of the transfer curve and the therefore predominantly 3rd harmonic it generates.  It seems this topology will always have this "flaw".  There are some interesting 4 transistor variations on the diff-pair presented, im going to study those more.

When he is talking about how to estimate distortion he develops a generalized expression for distortion products.  The higher order products have increasing powers of the amplitude term.  I think this is pretty interesting, but then further down he actually states what I was thinking:
"for a doubbling of amplitude, 2nd order distortion doubbles while 3rd order quadruples"  

Im trying to rationalize if this realy applies to all real circuits, or just his generalized case.  It does support what Ive often seen in real life measurements and in the simluator.  At increasing level 3rd rises faster than 2nd.  This seems siginificant to me as it probably contributes to audio sounding more "stressed" at higher levels.  so how do you fight it? keep voltages low?  Sounds like a job for a current amp.

The standard differential input pair seems to be the worst 3rd harmonic offender in a simple opamp.  It is a transconductance amplifier, volts in - current out.  Why not replace it with a current in - current out diff amp?  Ive done some experimenting with voltage input - current feedback amps and they have some good properties, but you can't make a low offsset or a high-CMR amp out of one, that I am aware of.  Im going to have a closer look at the LM3900 datasheet...

mike p


mikep

identifying sources of 3rd harmonic in discrete circuits
« Reply #10 on: March 03, 2006, 12:21:09 PM »
Um, is a differential current amplifier simply a current mirror?

bcarso

identifying sources of 3rd harmonic in discrete circuits
« Reply #11 on: March 03, 2006, 01:27:47 PM »
Heh.  You are off and running....

A current mirror by itself is sort of a diff amp---but the subtraction of the second current occurs at its output which is also the input of the following stage.  Look at the topology of the 3900 and its ilk for how they did it.  Also bear in mind that the input diode is a diode-connected transistor of the same geometry as the other input transistors.

Without getting too much into detail at the moment, one problem with many current amps is noise.  Also many sources are not designed to operate into low Z inputs.

Larrchild

identifying sources of 3rd harmonic in discrete circuits
« Reply #12 on: March 03, 2006, 01:55:03 PM »

"Hey, hey, Ralphie! I made a current opamp!"

Hey, what about TransNodal feedback?
I've always been a Jim Strickland (Acoustat) fan.

He later became Grand Poobah at Hafler:

"Hafler uses a variation of Class AB called trans-nova, designed by Jim Strickland in 1980. Jerry Cave, Hafler?s managing director, explains: "It?s a different way of using transistors in the circuit, requiring fewer gain stages and a much simpler signal path. This lets us get voltage and current gain out of both transistors"

Patent

mikep

identifying sources of 3rd harmonic in discrete circuits
« Reply #13 on: March 03, 2006, 03:32:07 PM »
Quote from: "bcarso"

Without getting too much into detail at the moment, one problem with many current amps is noise.  Also many sources are not designed to operate into low Z inputs.


There are two applications I was thinking of trying this that need high CMR: active line level M/S matrix (sum/difference) and balanced line receiver.

noise shouldn't be a problem in either one, right?  the low-z inputs is another story.  In the LM3900 datasheet they show alot of high value resistors around the amps. I suppose that is to keep the input-Z high.  I wonder about noise with 2M in the feedback loop.  I read somewhere about stabilizing a CFB amp by raising the Z of the feedback resistor instead of with a parallel cap like a voltage feedback system. So they could be doing it for that reason too.

I guess in the the M/S application there would be input buffers. in the line receiver case you could essentially make it into an instrumentation amp.

what about a high-level differential current amp as an OUTPUT stage? would that be feasible?

mike p

PRR

identifying sources of 3rd harmonic in discrete circuits
« Reply #14 on: March 03, 2006, 06:21:11 PM »
> This lets us get voltage and current gain out of both transistors"

Does that come with the Free Lunch?

It's a useful trick, but not earth-shattering.

Larrchild

identifying sources of 3rd harmonic in discrete circuits
« Reply #15 on: March 03, 2006, 06:27:46 PM »
I was more intrigued by that delta-shaped feedback network. And how they distribute the feedback.

PRR

identifying sources of 3rd harmonic in discrete circuits
« Reply #16 on: March 03, 2006, 06:37:16 PM »
> the S-shape of the transfer curve and the therefore predominantly 3rd harmonic it generates. It seems this topology will always have this "flaw".

Imagine an amplifier, for symmetrical signals, that won't eventually clip on both sides and splatt odd-order distortion. The only way to avoid that is to have an infinitely big amp, which is infinitely expensive.

We do tend to know our signal levels, and can often avoid gross clipping. Can we devise an amplifier that has dead-constant gain up to nearly the clipping point?

In general: probably not. All active devices have transconductance that varies with standing current. If they didn't, they would have transconductance at zero current, which is probably absurd. For very small signal variations around a large standing current, we can pretend that transconductance is constant. But it isn't: the rise on positive peaks does not cancel the drop on negative peaks. And in most practical amps, this soon becomes obvious, to the THD meter if not the o'scope.

> "for a doubbling of amplitude, 2nd order distortion doubbles while 3rd order quadruples" Im trying to rationalize if this realy applies to all real circuits

Is it quadruples? Probably depends which power-law you assume your devices follow.

And it would seem to assume that only one stage is distorting. (And that we are working SE; an ideal P-P amp has zero 2nd harmonic.)

It is true-enough that for Class-B radio linear amplifier specification, they assume it is always true (tube or transistor), and specify distortion by "3rd order intercept", an imaginary power level (above clipping) where the (extrapolated) 3rd-order tone equals the (extrapolated) fundamental. This fails for the new chip-amps because they have multiple stages under feedback. Distortion is low and then goes high very suddenly.

mikep

identifying sources of 3rd harmonic in discrete circuits
« Reply #17 on: March 07, 2006, 02:59:20 AM »
Quote from: "PRR"
The only way to avoid that is to have an infinitely big amp, which is infinitely expensive.


I think I like where this is going.  If you manufacture something infinitely expensive and the profit margin is non-zero as long as someone buys it, the profit is INFINITE.  I should have worked for a defense contractor after all. (I have an MSME, by the way, and alot of my friends from grad school now make bombs. not me!)

but seriously, I guess this is why SPL builds those mastering consoles that run on, what is it, +/- 48v?  what is the downside, other than cost? if you are willing to spend the $$ are there high voltage transistors with the same kind of bandwidth the little guys have?  

Quote from: "PRR"
All active devices have transconductance that varies with standing current.


here is a big part of the problem.  I thought the topology would play a bigger part, but it keeps coming back to the shape of this curve. It is pretty darn important if you want to control the different harmonics.  but they all look pretty similar on the datasheets.  roughly half of a  x=y^2 parabola.   what is there to do, test them all yourself? are there any rules of thumb I should know about general device types and their distortion characteristics?


mike


 

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