Conceptual problem about transfer flat-spots

Several audio related devices exhibit zero-crossing
"flat-spots", regions in their transfer curves near
zero crossing where the Y axis output is transitionally
flat. Poorly designed push-pull amplifiers exhibit
"crossover distortion", magnetic storage has poorly
characterized related effects, etc.

Question: is this electronic "backlash", to use an old
machinist's term, conceptually related (at all?) to the
well understood issue of quantizing distortion/ error?
And, if so, could classical dither be considered to be
a possible remedy?

Or, to put the question another way, could dither (of any
amount) correct a ferinstance problem of a D/A conversion
with zero output below some absolute level, but with correct output
above that level? Not an error in estimating a quantized
level, but rather zero output below some (unsigned) level.

I've approached an acquaintance from rec.audio.pro who's
the only person I know capable of answering the question.
He didn't have an off-the-cuff answer, but suggested that
I ask here, and specifically that I ask Randy Yates, as my
best bet.

Much thanks for any input, thoughts, insights. Anything currently
over my head will be studied into submission.

Great newsgroup; very impressive in so many ways,
(but sadly over my head)

Chris Hornbeck
6x9=42

On Sun, 10 Apr 2005 06:43:37 GMT, Chris Hornbeck
<chrishornbeckremovethis@att.net> wrote:

> a D/A conversion

Very sorry; thought this was fixed. Meant, of course,
"an A/D conversion"

Chris Hornbeck
6x9=42

"Chris Hornbeck" <chrishornbeckremovethis@att.net> wrote in
message news:ishh51lhk6vb86ovir3469i8fuh8aioh3p@4ax.com...
> Several audio related devices exhibit zero-crossing
> "flat-spots", regions in their transfer curves near
> zero crossing where the Y axis output is transitionally
> flat. Poorly designed push-pull amplifiers exhibit
> "crossover distortion", magnetic storage has poorly
> characterized related effects, etc.
>
> Question: is this electronic "backlash", to use an old
> machinist's term, conceptually related (at all?) to the
> well understood issue of quantizing distortion/ error?
> And, if so, could classical dither be considered to be
> a possible remedy?

Hysteresis is the electronic analog to gear lash.  It is
different from quantizing errors in several respects.
First, hysteresis is a property that shows up in the
dynamics of a process.  That is, it shows up when the
process is changing and its effect depends on the past and
current trajectory of the process.  (Gear lash only shows up
when the driven gear suddenly changes to become the driving
gear.)  Quantization error is minimally dynamic; it would
exist even if real devices had no dynamics.  It exists
because a discrete system cannot represent a continuum.

Dithering the input is hardly a "remedy" for quantization
error.  The dynamic effect of adding random dither before
quantizing is to blur the step locations.  The effect is to
cause sampled values to change value in response to input
changes that are too small to cause a change by themselves.
If the dither is random and unbiased, the digitized data can
be averaged to yield a better estimate of the analog value.
This effectively adds another bit or two to the low end of
the A/D converter at the expense of adding lag (and phase
distortion) to the system.

There are two better solutions to the problem: add more bits
to the A/D converter or add a preamplifier to raise the
analog level to take advantage of more of the dynamic range.

Chris Hornbeck wrote:
> Several audio related devices exhibit zero-crossing
> "flat-spots", regions in their transfer curves near
> zero crossing where the Y axis output is transitionally
> flat. Poorly designed push-pull amplifiers exhibit
> "crossover distortion", magnetic storage has poorly
> characterized related effects, etc.
> 
> Question: is this electronic "backlash", to use an old
> machinist's term, conceptually related (at all?) to the
> well understood issue of quantizing distortion/ error?
> And, if so, could classical dither be considered to be
> a possible remedy?
> 
> Or, to put the question another way, could dither (of any
> amount) correct a ferinstance problem of a D/A conversion
> with zero output below some absolute level, but with correct output
> above that level? Not an error in estimating a quantized
> level, but rather zero output below some (unsigned) level.
> 
> I've approached an acquaintance from rec.audio.pro who's
> the only person I know capable of answering the question.
> He didn't have an off-the-cuff answer, but suggested that
> I ask here, and specifically that I ask Randy Yates, as my
> best bet.
> 
> Much thanks for any input, thoughts, insights. Anything currently
> over my head will be studied into submission.
> 
> Great newsgroup; very impressive in so many ways,
> (but sadly over my head)
> 
> Chris Hornbeck
> 6x9=42

One manifestation of backlash is failure of a mechanical system's output 
to immediately follow a reversal of the input. I call the "flat spot" 
you describe in poorly biased class-B amplifiers "center clipping". It's 
not conceptually the same as backlash at all. On the other hand, like 
center clipping, quantizing loss is a failure of the output to move 
while the input continues in the same direction. For me, the similarity 
ends there, and I derive no insight from connecting the phenomena.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Chris Hornbeck wrote:

> Several audio related devices exhibit zero-crossing
> "flat-spots", regions in their transfer curves near
> zero crossing where the Y axis output is transitionally
> flat. Poorly designed push-pull amplifiers exhibit
> "crossover distortion", magnetic storage has poorly
> characterized related effects, etc.
> 
> Question: is this electronic "backlash", to use an old
> machinist's term, conceptually related (at all?) to the
> well understood issue of quantizing distortion/ error?

Only in as much as there is a flat spot involved, and an error between 
the input and the output representation.

> And, if so, could classical dither be considered to be
> a possible remedy?

Yes.
> 
> Or, to put the question another way, could dither (of any
> amount) correct a ferinstance problem of a D/A conversion
> with zero output below some absolute level, but with correct output
> above that level? Not an error in estimating a quantized
> level, but rather zero output below some (unsigned) level.

Probably not in either this case or your (corrected) A/D case -- reason 
being that dither _can_ be used to force a correct average value, but 
only if you can bracket the intended value.  Obviously if your intended 
value is outside of the range achievable then you're out of luck.
> 
> I've approached an acquaintance from rec.audio.pro who's
> the only person I know capable of answering the question.
> He didn't have an off-the-cuff answer, but suggested that
> I ask here, and specifically that I ask Randy Yates, as my
> best bet.
> 
> Much thanks for any input, thoughts, insights. Anything currently
> over my head will be studied into submission.
> 
> Great newsgroup; very impressive in so many ways,
> (but sadly over my head)
> 
> Chris Hornbeck
> 6x9=42


-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

John E. Hadstate wrote:

--snip--

> Dithering the input is hardly a "remedy" for quantization
> error.  The dynamic effect of adding random dither before
> quantizing is to blur the step locations.  The effect is to
> cause sampled values to change value in response to input
> changes that are too small to cause a change by themselves.
> If the dither is random and unbiased, the digitized data can
> be averaged to yield a better estimate of the analog value.
> This effectively adds another bit or two to the low end of
> the A/D converter at the expense of adding lag (and phase
> distortion) to the system.
> 
> There are two better solutions to the problem: add more bits
> to the A/D converter or add a preamplifier to raise the
> analog level to take advantage of more of the dynamic range.
> 
Neither of which can be used if you've already used up your power and 
space claim with the smallest, lowest power, decently fast converter 
chips that will fit in the design, and have chosen appropriate gain 
levels.  In that case then oversampling a 16-bit ADC and averaging works 
quite well to extend the ADC resolution (_not_, unfortunately, it's 
accuracy).  This technique is enhanced by the fact that almost any ADC 
that you can get that is at the limit of the current market's precision 
range will have random dither of the least significant bits thrown in 
_for free_!  It'll be called "noise" and it'll be in small print on the 
data sheet, but it'll be there.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

On Sun, 10 Apr 2005 12:20:14 -0700, Tim Wescott
<tim@wescottnospamdesign.com> wrote:

> dither _can_ be used to force a correct average value, but 
>only if you can bracket the intended value.  Obviously if your intended 
>value is outside of the range achievable then you're out of luck.

Thanks, Tim, this helps a lot to clear my thinking. Thanks
also to John and Jerry for reminding me that magnetic
hysteresis is a dynamic process.

My interest springs from iron-cored transformers, and now
I'm wondering if the convention solution to B-H zero crossing
flat spot, DC bias, is even approprite. I hadn't thought
that it was even related to hysteresis. Thanks!

Chris Hornbeck
6x9=42

Chris Hornbeck wrote:
 > [snip]
> 
> Thanks, Tim, this helps a lot to clear my thinking. Thanks
> also to John and Jerry for reminding me that magnetic
> hysteresis is a dynamic process.
> 

Is not "hysteresis" by definition "dynamic"?
I guess I'm *presuming* "path dependence"="dynamic".

On Sun, 10 Apr 2005 21:06:33 -0500, Richard Owlett
<rowlett@atlascomm.net> wrote:

>> for reminding me that magnetic
>> hysteresis is a dynamic process.

>Is not "hysteresis" by definition "dynamic"?
>I guess I'm *presuming* "path dependence"="dynamic".

Thanks for your thoughts. I'm still slightly uncertain
whether magnetic hysteresis is the physical phenomenon
I'm interested in. Iron cored magnetics have a zero-
crossing flat spot in their B-H curves that is often
ascribed to hysteresis.

I'd come to believe that that wasn't the case, but now
am a-sea without a paddle. If, as several knowledgeable
posters have said, the flat spot is an artifact of
hysteresis, then I need to work on my meager mental model
some (a lot) more.

Thanks to all,

Chris Hornbeck
6x9=42

"Chris Hornbeck" <chrishornbeckremovethis@att.net> wrote in message 
news:0coj51hjufkagslg58e96kt64h8q7cl8fe@4ax.com...
> On Sun, 10 Apr 2005 21:06:33 -0500, Richard Owlett
> <rowlett@atlascomm.net> wrote:
>
>
> If, as several knowledgeable
> posters have said, the flat spot is an artifact of
> hysteresis, then I need to work on my meager mental model
> some (a lot) more.

Chris,

I don't see where anyone said that......

The description you gave:

"Several audio related devices exhibit zero-crossing "flat-spots", regions 
in their transfer curves near zero crossing where the Y axis output is 
transitionally flat. Poorly designed push-pull amplifiers exhibit "crossover 
distortion", ..."

seems to be clear enough and the principle is at least implied by the 
amplifier example.  From the description and experience would suggest a 
"single trajectory plot" - that is, for every value of x, there is a single 
value of y with a shape like this:

                           |
                           |              /
                           |             /
                           |            /
                           |           /
                           |          /
                           |         /
                           |        /
                           |       /
                           |      /
                           |     /
     -----------------+----|----+------------------
                     /     |
                    /      |
                   /       |
                  /        |
                 /         |
                /          |
               /           |
              /            |
             /             |
            /              |
           /               |
          /                |
                           |

Hysteresis and backlash have a different kind of plot where there are 
families of curves such that for every curve and for every value of x, there 
are (mostly) two values of y (except at the end points).  Poorly meshed 
gears are a good example.  One can drive the gear train in one direction - 
when the direction is reversed the drive gear must move through the dead 
space until it engages the driven gear once more.  This means that the 
driven gear will stop moving while the drive gear does move.  The result is 
sort of an S-shaped double curve.  Note that there is one double curve for 
each value of maximum excursion and at each end of the excursions.  Thus, an 
infinity of round-trip curves with a general shape like this:

                           |
                           |    ----<-----+
                           |   /         /
                           |  /         /
                           | /         /
                           |/         /
                           /         /
                          /|        /
                         / |       /
                        /  |      /
                       /   |     /
     -----------------/----|----/------------------
                     /     |   /
                    /      |  /
                   /       | /
                  /        |/
                 /         /
                /         /|
               /         / |
              /         /  |
             /         /   |
            /         /    |
           /         /     |
          +---->-----      |
                           |


Unless there is some known relationship between hysteresis and a 
single-curve zero-crossing flat spot, I think the term "hysteresis" doesn't 
belong in this discussion.

Fred