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Class D Switching Power Amplifiers and Power D/A conversion

System_D_MD,  Class D is like chocolate
System_D_MD,  Class D is like chocolate
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Old 13th October 2012, 09:12 PM   #1
ChocoHolic is offline ChocoHolic  Germany
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Default System_D_MD, Class D is like chocolate

System_D_MD is a clocked design with post filter feedback, which uses parts of my private class D cook book.
Here MD does not mean Doctor of Medicine – it means Mostly Discrete.
I have audiophile concerns against irritating OP amps with large signals of the carrier frequency and decided to go for a discrete analogue input gain stage.
Further on I found that many integrated comparators have unpleasant jitter properties, which translate into poor noise figures in the audio band of the modulator. This pushed me to experiment with a discrete comparator in the triangle generator and the modulator as well.

Class_D is like chocolate. No need for fancy specials, but it has to be well balanced in its overall nature.
System_D_MD is intended to offer a pleasant balance of the properties below.
- Distortion
- Step response
- Noise
- Clipping recovery
- Carrier aliasing
The goal is to achieve reasonably good properties in all these fields, instead of pushing just a single topic to the extreme.

I have to apologize for the primitive way of scanned schematics and calculations, but during my spare time and hobby I enjoy to focus on the topic itself without winning a price for nice power point slides.

The listed references gave great inspiration to me and I am thanking the authors for their work:

Bruno Putzeys:
'The Bits In-Between. An EE's Guide to Survival Between Microphone and Voice Coil'
On the occasion of the 123rd AES Convention, Oct. 6th, 2007

Bruno Putzeys:
'Master Class, Life on the Edge, A Universal Grammar of Class D Amplification'
On the occasion of the 124rd AES Convention, May, 2007

Lars Risbo:
AES 27th International Conference, Copenhagen, Denmark, 2005 September 2–4

Lars Risbo and Claus Neesgaard:
'PWM Amplifier Control Loops with Minimum Aliasing Distortion'
AES 120th Convention, Paris, France, 2006 May 20–23

Stephen Cox:
'Mathematical models for class-D amplifiers'
School of Mathematical Sciences, University of Nottingham, UK
Presented @: School of Electrical & Electronic Engineering
NTU, Singapore, December 2009

Stephen M. Cox and Bruce H. Candy:
'Class-D Audio amplifiers with negative feedback'

Kaspar Sinding Meyer:
'Minimizing distortion in self-oscillating switching amplifiers'
Oersted DTU Department for Electric Power Engineering
Under guidance of:
Michael Andreas E. Andersen
Mikkel Christian Wendelboe Høyerby
Kgs. Lyngby, July 24, 2006

Nguyen Tranh T.:
Selfoscillating Switching Amplifier
Patent No.: US 7,221,216 B2
May 22nd, 2007

J. Lunze:
Regelungstechnik 1
DOI 10.1007/978-3-642-13808-9_8,
© Springer-Verlag Berlin Heidelberg 2010

Bruno Putzeys:
Selfoscillating Class D Amplification Device
Pub No.: US 2011/0068864 A1
March 24th, 2011
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Old 13th October 2012, 09:22 PM   #2
ChocoHolic is offline ChocoHolic  Germany
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Default Modulator Distortion

Many of the listed references focus on modulator distortion, so let's start with this.
The good old triangle modulator is known to offer a theoretical ideal linear transfer function, but application results often differ from this ideal world. There are two main reasons:
a) Imperfection of the triangle
b) Switching residuals which are injected to the modulator by the feedback.
While a) is most commonly blamed, b) is less popular in discussion - but often more crucial.

Inspired by Cox 'n Candy and Risbo and Neesgaard, I decided that it would be worth to think about less cumbersome ways of math description.
I started from the switching criteria of the comparator.
Please note that this is just a simplified model. Obviously instead of extending the term by a sum of constants, mathematically it would be allowed to extend by a sum of complex functions which sums up to 1 at any time. Such a more complex model might become necessary when digging deeper, but the simple model with constants is already opening eyes.
The new switching criteria is a sum of the well known ideal modulation mechanism and a second accidential modulation mechanism.
Well, I should not say accidential, because there are self resonant topologies that use this second modulation mechanism exclusively.

Key point: Whenever the shape of the feedback switching residual is not triangular or saw tooth, our second modulation mechanism will become substantially non linear.
There are two obvious paths to overcome this:
- Shoot with very high loop gain instead of moderate loop gain. Bruno is doing this in highest perfection.
- Shape the residuals to become triangular. That's more my cup of tea, because systems with extremely high loop gain and high order compensations, are tricky to handle when things came to carrier aliasing, step response and clipping recovery.
Attached Images
File Type: jpg TriMod_ideal.JPG (19.8 KB, 1379 views)
File Type: jpg TriMod_real.JPG (89.0 KB, 1357 views)
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Old 14th October 2012, 03:14 PM   #3
ChocoHolic is offline ChocoHolic  Germany
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Simulation shows that simple implementations can cause distortion between 0.1-1% already at medium modulation levels.

Attached two simulations.
The first three pictures show a system with triangle modulator and no feedback.
The output stage is an ideal switching stage +/-60V. Output sine wave +/-30V.
No carrier residuals, no distortion.

Picture 4, 5 and 6 show the same system with feedback.
Control theory is pointing to a P(I)D loop structure, whereas the integral portion is optional.
P and D are a must for proper loop design. In switch mode system D portions are not well regarded, because of noise issues.
Instead of the overall D portion, in motor drives and SMPS many designs use a nested current mode control loop , which is more rugged.
Basically it uses the same information, because the voltage across the output cap reflects the integral of the inductor current minus load current.
Discussion of this approach might also be valid for Audio, but here I will stay with the overall D.
The shown implementation is simple and offers 21db neg feedback, but is unfortunate regarding distortion (less distorting implementations in my next posting...).
The resulting carrier/switching residuals are not at all shaped triangular or sawtooth. Massive K3, K5 and a good portion of K2 and K7 are generated by this simple implementation of feedback.
Attached Images
File Type: jpg NoFeedback_schematic.JPG (31.3 KB, 1303 views)
File Type: jpg SWres_NoFeedback.JPG (54.5 KB, 1264 views)
File Type: jpg FFT_NoFeedback.JPG (38.6 KB, 1245 views)
File Type: jpg PDloop_simple_schematic.JPG (37.9 KB, 275 views)
File Type: jpg SWres_PDloop_simple.JPG (62.4 KB, 247 views)
File Type: jpg FFT_PDloop_simple.JPG (46.9 KB, 114 views)
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Old 14th October 2012, 03:16 PM   #4
AP2 is offline AP2  Italy
Join Date: Dec 2009
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Hi Choco,
this yours, it's a good clarification, given that some scholars, rowing against the pwm clocked, pushing more and more self-oscillating, saying it was the only way to get good performances.
As you know, I do not think so (though I have developed a good self-oscillating). certainly this development has "enlightened" me.
Today I'm right, that he insisted on pwm clocked, having solved the problem of nfb, just what you need, and not too much value in dB.
In my experience, I can say that:
Ultra precision triangle generator, solve the linearity, but has a high composition of noise. much of this noise is generated at the tips (narrow angle), the reason is obvious.
the same thing happens with fast comparators, (I need fast Comparators), then I saw that you can greatly reduce the "glish" using parallel comparators with very small shift (a res for each comparator output).

As always, you need many things, including a psu, to get a real good amp.

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Old 14th October 2012, 04:57 PM   #5
ChocoHolic is offline ChocoHolic  Germany
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The first obvious step to get more triangular carrier residuals is to build a proper differentiator.
Kaspar Sinding Meyer is listing multpile references, where this method is used to generate a linear carrier signal in self oscilating designs.

Instead of connecting the feedback cap to an oscillating node you will need a virtual AC ground,
this can reached by an OP amp or a gain stage with current input. Already this simple thing is a big step to reduce the distortion.
Picture 1, 2, 3 show an example.
There are many other points in the circuitry, which allow signal shaping.
Picture 4, 5, 6 show an example which uses a zobel to shape the residuals.

Overall it becomes obvious, that already simple (but not brainless/unreflected) methods allow a feedback structure, which won't be the bottle neck compared to other sources of distortion in class D amps.

Just take the design in picture 4 and use fast OP amps, proper comparators, IRS21xxx and a power stage and you are done?
Already this can allow good performance, but it would be ZD - means Zero Discrete, instead of MD.
Also carrier aliasing and clipping recovery are still waiting for special care.
Please note that the structure of picture 4 would already allow to add an integrating component to the loop gain by putting a cap in series to R1.
Any desired higher order loop gain behaviors can be implemented by the feedback network of E3.
For all who are waiting for MD - more to come in the next postings.

Oh yes, noise is a general headache in class D. Many PWM comparators have the unpleasant feature of translating HF-junk into audible PWM noise. Hm, paralleling comps - I never tried, but sounds to be worth a trial. Right now I am playing with discrete comparators, which seem to be especially helpful in order to shoot the component count through the roof....
Attached Images
File Type: jpg PDloop_VGND_schem.JPG (42.2 KB, 199 views)
File Type: jpg SWres_PDloop_VGND.JPG (64.0 KB, 164 views)
File Type: jpg FFT_PDloop_VGND.JPG (44.0 KB, 65 views)
File Type: jpg PDloop_VGND_zobel_schem.JPG (47.2 KB, 175 views)
File Type: jpg SWres_PDloop_VGND_zobel.JPG (58.2 KB, 159 views)
File Type: jpg FFT_PDloop_VGND_zobel.JPG (40.6 KB, 65 views)
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Old 14th October 2012, 05:47 PM   #6
darkfenriz is offline darkfenriz  Poland
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Keep them coming, excellent stuff.
One question: now you need an error amp with a flat gain up to several megahertz and output ripple signal completely free of any HF junk, don't you?
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Old 14th October 2012, 07:37 PM   #7
ChocoHolic is offline ChocoHolic  Germany
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Hi Adam,
right. Any HF-junk on the output will cause irritations, because of the D-portion... Challenge for the layout. One could soften the D portion by putting a series resistor to the D-portion-capacitor, but immediately will see increase modulator distortion again. Something to balance in real life.
The error amp E3 could be any fast OP amp. OPA2654 or LT1363 would be candidates, but also much slower types will already be fine - like AD8610/8620.
Or one could also experiment with current feedback OP amps...

I solved it discrete.
Instead of chasing poor OP amps with carrier residuals, MD is providing symetrically virtual GND to the capacitors for the D-portion with just two BJTs.
The current sources are shown simplified as ideal current sources, in reality I am designing them as discrete servo current sources in order to provide low output offset.

Version 1:
Most simple, but has a low input impedance and needs large driving signals.
Also it has no simple option to add an integrating portion for the the loop gain.

Version 2:
Uses an diamond buffer input stage and provides high input impedance and adjustable input sensitivity.
Feedback is a current feedback structure as I used in my Rookie amp.
R32 and C8 is defining the loop gain and allows for many more complex higher order structures.
If a pure PD without integrating gain is desired, simply jumper C8.
Q8 and Q7 provide excellent clipping recovery and the clipping level of this driver stage can be adjusted
by the choice of V8 and V9 close beyond the level of the triangle peaks.

Version 3:
Instead of a diamond buffer basically also two J-Fets can be used.
Greetings to Papa Nelson.
Attached Images
File Type: jpg System_D_MD_V1_schematic.JPG (33.4 KB, 265 views)
File Type: jpg System_D_MD_V2_schematic.JPG (42.4 KB, 352 views)
File Type: jpg System_D_MD_V3_schematic.JPG (40.9 KB, 376 views)
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Old 14th October 2012, 08:25 PM   #8
ChocoHolic is offline ChocoHolic  Germany
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Default Carrier Aliasing

Now let's talk about the other triangle....

There are many discussions about carrier aliasing and how to avoid or milden it.
Often discussed are gain control ideas, which change the gain of the error amp or the size of the triangle on the fly, in case of high signals.
Typically pretty complicated in real life.
Instead of above ideas we could also change the shape of the triangle.
Of course only at its peak area. The triangle shall have mostly or fully identical shape as an ideal triangle except for very high modulation levels. Around its peaks the triangle can be shaped more steep (==> reduction of gain).

Of course this effective reduction of loop gain close to clipping will affect the loop properties in this range.
In case of the 'barrier triangle' your amp will have a hard change from normal loop gain to no loop gain and the output can show the modes of the output filter, looking like in pre filter feedback systems.
In any case triangle shaping allows tons of desired shapes and makes it easy to settle the right trade off for most amps.

Attached some shapes for inspiration, feel free to create your own shaping ideas.
Attached Images
File Type: jpg Triangle_Mods_shrinked.JPG (35.1 KB, 357 views)
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Old 14th October 2012, 08:51 PM   #9
darkfenriz is offline darkfenriz  Poland
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Is there any difference between manipulating triangle shape and applying pre-distortion in a 'linear' way?
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Old 14th October 2012, 09:09 PM   #10
ChocoHolic is offline ChocoHolic  Germany
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In simulation the predistortion, by sort of soft clipping close to the peak level of the triangle, was also possible, but less flexible in its characteristic.
Also I think in reality it will be more difficult to adjust and handle tolerances and temperature drift. But I never tried such predistortion in reality.
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