# Q: Magic Sinewave short sequence

Discussion in 'Electronic Design' started by Henry Kiefer, Mar 31, 2007.

1. ### The PhantomGuest

In which one of the papers is the parameter "m" to be found?

2. ### Henry KieferGuest

| On Mon, 2 Apr 2007 23:10:33 +0200, "Henry Kiefer" <>
| wrote:
|
| >Can you explain what the parameter m means?
| >
| >regards -
| >Henry
|
| In which one of the papers is the parameter "m" to be found?
|

http://www.ece.utk.edu/~tolbert/publications/apec_2003_complete.pdf
Fig. 2, m is on the x-axis.

BTW the Fig.1 is wrong: Left over one transition.
Also at least the phase angle 1 is not on the correct position. Maybe just to clarify the picture for printing.

I constructed a bit-sequence out of the two figures but the result is not worth to mention. Way worse than my sequence.
I cannot find an explanation for m other than it connects the three phase angles to reduce the mathematics. Is this right?

How to read the correct three angles in Fig. 2 ?

In another paper m stands for modulation index and there Fig. 2 from the paper here is printed but not referenced in the text.

Confusing.
It's maybe better to run a noise generator to construct a sequence and let see FFT if it is good. Then repeat until there is no
better solution found.
Beginning with a short sequence up to a maximum chosen.
You need to simulate the first quadrant only. All others are symmetrical to it.

- Henry

3. ### The PhantomGuest

On page 596, right hand column, last line of text: "Given a desired
fundamental voltage V1..."; that is, V1 is the desired fundamental
amplitude.

On page 597, left hand column, top of the page, "...where m =
V1/(4*Vdc/pi)."

He has set up the equations in (2) to eliminate the 5th and 7th harmonics.
If you want to eliminate the 3rd, you will have to re-formulate the
equations, and also add more equations if you want to eliminate 3rd, 5th,
7th, 9th and 11th, for example.

4. ### Henry KieferGuest

| On page 596, right hand column, last line of text: "Given a desired
| fundamental voltage V1..."; that is, V1 is the desired fundamental
| amplitude.
|
| On page 597, left hand column, top of the page, "...where m =
| V1/(4*Vdc/pi)."

How does he come to this? And why there is a dependence of the absolute value voltage? After low-pass filtering the output stream I
can amplify the ouput as needed. So I don't understand why going another way than simple ratio output.

On the other side:
Setting V1=1 and Vdc=0 (No dc voltage) makes no sense.
Or setting Vdc=0.5 for shifting the output to dc voltage=0 is correct?
Hm "pi": Is V1 the desired Vrms=1? I remember loosely that Vpeak and Vrms are connected with pi and something...

|
| He has set up the equations in (2) to eliminate the 5th and 7th harmonics.
| If you want to eliminate the 3rd, you will have to re-formulate the
| equations, and also add more equations if you want to eliminate 3rd, 5th,
| 7th, 9th and 11th, for example.

Yeah. I think I can modify the equations as needed but how should I resolve them? Can I pass them to Scilab or such? I never played
with Scilab -> next problem

regards -
Henry

5. ### The PhantomGuest

Look at equation 1. Do you see the term 4 Vdc/pi in front of the curly
bracket? He wants to define m such that when m = 1, the output has the
maximum possible fundamental for the given available DC voltage.
The technique described in this paper is for high power inverters, where
it is not feasible to amplify the output, because amplifying the output
would introduce unacceptable losses and extra cost. Also, because of the
high power, it is desirable to keep the switching frequency as low as
possible while still suppressing harmonics.

If your application can use amplification after the generation of the
switching waveform, and a higher switching frequency, then perhaps a
different method might be better for you.

In fact, if you would tell us what your application is, we might be
better able to advise you. If you can use amplification of the switching
waveform, then why don't you just use a sine wave to start with?
This paper is describing high power inverters. Vdc will never be zero
when the inverter is operating; it will be whatever DC rail voltage is
available, possibly from batteries. The variable m will be varied to
create a switching pattern to generate the desired amplitude of the
fundamental.

On page 600 under "Experimental Results", he says he used a DC link
voltage of 48 volts, for example.
As he says on page 597 under "Elimination using Resultants", "A
systematic procedure to do this is known as elimination theory and uses the
notion of resultants [4][5][6][7]". You may have to look up some of the
references.

problem, but the various papers I've referred you to probably don't have
that. They only show you the methods to use, and you will have to do some
work to get the final answer.

6. ### Don LancasterGuest

The latest magic sinewave calculator appears at
http://www.tinaja.com/demo28a.asp

It is thousands of times faster and more precise than the earlier versions.

--
Many thanks,

Don Lancaster voice phone: (928)428-4073
Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552

Please visit my GURU's LAIR web site at http://www.tinaja.com

7. ### Henry KieferGuest

| The latest magic sinewave calculator appears at
| http://www.tinaja.com/demo28a.asp
|
| It is thousands of times faster and more precise than the earlier versions.

Hi Don -

OK. What is "delta friendly"?

I have 1-bit quantization. You smallest seems to be 8-bits.
My amplitude has no meaning. I need the ratio only

What I have to do?

regards -
Henry

8. ### Don LancasterGuest

Very specialized magic sinewaves are required to drive a three phase
motor or other three phase load in which you are not willing to isolate
each end of each phase.

In general, three phase sinewaves are trickier to understand, and zero
out fewer harmonics (typically 3n/4 or so rather than 4n). But they also
need only one half the storage and calculate much faster.

See http://www.tinaja.com/glib/deltams1.pdf for specifics.

--
Many thanks,

Don Lancaster voice phone: (928)428-4073
Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552

Please visit my GURU's LAIR web site at http://www.tinaja.com

9. ### Henry KieferGuest

| > I have 1-bit quantization. You smallest seems to be 8-bits.
| > My amplitude has no meaning. I need the ratio only
| >
| > What I have to do?
| >
| > regards -
| > Henry
| >
| >
|
|
| Very specialized magic sinewaves are required to drive a three phase
| motor or other three phase load in which you are not willing to isolate
| each end of each phase.
|
| In general, three phase sinewaves are trickier to understand, and zero
| out fewer harmonics (typically 3n/4 or so rather than 4n). But they also
| need only one half the storage and calculate much faster.
|
| See http://www.tinaja.com/glib/deltams1.pdf for specifics.

Your document shows a 3-phase motor control with 3 quantization steps per channel.
I need a 1-phase control with one channel. I mentioned that.

It is not for motor control. I control a class E amplifier. At the receiving end the magic sinewave will be AM-demodulated to get a
pure sinewave while the class E amp works with a much higher carrier frequency.

regards -
Henry

10. ### Henry KieferGuest

| >How does he come to this?
|
| Look at equation 1. Do you see the term 4 Vdc/pi in front of the curly
| bracket? He wants to define m such that when m = 1, the output has the
| maximum possible fundamental for the given available DC voltage.

OK. I understand. He means the ratio between input voltage and required output voltage.

|
| >And why there is a dependence of the absolute value voltage? After low-pass filtering the output stream I
| >can amplify the ouput as needed. So I don't understand why going another way than simple ratio output.
|
| The technique described in this paper is for high power inverters, where
| it is not feasible to amplify the output, because amplifying the output
| would introduce unacceptable losses and extra cost. Also, because of the
| high power, it is desirable to keep the switching frequency as low as
| possible while still suppressing harmonics.
|
| If your application can use amplification after the generation of the
| switching waveform, and a higher switching frequency, then perhaps a
| different method might be better for you.

Good question which?

|
| In fact, if you would tell us what your application is, we might be
| better able to advise you. If you can use amplification of the switching
| waveform, then why don't you just use a sine wave to start with?

It is not for motor control. I control a class E amplifier. At the receiving end the "magic sinewave" will be AM-demodulated to get
a pure sinewave while the class E amp works with a much higher carrier frequency.

regards -
Henry

11. ### Don LancasterGuest

Magic sinewaves, of course, COMPLETELY ELIMINATE any need for a class E
amplifier. A simple H bridge driver is substituted. With which variable
amplitude combined with astoundingly low distortion is utterly trivial.

--
Many thanks,

Don Lancaster voice phone: (928)428-4073
Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552

Please visit my GURU's LAIR web site at http://www.tinaja.com

12. ### Henry KieferGuest

| > | See http://www.tinaja.com/glib/deltams1.pdf for specifics.
| >
| > Your document shows a 3-phase motor control with 3 quantization steps per channel.
| > I need a 1-phase control with one channel. I mentioned that.
| >
| > It is not for motor control. I control a class E amplifier. At the receiving end the magic sinewave will be AM-demodulated to
get a
| > pure sinewave while the class E amp works with a much higher carrier frequency.
| >
| > regards -
| > Henry
| >
|
| Magic sinewaves, of course, COMPLETELY ELIMINATE any need for a class E
| amplifier. A simple H bridge driver is substituted. With which variable
| amplitude combined with astoundingly low distortion is utterly trivial.

Don!

Don't clutter me with marketing. I need facts! You know, I'm german ;-) So we love facts, getting strong, nihilism and other great
things.

You cannot make a pure sine waveform at 7MHz with a H bridge the easy way. Class E is much cheaper at this frequency.

But that is not the point!
The problem is that I need a bipolar bit-stream magic sinewave.
So, is this possible or not? The carrier is about 1500 times higher than the baseband, where your sine wave will live.
I think it should be possible to trade algorithmically resolution vs. oversamping here.

Henry

13. ### Henry KieferGuest

| So, is this possible or not? The carrier is about 1500 times higher than the baseband, where your sine wave will live.
"where your digital magic wave will live."

- Henry

14. ### jasenGuest

You have a different problem than the one Don aims to solve.

You dividte time finitely and place no limit on transitions,

Don divides it continuously but limits transistions to a finite count.
bipolar?
__ __ __ __ __ __ __
| |_ _| |_ _| |_ _| |_ _| |_ _| |_ _| |_ _
|__| |__| |__| |__| |__| |__| |__|

or unipolar?
____ _ _ _____ _ _ _____ _ _ _____ _
| | | | | | | | | | | | | | | | | | | | | |
_| |_| |_____| |_| |_| |_____| |_| |_| |_____| |_| |_| |____

I'd model it in a spreadsheet: 296 rows (or whatever), assume a stable starting point and calculate
the optimum value for each cell.

Bye.
Jasen