# Q: Magic Sinewave short sequence

H

#### Henry Kiefer

Jan 1, 1970
0
Hi all -

Is there any useful resource for exploring Magic Sinewaves other than Don's site? I read his pages but lost in the infos. His online
calculators deal with selfmade syntax I don't understand.

I need a short bit sequence not more than say 300 bits long. Lower harmonics are much more important to me. Behind say the 9th I
don't care.
The sequence must be a multiple of eight to run a simple controller reloaded shift register.
I prefer a short sequence.

Any help?

regards -
Henry

H

#### Henry Kiefer

Jan 1, 1970
0
It is a general kind of harmonic suppression.

I worked a little on and the simulation of the following sequence shows approx. 15dB harmonics suppression:

whole length is: 108
next binary length is: 216
So there are two sine/cosine periods in one 216 sequence.

Surely there are much better ones. Just I don't know exactly how to calculate them.

Just to drive the discussion on ;-)

regards -
Henry

F

#### [email protected]

Jan 1, 1970
0
I need a short bit sequence not more than say 300 bits long. Lower harmonics
are much more important to me. Behind say the 9th I
don't care.

Stupid suggestion:

How about brute force? Use a Genetic Algorithm to guess a bit sequence, express
it's fitness in the product of correlation to the desired output and the RMS of
the lower harmonics calculated as an FFT of the waveform.

To me, it does not matter if the computer have to run for a few days - this
gives time for fun things.

H

#### Henry Kiefer

Jan 1, 1970
0
FFT is the way, surely.
Working in the garden and let the pc done the work...

I don't the big programmer to write that prog.

Somewhere is surely a list of useful sequences.
You can find pi, e or similar values already done to 300 digits.

Or lists of the cross-correlation properties of CDMA sequences. Gold code, Baker, etc.

But where for Magic Sinewaves? Just the wrong name for it?

regards -
Henry

--
www.ehydra.dyndns.info

|
| |
|
| > I need a short bit sequence not more than say 300 bits long. Lower harmonics
| are much more important to me. Behind say the 9th I
| > don't care.
|
| Stupid suggestion:
|
| How about brute force? Use a Genetic Algorithm to guess a bit sequence, express
| it's fitness in the product of correlation to the desired output and the RMS of
| the lower harmonics calculated as an FFT of the waveform.
|
| To me, it does not matter if the computer have to run for a few days - this
| gives time for fun things.
|
|

H

#### Henry Kiefer

Jan 1, 1970
0
| What you want is papers on the subject of "harmonic elimination".
|
| Have a look at:
| http://www.ece.utk.edu/~tolbert/publications/apec_2003_complete.pdf
|
| He refers to the classic older reference:
|
| "Generalized Harmonic Elimination and Voltage Control in Thyristor
| Inverters: Part 1--Harmonic Elimination", H. S. Patel and R. G. Hoft, IEEE
| Transactions on Industrial Applications, Vol. IE-9, pp. 310-317, May/June
| 1973.
|
| Also look at all the rest of his material on:
| http://www.ece.utk.edu/~tolbert/pubs.htm

Interesting. I read it all but understood not very much ;-(

There are at least two main differences:
- He doesn't take care of the 3rd overtone. But this is a most important one for me.
- And he is using multilevels drive. My system is bipolar only. I cannot see an easy way to convert between the different systems.

So it is interesting but not useful.

Thanks again!

- Henry

T

#### The Phantom

Jan 1, 1970
0
Hi all -

Is there any useful resource for exploring Magic Sinewaves other than Don's site? I read his pages but lost in the infos. His online
calculators deal with selfmade syntax I don't understand.

I need a short bit sequence not more than say 300 bits long. Lower harmonics are much more important to me. Behind say the 9th I
don't care.
The sequence must be a multiple of eight to run a simple controller reloaded shift register.
I prefer a short sequence.

Any help?

regards -
Henry

What you want is papers on the subject of "harmonic elimination".

Have a look at:
http://www.ece.utk.edu/~tolbert/publications/apec_2003_complete.pdf

He refers to the classic older reference:

"Generalized Harmonic Elimination and Voltage Control in Thyristor
Inverters: Part 1--Harmonic Elimination", H. S. Patel and R. G. Hoft, IEEE
Transactions on Industrial Applications, Vol. IE-9, pp. 310-317, May/June
1973.

Also look at all the rest of his material on:
http://www.ece.utk.edu/~tolbert/pubs.htm

T

#### The Phantom

Jan 1, 1970
0
| What you want is papers on the subject of "harmonic elimination".
|
| Have a look at:
| http://www.ece.utk.edu/~tolbert/publications/apec_2003_complete.pdf
|
| He refers to the classic older reference:
|
| "Generalized Harmonic Elimination and Voltage Control in Thyristor
| Inverters: Part 1--Harmonic Elimination", H. S. Patel and R. G. Hoft, IEEE
| Transactions on Industrial Applications, Vol. IE-9, pp. 310-317, May/June
| 1973.
|
| Also look at all the rest of his material on:
| http://www.ece.utk.edu/~tolbert/pubs.htm

Interesting. I read it all but understood not very much ;-(

There are at least two main differences:
- He doesn't take care of the 3rd overtone. But this is a most important one for me.
- And he is using multilevels drive. My system is bipolar only.

Did you look at the first paper:
http://www.ece.utk.edu/~tolbert/publications/apec_2003_complete.pdf

He specifically discusses bipolar modulation. The method is certainly
capable of eliminating the 3rd harmonic; you will have to work out the
details yourself.

The paper:

"Multiple Sets of Solutions for Harmonic Elimination PWM Bipolar Waveforms:
Analysis and Experimental Verification", Agelidis, Balouktsis, and Cossar,
IEEE Transactions on Power Electronics, March 2006.

deals only with bipolar waveforms.

F

#### Fred Bartoli

Jan 1, 1970
0
Henry Kiefer a écrit :
FFT is the way, surely.
Working in the garden and let the pc done the work...

I don't the big programmer to write that prog.

Somewhere is surely a list of useful sequences.
You can find pi, e or similar values already done to 300 digits.

Here are 10000s of them for pi
Want e too?

3.1415926535897932384626433832795028841971693993751058209749445923078164062862\
089986280348253421170679821480865132823066470938446095505822317253594081284811\
174502841027019385211055596446229489549303819644288109756659334461284756482337\
867831652712019091456485669234603486104543266482133936072602491412737245870066\
063155881748815209209628292540917153643678925903600113305305488204665213841469\
519415116094330572703657595919530921861173819326117931051185480744623799627495\
673518857527248912279381830119491298336733624406566430860213949463952247371907\
021798609437027705392171762931767523846748184676694051320005681271452635608277\
857713427577896091736371787214684409012249534301465495853710507922796892589235\
420199561121290219608640344181598136297747713099605187072113499999983729780499\
510597317328160963185950244594553469083026425223082533446850352619311881710100\
031378387528865875332083814206171776691473035982534904287554687311595628638823\
537875937519577818577805321712268066130019278766111959092164201989380952572010\
654858632788659361533818279682303019520353018529689957736225994138912497217752\
834791315155748572424541506959508295331168617278558890750983817546374649393192\
550604009277016711390098488240128583616035637076601047101819429555961989467678\
374494482553797747268471040475346462080466842590694912933136770289891521047521\
620569660240580381501935112533824300355876402474964732639141992726042699227967\
823547816360093417216412199245863150302861829745557067498385054945885869269956\
909272107975093029553211653449872027559602364806654991198818347977535663698074\
265425278625518184175746728909777727938000816470600161452491921732172147723501\
414419735685481613611573525521334757418494684385233239073941433345477624168625\
189835694855620992192221842725502542568876717904946016534668049886272327917860\
857843838279679766814541009538837863609506800642251252051173929848960841284886\
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002501262285941302164715509792592309907965473761255176567513575178296664547791\
745011299614890304639947132962107340437518957359614589019389713111790429782856\
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853061422881375850430633217518297986622371721591607716692547487389866549494501\
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413260472156951623965864573021631598193195167353812974167729478672422924654366\
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272037343146531977774160319906655418763979293344195215413418994854447345673831\
624993419131814809277771038638773431772075456545322077709212019051660962804909\
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105859548702790814356240145171806246436267945612753181340783303362542327839449\
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442822772634659470474587847787201927715280731767907707157213444730605700733492\
436931138350493163128404251219256517980694113528013147013047816437885185290928\
545201165839341965621349143415956258658655705526904965209858033850722426482939\
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618766795240616342522577195429162991930645537799140373404328752628889639958794\
757291746426357455254079091451357111369410911939325191076020825202618798531887\
705842972591677813149699009019211697173727847684726860849003377024242916513005\
005168323364350389517029893922334517220138128069650117844087451960121228599371\
623130171144484640903890644954440061986907548516026327505298349187407866808818\
338510228334508504860825039302133219715518430635455007668282949304137765527939\
751754613953984683393638304746119966538581538420568533862186725233402830871123\
282789212507712629463229563989898935821167456270102183564622013496715188190973\
038119800497340723961036854066431939509790190699639552453005450580685501956730\
229219139339185680344903982059551002263535361920419947455385938102343955449597\
783779023742161727111723643435439478221818528624085140066604433258885698670543\
154706965747458550332323342107301545940516553790686627333799585115625784322988\
273723198987571415957811196358330059408730681216028764962867446047746491599505\
497374256269010490377819868359381465741268049256487985561453723478673303904688\
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513984425322341576233610642506390497500865627109535919465897514131034822769306\
247435363256916078154781811528436679570611086153315044521274739245449454236828\
860613408414863776700961207151249140430272538607648236341433462351897576645216\
413767969031495019108575984423919862916421939949072362346468441173940326591840\
443780513338945257423995082965912285085558215725031071257012668302402929525220\
118726767562204154205161841634847565169998116141010029960783869092916030288400\
269104140792886215078424516709087000699282120660418371806535567252532567532861\
291042487761825829765157959847035622262934860034158722980534989650226291748788\
202734209222245339856264766914905562842503912757710284027998066365825488926488\
025456610172967026640765590429099456815065265305371829412703369313785178609040\
708667114965583434347693385781711386455873678123014587687126603489139095620099\
393610310291616152881384379099042317473363948045759314931405297634757481193567\
091101377517210080315590248530906692037671922033229094334676851422144773793937\
517034436619910403375111735471918550464490263655128162288244625759163330391072\
253837421821408835086573917715096828874782656995995744906617583441375223970968\
340800535598491754173818839994469748676265516582765848358845314277568790029095\
170283529716344562129640435231176006651012412006597558512761785838292041974844\
236080071930457618932349229279650198751872127267507981255470958904556357921221\
033346697499235630254947802490114195212382815309114079073860251522742995818072\
471625916685451333123948049470791191532673430282441860414263639548000448002670\
496248201792896476697583183271314251702969234889627668440323260927524960357996\
469256504936818360900323809293459588970695365349406034021665443755890045632882\
250545255640564482465151875471196218443965825337543885690941130315095261793780\
029741207665147939425902989695946995565761218656196733786236256125216320862869\
222103274889218654364802296780705765615144632046927906821207388377814233562823\
608963208068222468012248261177185896381409183903673672220888321513755600372798\
394004152970028783076670944474560134556417254370906979396122571429894671543578\
468788614445812314593571984922528471605049221242470141214780573455105008019086\
996033027634787081081754501193071412233908663938339529425786905076431006383519\
834389341596131854347546495569781038293097164651438407007073604112373599843452\
251610507027056235266012764848308407611830130527932054274628654036036745328651\
057065874882256981579367897669742205750596834408697350201410206723585020072452\
256326513410559240190274216248439140359989535394590944070469120914093870012645\
600162374288021092764579310657922955249887275846101264836999892256959688159205\
60010165525637568

H

#### Henry Kiefer

Jan 1, 1970
0
Thanks Fred!
If I looked for a crypt key I can use the bible ;-)

- Henry

--
www.ehydra.dyndns.info

| Henry Kiefer a écrit :
| > FFT is the way, surely.
| > Working in the garden and let the pc done the work...
| >
| > I don't the big programmer to write that prog.
| >
| > Somewhere is surely a list of useful sequences.
| > You can find pi, e or similar values already done to 300 digits.
| >
|
| Here are 10000s of them for pi
| Want e too?
|
| 3.1415926535897932384626433832795028841971693993751058209749445923078164062862\

H

#### Henry Kiefer

Jan 1, 1970
0
| >Interesting. I read it all but understood not very much ;-(
| >
| >There are at least two main differences:
| >- He doesn't take care of the 3rd overtone. But this is a most important one for me.
| >- And he is using multilevels drive. My system is bipolar only.
|
| Did you look at the first paper:
| http://www.ece.utk.edu/~tolbert/publications/apec_2003_complete.pdf

I had a flight over all papers on this side. Never seen a short sequence and their counterpart in the spectrum.

|
| He specifically discusses bipolar modulation. The method is certainly
| capable of eliminating the 3rd harmonic; you will have to work out the
| details yourself.

That is the point: I need at least a week doing the math work. Install Mathlab, learn it, etc.

|
| The paper:
|
| "Multiple Sets of Solutions for Harmonic Elimination PWM Bipolar Waveforms:
| Analysis and Experimental Verification", Agelidis, Balouktsis, and Cossar,
| IEEE Transactions on Power Electronics, March 2006.
|
| deals only with bipolar waveforms.

Of interest BUT IEEE is closed source. If I can load it via their Xplore access system I can try to load it on the local
university - not at home.
Otherwise they can trash it if most of the world cannot there documents - useless! And useless things will go the dino way...

I just need a short table book having the sequences.
It is not for a fancy military project or Bin Laden's next secure mobile phone the IEEE trying to avoid ;-)

regards -
Henry

H

#### Henry Kiefer

Jan 1, 1970
0
Here are some pictures and LTspice simulation files:
www.ehydra.dyndns.info/en/HarmonicSuppression/

Outputs are filtered by a simple 1-pole low-pass. Same values.

You can see that sig(1) vs. sig(2) have approx. 10dB more harmonics for the first few harmonic orders.
(533mVrms vs. 514mVrms)
Interesting is that higher harmonics get more power and ground noise is reduced.

Don't ask about circuit values. Here LTspice is just a number cruncher and nothing is a real component.

Have fun -
Henry

--
www.ehydra.dyndns.info

| It is a general kind of harmonic suppression.
|
| I worked a little on and the simulation of the following sequence shows approx. 15dB harmonics suppression:
|
| whole length is: 108
| next binary length is: 216
| So there are two sine/cosine periods in one 216 sequence.
|
| Surely there are much better ones. Just I don't know exactly how to calculate them.
|
| Just to drive the discussion on ;-)
|
| regards -
| Henry
|
| --
| www.ehydra.dyndns.info
|
|

H

#### Henry Kiefer

Jan 1, 1970
0
| Magic sinewaves could be replaced by a simple delta-sigma modulator,
| no? That's easy to do in an FPGA.

I'm not sure if I can follow you. ds-m? I thought this is a a/d and d/a tech thing.

I use a lookup table in ROM and send it via SPI as a bit-stream. Just clock-synched DMA.
See my link posting for the bit-stream.

regards -
Henry

J

#### John Larkin

Jan 1, 1970
0
Hi all -

Is there any useful resource for exploring Magic Sinewaves other than Don's site? I read his pages but lost in the infos. His online
calculators deal with selfmade syntax I don't understand.

I need a short bit sequence not more than say 300 bits long. Lower harmonics are much more important to me. Behind say the 9th I
don't care.
The sequence must be a multiple of eight to run a simple controller reloaded shift register.
I prefer a short sequence.

Any help?

regards -
Henry

Magic sinewaves could be replaced by a simple delta-sigma modulator,
no? That's easy to do in an FPGA.

John

I

#### Ian

Jan 1, 1970
0
Henry Kiefer said:
Newsbeitrag | Magic sinewaves could be replaced by a simple delta-sigma modulator,
| no? That's easy to do in an FPGA.

I'm not sure if I can follow you. ds-m? I thought this is a a/d and d/a
tech thing.

I use a lookup table in ROM and send it via SPI as a bit-stream. Just
clock-synched DMA.
See my link posting for the bit-stream.

regards -
Henry
I believe John is suggesting implementing a digital only (no D/A or analog
A/D)
sigma-delta in an FPGA, and feeding it a sine wave in digits. The output
would then be a string of bits that would provide your required bipolar
signal in real time.

If you pick your oversampling as an integer multiple of the sine period, you
could do this as a math (or spice) simulation, and capture the output
sequence
for one complete cycle to store in a LUT.

You can evaluate how well it does with an FFT.

Regards
Ian

J

#### John Larkin

Jan 1, 1970
0
I believe John is suggesting implementing a digital only (no D/A or analog
A/D)
sigma-delta in an FPGA, and feeding it a sine wave in digits. The output
would then be a string of bits that would provide your required bipolar
signal in real time.

Right. A counter would scan a sine lookup table, producing, say,
12-bit sines. A delta-sigma stage then decimates that to a 1-bit
stream whose duty cycle tracks the sinewave. I think Xilinx has
appnotes.

We've done something like this to force a 12-bit dac to have 16-bit
resolution.

John

H

#### Henry Kiefer

Jan 1, 1970
0
| >sigma-delta in an FPGA, and feeding it a sine wave in digits. The output
| >would then be a string of bits that would provide your required bipolar
| >signal in real time.
|
| Right. A counter would scan a sine lookup table, producing, say,
| 12-bit sines. A delta-sigma stage then decimates that to a 1-bit
| stream whose duty cycle tracks the sinewave. I think Xilinx has
| appnotes.
|
| We've done something like this to force a 12-bit dac to have 16-bit
| resolution.

But how will this suppress the lower harmonics? I think the sprectrum of your solution is nothing else than a digital signal
spectrum: amplitude(n) = 1/n * f^n and n=2k-1

- Henry

J

#### John Larkin

Jan 1, 1970
0
| >sigma-delta in an FPGA, and feeding it a sine wave in digits. The output
| >would then be a string of bits that would provide your required bipolar
| >signal in real time.
|
| Right. A counter would scan a sine lookup table, producing, say,
| 12-bit sines. A delta-sigma stage then decimates that to a 1-bit
| stream whose duty cycle tracks the sinewave. I think Xilinx has
| appnotes.
|
| We've done something like this to force a 12-bit dac to have 16-bit
| resolution.

But how will this suppress the lower harmonics? I think the sprectrum of your solution is nothing else than a digital signal
spectrum: amplitude(n) = 1/n * f^n and n=2k-1

- Henry

Well, you'd have to read up on the delta-sigma math. But the summary
is that the process "noise shapes" the output spectrum, shifting the
noise energy (and distortions) up in the spectrum, where the high
stuff is easily filtered out. That's how a 1-bit dac can make good
audio, or how a cheap d-s adc can deliver 24 bit data.

John

J

#### John Larkin

Jan 1, 1970
0
Well, you'd have to read up on the delta-sigma math. But the summary
is that the process "noise shapes" the output spectrum, shifting the
noise energy (and distortions) up in the spectrum, where the high
stuff is easily filtered out. That's how a 1-bit dac can make good
audio, or how a cheap d-s adc can deliver 24 bit data.

John

Oh, yeah, if you used d-s, you can stick a multiplier after the sine

John

H

#### Henry Kiefer

Jan 1, 1970
0
| >Well, you'd have to read up on the delta-sigma math. But the summary
| >is that the process "noise shapes" the output spectrum, shifting the
| >noise energy (and distortions) up in the spectrum, where the high
| >stuff is easily filtered out. That's how a 1-bit dac can make good
| >audio, or how a cheap d-s adc can deliver 24 bit data.
| >
| >John
|
| Oh, yeah, if you used d-s, you can stick a multiplier after the sine

Interesting.

I cannot go in my actual project very high in frequency.

regards -
Henry

H

#### Henry Kiefer

Jan 1, 1970
0
Can you explain what the parameter m means?

regards -
Henry

--
www.ehydra.dyndns.info

| On Sat, 31 Mar 2007 22:30:38 +0200, "Henry Kiefer" <[email protected]>
| wrote:
|
| >| What you want is papers on the subject of "harmonic elimination".
| >|
| >| Have a look at:
| >| http://www.ece.utk.edu/~tolbert/publications/apec_2003_complete.pdf
| >|
| >| He refers to the classic older reference:
| >|
| >| "Generalized Harmonic Elimination and Voltage Control in Thyristor
| >| Inverters: Part 1--Harmonic Elimination", H. S. Patel and R. G. Hoft, IEEE
| >| Transactions on Industrial Applications, Vol. IE-9, pp. 310-317, May/June
| >| 1973.
| >|
| >| Also look at all the rest of his material on:
| >| http://www.ece.utk.edu/~tolbert/pubs.htm
| >
| >Interesting. I read it all but understood not very much ;-(
| >
| >There are at least two main differences:
| >- He doesn't take care of the 3rd overtone. But this is a most important one for me.
| >- And he is using multilevels drive. My system is bipolar only.
|
| Did you look at the first paper:
| http://www.ece.utk.edu/~tolbert/publications/apec_2003_complete.pdf
|
| He specifically discusses bipolar modulation. The method is certainly
| capable of eliminating the 3rd harmonic; you will have to work out the
| details yourself.
|
| The paper:
|
| "Multiple Sets of Solutions for Harmonic Elimination PWM Bipolar Waveforms:
| Analysis and Experimental Verification", Agelidis, Balouktsis, and Cossar,
| IEEE Transactions on Power Electronics, March 2006.
|
| deals only with bipolar waveforms.
|
| >I cannot see an easy way to convert between the different systems.
| >
| >So it is interesting but not useful.
| >
| >Thanks again!
| >
| >- Henry
|

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