Q: Magic Sinewave short sequence

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:

one quadrant is: 6-3-5-2-11 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

are much more important to me. Behind say the 9th I

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.

FFT is the way, surely. Working in the garden and let the pc done the work...

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

Second stupid answer: 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

--

"The Phantom" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com... | What you want is papers on the subject of "harmonic elimination". | | Have a look at: |

| | 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: |

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

--
www.ehydra.dyndns.info

site? I read his pages but lost in the infos. His online

are much more important to me. Behind say the 9th I

shift register.

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

Have a look at:

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:

news: snipped-for-privacy@4ax.com...

for me.

Did you look at the first paper:

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.

Henry Kiefer a écrit :

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\ 269456042419652850222106611863067442786220391949450471237137869609563643719172\ 874677646575739624138908658326459958133904780275900994657640789512694683983525\ 957098258226205224894077267194782684826014769909026401363944374553050682034962\ 524517493996514314298091906592509372216964615157098583874105978859597729754989\ 301617539284681382686838689427741559918559252459539594310499725246808459872736\ 446958486538367362226260991246080512438843904512441365497627807977156914359977\ 001296160894416948685558484063534220722258284886481584560285060168427394522674\ 676788952521385225499546667278239864565961163548862305774564980355936345681743\ 241125150760694794510965960940252288797108931456691368672287489405601015033086\ 179286809208747609178249385890097149096759852613655497818931297848216829989487\ 226588048575640142704775551323796414515237462343645428584447952658678210511413\ 547357395231134271661021359695362314429524849371871101457654035902799344037420\ 073105785390621983874478084784896833214457138687519435064302184531910484810053\ 706146806749192781911979399520614196634287544406437451237181921799983910159195\ 618146751426912397489409071864942319615679452080951465502252316038819301420937\ 621378559566389377870830390697920773467221825625996615014215030680384477345492\ 026054146659252014974428507325186660021324340881907104863317346496514539057962\ 685610055081066587969981635747363840525714591028970641401109712062804390397595\ 156771577004203378699360072305587631763594218731251471205329281918261861258673\ 215791984148488291644706095752706957220917567116722910981690915280173506712748\ 583222871835209353965725121083579151369882091444210067510334671103141267111369\ 908658516398315019701651511685171437657618351556508849099898599823873455283316\ 355076479185358932261854896321329330898570642046752590709154814165498594616371\ 802709819943099244889575712828905923233260972997120844335732654893823911932597\ 463667305836041428138830320382490375898524374417029132765618093773444030707469\ 211201913020330380197621101100449293215160842444859637669838952286847831235526\ 582131449576857262433441893039686426243410773226978028073189154411010446823252\ 716201052652272111660396665573092547110557853763466820653109896526918620564769\ 312570586356620185581007293606598764861179104533488503461136576867532494416680\ 396265797877185560845529654126654085306143444318586769751456614068007002378776\ 591344017127494704205622305389945613140711270004078547332699390814546646458807\ 972708266830634328587856983052358089330657574067954571637752542021149557615814\ 002501262285941302164715509792592309907965473761255176567513575178296664547791\ 745011299614890304639947132962107340437518957359614589019389713111790429782856\ 475032031986915140287080859904801094121472213179476477726224142548545403321571\ 853061422881375850430633217518297986622371721591607716692547487389866549494501\ 146540628433663937900397692656721463853067360965712091807638327166416274888800\ 786925602902284721040317211860820419000422966171196377921337575114959501566049\ 631862947265473642523081770367515906735023507283540567040386743513622224771589\ 150495309844489333096340878076932599397805419341447377441842631298608099888687\ 413260472156951623965864573021631598193195167353812974167729478672422924654366\ 800980676928238280689964004824354037014163149658979409243237896907069779422362\ 508221688957383798623001593776471651228935786015881617557829735233446042815126\ 272037343146531977774160319906655418763979293344195215413418994854447345673831\ 624993419131814809277771038638773431772075456545322077709212019051660962804909\ 263601975988281613323166636528619326686336062735676303544776280350450777235547\ 105859548702790814356240145171806246436267945612753181340783303362542327839449\ 753824372058353114771199260638133467768796959703098339130771098704085913374641\ 442822772634659470474587847787201927715280731767907707157213444730605700733492\ 436931138350493163128404251219256517980694113528013147013047816437885185290928\ 545201165839341965621349143415956258658655705526904965209858033850722426482939\ 728584783163057777560688876446248246857926039535277348030480290058760758251047\ 470916439613626760449256274204208320856611906254543372131535958450687724602901\ 618766795240616342522577195429162991930645537799140373404328752628889639958794\ 757291746426357455254079091451357111369410911939325191076020825202618798531887\ 705842972591677813149699009019211697173727847684726860849003377024242916513005\ 005168323364350389517029893922334517220138128069650117844087451960121228599371\ 623130171144484640903890644954440061986907548516026327505298349187407866808818\ 338510228334508504860825039302133219715518430635455007668282949304137765527939\ 751754613953984683393638304746119966538581538420568533862186725233402830871123\ 282789212507712629463229563989898935821167456270102183564622013496715188190973\ 038119800497340723961036854066431939509790190699639552453005450580685501956730\ 229219139339185680344903982059551002263535361920419947455385938102343955449597\ 783779023742161727111723643435439478221818528624085140066604433258885698670543\ 154706965747458550332323342107301545940516553790686627333799585115625784322988\ 273723198987571415957811196358330059408730681216028764962867446047746491599505\ 497374256269010490377819868359381465741268049256487985561453723478673303904688\ 383436346553794986419270563872931748723320837601123029911367938627089438799362\ 016295154133714248928307220126901475466847653576164773794675200490757155527819\ 653621323926406160136358155907422020203187277605277219005561484255518792530343\ 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

--
Thanks,
Fred.

Thanks Fred! If I looked for a crypt key I can use the bible ;-)

- Henry

--

"Fred Bartoli" schrieb im Newsbeitrag news:460f6c21$0$22425$ snipped-for-privacy@news.free.fr... | Henry Kiefer a écrit : | > FFT is the way, surely. | > Working in the garden and let the pc done the work... | >

| > Stupid answer: | > I don't the big programmer to write that prog. | >

| > Second stupid answer: | > 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\

"The Phantom" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com... | >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: |

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

--
www.ehydra.dyndns.info

Here are some pictures and LTspice simulation files:

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

--

"Henry Kiefer" schrieb im Newsbeitrag news:460e9da6$0$20287$ snipped-for-privacy@newsspool3.arcor-online.net... | 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: | | one quadrant is: 6-3-5-2-11 | 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 | | -- |

| |

"John Larkin" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com... | 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

--
www.ehydra.dyndns.info

site? I read his pages but lost in the infos. His online

are much more important to me. Behind say the 9th I

shift register.

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

John

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

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

"John Larkin" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com... | >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

--
www.ehydra.dyndns.info

Newsbeitrag news: snipped-for-privacy@4ax.com...

solution is nothing else than a digital signal

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

Newsbeitrag news: snipped-for-privacy@4ax.com...

solution is nothing else than a digital signal

Oh, yeah, if you used d-s, you can stick a multiplier after the sine lookup table and get high-resolution amplitude control for free.

John

"John Larkin" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com... | >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 | lookup table and get high-resolution amplitude control for free.

Interesting.

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

regards - Henry

--
www.ehydra.dyndns.info

Can you explain what the parameter m means?

regards - Henry

--

"The Phantom" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com... | On Sat, 31 Mar 2007 22:30:38 +0200, "Henry Kiefer" | wrote: | | >"The Phantom" schrieb im Newsbeitrag news: snipped-for-privacy@4ax.com... | >| What you want is papers on the subject of "harmonic elimination". | >| | >| Have a look at: | >|

| >| | >| 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: | >| | >

| >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: |

| | 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 |