Square + triangle = sine (almost)
in [Design]
|
Prev: Avalanche Photodetector
Next: Cheap potting alternative
From: whit3rd on 9 Mar 2010 19:15 On Mar 8, 6:40 pm, Phil Hobbs <pcdhSpamMeSensel...(a)electrooptical.net> wrote: > >>> You can do a pretty good job with an LM13700 producing the tanh shape, > >>> and then subtracting off a small amount of the original triangle wave to > >>> get rid of the cusps at the peaks. > >> The transfer characteristics of a BIPOLAR diff pair IS a TANH > >> function. > See http://electrooptical.net/www/sed/TanhSineShaper.pdf Whoa! That's brilliant, you should get a patent. Not just for what it is, but it REMOVES THE AUTOCORRELATION glitch. It follows, from the Wiener-Hopf theorem, that the crude XR2206 style diode shaping will now be VERY effective; if your triangle wave is accurate enough, and your summation really takes out the cusp, then the crude diode-array trim can get you much further, to -80 dB or better. The low level of high harmonic content in F-space looks nice, but it doesn't do justice to the full glory of the scheme, in the context of building a sinewave generator on a chip. Tanh and diodes are easy, so are triangles. Getting the coefficients accurate enough on the summation might want trimmed resistors, but that can be done on-chip, too.
From: Phil Hobbs on 9 Mar 2010 19:39 On 3/9/2010 7:15 PM, whit3rd wrote: > On Mar 8, 6:40 pm, Phil Hobbs<pcdhSpamMeSensel...(a)electrooptical.net> > wrote: > >>>>> You can do a pretty good job with an LM13700 producing the tanh shape, >>>>> and then subtracting off a small amount of the original triangle wave to >>>>> get rid of the cusps at the peaks. > >>>> The transfer characteristics of a BIPOLAR diff pair IS a TANH >>>> function. > >> See http://electrooptical.net/www/sed/TanhSineShaper.pdf > > Whoa! That's brilliant, you should get a patent. Not just for what > it > is, but it REMOVES THE AUTOCORRELATION glitch. > It follows, from the Wiener-Hopf theorem, that the crude XR2206 style > diode shaping will now be VERY effective; if your triangle > wave is accurate enough, and your summation really takes > out the cusp, then the crude diode-array trim can get you > much further, to -80 dB or better. > > The low level of high harmonic content in F-space looks nice, but it > doesn't do justice to the full glory of the scheme, in the context of > building a sinewave generator on a chip. Tanh and diodes are > easy, so are triangles. Getting the coefficients accurate enough > on the summation might want trimmed resistors, but that can > be done on-chip, too. Thanks, but I very much doubt that I'm the first one to think of it. Works great though. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal ElectroOptical Innovations 55 Orchard Rd Briarcliff Manor NY 10510 845-480-2058 hobbs at electrooptical dot net http://electrooptical.net
From: Bitrex on 9 Mar 2010 23:36 Jim Thompson wrote: > On Tue, 09 Mar 2010 10:10:26 -0500, Phil Hobbs > <pcdhSpamMeSenseless(a)electrooptical.net> wrote: > >> On 3/9/2010 9:59 AM, Jim Thompson wrote: >>> On Mon, 08 Mar 2010 21:42:22 -0800, >>> "JosephKK"<quiettechblue(a)yahoo.com> wrote: >>> >>>> On Mon, 08 Mar 2010 09:25:15 -0700, Jim Thompson<To-Email-Use-The-Envelope-Icon(a)My-Web-Site.com> wrote: >>>> >>>>> On Mon, 08 Mar 2010 00:01:44 -0800, Muzaffer Kal<kal(a)dspia.com> >>>>> wrote: >>>>> >>>>>> On Sun, 07 Mar 2010 23:11:20 -0800, >>>>>> "JosephKK"<quiettechblue(a)yahoo.com> wrote: >>>>>> >>>>>>> On Sat, 6 Mar 2010 20:21:10 -0800, D from BC<myrealaddress(a)comic.com> wrote: >>>>>>> >>>>>>>> In article<4b9324ee.4432562(a)news.tpg.com.au>, rontanner(a)esterbrook.com >>>>>>>> says... >>>>>>>>> On Sun, 7 Mar 2010 14:31:48 +1100, "Phil Allison"<phil_a(a)tpg.com.au> >>>>>>>>> wrote: >>>>>>>>> >>>>>>>>>> "Harold Larsen" >>>>>>>>>>> If a squarewave contains all odd harmonics of the fundamental >>>>>>>>>>> frequency, and a triangle all even, >>>>>>>>>> >>>>>>>>>> ** Sorry - that is WRONG . >>>>>>>>>> >>>>>>>>>> A triangle wave contains only odd harmonics too. >>>>>>>>>> >>>>>>>>>> http://en.wikipedia.org/wiki/Triangle_wave >>>>>>>>>> >>>>>>>>>> A "sawtooth" wave contains all integer harmonics. >>>>>>>>>> >>>>>>>>> OK thanks for the pull-up, but how about using a triangle-square wave >>>>>>>>> mix, in place of a filter, to simulate a sinewave . >>>>>>>>> >>>>>>>>> I have not seen that method applied or described anywhere, but it >>>>>>>>> makes a fair approximation, at least to my eye. >>>>>>>>> >>>>>>>>> Harold Larsen >>>>>>>> >>>>>>>> This reminds of the XR2206 chip that makes square, triangle and sine >>>>>>>> using analog technology. >>>>>>> Sure enough, as does the ICL8038. Part of the question is how it is done. >>>>>> The datasheet at http://www.intersil.com/data/FN/FN2864.pdf has a >>>>>> pretty good schematic and explanation which shows how it's done. >>>>> Yep. "Piecewise-Linear", aka break-point analysis... taught in better >>>>> engineering schools ;-) >>>>> >>>>> ...Jim Thompson >>>> I first saw it in a synchro to digital converter about 1973. I had to think >>>> hard for a while before i "got" it. >>> The only place I can remember using it in an actual product was for >>> linearizing a flat-face CRT sweep (RADAR)... and there it was >>> piecewise _curve_ fitting. >>> >>> ...Jim Thompson >> Breakpoint amps are nearly always a crutch. One poor guy I tried to >> help (15 years back) ignored my advice and wound up with a multi-diode >> breakpoint amp stuck inside a crystal oven to keep the breakpoints from >> going all over the place with temperature. Blech. (It was in a fancy >> measurement system, too. Got all sorts of industry awards.) >> >> The Widlar approach (National AN4, Figure 8) uses BJT saturation to make >> nice sharp breakpoints that don't drift much. Of course you have to >> wait for the transistor to come out of saturation. >> >> About the only good use of breakpoint amps I've seen is inside >> complicated FB loops, e.g. to approximately correct for the nonlinearity >> of VCOs and heaters. This reduces the variation of loop gain and so >> makes frequency compensation easier. Drift and inaccuracy are not a big >> problem in those sorts of applications. >> >> Cheers >> >> Phil Hobbs > > Ah, yes! Thanks for the reminder! I also linearized a frequency > hopping VCO for OmniSpectra _many_ years ago... for jumping close to > desired frequency, so the PLL lock was faster... a cavity beast :-) > > I would never use _just_ diodes, rather use them with OpAmps or > comparators, such as... > > http://analog-innovations.com/SED/ClampForLarkin.pdf > > (A Christmas gift, 2007. But he remains a cranky old git :-) > > http://analog-innovations.com/SED/LevelDetectAndFollow-LM339.pdf > > http://analog-innovations.com/SED/LevelDetectAndFollow-TL431.pdf > > http://analog-innovations.com/SED/PerfectDiodeForChargerIsolation.pdf > > ...Jim Thompson The first schematic looks like the start of a decent guitar fuzzbox pedal! I think one could set more breakpoints with different slopes by using more comparators with the breakpoint voltage on the non inverting inputs and putting resistors in series with the diodes, right? Back before guitar practice amps with DSP became commodity hardware, Peavey had a patented technology called "TransTube" that purported to make a solid state amp have a tone more like a tube amp. I wonder if they used a similar piecewise linear technique to make the amp have a softer clipping characteristic.
From: JosephKK on 10 Mar 2010 00:38 On Tue, 9 Mar 2010 06:35:44 -0800 (PST), MooseFET <kensmith(a)rahul.net> wrote: >On Mar 9, 12:22 am, Fred Bartoli <myname_with_a_dot_inbetw...(a)free.fr> >wrote: >> MooseFET a écrit : >> >> >> >> > On Mar 8, 8:28 am, "Tim Williams" <tmoran...(a)charter.net> wrote: >> >> "MooseFET" <kensm...(a)rahul.net> wrote in message >> >> >>news:c968f0a3-64bc-46e1-8a14-7b36a8e75d0f(a)b9g2000pri.googlegroups.com.... >> >> >>> If you use a quad comparator, you can do some interesting stuff. With >> >>> just 2 more comparators, you can make this: >> >>> ------ ------ >> >>> --- --- --- --- >> >>> ------ >> >> I recollect something from Don Lancaster about Magic Sinewaves and how you >> >> can get arbitrarily low harmonics from certain optimal patterns of on and >> >> off, given sufficiently accurate timing, and I suppose some sort of >> >> filtering. I never did figure out if it's supposed to be a tristate >> >> waveform (as above) >> >> > The waveform I drew can be made by simply adding two pulse trains >> > with >> > different duty cycles. The fact that 3 time 60 degrees is 180 degrees >> > is how you can get the 3rd harmonic to go away. >> >> > If you use more steps, you can get the first N harmonics to drop to >> > zero. The same is true for line segments instead of steps. >> >> Which is nothing more than the analog variant of a transversal filter >> that you can build from a divider, a shift register and a few weighted >> summing resistors. > >It is the same idea but in this case, it is made from a triangle wave >which we have to start with instead of needing to make a higher >frequency >first. > > >> >> -- >> Thanks, >> Fred. Just to be off the wall, what is the integral of a triangle wave? How about the second and third integrals?
From: MooseFET on 10 Mar 2010 01:35
On Mar 9, 8:36 pm, Bitrex <bit...(a)de.lete.earthlink.net> wrote: > Jim Thompson wrote: > > On Tue, 09 Mar 2010 10:10:26 -0500, Phil Hobbs > > <pcdhSpamMeSensel...(a)electrooptical.net> wrote: > > >> On 3/9/2010 9:59 AM, Jim Thompson wrote: > >>> On Mon, 08 Mar 2010 21:42:22 -0800, > >>> "JosephKK"<quiettechb...(a)yahoo.com> wrote: > > >>>> On Mon, 08 Mar 2010 09:25:15 -0700, Jim Thompson<To-Email-Use-The-Envelope-I...(a)My-Web-Site.com> wrote: > > >>>>> On Mon, 08 Mar 2010 00:01:44 -0800, Muzaffer Kal<k...(a)dspia.com> > >>>>> wrote: > > >>>>>> On Sun, 07 Mar 2010 23:11:20 -0800, > >>>>>> "JosephKK"<quiettechb...(a)yahoo.com> wrote: > > >>>>>>> On Sat, 6 Mar 2010 20:21:10 -0800, D from BC<myrealaddr...(a)comic.com> wrote: > > >>>>>>>> In article<4b9324ee.4432...(a)news.tpg.com.au>, rontan...(a)esterbrook.com > >>>>>>>> says... > >>>>>>>>> On Sun, 7 Mar 2010 14:31:48 +1100, "Phil Allison"<phi...(a)tpg.com.au> > >>>>>>>>> wrote: > > >>>>>>>>>> "Harold Larsen" > >>>>>>>>>>> If a squarewave contains all odd harmonics of the fundamental > >>>>>>>>>>> frequency, and a triangle all even, > > >>>>>>>>>> ** Sorry - that is WRONG . > > >>>>>>>>>> A triangle wave contains only odd harmonics too. > > >>>>>>>>>>http://en.wikipedia.org/wiki/Triangle_wave > > >>>>>>>>>> A "sawtooth" wave contains all integer harmonics. > > >>>>>>>>> OK thanks for the pull-up, but how about using a triangle-square wave > >>>>>>>>> mix, in place of a filter, to simulate a sinewave . > > >>>>>>>>> I have not seen that method applied or described anywhere, but it > >>>>>>>>> makes a fair approximation, at least to my eye. > > >>>>>>>>> Harold Larsen > > >>>>>>>> This reminds of the XR2206 chip that makes square, triangle and sine > >>>>>>>> using analog technology. > >>>>>>> Sure enough, as does the ICL8038. Part of the question is how it is done. > >>>>>> The datasheet athttp://www.intersil.com/data/FN/FN2864.pdfhas a > >>>>>> pretty good schematic and explanation which shows how it's done.. > >>>>> Yep. "Piecewise-Linear", aka break-point analysis... taught in better > >>>>> engineering schools ;-) > > >>>>> ...Jim Thompson > >>>> I first saw it in a synchro to digital converter about 1973. I had to think > >>>> hard for a while before i "got" it. > >>> The only place I can remember using it in an actual product was for > >>> linearizing a flat-face CRT sweep (RADAR)... and there it was > >>> piecewise _curve_ fitting. > > >>> ...Jim Thompson > >> Breakpoint amps are nearly always a crutch. One poor guy I tried to > >> help (15 years back) ignored my advice and wound up with a multi-diode > >> breakpoint amp stuck inside a crystal oven to keep the breakpoints from > >> going all over the place with temperature. Blech. (It was in a fancy > >> measurement system, too. Got all sorts of industry awards.) > > >> The Widlar approach (National AN4, Figure 8) uses BJT saturation to make > >> nice sharp breakpoints that don't drift much. Of course you have to > >> wait for the transistor to come out of saturation. > > >> About the only good use of breakpoint amps I've seen is inside > >> complicated FB loops, e.g. to approximately correct for the nonlinearity > >> of VCOs and heaters. This reduces the variation of loop gain and so > >> makes frequency compensation easier. Drift and inaccuracy are not a big > >> problem in those sorts of applications. > > >> Cheers > > >> Phil Hobbs > > > Ah, yes! Thanks for the reminder! I also linearized a frequency > > hopping VCO for OmniSpectra _many_ years ago... for jumping close to > > desired frequency, so the PLL lock was faster... a cavity beast :-) > > > I would never use _just_ diodes, rather use them with OpAmps or > > comparators, such as... > > >http://analog-innovations.com/SED/ClampForLarkin.pdf > > > (A Christmas gift, 2007. But he remains a cranky old git :-) > > >http://analog-innovations.com/SED/LevelDetectAndFollow-LM339.pdf > > >http://analog-innovations.com/SED/LevelDetectAndFollow-TL431.pdf > > >http://analog-innovations.com/SED/PerfectDiodeForChargerIsolation.pdf > > > ...Jim Thompson > > The first schematic looks like the start of a decent guitar fuzzbox > pedal! I think one could set more breakpoints with different slopes by > using more comparators with the breakpoint voltage on the non inverting > inputs and putting resistors in series with the diodes, right? > > Back before guitar practice amps with DSP became commodity hardware, > Peavey had a patented technology called "TransTube" that purported to > make a solid state amp have a tone more like a tube amp. I wonder if > they used a similar piecewise linear technique to make the amp have a > softer clipping characteristic. At lowish frequencies, you can do this: ---------------------------------------/\/\---+----Out ! ! +-----------------/\/\----+-/\/\---+---/\/\----+ ! ! ! ! ! --!-\ ! ! In ---+--------!+\ ! >-- ! ! >---+--/\/\--+---!+/ ! --!-/ ! ! ! ! ! ---/\/\--GND ! GND--/\/\--+--/\/\---+------------------------/\/\-- With rail to rail op-amps, you can get a total of 6 knees from Vee to Vcc in the output swing. |