Square + triangle = sine (almost)
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From: JosephKK on 10 Mar 2010 16:00 On Wed, 10 Mar 2010 09:56:55 -0000, "Somebody" <why.do.you.want(a)to.know.invalid> wrote: >>>>>>>>>>> Sure enough, as does the ICL8038. > >Avoid this chip like the plague. At the transiition from >one quadrant to the next there is one almighty noise >spike. > Dude, the chip was new maybe 40 years ago and quite obsolete. Is someone wildcatting poor work alikes out there?
From: JosephKK on 10 Mar 2010 16:09 On Wed, 10 Mar 2010 08:18:25 -0700, Jim Thompson <To-Email-Use-The-Envelope-Icon(a)My-Web-Site.com> wrote: >On Tue, 09 Mar 2010 21:38:56 -0800, >"JosephKK"<quiettechblue(a)yahoo.com> wrote: > >>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? > >Gradually becomes sine, though smaller and smaller amplitude. I've >used such a scheme over small frequency ranges... in an ASIC, of >course, where parts are cheap :-) > > ...Jim Thompson That is what integrating the Fourier series term by term tells us.
From: whit3rd on 10 Mar 2010 16:47 On Mar 9, 9:38 pm, "JosephKK"<quiettechb...(a)yahoo.com> wrote: > Just to be off the wall, what is the integral of a triangle wave? > How about the second and third integrals? To close the loop and make an oscillator, using a square wave from a Schmitt trigger, one can use one stage of integration (to a triangle wave) or three, but not two. Two stages gets to a double-parabola, three stages to a double-cubic. The double-cubic has its small pointy defect at the crest as does the triangle wave. The three-stage thing is called a phase shift oscillator if you make it without the Schmitt trigger part. Alas, those all require multiple-gang variable resistors instead of a single knob to adjust. Have you ever priced a good three-gang pot? Or capacitor, for that matter?
From: Tim Williams on 10 Mar 2010 18:58 "JosephKK" <quiettechblue(a)yahoo.com> wrote in message news:kf2gp5deumuuqu0i2lr175n3c5bdnn5mk7(a)4ax.com... > That is what integrating the Fourier series term by term tells us. Or quite simply, when you stack up n integrators, you get 20*n dB/decade attenuation for frequencies away from fT. For convinience, set your integrators' fTs to the fundamental. I suppose you could do the same with differentiators if you had a lot of LF noise on your signal too (or wanted to bandpass to a harmonic). Of course, n differentiators and integrators, with the same fT (actually, with any fT, as long as the total has the desired gain at the peak), is an excellent description of a particularly narrow bandpass filter. As n --> infty, you get a delta response, so the circuit's impulse response is a sinewave, regardless of past or present state. It's an oscillator! Tim -- Deep Friar: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms
From: MooseFET on 10 Mar 2010 21:18
On Mar 10, 1:50 am, Bitrex <bit...(a)de.lete.earthlink.net> wrote: > MooseFET wrote: > > 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.pdfhasa > >>>>>>>> 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. > > I'm having trouble following that circuit - it looks clever, but how > does it work? Start with Vin = 0 Both op-amps are working normally. A small change in Vin is given gain as it goes towards output Increase Vin and at some point the 2nd op-amp hits the rail. Now the gain is less. Increase Vin and the 1st opamp hits the rail. Now the gain is even lower. Increase Vin and the (-) input of the 2nd opamp is going up to where the 2nd opamp comes off the rail and swings downwards The gain is further reduced. The same works in the other direction. |