Square + triangle = sine (almost)
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From: Tim Williams on 9 Mar 2010 04:17 "George Herold" <ggherold(a)gmail.com> wrote in message news:b7230e3e-874b-470b-b02a-a814d8409657(a)z35g2000yqd.googlegroups.com... > That's Great! Thanks, I tried to filter a square wave into a sine and > was deeply disappointed. (If you filtered it hard enough there was > just not enough left.) You need a high Q filter, of course. My induction heater makes an excellent sine wave from a fairly sharp square input (t_r = 100ns, so there's plenty of harmonics). The tank has Q around 10-20 depending on load, and obviously enough, since the fundamental is key to induction heating, there is plenty of signal left. :-) If you filtered a square with, say, a row of RCRC's, you'd get terrible results because the asymptotic attenuation is pretty weak and the knee is too soft (you can't make a Q > 1/3 or something like that). In time-domain terms, you're turning square into triangle with one RC (integrator), then triangle into parabola, then parabola into cubic, and so on. Eventually you'll get a fair approximation of a sine wave (i.e., the harmonics are attenuated sufficiently), but because you need to be in the asymptotic region to get useful attenuation of the harmonics, your signal of interest disappears almost as much. Tim -- Deep Friar: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms
From: MooseFET on 9 Mar 2010 09:35 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.
From: MooseFET on 9 Mar 2010 09:39 On Mar 8, 6:48 pm, George Herold <ggher...(a)gmail.com> wrote: > On Mar 8, 8:57 am, MooseFET <kensm...(a)rahul.net> wrote: > > > > > On Mar 7, 4:10 pm, whit3rd <whit...(a)gmail.com> wrote: > > > > On Mar 6, 8:04 pm, rontan...(a)esterbrook.com (Ron Tanner) wrote: > > > > > On Sun, 7 Mar 2010 14:31:48 +1100, "Phil Allison" <phi...(a)tpg.com.au> > > > > wrote: > > > > >> 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. > > > > OK thanks for the pull-up, but how about using a triangle-square wave > > > > mix, in place of a filter, to simulate a sinewave . > > > > To generate a square wave and triangle wave together, just hook a > > > Schmitt trigger to an op amp configured as integrator (resistor from > > > input to (-) node, feedback capacitor from op amp output to (-) node. > > > The output of the op amp then is fed to the Schmitt trigger (a '555 > > > does this without the op amp, but its triangle waves are curvey > > > because of that). > > > > The result is a square wave and a triangle wave, both of constant > > > amplitude, which changes frequency with a single variable resistor > > > (the integrator input resistor). > > > > SO, now you want to mix a square and triangle? If you generate them > > > by the method above, fundamentals ARE OUT OF PHASE by ninety degrees, > > > and so are all of the harmonics. You get neither cancellation nor > > > reinforcement > > > by any simple summing. > > > If you use a quad comparator, you can do some interesting stuff. With > > just 2 more comparators, you can make this: > > > ------ ------ > > --- --- --- --- > > ------ > > > It will be in phase with the triangle wave. It can be made to have no > > 3rd harmonic fairly easily. By trading off the 3rd you can have a > > reduced > > 5th. > > > It is too early in the morning for me to be sure, but I think that if > > you > > fiddle it just right and add in some of the triangle wave, you can get > > low > > values for both the 3rd and 5th. > > > It also seems to me that there should be a way to make a very > > nonlinear > > PWMing action that when low pass filtered leaves a moderately good > > estimate > > of a sine wave. This could allow you to hold the sine wave shape over > > perhaps > > a couple of decades.- Hide quoted text - > > > - Show quoted text - > > That's neat, are you making a 'few' bit DAC? The first idea: The comparators are a few bit ADC and the resistors to make the waveform are a few bit DAC. The second idea: The idea is that a PWM signal at perhaps a few MHz can be made. This PWM signal would be nonlinear with the triangle's voltage and thus make it into a more rounded shape. > > George H.
From: Jim Thompson on 9 Mar 2010 09:59 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 -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice:(480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | The only thing bipartisan in this country is hypocrisy
From: Phil Hobbs on 9 Mar 2010 10:10
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 -- 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 |