Square + triangle = sine (almost)
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From: Jim Thompson on 9 Mar 2010 10:39 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 -- | 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 11:48 On 3/9/2010 10:39 AM, 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 Try knitting him some mittens this year, maybe? Active diode clamps have been round for a day or too! 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: Jim Thompson on 9 Mar 2010 13:30 On Mon, 08 Mar 2010 21:40:09 -0500, Phil Hobbs <pcdhSpamMeSenseless(a)electrooptical.net> wrote: >On 3/8/2010 9:07 PM, whit3rd wrote: >> On Mar 8, 1:35 pm, Jim Thompson<To-Email-Use-The-Envelope-I...(a)My-Web- >> Site.com> wrote: >>> On Mon, 08 Mar 2010 16:26:04 -0500, Phil Hobbs >> >>>> 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. >> >>> The tricky part is containing the signal within the >>> temperature-dependent operating range. >> >> Err... did I miss something? I've squinted at the referenced paper, >> but >> what you want to convert a triangle wave to a sine is sine, not >> hyperbolic tangent... the tricky part is that it's not the right >> function >> and ALSO that it's temperature-dependent. >> >> The only 'pure' way to convert to a sine is to filter somehow. >> Motor/flywheel/generator is a pretty good filter... and it >> keeps any frequency of sine pure after it comes up to speed. >> Alas, there's no non-moving-part flywheel equivalent (high Q >> at a large range of frequencies). > >See http://electrooptical.net/www/sed/TanhSineShaper.pdf > >Cheers > >Phil Hobbs See http://analog-innovations.com/FuncGen.zip ;-) ;-) ;-) ...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: Don Lancaster on 9 Mar 2010 15:23 MooseFET wrote: > 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. > <http://www.tinaja.com/glib/hackar4.pdf> (page 85.2) <http://www.tinaja.com/magsn01.asp> -- Many thanks, Don Lancaster voice phone: (928)428-4073 Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552 rss: http://www.tinaja.com/whtnu.xml email: don(a)tinaja.com Please visit my GURU's LAIR web site at http://www.tinaja.com
From: whit3rd on 9 Mar 2010 18:59
On Mar 9, 7:39 am, Jim Thompson <To-Email-Use-The-Envelope-I...(a)My-Web- Site.com> wrote: > On Tue, 09 Mar 2010 10:10:26 -0500, Phil Hobbs > > >>>> Yep. "Piecewise-Linear", aka break-point analysis... taught in better > >>>> engineering schools ;-) > I would never use _just_ diodes, rather use them with OpAmps or > comparators, such as... Oh, they work dandy with just diodes, especially with +/-24V power. I learned on NIM bin power (highly regulated +/- 24V, highly regulated +/- 12V) and you can get away with a lot of things that newbies using 3.3V aren't gonna like. Nor IC designers, apparently. For current sources, we just hung a resistor from +24 to a PNP emitter, and wired the base to +12. The only thing more convenient would be (and it HAS been done) +/- 200V supplies. With those, you omit the transistor. More volts means less bother. It's a great relief; when something has to work on a single +2V supply, my blood pressure rises and I snarl at my squirrels. |