Square + triangle = sine (almost)
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From: Somebody on 10 Mar 2010 04:56 >>>>>>>>>> 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.
From: Ban on 10 Mar 2010 07:10 MooseFET wrote: > > 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. This is indeed a very cute circuit, in fact I had built something similar, but with one more opamp. ciao Ban
From: Jim Thompson on 10 Mar 2010 10:18 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 �crit : >>> >>> >>> >>> > 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 -- | 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: Jim Thompson on 10 Mar 2010 10:20 On Tue, 09 Mar 2010 23:36:12 -0500, Bitrex <bitrex(a)de.lete.earthlink.net> wrote: >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? Yep, It's the sort of circuit arrangement where you can continue pretty much forever :-) > >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. Possibly. ...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: Bob Monsen on 10 Mar 2010 13:13
"Phil Hobbs" <pcdhSpamMeSenseless(a)electrooptical.net> wrote in message news:4B96EA4D.9070300(a)electrooptical.net... > 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 > Very similar to the Gilbert sine shaper. It uses the fact that the tanh function's maclauren series is similar to the sin maclauren series sin x = x - x^3/3! + x^5/5! - ... tanh x = x - x^3/3 + 2x^5/15 - 17x^7/315... so by summing the result of tanh x + tanh x/a - tanh -x/a you end up with a result that is closer to the sin, assuming you only use the values generated by the range -PI/2 to PI/2. Here is an LTSpice simulation that implements it. No idea how well it works over temp ranges etc. Regards, Bob Monsen Version 4 SHEET 1 1320 680 WIRE -384 -224 -576 -224 WIRE 176 -224 -384 -224 WIRE 320 -224 176 -224 WIRE 832 -224 320 -224 WIRE -384 -208 -384 -224 WIRE 176 -208 176 -224 WIRE 320 -208 320 -224 WIRE 832 -208 832 -224 WIRE -384 -112 -384 -128 WIRE 176 -112 176 -128 WIRE 320 -112 320 -128 WIRE 832 -112 832 -128 WIRE 112 -64 -320 -64 WIRE 768 -64 384 -64 WIRE -576 -48 -576 -224 WIRE 112 -16 112 -64 WIRE 176 -16 112 -16 WIRE 384 -16 384 -64 WIRE 384 -16 320 -16 WIRE 176 16 176 -16 WIRE 176 16 -16 16 WIRE 688 16 176 16 WIRE -384 32 -384 -16 WIRE 832 32 832 -16 WIRE 320 48 320 -16 WIRE 320 48 -160 48 WIRE 544 48 320 48 WIRE -160 80 -160 48 WIRE -16 80 -16 16 WIRE 176 80 176 16 WIRE 320 80 320 48 WIRE 544 80 544 48 WIRE 688 80 688 16 WIRE -224 128 -272 128 WIRE 64 128 48 128 WIRE 400 128 384 128 WIRE 480 128 464 128 WIRE 768 128 752 128 WIRE -576 160 -576 32 WIRE -272 160 -272 128 WIRE 464 160 464 128 WIRE -80 176 -160 176 WIRE -16 176 -80 176 WIRE 240 176 176 176 WIRE 320 176 240 176 WIRE 624 176 544 176 WIRE 688 176 624 176 WIRE 944 176 944 16 WIRE -576 192 -576 160 WIRE -528 192 -576 192 WIRE -320 192 -448 192 WIRE 64 192 64 128 WIRE 64 192 -320 192 WIRE 400 192 400 128 WIRE 400 192 64 192 WIRE 768 192 768 128 WIRE 768 192 400 192 WIRE -384 208 -384 32 WIRE -80 208 -80 176 WIRE 240 208 240 176 WIRE 624 208 624 176 WIRE 832 208 832 32 WIRE -576 224 -576 192 WIRE -272 256 -272 240 WIRE 464 256 464 240 WIRE -576 320 -576 304 WIRE -384 320 -384 288 WIRE -384 320 -576 320 WIRE -80 320 -80 288 WIRE -80 320 -384 320 WIRE 240 320 240 288 WIRE 240 320 -80 320 WIRE 624 320 624 288 WIRE 624 320 240 320 WIRE 832 320 832 288 WIRE 832 320 624 320 WIRE 944 320 944 256 WIRE 944 320 832 320 FLAG 112 128 0 FLAG -576 160 0 FLAG -320 192 c FLAG -384 32 a FLAG 832 32 b FLAG 944 16 out FLAG -272 256 0 FLAG 464 256 0 SYMBOL npn 384 80 M0 SYMATTR InstName Q3 SYMBOL npn 112 80 R0 SYMATTR InstName Q4 SYMBOL current 240 208 R0 SYMATTR InstName I2 SYMATTR Value 50� SYMBOL voltage -576 208 R0 SYMATTR InstName V1 SYMATTR Value 5 SYMBOL voltage -576 -64 R0 SYMATTR InstName V2 SYMATTR Value 5 SYMBOL voltage -432 192 R90 WINDOW 123 0 0 Left 0 WINDOW 39 0 0 Left 0 WINDOW 3 24 104 Invisible 0 SYMATTR InstName Vtri SYMATTR Value PULSE({-Va} {Va} 0 .5 .5 0 1) SYMBOL npn 480 80 R0 SYMATTR InstName Q1 SYMBOL npn 752 80 M0 SYMATTR InstName Q2 SYMBOL current 624 208 R0 SYMATTR InstName I1 SYMATTR Value 50� SYMBOL npn -224 80 R0 SYMATTR InstName Q5 SYMBOL npn 48 80 M0 SYMATTR InstName Q6 SYMBOL current -80 208 R0 SYMATTR InstName I3 SYMATTR Value 50� SYMBOL pnp 112 -16 M180 SYMATTR InstName Q7 SYMBOL pnp -320 -16 R180 SYMATTR InstName Q8 SYMBOL res 160 -224 R0 SYMATTR InstName R1 SYMATTR Value 10 SYMBOL res -400 -224 R0 SYMATTR InstName R2 SYMATTR Value 10 SYMBOL pnp 384 -16 R180 SYMATTR InstName Q9 SYMBOL pnp 768 -16 M180 SYMATTR InstName Q10 SYMBOL res 336 -224 M0 SYMATTR InstName R3 SYMATTR Value 10 SYMBOL res 848 -224 M0 SYMATTR InstName R4 SYMATTR Value 10 SYMBOL res 816 192 R0 SYMATTR InstName R5 SYMATTR Value 100k SYMBOL res -400 192 R0 SYMATTR InstName R6 SYMATTR Value 100k SYMBOL bv 944 160 R0 SYMATTR InstName B1 SYMATTR Value V={5+V(a)-V(b)} SYMBOL voltage -272 144 R0 SYMATTR InstName V3 SYMATTR Value {E} SYMBOL voltage 464 144 R0 SYMATTR InstName V4 SYMATTR Value {-E} TEXT 72 384 Left 0 !.tran 0 100 0 500u TEXT -432 352 Left 0 ;Barrie Gilbert's Sine Shaper TEXT 960 48 Left 0 !.four 1 v(out) 10 TEXT 440 376 Left 0 !.param E=100m TEXT 232 376 Left 0 !.param Va 50m TEXT -528 392 Left 0 ;I1 - I2 = I * 2 * exp(-Vt*PI*PI/2/E)*sin(PI*Va/(N-1)/E)\nN = number of pairs, Va amplitude of triangle, E amplitude of correction. TEXT -376 0 Left 0 ;I1 TEXT 840 -8 Left 0 ;I2 |