Square + triangle = sine (almost)
in [Design]
|
Prev: Avalanche Photodetector
Next: Cheap potting alternative
From: Phil Allison on 8 Mar 2010 05:27 "Frank-Stefan M�ller" > In Gemany, the angle is 56.789 degrees, because the mains voltage is > higher... ** Das Fuhrer has spoken.... ...... Phil
From: MooseFET on 8 Mar 2010 08:57 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.
From: Jim Thompson on 8 Mar 2010 11:25 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 -- | 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: Tim Williams on 8 Mar 2010 11:28 "MooseFET" <kensmith(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) or PWM (on/off for varying rates) or multivalued (minimal bit DAC?) or what. http://www.tinaja.com/glib/stepsynt.pdf Ugh. Why does Don. Always have to write. Fragmented sentences. Looks like it's a PWM tristate thing (requiring an always-on H bridge), but not really PWM as the edge timings are arbitrary through the cycle. Rather than microcomputer friendly as claimed in the introduction, I expect such a generator would be easier to synthesize in an FPGA, since microcontrollers don't offer timers with lots and lots of counter compare units, and general microcomputers have awful timing (at best, you'll get single cycle accuracy in a single-cycle-instruction microcontroller with no possible interrupt service). Tim -- Deep Friar: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms
From: Don Klipstein on 8 Mar 2010 14:36
In article <om89p51rdgbhc1eaqipbvieu4oceoortut(a)4ax.com>, JosephKK 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. I have played around with the XR2206 before. It appears to me that the square and triangle have a derivative/integral relationship to each other. I seem to think that the triangle is generated current source switching polarity periodically, such that the current waveform is a squarewave, alternately charging and discharging a capacitor. And it appears to me that the sine wave is derived by feeding the triangle wave through a resistor in series with an inverse-paralleled pair of diodes or something having similar effect. The sinewave is found across the antiparallel pair of diodes (or similar circuitry). This results in the tips of the triangle wave being "squashed" to obtain an approximation of a sinewave. The peaks of the resulting sinewave are not perfectly rounded, but show a trace of the pointy tips of the triangle wave. The XR2206 has provisions to adjust the symmetry and the degree of squashing of the sine-to-triangle conversion. When my hearing is in a good mood, I can adjust the symmetry to minimize even harmonics, and the degree of squashing to get the 3rd and 5th harmonic low. (The 3rd and 5th cannot be both reduced to zero simultaneously in my experience). Traces of odd harmonics higher than the 5th will remain since the peaks of the sinewave cannot be perfectly smoothed by the triangle-to-sine conversion circuitry in the XR2206. - Don Klipstein (don(a)misty.com) |