Square + triangle = sine (almost)
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From: Tim Williams on 8 Mar 2010 17:58 "whit3rd" <whit3rd(a)gmail.com> wrote in message news:7f952719-ece0-4a91-bd65-9e981f5c058f(a)v20g2000yqv.googlegroups.com... > The 'magic sinewaves' approach is a variant on the digital filter > theme, using calculated ON/OFF pulses to cancel two or three > of the harmonics... but that only buys you a small reprieve > from the problem, a low-pass filter to take out the higher > harmonics is assumed. Alas, that kills the adjustable- > frequency range, unless you make a (expensive) tracking filter. Sure, but you could do it adaptively, using higher order magic sines for lower frequencies. I don't know how much computation or memory that would require. Sufficiently low frequencies could be driven by PWM instead (basically DDS with PWM or d-s output). So instead of an expensive tracking filter, you write a (potentially expensive) sinewave generator. Practical considerations can change things of course... driving a motor, it's not really going to matter much, as winding inductance will filter harmonics, at some expense to efficiency; at low frequencies, the drive will be rather coggy and the harmonics will be lossy, but the power output is small, too (think VFD), so efficiency doesn't matter as much. On the other hand, driving something like a voice coil shaker table, you *must* have harmonics above a fixed frequency, or else they'll screw up your test results. Tim -- Deep Friar: a very philosophical monk. Website: http://webpages.charter.net/dawill/tmoranwms
From: whit3rd on 8 Mar 2010 19:42 On Mar 8, 2:58 pm, "Tim Williams" <tmoran...(a)charter.net> wrote: > "whit3rd" <whit...(a)gmail.com> wrote in message > > news:7f952719-ece0-4a91-bd65-9e981f5c058f(a)v20g2000yqv.googlegroups.com... > > > The 'magic sinewaves' approach is a variant on the digital filter > > theme, ..., a low-pass filter to take out the higher > > harmonics is assumed. Alas, that kills the adjustable- > > frequency range, > Sure, but you could do it adaptively, using higher order magic sines for > lower frequencies. Oh, I just use brute force instead of adapting; my iPod has a complement of sinewaves, both pure and swept, ready for any occasion.
From: MooseFET on 8 Mar 2010 20:51 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. (time for dinner) > 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: whit3rd on 8 Mar 2010 21:07 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).
From: Phil Hobbs on 8 Mar 2010 21:40
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 -- 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 |