Square + triangle = sine (almost)
in [Design]
|
Prev: Avalanche Photodetector
Next: Cheap potting alternative
From: Richard Henry on 7 Mar 2010 00:09 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: > > > > >"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 Why would you need to simulate a sine wave? It is well characterized in the literature and there are lots of extra ones lying around unused.
From: Bitrex on 7 Mar 2010 00:23 Ron Tanner wrote: > 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 > > You can approximate a sine wave by putting a triangle wave through a circuit that has a hyperbolic tangent shaped transfer function. The following circuit (from "Musical Applications of Microprocessors " by Hal Chamberlin)approximates that function by using the conduction characteristics of two back to back diodes at low currents: Triangle in 14V pk-pk o-------o-------------------- .-. | .-. | | - | | 1M | | ^ | | 150 '-' | '-' | | | | | | | | |-+ | | | -o--------o------>|-+ Sine out 1V pk-pk | | | | o---------o .-. | .-. 1M | | | | | | | V | | 150 '-' - '-' | - | ---------|----------- === GND (created by AACircuit v1.28.6 beta 04/19/05 www.tech-chat.de) Though I haven't tried to do it the author claims that with precision components and adjustment the circuit can be adjusted to under 1% harmonic distortion. You could do a similar thing with a differential amplifier or an OTA.
From: Kevin McMurtrie on 7 Mar 2010 00:44 In article <4b931859.1212000(a)news.tpg.com.au>, haroldlarsen(a)porterland.com (Harold Larsen) wrote: > If a squarewave contains all odd harmonics of the fundamental > frequency, and a triangle all even, will I get ALL harmonics if I mix > the two waveforms? > > It looks like a cross between a squarewave and sinewave. > > I have not seen any tech references to the practical value of this. > Does it have any? > > For example, to roughly approximate a sinewave without filtering. > > Harold Larsen Heh, no that doesn't work. The usual way to approximate a sine wave is to blunt the sharp tips off a triangle wave with diodes. With enough tweaking it gets very close. -- I won't see Google Groups replies because I must filter them as spam
From: Ban on 7 Mar 2010 03:12 Bitrex wrote: >> > > You can approximate a sine wave by putting a triangle wave through a > circuit that has a hyperbolic tangent shaped transfer function. The > following circuit (from "Musical Applications of Microprocessors " by > Hal Chamberlin)approximates that function by using the conduction > characteristics of two back to back diodes at low currents: > > > Triangle in 14V pk-pk > > o-------o-------------------- > .-. | .-. > | | - | | > 1M | | ^ | | 150 > '-' | '-' > | | | > | | | > | | |-+ > | | | > -o--------o------>|-+ Sine out 1V pk-pk > | | > | | o---------o > .-. | .-. > 1M | | | | | > | | V | | 150 > '-' - '-' > | - | > ---------|----------- > === > GND > > (created by AACircuit v1.28.6 beta 04/19/05 www.tech-chat.de) > > > Though I haven't tried to do it the author claims that with precision > components and adjustment the circuit can be adjusted to under 1% > harmonic distortion. You could do a similar thing with a differential > amplifier or an OTA. If this circuit is really published the way you drew it, it shows how little a uP guy knows about analogue. The distortion may be even higher than of the triangle wave at the input, and <1% you can get only with 6 turn points if adjusted well. A differential transistor stage OTOH is capable of sine-shaping with a minimum of 1.3% THD, with an additional clipping of the tops you can reach almost 0.4%. Another possibility is to develop the sine function into a power series sinx = x - x^3/3! + x^5/5! - ... using only the first 2 terms you get 0.6% THD, but you need 2 analog multipliers for that. Slightly modifying the coefficients even 0.25% can be reached. This is very useful if the sin is to be differentiated later. ciao Ban
From: Darwin on 7 Mar 2010 04:25
On 7 Mar, 04:12, haroldlar...(a)porterland.com (Harold Larsen) wrote: > For example, to roughly approximate a sinewave without filtering. As pointed out by other participants, you can obtain a sine wave from a triangle wave thanks to a nonlinear transform of the signal. The National Semiconductor application note 263 is worth reading and contains a paragraph dedicated to those techniques: http://www.national.com/an/AN/AN-263.pdf (see "Approximation Methods" paragraph beginning at page 8) Hope it helps. |