From: Richard Henry on
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
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
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
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
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.
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