On Fri, 18 May 2001, David Cary wrote:

> Have you heard about "Magic Sinewaves" ? It's a way of generating sine waves
> from a 1 bit digital output, very similar to PWM, except that PWM has to use
> *many* more edges to generate equivalent-quality sinewaves. Lancaster claims
> that using fewer edges also reduces power transistor "switching loss".
>
>   Don  Lancaster's Magic Sinewave Library
>   http://www.tinaja.com/magsn01.html

Yep, definitely heard about it. There ain't nothin' magic about it though.

> Is there some connection between PWM, "magic sinewaves", and sigma-delta
> converters ?

In fact, there is. Take a look at:

http://www.dattalo.com/technical/theory/sqwave.html

In particular, the section titled: "011 Harmonic Content of a Periodic Pulse
Train" discusses this very issue. Within this section are links to a couple of
Octave (the GNU version of MATLAB) programs that assist in the synthesis and
analysis of "magic sine waves".

>
> The only flaw I see with "Magic Sinewaves" is that it seems to work only with a
> fixed number of samples/cycle. If I'm trying to generate several sinewaves
> (DTMF), it looks like I'm forced to store a separate table for each possible
> frequency (DTMF uses 8 frequencies), and output them independently on 2
> different pins. (With PWM, I can sum 2 analog values from a single table
> (different offsets) and emit it from a single PWM output). Am I missing
> something clever ?

The difference between PWM synthesis of sine waves and harmonic cancellation
techniques (like magic sine waves), is that the latter attempts to maximize the
"carrier" frequency while the former attempts to minimize it. If you're
controlling "things" that can't switch fast (say like large inverters) then you
want to minimize the switching and would choose the magic sinewave approach. On
the other hand, if you have a hardware PWM and just want to create a variable
frequency tone, then you'd use the PWM technique.

Another difference is that the PWM synthesis is flexible. It's conducive to
dynamic algorithms (e.g. lookup tables). However, the pulse stream for a magic
sinewave has to be pre-calculated - or I should say that generating optimum
pulse streams is computationally expensive.

Scott

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