Re: Digital Sine Wave Generation

From: Jim Thompson (thegreatone_at_example.com)
Date: 07/05/04 

Date: Mon, 05 Jul 2004 09:21:50 -0700

On Mon, 05 Jul 2004 15:22:06 GMT, Fred Bloggs <nospam@nospam.com>
wrote:

>
>
>Scrim wrote:
>> I'm hoping to use a modification to this circuit from "The Art of
>> Electronics" but I can't sort out the maths:
>>
>> http://www.scitech.pwp.blueyonder.co.uk/Digital-Sine-Wave-Generatio.gif
>>
[snip]
>> After spending some time using the trig functins on my calculator I havn't
>> yet been able to find exactly how these values were selected. Any one know
>> the answer?
>>
>> Scrim
>>
>>
>
>Those values are computed easily once you have the digital weighting
>function for the sinewave- it is a digital filtering application- the
>example circuit is not a uniform weighting function:
> View in a fixed-width font such as Courier.
>
>
>
>
>
> SHIFT REG
> +------------+
> | | R1
> | B |---/\/\-------+----->VOUT
> | 1 | |
[snip]
> +------------+ |
> |
> FDBK<----------------+
>
>
>
>
>
> ITERATIVE COMPUTATION OF R I=1,2,3,..N :
> I
>
> Denote Y = 1/R
> I I
>
> and Y = Y + Y + ...+ Y
> T 1 2 N
>
> and R = 1/Y or R x Y =1
> P T P T
>
>
> When B = Vdd='1' then contribution to VOUT is
> I
>
> | 1
> VOUT/Vdd| = -------------------------------------------
> |B 1+ R x(Y + Y +...Y + Y + ...+ Y )
> I I 1 2 I-1 I+1 N
>
[snip]
> y + y + y = W x SIN (ANGLE )
> 1 2 3 3 3
>
> ETC...
>
> y + y +... + y = W x SIN(ANGLE )=1
> 1 2 N N N
>
>
> From this, it is clear how to solve for ratios y in
> I
> succession. So that when you fix Y by consideration
> T
> of loading constraints, then each
>
>
> 1 1
> R = - = ------
> I Y y x Y
> I I T
>

Show-off ;-)

However, it is refreshing to see math instead of guess-work!

But no surprise coming from Fred!

                                        ...Jim Thompson 

-- 
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.