Re: DDS issues...was sine generator ic solution

From: John Larkin (jjSNIPlarkin_at_highTHISlandPLEASEtechnology.XXX)
Date: 01/31/05 

Date: Sun, 30 Jan 2005 17:26:03 -0800

On Sun, 30 Jan 2005 16:28:50 -0800, mike <spamme0@netscape.net> wrote:

>John Larkin wrote:
>> On Sun, 30 Jan 2005 14:47:13 -0800, mike <spamme0@netscape.net> wrote:
>>
>>
>>>DDS issues???
>>>
>>>The concept of DDS frequency synthesizers comes up frequently.
>>>I can't figure out what they're good for.
>>>I took apart the prototype hardware, so you'll have to be
>>>content with an Excel simulation.
>>>Here's a plot of a DDS simulation.
>>>
>>>http://nm7u.tripod.com/homepage/sine.jpg
>>>
>>>If you looked at it on a real-time scope, you'd likely
>>>be impressed. All the points lie exactly on the sine wave,
>>>(within D/A resolution)
>>>so statistically it's a real sinewave. Averaged over time
>>>the AVERAGE frequency can be very precise.
>>>
>>>But if you look at it on a storage scope, you can see that
>>>each cycle is different. And the difference can change dramatically for
>>>small changes in frequency. The graph shows how for some frequencies, the
>>>output is amplitude modulated at a much lower frequency. You can't
>>>take that out with a low-pass filter.
>>>
>>>The graph is deceptive cause it
>>>linearly interpolates the points. In actuality, there's a big
>>>ole step at each point. This becomes painfully clear if you try to use
>>>a comparator to generate a square wave. Or if you try to DDS anything
>>>other than a sine wave.
>>>
>>>Yes, if you filter it enough, you can make anything into
>>>a sinewave. And if your hardware is a few orders of magnitude
>>>faster than your ouput requirement, the filter is easier.
>>>
>>>What am I missing that makes DDS useful in any time-domain application
>>>or wideband frequency-domain application?
>>>mike
>>
>>
>>
>> I can't see the pic, but a raw DDS output does indeed look nasty, and
>> gets worse as you approach Fclk/2, the Nyquist frequency. But if you
>> run it through a lowpass filter, you get a nice sine wave with
>> respectably low jitter. The Sampling Theorem says so, and it works.
>>
>> We build an arbitrary waveform generator that includes four DDS clock
>> sources. The crystal oscillator freq is 40 MHz, and we synthesize
>> wavegen clocks up to 15 MHz. The DDS chip output feeds a 4-pole LC
>> filter and a schmitt trigger gate and makes a pretty nice clock.
>
>Since you're triggering at the high slew rate part of the waveform, a
>little amplitude modulation probably won't affect you much.
>

It's not amplitude modulation; it's the presence of a summed image,
which is fixable with a lowpass filter. The horrible slithering
effects you see near submultiples of the clock are really an optical
illusion.

>I don't know whether to describe it as a mix or as an alias.
>It's most observable where the sampling frequency is not quite
>exactly a multiple of the output frequency. Modulation depth
>is a function of frequency. I found it took a big chunk out
>of the top end I was expecting. I don't think most people would
>notice the problem or object until they wanted to use those frequencies
>in some test that counted on stable amplitude.

Again, a lowpass filter will take what looks like hell and fix it up
into a beautiful sine wave. A telephone or a CD player is exactly the
same: a digitized, sampled-data telemetry link, reconstructed by a dac
and a lowpass filter. A DDS is no different from playing a sine wave
on a CD player.

If you stay below, say, half of Nyquist (namely Fclk/4) it doesn't
take much of a filter to clean it up nicely. The highest signal
frequency will be 0.25*Fclk, and the image you need to kill will be at
0.75*Fclk, three times the fundamental. As you approach the Nyquist
frequency, the filter becomes impossible.

>
>Does this work any better?
>
>http://www.geocities.com/SiliconValley/Monitor/4710/sine.jpg
>

Yup, but it's kind of small. A lowpass filter will connect (actually,
extrapolate) the points better than these straight lines; it will make
a nice flat sine wave.

John