Re: DDS question: why sine lookup?

From	john larkin <jl@glen--canyon.com>
Newsgroups	sci.electronics.design, comp.dsp
Subject	Re: DDS question: why sine lookup?
Date	2025-05-07 06:32 -0700
Organization	A noiseless patient Spider
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On Wed, 7 May 2025 11:44:23 +0200, Arie de Muijnck <noreply@ademu.nl>
wrote:

>On 2025-05-07 00:50, john larkin wrote:
>> On Tue, 6 May 2025 16:46:16 -0400, Phil Hobbs
>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>> 
>>> On 2025-05-06 15:00, Jeroen Belleman wrote:
>>>> On 5/6/25 17:48, john larkin wrote:
>>>>> A DDS clock generator uses an NCO (a phase accumulator) and takes some
>>>>> number of MSBs, maps through a sine lookup table, drives a DAC and a
>>>>> lowpass filter and finally a comparator. The DAC output gets pretty
>>>>> ratty near Nyquist, and the filter smooths out and interpolates the
>>>>> steps and reduces jitter.
>>>>>
>>>>> But why do the sine lookup? Why not use the phase accumulator MSBs
>>>>> directly and get a sawtooth, and filter that?
>>>>>
>>>>> The lowpass filter looks backwards in time for a bunch of ugly samples
>>>>> to average into a straight line. The older sine samples are the wrong
>>>>> polarity! If the filter impulse response is basically zero over the
>>>>> period of the sawtooth, and we compare near the peak, we'll average a
>>>>> lot of steps and forget the big sawtooth reset. [...]
>>>>
>>>> Two things are immediately obvious: First, the sawtooth will have
>>>> a variable frequency, and the filter won't have a zero response
>>>> for all possible frequencies.
>>>>
>>>> Second, the usual reconstruction filters do *not* interpolate
>>>> into straight lines.
>>>>
>>>> Beyond that, I would have to think this over a bit more.
>>>>
>>>> Jeroen Belleman
>>>>
>>>>
>>>>
>>>
>>> You don't want to use a sawtooth if you can help it, because it has huge
>>> contributions from all harmonic orders.  It also puts a lot of demands
>>> on the slew rate and settling of the DAC and any amplifiers used in the
>>> filtering.  Errors there are of course nonlinear, because once an amp is
>>> in slew limiting, it stops responding to its inputs for a bit.
>> 
>> I was thinking that my DAC is just 5 or 6 resistors hanging off some
>> FPGA pins, and that drives a 3rd order (CLC) LC filter and the
>> comparator. So no opamps.
>> 
>> 
>> 
>>>
>>> It also emphasizes the close-in spurs.  Say you have two N-bit DDSes
>>> running at the same average frequency but different phases.  The DAC
>>> samples only the M high-order bits. It happens that at time t=0 the
>>> accumulator overflows on the same clock cycle on both.
>>>
>>> This will continue to happen until one of them overflows a cycle early
>>> because the bottom N-M bits rolled over.
>>>
>>> The resulting voltage difference between them is a full-scale,
>>> one-clock-wide pulse, followed by a noisy baseline as the bottom N-M
>>> bits roll over into the DAC's LSB at different times.  This will repeat
>>> every cycle until the other DDS catches up.  This scenario will play out
>>> some number of times in a full period, i.e. the least common multiple of
>>> the accumulator size and the increment in clocks.
>>>
>>> The energy in that glitch is much larger than in the noisy baseline, and
>>> its timing is variable in complicated ways.
>>>
>>> A triangle would be better, and of course that could be done pretty
>>> simply, e.g. with a flip flop controlling a bunch of XOR gates, if you
>>> don't mind halving the frequency.
>>>
>>> Once you have a lookup table, a sine is as easy as anything else, and
>>> minimizes the demands on the DAC, filters and amplifiers.
>>>
>>> Cheers
>>>
>>> Phil Hobbs
>> 
>> If I'm using, say, 8 MS phase accumulator bits and a 5-bit DAC and
>> synthesizing one octave of frequency, the sine table is no big deal.
>> 256 bytes of RAM per DDS unfolded.
>> 
>> I've been playing with sims. The sawtooth works OK but may be too
>> cute. I'll compare it to sines.
>> 
>> The pseudo-DAC output is always positive. It can go into one
>> comparator input and I can RC lowpass filter same into the other, to
>> switch on the waveform midpoint.
>> 
>> I reall need to get my FPGA kids to run the phase accumulator at 160
>> MHz. Run way below Nyquist.
>> 
>
>
>Can't you fold the LIN to SIN conversion in the resistor values?
>
>Arie

I don't know. I can buy a small cheap R-2R resistor network, and a 8-8
bit sine lookup is easy in an FPGA.

Resistors are linear and sine is nonlinear.

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Thread

DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-06 08:48 -0700
  Re: DDS question: why sine lookup? Jeroen Belleman <jeroen@nospam.please> - 2025-05-06 21:00 +0200
    Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-06 12:33 -0700
    Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-06 16:46 -0400
      Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-06 15:50 -0700
        Re: DDS question: why sine lookup? Arie de Muijnck <noreply@ademu.nl> - 2025-05-07 11:44 +0200
          Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-07 06:32 -0700
            Re: DDS question: why sine lookup? Bill Sloman <bill.sloman@ieee.org> - 2025-05-08 01:58 +1000
      Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-07 06:55 -0700
        Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-07 11:31 -0400
          Re: DDS question: why sine lookup? Bill Sloman <bill.sloman@ieee.org> - 2025-05-08 02:11 +1000
  Re: DDS question: why sine lookup? Gerhard Hoffmann <dk4xp@arcor.de> - 2025-05-06 21:27 +0200
    Re: DDS question: why sine lookup? "Don" <g@crcomp.net> - 2025-05-06 20:10 +0000
    Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-06 13:35 -0700
  Re: DDS question: why sine lookup? Bill Sloman <bill.sloman@ieee.org> - 2025-05-07 16:27 +1000
  Re: DDS question: why sine lookup? Martin Brown <'''newspam'''@nonad.co.uk> - 2025-05-07 20:32 +0100
    Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-07 13:01 -0700
      Re: DDS question: why sine lookup? bitrex <user@example.net> - 2025-05-07 20:27 -0400
        Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-07 19:21 -0700
          Re: DDS question: why sine lookup? Bill Sloman <bill.sloman@ieee.org> - 2025-05-08 22:49 +1000
          Re: DDS question: why sine lookup? Joe Gwinn <joegwinn@comcast.net> - 2025-05-08 11:01 -0400
          Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-08 14:20 -0400
            Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-08 11:58 -0700
              Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-08 16:24 -0400
                Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-08 14:18 -0700
                Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-08 22:28 +0000
                Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-08 16:24 -0700
                Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-08 23:57 +0000
                Re: DDS question: why sine lookup? piglet <erichpwagner@hotmail.com> - 2025-05-09 04:48 +0000
                Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-09 12:53 -0700
                Re: DDS question: why sine lookup? Bill Sloman <bill.sloman@ieee.org> - 2025-05-10 18:53 +1000
                Re: DDS question: why sine lookup? Lasse Langwadt <llc@fonz.dk> - 2025-05-10 19:52 +0200
                Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-10 11:53 -0700
                Re: DDS question: why sine lookup? dplatt@coop.radagast.org (Dave Platt) - 2025-05-10 16:50 -0700
                Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-10 17:39 -0700
                Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-11 16:27 -0400
                Re: DDS question: why sine lookup? Bill Sloman <bill.sloman@ieee.org> - 2025-05-11 16:55 +1000
                Re: DDS question: why sine lookup? Lasse Langwadt <llc@fonz.dk> - 2025-05-11 22:03 +0200
                Re: DDS question: why sine lookup? Bill Sloman <bill.sloman@ieee.org> - 2025-05-09 15:52 +1000
        Re: DDS question: why sine lookup? Lawrence D'Oliveiro <ldo@nz.invalid> - 2025-05-10 00:44 +0000
      Re: DDS question: why sine lookup? Martin Brown <'''newspam'''@nonad.co.uk> - 2025-05-09 09:32 +0100
  Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-10 17:00 -0700
  Re: DDS question: why sine lookup? antispam@fricas.org (Waldek Hebisch) - 2025-05-13 23:25 +0000
    Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-13 20:22 -0400
      Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-13 18:40 -0700
      Re: DDS question: why sine lookup? antispam@fricas.org (Waldek Hebisch) - 2025-05-14 15:35 +0000
        Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-14 15:05 -0400
          Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-14 14:53 -0700
            Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-14 19:16 -0400
              Re: DDS question: why sine lookup? john larkin <jl@glen--canyon.com> - 2025-05-14 17:10 -0700
                Re: DDS question: why sine lookup? Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> - 2025-05-15 12:40 -0400
          Re: DDS question: why sine lookup? Bill Sloman <bill.sloman@ieee.org> - 2025-05-15 17:23 +1000

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