dac dithering

Den lørdag den 30. november 2013 03.37.01 UTC+1 skrev John Larkin:

I'd try the delta-sigma, maybe skip the "bad bit"

Analog Devices uses something called "data directed scrambling" I think the re is some patents explaining it if you google

-Lasse

Making 20 bits out of 14 bits = oversampling of factor 4096 ballpark.

Really really fast.

Vladimir Vassilevsky DSP and Mixed Signal Designs

a few hundred MHz is not such a big problem

-Lasse

If you have a CPU generating the bits, it could run a linear congruential generator with little cost. I recommend initializing with a constant seed so that you can guarantee the results. The result is hardly random but it looks and sounds random when used for dithering. I've used it in photo processing algorithms to prevent blue sky and greyscale banding when generating ARGB packed in 32 bits.

LCGs can be done with feedback loops in shift registers too.

It's all in an FPGA, so a pseudo-random shift register, plus the DC offset, could all be done in hardware. The low N bits of the random number could be added to the 24-bit stuff, where N is, say, 11 or thereabouts, to dither the DAC maybe 3 bits.

I guess I could simulate this to tune it.

I mean seriously, this was so much already invented that I gave up after the first paragraph.

Then you didn't read the interesting stuff.

For uncorrelated, unshaped noise, yes. For a first-order sigma delta, the minimum oversampling is more like 64 (and you wouldn't want to get that close -- but 200x would probably be OK).

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com

You probably want to noise-shape the dithering, which means sigma-delta, which means some arithmetic. But it means a much lower oversampling ratio.

The non-monotonicity comes from the DAC's differential nonlinearity, which will be with you no matter what. So you're hardly going to be able to get an accuracy of 120dB down from full scale, and you probably won't be able to achieve a 120dB dynamic range by any but a very forgiving specification of dynamic range.

If all you're looking for is single-tone reproduction, and you don't mind some considerable gain errors when you're down in that -120dB range, well, maybe you can achieve it.

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com

I forgot to add one thing:

When I was converting 32 bit float to 8 bit integers for graphics, only a tiny amount of dither was added. The mathematically correct number produced visible noise in certain solid colors where the eye is sensitive. A very small amount, however, softened transitions from one value to another in nearly solid colors to make banding invisible.

The same might hold true if this is audio. Fixing sharp steps in low frequencies might sound good with less filtering effort.

If I bias the DAC into a zone without major transitions, it will likely be monotonic to 16 bits, at least when I'm making smallish signals. And if the added noise spans several LSBs, it gets better. So I only have to make 20 out of 16.

The LTC1668 has sub-LSB DNL in zones, with a spike at major code crossings... looks like about 32 big DNL spikes. That makes sense for a classic R-2R ladder architecture. I just need to center the system "zero" in one of those nice regions.

50 MHz, for a signal bandwidth around 100 KHz. Might work.

That is sort of the situation. The system resolution will be tested when there is a small signal, probably a single sine, because that's the obvious way to measure things. If I dither several LSBs, the gain is likely to be more accurate than a classic delta-sigma that just dithers one bit.

OK, it sounds like I need a black box that generates a stream of

24-bit dither codes at 50 MHz, the DAC rate.

The codes should have a DC offset to push the DAC into one of its low-DNL zones.

A triangular (maybe Gaussian?) probability distribution would probably be good, several (4? 16?) DAC LSBs p-p.

The dither stream should have low noise density in the passband of the post-DAC lowpass filter. Gotta consider aliasing down-conversion too.

One way to do this is to compute it on a PC, in PowerBasic or Matlab or something, and program an FPGA lookup table from the computed points. One could work in floats and invoke the RND function to make a stream of random numbers, then warp them through some function to change the probability density from rectangular to triangular. Then highpass (or bandpass?) filter, scale, convert to 24 bit integers, and dump into the FPGA tools. A 4K point table in the FPGA, walked by a counter, should do.

My 24-bit signal points would then be summed with this noise stream, truncated to 16 bits, and fed to the DAC.

Might work.

You'll have a distinct speed vs. quality trade-off, exactly because using more bits means you need more noise (and hence more filtering, and hence higher speed). Random white noise fed into a high-pass filter may be your friend, here.

Are you interested in a system that passes tests, or one that succeeds in your customer's hands? In most of the contexts that I'm used to, dynamic range means, essentially, "picking out a little signal that's buried in a big signal", not "being able to make a little signal or a big one". For the former definition, nonlinearities cause harmonics or other products of the big signal to interfere with the little signal, so in that context "dynamic range" is a measure of linearity.

--
Tim Wescott 
Control system and signal processing consulting 
www.wescottdesign.com

Right, the dither waveform shouldn't have low-frequency components that would get through the post-DAC analog lowpass filter.

It maybe shouldn't have any energy within a band around the sample rate, because that could be aliased down into the passband.

So the noise points should be generated as if they were passed through a bandpass filter from, say, 5 to 45 MHz. There must be a way to do that. I have an intern who claims to be good with Matlab. Can Matlab do filtering of sample sets?

Hmmm, what if the dither waveform were a single sine wave around, say,

7 MHz or something? Or a bunch of sine waves all well within the stopband of the post-DAC lowpass filter? That's easy to compute. With a bunch of them, the mess approaches strictly bandlimited Gaussian noise.

Well, both. There will be big booms and small booms, but I don't need PPM precision on the details of a big boom. But I need to make small booms that look pretty good.

The previous vendor tried for a couple of years to get this to work with a mostly-analog design. We're going ADC-FPGA-DAC. The customer will be overjoyed to get anything that works. It's sort of a rescue/charity job, so the customer won't be hard-headed about specs.

In most of the contexts that I'm used to, dynamic

I think the latter will do.

For

The biggest nonlinearity of that sort, keeping the small stuff accurate on top of big stuff, will mostly depend on the 14-bit DNL of the DAC. It's really very good, fractional LSB, on most code transitions, but has about 32 big spikes across the code range. So I need to avoid them as much as possible. The best DC offset is then

1/64 of full scale.

Yes, Matlab will do the filtering. If you do the filtering in the sampled-time domain at your sampling rate you'll automatically get the bandpass effect that you want.

Or you can generate your collection of sine waves -- but doing so is kind of like making your own pieces of wood out of cotton thread and resin because you don't like saws.

A 1st-order highpass filter is Really Freaking Easy to write in C; given the "really long table" vs. "a few lines of code" tradeoff, I'd go for the few lines of code. But you could generate a table of values and run with that.

--

Tim Wescott 
Wescott Design Services 
http://www.wescottdesign.com

tl;dr

sas

If anyone's interested, there's an LT Spice thing below.

I'm trying to get microvolt waveforms out of a 16 bit DAC that has 1 volt p-p range, which is 15 microvolt steps.

This uses two summed sines as the dither. Two sines has a better probability distribution than one, and more don't seem to help. I tried writing an LT SPice thing to graph the probability distribution of summed sines, but it was too slow to be useful. Maybe my intern can Matlab it.

The dither sines get intermodulated by the quantizer, generates sums and differences, and the IM products have to be kept away from the 1 MHz passband.

Finding the optimum sinewave dither amplitudes and frequencies would take either a lot of theory or a lot of fiddling. The values I'm using seem to work pretty well. I can make a decent 6 uV p-p sine wave.

I'm thinking that, if the dither were bandlimited gaussian noise, there would be an infinite number of IM products folding the noise back into the 1 MHz passband. Maybe the discrete sines are better.

I didn't include the dac clock yet. I guess a s/h clocked at 50 MHz would be a pretty good model.

Sorry if I'm boring you, miso.

Version 4 SHEET 1 1316 680 WIRE 224 -400 160 -400 WIRE 256 -400 224 -400 WIRE 464 -400 336 -400 WIRE 160 -368 160 -400 WIRE 160 -272 160 -288 WIRE 224 -160 160 -160 WIRE 256 -160 224 -160 WIRE 464 -160 464 -400 WIRE 464 -160 336 -160 WIRE 544 -160 464 -160 WIRE 160 -128 160 -160 WIRE 688 -96 656 -96 WIRE 768 -96 688 -96 WIRE 896 -96 848 -96 WIRE 944 -96 896 -96 WIRE 1088 -96 1024 -96 WIRE 1152 -96 1088 -96 WIRE 1200 -96 1152 -96 WIRE 160 -32 160 -48 WIRE 656 -32 656 -96 WIRE 896 -32 896 -96 WIRE 1088 -32 1088 -96 WIRE 224 48 160 48 WIRE 256 48 224 48 WIRE 464 48 464 -160 WIRE 464 48 336 48 WIRE 160 80 160 48 WIRE 656 96 656 48 WIRE 896 96 896 32 WIRE 1088 96 1088 32 WIRE 160 176 160 160 FLAG 544 -160 Z FLAG 160 176 0 FLAG 160 -32 0 FLAG 160 -272 0 FLAG 224 48 D1 FLAG 224 -160 D2 FLAG 224 -400 SIG FLAG 656 96 0 FLAG 896 96 0 FLAG 688 -96 DACOUT FLAG 1088 96 0 FLAG 1152 -96 LPF SYMBOL voltage 160 64 R0 WINDOW 0 -165 44 Left 2 WINDOW 3 -275 96 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value SINE(0 40 13.3e6) SYMBOL voltage 160 -144 R0 WINDOW 0 -165 51 Left 2 WINDOW 3 -275 96 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V2 SYMATTR Value SINE(0 40 21.7e6) SYMBOL voltage 160 -384 R0 WINDOW 0 -177 26 Left 2 WINDOW 3 -257 73 Left 2 WINDOW 123 0 0 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V3 SYMATTR Value SINE(0 3u 100K) SYMBOL res 352 32 R90 WINDOW 0 76 77 VBottom 2 WINDOW 3 48 26 VTop 2 SYMATTR InstName R2 SYMATTR Value 1e6 SYMBOL res 352 -176 R90 WINDOW 0 70 78 VBottom 2 WINDOW 3 42 25 VTop 2 SYMATTR InstName R3 SYMATTR Value 1e6 SYMBOL res 352 -416 R90 WINDOW 0 71 71 VBottom 2 WINDOW 3 43 33 VTop 2 SYMATTR InstName R5 SYMATTR Value 1 SYMBOL bv 656 -48 R0 WINDOW 3 -98 192 Left 2 WINDOW 0 13 111 Left 2 SYMATTR Value V=int(65536*V(Z)) / 65536 SYMATTR InstName B1 SYMBOL res 864 -112 R90 WINDOW 0 68 55 VBottom 2 WINDOW 3 79 55 VTop 2 SYMATTR InstName R6 SYMATTR Value 1 SYMBOL ind 928 -80 R270 WINDOW 0 -31 55 VTop 2 WINDOW 3 -36 59 VBottom 2 SYMATTR InstName L1 SYMATTR Value 220n SYMBOL cap 880 -32 R0 WINDOW 0 32 64 Left 2 WINDOW 3 29 97 Left 2 SYMATTR InstName C1 SYMATTR Value 83n SYMBOL cap 1072 -32 R0 WINDOW 0 39 63 Left 2 WINDOW 3 31 96 Left 2 SYMATTR InstName C2 SYMATTR Value 250n TEXT 256 208 Left 2 !.tran 0 20u 0 500p TEXT 648 -224 Left 2 ;QUANTIZER TEXT 856 -224 Left 2 ;1 MHZ BUTTERWORTH TEXT 640 -184 Left 2 ;15 uV STEPS TEXT 256 -296 Left 2 ;SIGNAL TEXT 256 -48 Left 2 ;DITHER TEXT 880 -184 Left 2 ;LOWPASS FILTER TEXT 680 -408 Left 2 ;SINEWAVE DAC DITHERING TEXT 712 -352 Left 2 ;J LARKIN DEC 1, 2013