How does a pulse array DAC work, how does it differ from R2R and delta-sigma, and why is it insensitive to jitter?
Short answer
Watts describes pulse array, which he dates to 1994 or 1995, as a type of delta-sigma DAC: a fast noise shaper drives an array of identical PWM elements (discrete flip-flops and resistors) arranged so that a rising edge in one element is balanced by a falling edge in another, giving switching activity that does not depend on the signal Head-Fi, May 2016Passion for Sound 3:22HIFICLUB 40:43. He contrasts this with R2R, whose resistors can never be matched and whose switches are slow, and with DSD and conventional multi-bit delta-sigma, whose switching activity varies with the signal HIFICLUB 35:53HIFICLUB 41:34Head-Fi, Jan 2018. On jitter, he has said since 2015 that random master clock jitter only adds a fixed noise, and from 2015 to 2026 that switching the array to DC improves noise by only about 0.5 dB Head-Fi, Oct 2015Head-Fi, May 2017Head-Fi, Jul 2019HiFi Buys 1:12:47. His wording has varied rather than moved in one direction: "innately jitter insensitive" (2016), "jitter immune innately" (2022, Dave), and "that reduced jitter sensitivity" (2026); he has also said no DAC architecture can fix low-frequency master clock jitter (2024) Head-Fi, May 2016Upscale Audio 3:16HiFi Buys 1:43:13Head-Fi, Jun 2024.
What it is
Watts calls pulse array his own DAC technology and "a type of Delta Sigma" (2019) Passion for Sound 3:22. In 2024 he put it more precisely: "Pulse array is also an n-bit delta sigma. It's a particular type of n-bit delta sigma" HIFICLUB 40:43. He has given its origin as 1995 ("pulse array DAC was born, which had a 16 element discrete DAC and an FPGA noise shaper", 2014) and elsewhere as 1994, or "1994, 1995" (2026) article, Aug 2014Head-Fi, Jun 2017HiFi Buys 1:41:42.
He says he invented it to keep what he saw as the benefit of DSD, a single element with no resistors to match, while adding resolution and removing signal-dependent switching Passion for Sound 3:58Pursuit Perfect System 17:18. Before it he used PDM256 (the same as DSD256) chips, multiple dithered noise shapers summed in the analog domain, and in the early 1990s "32 element DSD conversion to analogue" Head-Fi, Apr 2015Head-Fi, Feb 2019HiFi Buys 1:41:42.
How it works, in his words
The noise shaper's output goes to a "pulse array modulator", which he describes in 2016 as "the digital circuit that converts the data output (6 bits) from the noise shaper into an array of PWM signals"; its output is fed back into the noise shaper, and each element is an output flip-flop plus a resistor Head-Fi, Mar 2016. The next day he said the 6 bits include overload bits, so that for 20 elements the range is 0 to 20 Head-Fi, Mar 2016; in 2015 he had given the noise shaper as 5 bits at 104 MHz Head-Fi, Jul 2015. He uses discrete flip-flops, re-timed by the master clock, "so that the jitter from the FPGA is eliminated" Head-Fi, Mar 2016Head-Fi, Jul 2019Head-Fi, Mar 2025.
His core description (May 2016, in a post on his Watts Up blog thread) is that with 16 PWM time states and 16 elements with different timing, "we can arrange the system so that a rising edge is always balanced by a falling edge for a constant OP", which he calls "in a nutshell is how pulse array works" Head-Fi, May 2016. In 2019, using Qutest as the example, he said the ten elements are "arranged so that 1 element will rise, the other element will fall" to give "a clock cancellation effect" Passion for Sound 3:58Passion for Sound 5:02.
Because each element is PWM, it switches at a constant rate, so glitch energy becomes "a DC component, a fixed level of noise" (2019) Passion for Sound 5:29. In 2016 he listed the consequences on Dave: switching errors end up as a DC value that the digital DC servo removes; resistor tolerance only creates "a completely fixed and unvarying noise signal, with zero distortion"; and voltage switching lets the noise shaper run at 104 MHz Head-Fi, Mar 2016. He does not run the array in voltage mode, because "it creates too much distortion"; the resistors feed a single I to V converter instead Head-Fi, Oct 2016Head-Fi, Aug 2018.
He has explained why the array is not plain PWM. Plain PWM still swings fully positive to fully negative, so master clock jitter creates noise, and its timing depends on amplitude Head-Fi, May 2016. In 2024 he said of PWM DACs "a high amplitude signal comes earlier than a low amplitude signal", and that pulse array avoids this because the array tracks each change in the noise shaper output HIFICLUB 42:28HIFICLUB 43:18. In 2021 he added that a PWM noise shaper is limited to the PWM switching frequency, whereas his "produces a new value every 9.6 nS not every 354nS with a PWM noise shaper" Head-Fi, Mar 2021. In 2026 he said one element can change every 9.6 ns, so transient timing is reproduced to 9.6 ns accuracy (check the recording) HiFi Buys 1:46:24HiFi Buys 1:47:22.
Element counts by product
He has given these counts: the original 1995 design had 16 elements; Hugo (2014) and the original Mojo share "exactly the same 4e pulse array"; Hugo 2 ("10 elements from 4 elements" against Hugo 1), Qutest and Hugo TT2 use 10 elements; Dave uses 20 article, Aug 2014Head-Fi, Feb 2018Head-Fi, Jun 2017Passion for Sound 3:58Head-Fi, Feb 2018Head-Fi, Oct 2018Head-Fi, Mar 2016Head-Fi, Jul 2022. The Davina ADC project "uses 40 elements as the pulse array reference for the ADC" (2018) Head-Fi, Jan 2018.
Dave has 20 rather than 16 elements for headroom, because "when you approach zero or 100% output, the switching activity stops, then you get distortion"; of the QBD76 he said "an overhead was built in as its a fixed level DAC" (2016) Head-Fi, Mar 2016Head-Fi, Mar 2016Head-Fi, Jan 2018. He described the 4e design as involving compromises, which is why he gave "Mojo is at 0.00017% but Dave is 0.000015% THD" (2016, original Mojo) Head-Fi, Mar 2016. In 2019 he said the Mojo 4e encodes extra resolution in the PWM, giving 7-bit truncator resolution, and that "the raw truncator output resolution is no indicator of overall performance" Head-Fi, Oct 2019Head-Fi, Oct 2019. In 2018 he said that doubling the number of elements "halves the correlated jitter error (reduces random jitter error by 3dB)" Head-Fi, Jan 2018.
Mojo 2 keeps four elements. At its 2022 launch he listed an "Improved 4 element pulse array DAC" among its changes, aimed at a distortion bump between about 70 kHz and 200 kHz (check the recording) MFG Audio Reviews 28:30. In 2023 he wrote "Mojo 2 is a 4e pulse array", adding that its noise shaper runs at a slower rate to keep distortion low, so noise starts rising around 100 kHz Head-Fi, Feb 2023. In February 2022, in a post that does not name the product, he gave "The 4e noise shaper" as 250 dB against Dave's 350 and said "You are correct in that 4 elements limits the performance" Head-Fi, Feb 2022; he describes both Mojo and Mojo 2 as 4e designs Head-Fi, Feb 2018Head-Fi, Feb 2023. Mojo 2 uses discrete flip-flops, reference supplies and resistors, and he said all his DACs "from Mojo right up to Dave" run at 104 MHz Darko.Audio 12:12AVstore 27:43.
How it differs from R2R
His recurring objections to R2R are that "you can never match the resistors", that the FET switches are slow, and that switching activity varies with the signal (2024) HIFICLUB 35:53HIFICLUB 36:40. He said in 2015 that R2R "in practice you can't run them above 16 FS - but I can run mine at 2048 FS so the digital domain is much closer to the original un-sampled analogue waveform", and in 2023 that "the fastest rate of operation is 16 times oversampled" Head-Fi, Apr 2015Soundnews 22:52. On jitter, he said in 2015 that R2R DACs "create noise floor modulation from jitter proportionate to the rate of change of signal" Head-Fi, Oct 2015. By contrast, he says pulse array elements are identical, each carries the audio signal, and so "we do not need to worry about element matching in terms of distortion" (2019) Head-Fi, Oct 2019.
How it differs from DSD and other delta-sigma
He says DSD's switching rate depends on the signal: maximum when reproducing zero, none at full positive or negative output, which makes jitter and glitch errors signal dependent Passion for Sound 2:28Passion for Sound 3:12Head-Fi, Nov 2018. He also says DSD has amplitude-dependent transient delay, while his 5-bit, 2048 FS design showed in simulation that "a -60dB step change has no consistent delay compared to 0dB step change" (2017) Head-Fi, Dec 2017.
In 2018 he sorted multi-bit delta-sigma DACs into R2R-backed, thermometer code, and thermometer code with constant switching activity, saying "pulse array is the only example that uses this approach" Head-Fi, Jan 2018. He said ordinary thermometer-code designs reduce mismatch with element rotation or DEM, but their switching activity is still signal dependent, while pulse array has "zero distortion associated with element mismatch" without DEM Head-Fi, Jan 2018Head-Fi, May 2019. In 2024 he said other n-bit designs that switch elements in and out have noise floor modulation and distortion problems HIFICLUB 41:34.
Why he says it is insensitive to jitter
His argument, stated from 2015 onward, is that switching activity does not depend on the signal, so random master clock jitter produces only a fixed noise rather than distortion or noise floor modulation Head-Fi, Apr 2015Head-Fi, Oct 2015Head-Fi, May 2016. In 2016 he wrote "the array is fundamentally jitter immune as rising edges are cancelled by falling edges within the array" Head-Fi, Mar 2016. The blog post the same year was more qualified: for a constant noise shaper value "the clock jitter has no effect whatsoever", and the only way for jitter to play a part is when the noise shaper output changes, where "the error is 1/16 of the DSD or PWM error" Head-Fi, May 2016. In 2019 he added that this requires a noise shaper whose activity rate is signal independent, "and my design of the noise shaper ensures this" Head-Fi, Oct 2019.
He bases the claim on simulation and on a test he says he runs on his designs at the prototype stage or on completion Head-Fi, May 2017Head-Fi, Jul 2019. In simulation, adding random jitter "creates zero signal correlated effects to pulse array" (2016, Dave) Head-Fi, May 2016. In the test, he switches the array to DC with half the elements high and half low, and compares the noise Head-Fi, May 2017Head-Fi, Jul 2019. He reported the change as about 0.5 dB: "127 dB to 127.5 dB" (2015), and "Dave goes from 128 dB to 128.5 dB" (2017) Head-Fi, Oct 2015Head-Fi, Dec 2017. He also said "clock jitter and element mis-match is an identical error" in this test, and that a Hugo 2 prototype channel that degraded by 1 dB was traced to a layout difference and fixed (2017) Head-Fi, May 2017. In an October 2017 talk (video published December 2017) he gave the figure as half a dB off 126 dB, and for DAVE "128.5 dB goes to 129 dB", against 128 dB to 128.5 dB in the December 2017 post (check the recording) RMAF 42:18RMAF 43:11. He repeated the 0.5 dB figure in 2020 ("turning the clocks off only gives a 0.5dB improvement in noise", Hugo 2 context) and in talks in 2023 and 2026 ("half a dB") Head-Fi, Sep 2020The Headphone Show 46:38HiFi Buys 1:12:47.
He separates random jitter from correlated jitter: "as soon as we get jitter that is correlated, or signal dependent, then we are in massive trouble" (2017, Hugo 2) Head-Fi, May 2017. His answer is discrete flip-flops "only one buffer away from the crystal oscillator" with their own power, and he said "This issue of correlated jitter problems can't be solved on-chip" (2016) Head-Fi, May 2017Head-Fi, Sep 2016. Source jitter he attributes to a separate mechanism, the DPLL, not to pulse array Head-Fi, Oct 2015Head-Fi, Dec 2017.
How his wording changed
From 2015 to 2019 he called pulse array "innately jitter insensitive", "jitter immune" and "inherently jitter immune" Head-Fi, May 2016Head-Fi, Mar 2016Head-Fi, May 2017. He kept the strong form later: "pulse array is inherently immune from master clock jitter" (2020) and "jitter immune innately" (2022, of Dave) Head-Fi, Sep 2020Upscale Audio 3:16. In the same period he also limited the claim: the array is "innately much less sensitive to master clock jitter", but "like all DAC's there is nothing I can do about LF drift" from a PLL (2016) Head-Fi, Sep 2016. In 2024 he said "With low frequency master clock jitter no DAC architecture can fix it"; the DPLL handles that, leaving cycle-to-cycle jitter, which is architecture dependent, and "with the appropriate number of pulse array elements, we can make this error become unmeasurable" Head-Fi, Jun 2024. In talks in 2023 and 2026 he described the edge balancing as reducing jitter sensitivity ("that reduced jitter sensitivity") The Headphone Show 45:40HiFi Buys 1:43:13. In 2024 he also said n-bit delta-sigma in general is "less sensitive to jitter" than DSD because it has many levels HIFICLUB 40:43. This archive does not show him explaining the difference between the immune and reduced-sensitivity wordings; both appear within a few years of each other. Similarly, in 2024 he said "I've succeeded in eliminating measurable noise floor modulation. I've not succeeded in eliminating noise floor modulation" HIFICLUB 34:29.
What he has not said: this archive has no full public description of the noise shaper (he calls parts of it too complex or proprietary), and no published jitter-test figures for each product beyond the 0.5 dB DC-test statement he says applies to all his DACs Head-Fi, Apr 2015Head-Fi, Mar 2016Head-Fi, Oct 2015.
Quotes
“In short, with 16 elements and 16 PWM time states we can completely balance switching activity - this in a nutshell is how pulse array works.”2016-05-17 Head-Fi, May 2016
“…it has a number of equal value elements, that are PWM encoded, with a fixed switching activity - so switching errors become constant irrespective of signal activity.”2018-01-19 Head-Fi, Jan 2018
“…adding random jitter creates zero signal correlated effects to pulse array - no distortion, noise floor modulation at all - just an insignificant level of unvarying random noise.”2016-05-13 Head-Fi, May 2016
“With low frequency master clock jitter no DAC architecture can fix it - it's like wow and flutter from tape…”2024-06-10 Head-Fi, Jun 2024
Dated positions
| When | Products | Position |
|---|---|---|
| 1994 to 1995 | pulse array (original 16e) | He developed pulse array, a 16-element discrete DAC with an FPGA noise shaper, to solve the resolution, jitter and switching problems of his earlier PDM/DSD designs. article, Aug 2014HiFi Buys 1:41:42Head-Fi, Nov 2018 |
| 2015 to 2022 | Hugo (original), DAVE, Hugo 2, Qutest, hugo-tt-2 | Pulse array is innately jitter insensitive or immune: random master clock jitter yields only a fixed noise, shown by a roughly 0.5 dB noise change when the array is switched to DC. Head-Fi, Apr 2015Head-Fi, Oct 2015Head-Fi, Mar 2016Head-Fi, May 2017Head-Fi, Jul 2019Head-Fi, Sep 2020Upscale Audio 3:16 |
| 2016 | DAVE | For a constant noise shaper value edge balancing cancels jitter entirely; jitter only matters when the output changes, at 1/16 of the DSD or PWM error. Head-Fi, May 2016 |
| 2016 | DAVE, Mojo (original), QBD76 | Dave has 20 elements rather than 16 for headroom; QBD76 had overhead built in as a fixed-level DAC; Mojo's 4e design involved compromises. Head-Fi, Mar 2016Head-Fi, Mar 2016 |
| 2018 | pulse array (all) | Pulse array is the only thermometer-code multi-bit delta-sigma with constant switching activity, and element mismatch causes noise but no distortion, without DEM. Head-Fi, Jan 2018 |
| 2016 to 2024 | DAVE, all chord dacs | No DAC architecture can fix low-frequency master clock jitter; the DPLL handles it, and cycle-to-cycle jitter can be made unmeasurable with enough elements. Head-Fi, Sep 2016Head-Fi, Jun 2024 |
| 2023 to 2026 | pulse array (all) | In talks he describes rising and falling edge balancing as reducing jitter sensitivity. The Headphone Show 45:40HiFi Buys 1:43:13 |
| 2017 to 2024 | pulse array (all) | R2R suffers from unmatched resistors, slow switches limited to about 16 FS, and signal-dependent switching; DSD's switching rate varies with signal. HIFICLUB 35:53Soundnews 22:52Passion for Sound 3:12 |
| 2022 to 2023 | Mojo 2 | Mojo 2 uses an improved 4-element pulse array, with a slower noise shaper to keep distortion low; four elements limit performance relative to larger arrays (the last from a February 2022 post on the 4e design that does not name the product). MFG Audio Reviews 28:30Head-Fi, Feb 2023Head-Fi, Feb 2022 |
Caveats and open points
- He has given the invention year as 1995 and as 1994; both are reported.
- Transcript figures (126 dB, 'about 70 dB' with one resistor removed, 9.6 ns) come; check the recordings.
- His jitter wording shifts between 'immune' and 'reduced sensitivity'; he separates random, correlated and low-frequency jitter, and his claims differ for each.
- The 0.5 dB DC-switching test is his own reported measurement; this archive has no independent figures.
- Mojo 2's element count (4e) rests on a 2023 forum post and a 2022 talk.
Topics: Pulse array DAC, Other DAC architectures (R2R, delta-sigma, chips, 1-bit), Jitter, clocks and the DPLL