Pulse array DAC

Noise shaping, accuracy and conversion hardware

Answers on this topic

• How does a pulse array DAC work, how does it differ from R2R and delta-sigma, and why is it insensitive to jitter?
• How many taps and pulse array elements does each Chord DAC have?

Everything he said on this topic (96)

One-line summaries in our words, oldest first. Each link opens the original.

• 2014-04-15Watts says Hugo's DAC is a pulse array with a 104 MHz noise shaper, the DPLL eliminates source jitter, and more taps keep helping, guessing 1M taps for 16-bit accuracy. Head-Fi, Apr 2014
• 2014-08-03Watts recounts moving from disliking digital in 1989 to the PDM1 and PDM 1024, then creating the pulse array DAC in 1995 to fix noise shaper resolution and jitter. article, Aug 2014
• 2015-04-20Watts explains Hugo's discrete Class A output stage, his path from 1989 PDM DACs to the 16-element pulse array, its jitter immunity, time-domain reconstruction, and R2R's flaws. Head-Fi, Apr 2015
• 2015-06-18Watts explains the pulse array's analog-like distortion, why half-band filters keep original samples, and how a 256-tap WTA beat a 2048-tap half-band Kaiser filter in the late 90s. Head-Fi, Jun 2015
• 2015-10-02Watts says a femto clock sounded brighter due to low-frequency jitter, and DAC architecture, logic stages and pulse array's fixed-noise response matter more than headline clock jitter. Head-Fi, Oct 2015
• 2015-10-03Watts says pulse array's constant switching makes it immune to jitter, and USB purifiers are pointless for galvanically isolated Dave, Hugo TT and 2Qute; Hugo's issue is RF noise. Head-Fi, Oct 2015
• 2016-01-11Watts says Dave has 20 elements, not 16, for overload margin: -3 dB gives 3 V RMS, +3 dB 6 V RMS, and clipping starts at +4 dB. Head-Fi, Jan 2016
• 2016-03-04Watts explains the pulse array modulator and seven benefits (constant switching, jitter immunity, signal-unrelated currents, 104 MHz noise shaping), why Dave has 20 elements, and Mojo versus Dave THD. Head-Fi, Mar 2016
• 2016-03-05Watts explains the 6-bit noise shaper output spans 0 to 20 elements with clamping, and the 4 elements beyond 16 keep every element switching and give headroom. Head-Fi, Mar 2016
• 2016-04-01Watts says the Davina ADC will have 40 elements to reach 350 dB noise-shaper resolution and DAVE-level distortion; generally, doubling elements cuts noise 3 dB and improves resolution 6 dB. Head-Fi, Apr 2016
• 2016-05-13Watts gives four reasons jitter is a non-issue on DAVE, including the pulse array's jitter insensitivity, and says reducing RF noise sounds warmer and softer and is more transparent. Head-Fi, May 2016
• 2016-05-17Watts explains DSD's and PWM's switching, jitter and amplitude-timing errors, how pulse array balances switching to avoid them, and why DAVE needs 350 dB noise shapers for depth. Head-Fi, May 2016
• 2016-09-04Watts recalls using multiple dithered noise shapers for DSD256 in the early 1990s, explains that his 1995 pulse array eliminates correlated jitter, and why discrete flip-flops beat on-chip shift registers. Head-Fi, Sep 2016
• 2016-10-21Watts explains DAVE's 20-element pulse array feeds current into a single I-to-V converter rather than using voltage mode, and why keeping the node and reference voltage noise-free was hard. Head-Fi, Oct 2016
• 2017-03-15Watts says Hugo 2 noise is mostly resistor thermal noise, so units match within 0.2 dB; halving it would raise distortion 16 times, and he hears no warm-up or break-in. Head-Fi, Mar 2017
• 2017-03-19Watts says the limit is timing closure between discrete flip-flops and FPGA output delay, unchanged in 15 years; FPGA clocks run near 800 MHz, WTA modules at 208 MHz. needs context Head-Fi, Mar 2017
• 2017-05-25Watts explains why pulse array DACs are jitter immune, why femto clocks with PLLs degrade sound, and how a Hugo 2 prototype jitter and element-mismatch test exposed a layout fault. Head-Fi, May 2017
• 2017-12-02Watts calls the reference voltage the key internal supply, explains 2Qute's upgraded regulation and RF filtering, his jitter-removing DPLL, and pulse array jitter tolerance (DAVE 128 to 128.5 dB). Head-Fi, Dec 2017
• 2017-12-05Watts says pulse array eliminated the fundamental linearity problem of his 1990s DSD256 DACs; a minus 120 dB signal now measures within a thousandth of a dB, Mojo to DAVE. RMAF 18:43
• 2017-12-05Watts says PWM and pulse array have signal-independent switching, so jitter and glitch errors become DC, avoiding anharmonic distortion and noise floor modulation. RMAF 27:38
• 2017-12-05Watts recounts a project specified at 120 dB with 4 picoseconds of jitter, later changed to 15 picoseconds, which he met by changing the number of elements. RMAF 28:20
• 2017-12-05Watts asks why he invented pulse array in 1995. RMAF 40:43
• 2017-12-05Watts says he invented pulse array to improve DSD's high-frequency and small-signal resolution while keeping single-resistor freedom from distortion, running at 2048 times rather than 64 times. RMAF 40:50
• 2017-12-05Watts says the first pulse array used 16 resistors carrying PWM, giving about 5 bits; removing a resistor leaves distortion unchanged and only adds fixed noise at about 70 dB. RMAF 41:34
• 2017-12-05Watts says pulse array needs no resistor matching; a DC test shows resistor tolerance and clock jitter degrade the 126 dB noise figure by only half a dB. RMAF 42:18
• 2017-12-05Watts says Hugo 2 goes from 126 to 126.5 dB and DAVE from 128.5 to 129 dB; Chord uses femto clocks without fuss, and better clocks are not worth it. RMAF 43:11
• 2017-12-05Watts says clamping makes DSD's noise shaper unstable unless first order, whereas pulse array allows overload so its noise shaper works; the coefficients strongly affect measurements and sound. RMAF 44:33
• 2017-12-05Watts says the pulse array noise shaper is always stable, irrespective of signal conditions. RMAF 45:21
• 2017-12-25Watts explains DSD's 1-bit problems: lower resolution, modulator instability causing noise floor modulation, and small-transient delays, versus his 5-bit 2048FS pulse array and DAVE's -301 dB noise shaper. Head-Fi, Dec 2017
• 2018-01-10Watts lists noise and distortion pass criteria, says Hugo 2 and Qutest are within 0.5 dB of theoretical noise, and explains setting pulse array resistors at a distortion tipping point. Head-Fi, Jan 2018
• 2018-01-19Watts compares R2R, thermometer-code and constant-switching approaches to multibit delta-sigma, explaining that the pulse array's equal PWM elements give signal-independent switching, mismatch as noise only, and jitter insensitivity. Head-Fi, Jan 2018
• 2018-01-19Watts says doubling pulse array elements halves correlated jitter error, cuts noise 3dB and improves THD and small-signal resolution; Davina uses 40 elements to reach 135dB dynamic range. Head-Fi, Jan 2018
• 2018-01-19Watts says he uses 10 or 20 pulse array elements rather than 8 or 16 for headroom, since a noise shaper must exceed full scale to stay stable. Head-Fi, Jan 2018
• 2018-02-26Watts points to Chord's simplified 10-element pulse array video and says the noise shaper truncator outputs 7 bits, with a 4-bit feedback path at 104MHz. Head-Fi, Feb 2018
• 2018-05-03Watts says pulse array was designed so every unit measures identically, attributes perceived break-in to the brain, notes a slight warming after ten minutes, and says 192k remains inaccurate. Head-Fi, May 2018
• 2018-10-24Watts summarizes TT2's 10-element pulse array: 300 dB noise shapers at 104MHz, jitter insensitivity, no measurable noise floor modulation or non-linearity, and minimal analog filtering. Head-Fi, Oct 2018
• 2018-10-27Watts says 10 versus 20 pulse array elements helps Dave's transparency, and his noise-shaped volume control is not bit perfect but passes a -301 dB test. Head-Fi, Oct 2018
• 2018-12-12Watts says he invented the pulse array in 1995, using an FPGA plus discrete components for conversion, and that silicon DAC chips struggle to reach good measured performance. Pursuit Perfect System 14:00
• 2018-12-12Watts says a discrete FPGA-based DAC measures and sounds better, the pulse array eliminates noise floor modulation by constant switching, and a DSD modulator switches most when reproducing zero. Pursuit Perfect System 15:43
• 2018-12-12Watts says he wanted the pulse array to keep DSD's single-element benefit over R2R resistor matching, which never gets small-signal accuracy right, while constant switching removes signal-dependent glitch noise. Pursuit Perfect System 17:18
• 2018-12-12Watts says one switching element gives accurate small signals, and the pulse array adds clock cancellation and constant switching rate at far higher resolution than DSD. Pursuit Perfect System 17:57
• 2018-12-12Watts says simpler analog improves depth and detail; the pulse array's 104 MHz rate gives noise shaper resolution and allows an output of one amplifier, two resistors and two capacitors. Pursuit Perfect System 30:58
• 2018-12-12Watts says a conventional DAC uses four amplifiers versus his one, says TT2 has a 10-element pulse array, and explains elements as ten offset 1-bit streams whose clock edges cancel. Pursuit Perfect System 32:30
• 2018-12-12Watts says canceling clock edges eliminates master-clock jitter effects, and explains the reference supply: a DAC modulates a reference voltage, so its noise or variation directly affects performance. Pursuit Perfect System 33:24
• 2019-02-20Watts says Qutest is surge protected, element count does not set resolution, Davina has no date, DSD sounds unnaturally soft, and explains FIR for reconstruction versus IIR for EQ. Head-Fi, Feb 2019
• 2019-05-05Watts says DDFA did not use a pulse array, being a PWM switching output, whereas his pulse array DACs have linear outputs with analog-only feedback. Head-Fi, May 2019
• 2019-05-17Watts says separate supply pins on DAC chips do not solve substrate noise; pulse array mismatch creates only fixed noise, and Davina will record at 705/768 kHz. Head-Fi, May 2019
• 2019-05-18Watts gives three reasons DSD must be converted to PCM, notes Chord knows of the Linux DSD512 issue, and says 44.1 via M scaler sounds better. Head-Fi, May 2019
• 2019-07-25Watts says his DPLL uses only frequency once locked, so even 2 uS of source jitter has no effect, and external flip-flops remove FPGA jitter, verified with switching stopped. Head-Fi, Jul 2019
• 2019-10-06Watts explains 16 pulse array elements encode 5 bits, that 64-clock PWM switching raises truncator resolution to 7 bits as on Mojo, and that raw resolution is no performance indicator. Head-Fi, Oct 2019
• 2019-10-07Watts says noise shaper activity must be signal independent so pulse array jitter noise stays fixed, and that his 2nd-order analog noise shaper amplifier eliminates crossover distortion in Class B. Head-Fi, Oct 2019
• 2019-10-08Watts says he has not done a Canada show, and explains that 16 identical pulse array elements, unlike binary-weighted PCM bits, avoid distortion from element matching. Head-Fi, Oct 2019
• 2019-12-10Watts says Pulse Array, his DAC technology, is a type of delta sigma. Passion for Sound 3:22
• 2019-12-16Watts says he wanted DSD's single-element benefit without signal-dependent switching, leading to the pulse array; Qutest has ten PWM elements arranged so one rises as another falls. Passion for Sound 3:58
• 2019-12-16Watts says this gives clock cancellation, so clock jitter has no effect. needs context Passion for Sound 4:44
• 2019-12-16Watts explains that when reproducing zero, one PWM element has five positive and five zero while another has the reverse, arranged to transition together, giving a clock cancellation effect. Passion for Sound 5:02
• 2019-12-16Watts says PWM switches at a constant rate whatever the signal, so glitch energy becomes fixed noise instead of signal-dependent noise that creates noise floor modulation and distortion. Passion for Sound 5:29
• 2019-12-16Watts says eight or ten elements (ten on Qutest) give a 4-bit signal and better small signals, then starts explaining how a noise shaper maps 32 bits to 4. Passion for Sound 6:09
• 2020-01-01Watts says the DACs use a third overtone crystal by the flip-flops and no PLLs, so measurements need no warm-up, though Hugo 2 seemed slightly different after ten minutes. Head-Fi, Jan 2020
• 2020-05-13Watts says GaN transistors help Class D but cannot fix its transient timing problems, are unavailable for logic, and his discrete flip-flops have not improved in twenty years. Head-Fi, May 2020
• 2021-03-29Watts declines to discuss future products, describes a -350dB artifact his son identified blind, and says pulse array residual noise is resistor thermal noise traded against distortion. Head-Fi, Mar 2021
• 2021-06-04Watts says metal-to-metal interfaces attenuate small signals, his analog noise shaper gives TT2 20GHz and Dave 0.5THz gain bandwidth, and the pulse array creates no noise floor modulation. Head-Fi, Jun 2021
• 2021-12-31Watts says the pulse array modulator takes two's complement PCM so it can be filtered and decimated, with 10 elements on and 10 off at zero, internally using offset binary. Head-Fi, Dec 2021
• 2022-01-31Watts says conversion uses discrete flip-flops, references and resistors, separating digital noise from the analog, giving very low distortion, and is the only way to eliminate measurable noise floor modulation. Darko.Audio 12:12
• 2022-03-19Watts says conventional DACs do not reach 140 dB, and that he invented the pulse array in 1995 to solve small signal non-linearity and eliminate noise floor modulation. MFG Audio Reviews 12:31
• 2022-03-19Watts says the FPGA is not the DAC: discrete flip-flops and resistors do the conversion, avoiding the substrate noise in silicon DAC chips that causes noise floor modulation. MFG Audio Reviews 13:14
• 2022-08-19Watts says Chord's pulse array DACs, Mojo to DAVE, run a 104 MHz clock and reproduce 52 MHz; R2R mishandles 768 kHz; delta-sigma caps at 3 or 6 MHz. AVstore 27:43
• 2022-10-12Watts says noise floor modulation is controlled by isolating the digital and analog domains and by the conversion architecture, the pulse array inside DAVE. Upscale Audio 2:50
• 2022-10-12Watts says it solves many issues: it is innately jitter immune and has constant switching activity. needs context Upscale Audio 3:16
• 2023-03-28Watts says pulse array, improved over 25 years, addresses transients, small-signal accuracy and NFM, using discrete flip-flops and resistors with PWM edges balanced to reduce jitter sensitivity. The Headphone Show 45:40
• 2023-03-28Watts says the pulse array's constant PWM switching activity avoids signal-correlated glitch noise. The Headphone Show 46:23
• 2023-03-28Watts says noise changes only half a dB when pulse array elements are fed DC, and pulse array lets the noise shaper run at 104 MHz, reproducing 52 MHz. The Headphone Show 46:38
• 2023-03-28Watts says at 104 MHz the noise shaper digitally reproduces -301 dB with perfect amplitude and phase, has no noise floor modulation, and shows no transient timing errors in simulation. The Headphone Show 47:23
• 2024-04-16Watts says RF noise scales with circuit power, Toslink lowest and USB two orders worse; he still RF-filters optical, and more pulse array elements give lower noise, distortion and impedance. Head-Fi, Apr 2024
• 2024-06-10Watts says the DPLL fixed low-frequency master clock jitter (DAC64 used a buffer), while cycle-to-cycle jitter is made unmeasurable by enough pulse array elements. Head-Fi, Jun 2024
• 2024-07-12Watts says all DACs create noise floor modulation; the pulse array was invented to improve small-signal resolution and eliminate measurable noise floor modulation, though some unmeasurable remains. HIFICLUB 34:29
• 2024-07-12Watts says n-bit delta-sigma, of which the pulse array is a type, uses many levels (typically 32), giving higher resolution, less jitter sensitivity and better small-signal accuracy. HIFICLUB 40:43
• 2024-07-12Watts says PWM DACs sound analytical from timing issues; the pulse array uses many PWM elements at 104 MHz, can reproduce a 52 MHz sine, and avoids those timing problems. HIFICLUB 43:18
• 2024-07-12Watts says the pulse array avoids noise floor modulation and element distortion because all elements carry the signal with constant switching; its 104 MHz noise shaper reproduces minus 301 dB. HIFICLUB 44:15
• 2024-07-12Watts says the pulse array, which he invented in 1995, solves all three major issues unlike PWM, n-bit delta-sigma or R2R, and no one else appears to have copied it. HIFICLUB 44:59
• 2025-03-19Watts says the FPGA-to-flip-flop path delay is irrelevant without setup and hold violations, because the pulse array flip-flop outputs are retimed by the 104MHz master clock. Head-Fi, Mar 2025
• 2026-03-17Watts says higher rates hit hardware limits: FPGA speed and processing, and discrete flip-flops that lose accuracy above 100 MHz, so about 100 MHz is the sweet spot. ecoustics 9:37
• 2026-03-17Watts explains that a 32-bit signal cannot drive millions of switches, so a noise shaper reduces it to about 4.5 or 5 bits for, in DAVE's case, twenty switches. ecoustics 34:09
• 2026-05-03Watts says the pulse array's small-signal accuracy and lack of noise floor modulation matter for ADCs too; Quartet is the first product using his pulse array ADC, and a Pro Audio ADC is in development. Audio Force 16:00
• 2026-10-02Watts says in R2R and DSD DACs switching activity depends on the music, creating signal-dependent noise and NFM, so conversion needs constant switching activity. HiFi Buys 1:11:40
• 2026-10-02Watts says one way to get constant switching activity is PWM, where small signals use narrow pulses and big signals wider ones at the same switching rate. HiFi Buys 1:12:31
• 2026-10-02Watts says the pulse array, an array of PWM signals, has constant glitch energy: half the elements on changes output noise by only half a dB, unlike R2R or delta-sigma. HiFi Buys 1:12:47
• 2026-10-02Watts says he developed the pulse array in 1994 to 1995, using PDM256 (DSD256) chips fed by several randomized noise shapers summed in the analog domain. HiFi Buys 1:41:42
• 2026-10-02Watts says DSD sounds natural as distortion vanishes into noise, but he wanted its benefits without its problems: a faster noise shaper and no signal-dependent switching causing NFM. HiFi Buys 1:42:15
• 2026-10-02Watts says an array of PWM schemes, rising edges canceling falling edges, made switching signal-independent, cut jitter sensitivity and let the noise shaper run at 104 MHz. HiFi Buys 1:43:13
• 2026-10-02Watts says low-distortion flip-flops have not improved in 30 years, so faster ones would add distortion and 104 MHz remains the sweet spot. HiFi Buys 1:44:04
• 2026-10-02Watts says he does not use plain PWM because a high positive transient makes the pulse early and a negative one late. HiFi Buys 1:44:40
• 2026-10-02Watts says with many elements one can change every 9.6 nanoseconds, and a band-limited system need not reproduce 52 MHz at 0 dBFS. HiFi Buys 1:46:24
• 2026-10-02Watts says the pulse array resolves timing to 9.6 nanoseconds, and analog filtering in the amplifier and I/V decoupling, outside the feedback loop, turns this into an unsampled linear signal. HiFi Buys 1:47:22
• 2026-10-14Watts says ladder DACs create much HF distortion and worse timing from FET switching, while his pulse array (developed 1994 on FPGAs) avoids noise floor modulation and timing problems. Part-Time Audiophile 38:10
• 2026-10-14Watts says a PDM DAC built from eight individually dithered PDM DACs showed PDM resolution was insufficient, leading him to develop the pulse array on mid-nineties FPGAs. Part-Time Audiophile 45:20