Other DAC architectures (R2R, delta-sigma, chips, 1-bit)

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?
• Why does Chord use FPGAs and discrete conversion instead of DAC chips or a custom ASIC?

Everything he said on this topic (182)

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

• 2014-04-16Watts says calling something delta sigma hides a lot, since performance depends on factors such as oversampling rate, with 64FS to 2048FS a huge change. needs context Head-Fi, Apr 2014
• 2014-07-02Watts rebuts a poster: he consults for silicon companies, Hugo's 16 cores at 208 MHz dwarf ASIC DACs, and FFTs at -40 and -140 dB show no distortion or NFM. Head-Fi, Jul 2014
• 2014-08-20Watts explains chip DACs are differential for substrate and reference noise reasons, while Hugo is fully single-ended with one output stage, so balanced adds complexity. Head-Fi, 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
• 2015-07-14Watts says balanced doubles signal-path components and costs transparency; silicon DACs need differential operation, but his discrete DACs are single-ended, which forced solving problems differential hides. Head-Fi, Jul 2015
• 2016-01-09Watts says silicon chip design is budget-limited and suffers non-linear silicon and capacitors, while an FPGA plus discrete components lets him build his own chip in Mojo without those problems. What Hi-Fi? 3:29
• 2016-01-29Watts gives DAVE's noise as -127 dB A-weighted at 2.5 V and distortion 0.000015 percent, and says his converters' distortion falls with signal level, unlike ladder, DSD or chip DACs. article, Jan 2016
• 2016-04-02Watts contrasts fixed analog noise with signal-dependent small-signal distortion in R2R, delta-sigma and DSD DACs, and says DAVE's -127 dB dynamic range is set by hiss alone. Head-Fi, Apr 2016
• 2016-04-26Watts says DAVE adds no artificial depth, since flat recordings stay flat, and attributes compressed depth in DACs to small-signal amplitude errors rather than ringing. Head-Fi, Apr 2016
• 2016-04-28Watts calculates that an R2R DAC matching DAVE's -350 dB accuracy would need 0.000000000000003% resistors and 40 fS timing, and argues this cannot be achieved. Head-Fi, Apr 2016
• 2016-06-10Watts says R2R DACs create large amounts of distortion that their fans like, whereas he wants un-amplified music as in the original acoustic, which Hugo brought him closer to. Head-Fi, Jun 2016
• 2016-07-24Watts says his DACs from Mojo to DAVE show no measurable noise floor modulation or anharmonic distortion, with distortion falling as signal falls, unlike R2R, DSD and silicon DACs. Hifistatement 44
• 2016-08-05Watts describes DAVE's power system: multistage RF filtering, a 3 milliohm output-stage supply and a discrete reference under 0.1 milliohm; he says noise floor modulation is audible to -200 dB. Head-Fi, Aug 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
• 2016-09-05Watts says Head-Fi rules stop him criticizing an obviously Mola-Mola graphic, and notes he designed PWM chip DACs in 2002 but met fundamental limits on noise shaping and transients. Head-Fi, Sep 2016
• 2017-05-12Watts explains that an ADC contains a DAC, a delta-sigma noise shaper serving as either, and that the poor DAC inside an ADC chiefly limits ADC performance. Head-Fi, May 2017
• 2017-08-17Watts says chip DACs suffer noise floor modulation, jitter sensitivity, poor small-signal resolution and short filters versus Hugo 2's 49,152 taps, factors far outweighing passive part quality. Head-Fi, Aug 2017
• 2017-12-05Watts says R2R DAC FETs take about a microsecond to switch and vary by about 10%, giving 100 nanoseconds of timing uncertainty that dwarfs 75 femtoseconds. RMAF 26:17
• 2017-12-05Watts says jitter affects DAC architectures differently: R2R and DSD switching activity depends on the signal, R2R switching all FETs near zero and DSD switching most at zero. RMAF 26:53
• 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 says silicon DACs suffer nonlinear resistors and capacitors, phase intermodulation distortion, and digital noise coupling through a roughly three kilohm substrate, only partly fixed by triple well isolation. RMAF 29:34
• 2017-12-05Watts says chip simulation tools capture parasitics poorly, and that the on-chip reference voltage, which the data modulates, is noisy and high impedance. RMAF 30:26
• 2017-12-05Watts says chips cancel reference noise with a differential structure, but it cancels only at zero, not full scale, making it a big source of noise floor modulation. RMAF 31:09
• 2017-12-05Watts describes the R2R ladder DAC with FET switches and an I to V converter, and says a switched FET takes a long time to reach full saturation. RMAF 31:35
• 2017-12-05Watts says R2R switch resistance keeps changing for up to a microsecond, and parasitic capacitances create glitches, making even 16-bit performance a nightmare; resistor matching is another problem. RMAF 32:23
• 2017-12-05Watts says 144 dB distortion would need R2R resistors matched to fifty micro-ohms on 1 kilohm, which will never happen, and mismatch also ruins fundamental linearity. RMAF 33:05
• 2017-12-05Watts says R2R switches change most for small signals, adding glitch energy that degrades small-signal integrity and depth; he calls DSD widely misunderstood, though he loves it. RMAF 33:54
• 2017-12-05Watts says DSD avoids resistor mismatch and higher-order harmonics, giving fairly good depth and refinement, while R2R's higher-order harmonics sound hard, forced, aggressive and flat to him. RMAF 35:56
• 2017-12-05Watts says the analog stage matters as much as the digital, and R2R and DSD DACs need a lot of post filtering. RMAF 45:30
• 2017-12-09Watts says the best sound is only achievable with FPGAs and discrete DACs; after 14 years trying with silicon, he says superior performance is not possible from chips. article, Dec 2017
• 2017-12-15Watts says Philips Bitstream chips equal DSD256; his 1992 PDM1024 summed multiple PDM noise shapers, leading to pulse array in 1995 and WTA by 1999, neither patented. Head-Fi, Dec 2017
• 2017-12-25Watts rejects the claim that DSD needs no DAC, saying a simple low-pass filter would have huge THD and noise, and his DSD DAC designs never measured reasonably. Head-Fi, Dec 2017
• 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 he and the poster are not converging, and that R2R sounds exactly as bad as it measures; some people simply like the sound of distortion. Head-Fi, Jan 2018
• 2018-02-11Watts says passive volume controls add small-signal non-linearity via contacts and joints, conventional R2R and delta-sigma DACs resolve small signals poorly, so he ensures -301 dB resolution. Head-Fi, Feb 2018
• 2018-04-04Watts says an FPGA lets a designer build his own digital circuits, so FPGA plus discrete analog parts escapes the subjective and technical limits of DAC chips. article, Apr 2018
• 2018-04-04Watts says DAC chips have few FIR taps, perfect reconstruction needs infinite taps, and a brain-matched filter needs 1,000,000, realized last year in WTA M scaler technology (1,015,808 taps). article, Apr 2018
• 2018-04-04Watts says that because the FPGA is entirely digital and cannot have analog outputs, the analog components are implemented discretely. article, Apr 2018
• 2018-07-27Watts explains dual-data and DX modes, M scaler DSD-to-PCM conversion with Hugo 2's 220 dB filter, says algorithm beats tap length, and compares R2R and delta-sigma timing errors. Head-Fi, Jul 2018
• 2018-08-27Watts explains he avoids voltage mode DACs because output voltage modulates switching delays, giving about 0.03% THD and HF noise; his single stage combines I to V and drive. Head-Fi, Aug 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 chip DACs suffer digital noise coupled through the silicon substrate, even with triple-well isolation, plus non-linear on-chip resistors and capacitors, which discrete analog parts avoid. Pursuit Perfect System 14:47
• 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 a DSD output's switching varies with signal; each switch makes glitch noise, plus N/P FET speed asymmetry, so signal-dependent glitch noise creates distortion and noise floor modulation. Pursuit Perfect System 16:35
• 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 chip DACs need differential I-to-V stages to cancel substrate noise, four or five amplifiers in all, while his FPGA and discrete parts let him run single-ended. Pursuit Perfect System 31:42
• 2018-12-16Watts explains why a DAC's reference supply needs zero noise and impedance, says chip DACs hide poor references, and describes TT2's DAVE-standard discrete reference and its warmer sound. Head-Fi, Dec 2018
• 2019-02-22Watts says he used DSD256-equivalent PDM DACs with 32 elements in the early 90s and invented pulse array to fix DSD's resolution, noise floor modulation and amplitude-dependent timing. Head-Fi, Feb 2019
• 2019-04-03Watts says his 768k recording resembles M scaled 44.1k, doubling the rate cuts the error area fourfold, and R2R or 2.8 MHz noise-shaped DACs limit accuracy above 768k. Head-Fi, Apr 2019
• 2019-05-11Watts says chip DACs suffer substrate noise, NFM and jitter, while his discrete DACs measure -120dB signals to +/-0.001 dB and resolve -186 dB within 1dB. 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
• 2019-12-10Watts says there are really only two types of DAC: delta sigma and R2R. Passion for Sound 2:04
• 2019-12-10Watts says Pulse Array, his DAC technology, is a type of delta sigma. Passion for Sound 3:22
• 2019-12-10Watts says delta sigma divides into two major types, the first being DSD, which is 1 bit. Passion for Sound 3:26
• 2019-12-10Watts says the second delta-sigma type is n-bit, typically four or 5 bits, and that 1-bit modulators have huge problems because they very easily go unstable. Passion for Sound 3:35
• 2019-12-10Watts says chip DACs are all delta sigma and pretty much all of them n-bit. Passion for Sound 4:04
• 2019-12-10Watts says chip designers implement the four or 5-bit output in many ways, such as switched capacitor networks, switched resistors or switched current sources. Passion for Sound 4:15
• 2019-12-10Watts says chip DACs are all n-bit delta sigma with noise shapers around 3 MHz, and that before 1995 designers chose between Philips R2R chips and 1-bit PDM chips. Passion for Sound 4:42
• 2019-12-10Watts says chip makers abandoned 1-bit DSD/PDM in the mid nineties for its instability, distortion, noise, gurgle tones and modulation noise, so Sony and Philips's DSD was a backward step. Passion for Sound 5:25
• 2019-12-10Watts says the pro of R2R is that a designer without his own chip can easily build one from accurate resistors and FETs, but good measurements are very hard since tolerances must match. Passion for Sound 7:43
• 2019-12-10Watts says R2R FET switching timing, drive and parasitic capacitance must all be matched, creating glitch energy that is noise and signal-correlated distortion: a horrendous number of problems. Passion for Sound 8:34
• 2019-12-10Watts says an R2R DAC is a very simple way for a designer to create his own DAC without using somebody else's chip. Passion for Sound 9:32
• 2019-12-10Watts says delta sigma is harder because you must design noise shapers, for example with MATLAB generating coefficients, then implement them in code on an FPGA or DSP. Passion for Sound 9:43
• 2019-12-10Watts says 'this' is fundamentally much more difficult and complicated to do than an R2R DAC, which is relatively easy. needs context Passion for Sound 13:14
• 2019-12-10Watts says R2R's only benefit is having no noise shaper, which might help small signals, but measured R2R small-signal accuracy is awful and chip delta-sigma DACs do much better. Passion for Sound 14:05
• 2019-12-10Watts says he does not understand the appeal of R2R DACs; those he has heard sounded flat and distorted to him. Passion for Sound 14:50
• 2019-12-10Watts says the host has much more experience listening to other DACs, and that he has listened to only one R2R DAC in the last 5 years. Passion for Sound 15:39
• 2019-12-10Watts says he cares about competitors' technology, not their sound, and that R2R distortion extends to infinite frequencies and stays constant as signal falls until it exceeds the signal, very audibly. Passion for Sound 15:47
• 2019-12-10Watts says delta-sigma distortion has fewer harmonics and falls naturally as the signal level is reduced. Passion for Sound 16:37
• 2019-12-10Watts says chip DACs have a problem in that some distortion always remains as the signal gets smaller. Passion for Sound 16:49
• 2019-12-10Watts says signal-correlated substrate noise leaches into chip DACs' analog sections, whereas his FPGA does the digital processing and discrete components do conversion, isolating the two domains. Passion for Sound 17:00
• 2019-12-10Watts adds 'if you haven't got a common substrate', then says the major problem is that tolerances can never be made accurate enough. needs context Passion for Sound 17:39
• 2019-12-10Watts says R2R uses 0.01% resistors, about -80 dB; 144 dB would need impossible tolerances, while his noise shapers reach 64-bit accuracy or 350 dB. Passion for Sound 17:48
• 2019-12-16Watts recalls that in 1989 Philips PDM chips sounded more musical, deeper and warmer than R2R, but he questioned how DSD256 could work with only 256 pulses. Passion for Sound 56
• 2019-12-16Watts says he doubted 256 pulses could encode 20 kHz at 120 dB, so PDM1024 summed four or eight randomized PDM DACs, improving depth and detail resolution. Passion for Sound 1:36
• 2019-12-16Watts says each DSD DAC sounded and measured different and needed tweaking, and that DSD DACs are very sensitive to clock jitter and parasitics because switching activity varies with signal. Passion for Sound 2:28
• 2019-12-16Watts explains that DSD switching activity falls as signal rises, making jitter and glitches signal dependent and causing distortion, and that DSD and R2R DACs are both highly jitter sensitive. Passion for Sound 3:12
• 2020-01-06Watts says the Dubai events are public; his DACs are innately single-ended so balanced adds circuitry, while chip DACs must be balanced to reject substrate noise. Head-Fi, Jan 2020
• 2020-01-30Watts agrees DSD may beat PCM on a modest DSD-optimized chip DAC, but says PCM is much better on Hugo 2, DSD being format limited and PCM conversion limited. Head-Fi, Jan 2020
• 2020-06-25Watts says semiconductor work aims at good enough rather than best performance, and silicon brings substrate noise and nonlinear resistors and capacitors that FPGA discrete DACs avoid. Part-Time Audiophile 4:58
• 2020-10-10Watts says R2R DACs sound as bad as they measure, and that subjective listening can be objectively quantified if parameters are evaluated separately, though it is hard. Head-Fi, Oct 2020
• 2020-11-23Watts compares Hugo 2's out-of-band noise with the APx555's 192kHz DAC, explains the 104MHz noise shaper hump, and why gentle analog filtering needs only 4 passive components. Head-Fi, Nov 2020
• 2021-03-15Watts says quick measurements on non-APx555 gear reveal little, measurements matter but interpretation is paramount, and chip DACs fail on brick-wall response, small-signal accuracy and noise floor modulation. Head-Fi, Mar 2021
• 2021-03-29Watts says Linn-style PWM FPGA DACs have amplitude-dependent transient timing errors and a roughly 3MHz noise shaper, unable to reach the 350dB accuracy of his pulse array. Head-Fi, Mar 2021
• 2021-03-29Watts says Linn products are well engineered, but a PWM FPGA DAC is easy to cobble together, and state-of-the-art discrete DAC performance takes decades of work. Head-Fi, Mar 2021
• 2021-06-22Watts says R2R cannot cancel resistor mismatch, since -301dB accuracy needs 400 dB matching, and NOS and R2R fans are enjoying distortion; rival DACs at shows sound as expected. Head-Fi, Jun 2021
• 2021-11-08Watts disputes that DAPs have closed the gap on Mojo, citing its zero measurable noise floor modulation, transient timing and small-signal accuracy, which DAC chips have not improved. Head-Fi, Nov 2021
• 2022-01-31Watts names three issues separating his DACs from others: small-signal accuracy, important for depth and detail, and noise floor modulation, which other DACs show heavily; he begins defining it. Darko.Audio 6:56
• 2022-01-31Watts says he controls everything from the digital inputs through to the analog outputs, and the three factors he described are only achievable with that control. Darko.Audio 11:29
• 2022-01-31Watts agrees and adds that the FPGA is a digital chip, not an analog one. Darko.Audio 12:01
• 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
• 2022-01-31Watts says chip DACs use noise shapers of -140 dB and lose anything lower, and DSP EQ is worse because bass EQ multiplies the signal by very small coefficients. Darko.Audio 23:00
• 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
• 2022-03-19Watts says discrete conversion allows single-ended operation, his noise shapers resolve small signals a billion times better than chips, and running at 104 MHz permits minimal analog filtering. MFG Audio Reviews 14:03
• 2022-06-27Watts says pure DSD and R2R DACs are fundamentally limited, DAVE's noise shaper is not capped at 17th order, the HF filter sits after WTA2, and car batteries are ideal. Head-Fi, Jun 2022
• 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
• 2022-08-19Watts says a DAC is limited not only by accepting 768 kHz but by its own ability to resolve transient timing, because of errors inside the DAC. AVstore 29:25
• 2022-10-12Watts says another benefit is that conversion to analog is done with discrete components rather than on a chip. Upscale Audio 2:22
• 2022-10-12Watts explains that in a normal DAC component switching depends on the signal, each switch adds a noise glitch, and the changing noise produces noise floor modulation. Upscale Audio 3:28
• 2022-12-17Watts says pairing a digital front-end chip with a mostly analog chip reduces digital noise, as Philips did in the 90s, since substrate noise in single-chip designs cannot be eliminated. Head-Fi, Dec 2022
• 2023-02-05Watts says from 1984 to 1989 DACs were all R2R DACs. Soundnews 20:12
• 2023-02-05Watts says R2R DACs sounded dreadful, flat and hard compared with more musical vinyl, until Philips launched Bitstream in 1988. Soundnews 20:24
• 2023-02-05Watts says Bitstream was effectively DSD256, a simple second-order noise shaper at 1 bit, 256 times, and was the first digital he heard sound musical and smooth. Soundnews 20:51
• 2023-02-05Watts says Bitstream's 256 one-bit pulses seemed too few for a 20 kHz waveform, so he modeled noise shapers and paralleled dithered noise shapers in early FPGAs. Soundnews 21:31
• 2023-02-05Watts says that work led to the pulse array; turning to R2R, its first fundamental problem is that the resistors can never be matched. Soundnews 22:19
• 2023-02-05Watts says R2R tops out at 16 times oversampling because FETs switch too slowly, causing high distortion; the ear is very sensitive to high-frequency distortion, even at 10 MHz. Soundnews 22:52
• 2023-02-05Watts says transient performance at 10 nanoseconds is critical to sound quality and physically impossible for R2R DACs, a fundamental limitation. Soundnews 24:20
• 2023-03-01Watts shares his NYC CanJam seminar on DAC types, with more detail on differing DAC topologies. Head-Fi, Mar 2023
• 2023-03-28Watts says when the client changed the spec to 15 picoseconds he redesigned the DAC and still got 120 dB, so jitter sensitivity depends on the DAC design. The Headphone Show 4:01
• 2023-03-28Watts says chip DACs share a roughly 3 kilohm substrate, so signal-correlated digital noise corrupts the analog side, causing distortion and noise floor modulation; silicon resistors are also nonlinear. The Headphone Show 6:58
• 2023-03-28Watts adds that capacitors are nonlinear too, a particular issue in chip design. The Headphone Show 7:45
• 2023-03-28Watts divides DACs into R2R (ladder) and delta-sigma, the latter either 1-bit (DSD) or multi-bit, and says an R2R DAC is not too difficult to build. The Headphone Show 7:54
• 2023-03-28Watts says R2R DACs are extremely hard to make measure well, delta-sigma design needs digital logic and FPGA skills, and delta-sigma DACs come in too many flavors to sound alike. The Headphone Show 8:44
• 2023-03-28Watts describes how an R2R DAC works: FET switches select resistors whose current feeds an I-to-V converter (virtual ground) to produce the output voltage. The Headphone Show 9:34
• 2023-03-28Watts says low-impedance FETs bring gate capacitance that injects switching glitch noise, and R2R's two basic problems are resistor matching and this glitch noise, causing distortion and noise. The Headphone Show 10:20
• 2023-03-28Watts says R2R DACs can only run at 16 times oversampling, not 104 MHz, limiting transient reconstruction to microseconds rather than the nanoseconds pulse array achieves. The Headphone Show 11:03
• 2023-03-28Watts shows a plot of a monotonic 4-bit R2R DAC whose transfer function has knee points caused by resistor matching. The Headphone Show 11:27
• 2023-03-28Watts says R2R knee points make the differential transfer function go to infinity, creating high-frequency distortion, much like the sharp knees of Class B output stages. The Headphone Show 12:08
• 2023-03-28Watts says R2R distortion rises as signal level falls, the opposite of the ear, harming soundstage and detail and sounding harder and brighter; he is not a fan. The Headphone Show 12:57
• 2023-03-28Watts explains a delta-sigma DAC as a noise shaper plus an analog output stage, reducing 32-bit data to 1 bit for DSD or about 5 bits for multi-bit. The Headphone Show 13:44
• 2023-03-28Watts says DSD's single element avoids R2R mismatch, and its distortion disappears below about -60 dB as signals get smaller, matching how the ear behaves. The Headphone Show 19:51
• 2023-03-28Watts says multi-bit delta-sigma DACs let the noise shaper go beyond plus or minus one, keeping it stable and consistent, which eliminates DSD's noise shaper noise floor modulation. The Headphone Show 24:08
• 2023-03-28Watts says more bits improve resolution and reduce jitter sensitivity; his answer to the 4 to 15 picosecond jitter spec was to add more DAC elements. The Headphone Show 24:55
• 2023-03-28Watts says multi-bit also reduces RF noise injected into the analog section, and names three multi-bit types: unitary elements, PWM, and his pulse array. The Headphone Show 25:39
• 2023-03-28Watts explains unitary-value DACs: a 5-bit design uses 32 equal elements, half on for zero, with a thermometer DAC simply switching more elements on as level rises. The Headphone Show 26:20
• 2023-03-28Watts says unitary DACs suffer element mismatch distortion, partly averaged by rotating element selection, which still leaves distortion and noise, or by random multiplexing. The Headphone Show 27:07
• 2023-03-28Watts says random element selection still distorts, and the best method noise-shapes each element, selecting elements based on past use. The Headphone Show 27:50
• 2023-03-28Watts says unitary DACs have signal-dependent switching activity causing noise floor modulation, noise shapers limited to 64 or 128FS (6 MHz), and transient resolution of hundreds of nanoseconds. The Headphone Show 28:14
• 2023-03-28Watts describes PWM DACs, which he has used, as like Class D: a 64FS (3 MHz) noise shaper embedded in PWM at a 98 MHz clock, with fixed switching frequency. The Headphone Show 29:13
• 2023-03-28Watts says PWM switching glitches become a DC offset and a single element avoids mismatch, but PWM can be jitter sensitive as the signal swings fully positive to negative. The Headphone Show 30:06
• 2023-03-28Watts says PWM can give excellent measured performance. The Headphone Show 31:02
• 2023-03-28Watts says PWM has a fatal flaw: pulse edges shift earlier as the signal goes more positive, so transient timing moves with signal level. The Headphone Show 31:11
• 2023-03-28Watts says PWM's timing shift is a major transient reconstruction error that analog filtering cannot fix, and the brain uses transient timing for timbre, separation and bass pitch. The Headphone Show 32:01
• 2023-03-28Watts says degraded transient timing harms timbre variation, separation, focus, pitch and the starting and stopping of notes, noting he used PWM DACs in low-cost chip designs. The Headphone Show 32:45
• 2023-03-28Watts says his PWM DACs sounded clinical and analytical, lacking musicality, and states his goal for pulse array: recapturing the emotion of a live acoustic event. The Headphone Show 33:27
• 2023-09-19Watts says only one filter set minimizes transient timing error, and the ESS9038 Pro's 128 taps use only 8 original samples, inadequate for transient reconstruction. Head-Fi, Sep 2023
• 2023-12-06Watts says chip makers had no interest in a high-end DAC chip, and a WTA ASIC would need a 1M USD mask set in a 2M USD project. Head-Fi, Dec 2023
• 2024-07-12Watts says R2R resistors can never be matched, giving large small-signal errors that hurt depth and detail, and switching limits R2R to 768 kHz and poor timing. HIFICLUB 35:53
• 2024-07-12Watts says R2R's 768 kHz limit gives 1.3 microsecond timing resolution and signal-dependent switching causes anharmonic distortion and noise floor modulation; DSD's single element avoids distortion between elements. HIFICLUB 36:40
• 2024-07-12Watts says DSD's distortion falls as signal falls, matching how the ear works, whereas R2R distortion stays fixed and can exceed very small signals. HIFICLUB 37:45
• 2024-07-12Watts says DSD64 is very noisy at high frequencies (about minus 20 dB near 100 kHz), with signal-correlated noise that damages transient timing. HIFICLUB 38:29
• 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 n-bit delta-sigma comes as switched fixed elements, which give distortion and noise floor modulation, or as PWM, encoding 32 levels in 1-bit switching. HIFICLUB 41:34
• 2024-07-12Watts says PWM DACs (98 MHz clock, 3 MHz noise shaper) have constant switching and no noise floor modulation, but amplitude modulates transient timing. HIFICLUB 42:28
• 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, 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
• 2024-08-01Watts says FPGA silicon costs more but gives freedom, and that chip DACs suffer digital noise through the substrate into the analog section, mitigated but never solved by differential structures. Audiophilesdoteu 1:31
• 2024-08-01Watts says differential chip DACs need complex analog stages, whereas in his designs the FPGA only makes data and discrete parts on a separate supply do conversion, avoiding digital noise. Audiophilesdoteu 2:13
• 2024-08-01Watts says his analog section is one single-ended amplifier doing I to V and output, and his 104 MHz noise shaper, versus 3 MHz delta-sigma, eases filtering. Audiophilesdoteu 3:07
• 2025-02-17Watts says he spent 14 years consulting for semiconductor companies on digital amplifiers with patented feedback, and that substrate noise from digital sections corrupts a chip's analog section. audio-2G 1:20
• 2025-02-17Watts says chip DACs cannot eliminate substrate noise; in an FPGA-based DAC the FPGA only creates digital signals and conversion is discrete, with flip-flops, resistors, separate supply and grounds. audio-2G 2:10
• 2025-02-17Watts says chip design is driven by price down to a few cents, while with FPGAs he can buy a bigger FPGA or use several to get processing power. audio-2G 2:58
• 2026-05-03Watts, who has designed chip DACs as a semiconductor consultant, says chip DACs are cost-limited to simple digital circuitry and suffer digital noise through the substrate upsetting analog parts. Audio Force 1:42
• 2026-05-03Watts says discrete components with FPGAs outperform chips, allow digital complexity thousands of times greater, and free design choices such as 192 bits internal accuracy. Audio Force 2:28
• 2026-10-02Watts says audio chips must sell at least 100,000 devices a year, so cost is severely limited and his designs would need far too much die area. HiFi Buys 30:07
• 2026-10-02Watts says silicon's bulk resistance lets digital noise leak into on-chip analog sections despite isolation, and on-chip capacitors and polysilicon resistors are nonlinear. HiFi Buys 30:47
• 2026-10-02Watts says these chip mechanisms create signal-correlated noise and thus noise floor modulation, while a discrete DAC fed pulses from an FPGA avoids substrate noise and uses linear parts. HiFi Buys 31:32
• 2026-10-02Watts says discrete design separates digital and analog noise and allows billion-transistor FPGAs; FPGAs are slower and use more power than silicon but less than microprocessors. HiFi Buys 32:15
• 2026-10-02Watts says the disadvantage is man effort, citing 10 to 29 years' worth per device; chips measure very well, and he could build a DAC from scratch after 40 years. HiFi Buys 33:52
• 2026-10-02Watts says a designer who knocks together an FPGA design in a year with marketing will almost certainly sound worse than a competent but limited chip design. HiFi Buys 34:45
• 2026-10-02Watts says R2R DACs are popular with specialist audiophile firms because they are easy to assemble but very hard to make measure well, unlike a properly done delta-sigma modulator. HiFi Buys 35:27
• 2026-10-02Watts says R2R DACs have two main issues, the first being resistor matching. HiFi Buys 37:28
• 2026-10-02Watts says 24-bit accuracy needs resistors matched to about 0.00006 percent. HiFi Buys 37:34
• 2026-10-02Watts says such matching is impossible because resistors drift with temperature and time. HiFi Buys 37:46
• 2026-10-02Watts says R2R resistors drift and age differently, and low-RDS-on switching FETs have high capacitance that injects signal-dependent glitches, causing signal-dependent distortion. HiFi Buys 37:55
• 2026-10-02Watts says this is a very non-linear distortion, and the principal problem of R2R DACs is that distortion grows relative to the signal as the signal gets smaller. HiFi Buys 38:40
• 2026-10-02Watts says R2R distortion is fixed, reaching thousands of percent at low levels, while delta-sigma distortion vanishes as signals shrink, as the ear's does. HiFi Buys 38:50
• 2026-10-02Watts says R2R DACs have the opposite distortion characteristics to the ear. HiFi Buys 39:38
• 2026-10-02Watts says R2R glitch energy makes noise vary with the signal, and some delta-sigma DACs share this because their low-bit conversion creates signal-dependent noise. HiFi Buys 40:29
• 2026-10-02Watts says R2R DACs are made to sound warm by using other distortions. HiFi Buys 41:30
• 2026-10-02Watts says a chip DAC's bandgap reference, decoupled by a capacitor, pumps with current draw, carries RF noise and modulates dynamically, unseen in static measurements. HiFi Buys 1:10:51
• 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 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
• 2026-10-14Watts says ESS chips have half a dozen filters and at most a few hundred taps, versus 4 million on Quartet and, he thinks, about 44 thousand on Mojo 2. Part-Time Audiophile 33:10
• 2026-10-14Watts says one could upsample 48 kHz to 768 kHz with one's own filter into a chip DAC; ESS measure well, but he rates chip DACs as similar sounding. Part-Time Audiophile 34:54
• 2026-10-14Watts says a perfect 768 kHz filter would improve a chip DAC but not match his FPGA DACs, which filter up to 104 MHz, leaving 9.6 nanoseconds of uncertainty. Part-Time Audiophile 35:47
• 2026-10-14Watts says chip DACs handle the step from 768 kHz up to about 12 MHz poorly, a major focus of his FPGA pulse array DACs. Part-Time Audiophile 36:44
• 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 that warmth suits ladder DACs because a soft, bloated bass masks their high frequency distortion, one distortion covering another. Part-Time Audiophile 39:45
• 2026-10-14Watts says in the very beginning they used 14-bit ladder DACs. needs context Part-Time Audiophile 43:06
• 2026-10-14Watts says Philips's PDM DAC, equivalent to DSD256, sounded musical and warm, and he could not understand how 256 one-bit pulses could encode a 22 kHz sine wave. Part-Time Audiophile 44:32
• 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