The digital-to-analogue converter (D/A converter or DAC) converts digital (discrete-modulated) audio signals into analogue (continuous) audio signals. It is of crucial importance for the quality of the digital playback chain. Just as the analogue-to-digital converter (A/D converter or ADC) largely determines the quality of the modulated signal, the D/A converter determines how faithfully the digital signal is transmitted back into the analogue domain. In principle, a number of different concepts for technical realisation are available. In the audio field, two concepts play a role: R-2R ladder and delta sigma DACs. As an alternative, the none-oversamplig (NOS) DAC concept has also become established in recent times, which is usually a special variant of the R-2R concept.
I. R-2R-LADDER DACS
At the beginning of the digital audio era, D/A converters were predominantly based on the R-2R ladder principle. It was patented in 1955 (US patent: “Signal Conversion Apparatus”, July 22, 1955). An R/2R ladder DAC is a network of resistors with the values R and 2R for converting digital signals into analogue signals. These networks can either be discrete (e.g. dCS converters) or integrated in ICs (as in all converters based on the Philips TDA1541/TDA1543). The individual input bits are either connected to ground or to the reference voltage Vcc and feed in via resistors (2R) that are exactly twice as large as the horizontal part (R) of the network. Each bit thus contributes its own weighted contribution to the resulting analogue output voltage. Output impedance is always equal to R, regardless of the number of bits, simplifying filtering and further analogue signal processing circuit design.
Graph 1: Schema of a 4Bit R-2R Ladder DAC
Although this converter principle is characterised by very high speed and bandwidth as well as signal-to-noise ratios, it was not able to establish itself. The reason for this was not quality considerations – quite the contrary – but cost aspects. The R-2R concept places very high demands on the quality of the components and is therefore relatively expensive. Many high-end companies, such as MSB Technology, dCS, 47Labs, Zanden, Audio Note and AMR use R-2R ladder concepts in their DACs.
II. DELTA-SIGMA DACS
The operating principles of delta-sigma converters (ΔΣ ) is covered in detail in the article ” Digital Audio Basics”. In order to avoid the problems associated with analogue reconstruction filters, delta -sigma converters are mostly used nowadays. Although they are expensive to develop, they are much cheaper to produce than, for example, R-2R converters. For delta -sigma converters, the digital signal is first oversampled to usually 4-8 times the standard sampling rate (with the help of an interpolation filter), after the ΔΣ-modulator with its negative feedback loop, the one-bit stream signal is available again. Finally, it is pre-filtered to analogue by an internal switched-capacitor filter.
Graph 2: Modern PCM D/A conversion process
However, digital filters lead to a new phenomenon: pre-ringing, in which the impulse response, exhibits – in addition to the post-ringing (which also occurs with analogue filters) – also an unnatural pre-ringing before the actual signal enters. Hence, the filter “smears” the signal over time. In the following graphs 4 & 5, the original Dirac pulse with a width of exactly 1 sample is smeared in time by the filter over many samples. This phenomenon is mainly held responsible for the sometimes unnatural sound quality of digital recordings (hard sound textures, flat spatiality, high frequencies that sound narrow and brilliant at the same time, etc.):
Graph 3: Original Impulse of 1 Sample
Graph 4: Impulse after application of a linear phase filter
III. NON-OVER-SAMPLING DACS
Non-oversampling (“NOS”) D/A converters use neither oversampling nor digital filters. The concept goes back to Ryohei Kusunoki’s 1996 paper, where he deliberately ignored the doctrines of the time regarding digital-to-analogue conversion based on a multi-bit converter of the Philips TDA1543 chip type (which can also be operated without oversampling).
Based on the observation that the unnatural digital sound is essentially due to oversampling and the necessary digital reconstruction filters with their peculiarity of smearing the signal in the time domain (pre- and post-ringing), he experimented with DAC variants without oversampling and filters
In the NOS DAC concept he output signal goes directly to the analogue output without any digital filtering or other output stage. NOS DACs thus avoid the problems caused by digital filters in sigma-delta converters, especially filter pre-ringing. Without oversampling and digital filters, the aliasing effects start just above the usable frequency band (e.g. with Red Book standard, at 22.05kHz or with 96Khz sampling frequency at 48kHz) and are not filtered out. Kusunoki’s reasoning is that there is no need for a digital reconstruction filter, since the human auditory system itself – due to its clearly defined auditory area with a maximum of 20kHz) – functions like a low-pass filter with a passband of 20kHz. Thus, in the NOS concept, the human ear itself becomes part of the digital-to-analogue converter. The NOS concept only provides for a mild analogue low-pass filter (1st order) at the output to protect subsequent electronics from high-frequency aliasing frequencies
The end result is a transducer concept that delivers a particularly realistic, spatial and natural sound image, with a minimum of components, the shortest possible signal paths and the least necessary signal interference. Thereby NOS DACs come closer to analogue standards than most other transducer concepts – at least with comparable effort. Audiophile companies such as 47Labs, Zanden, Audio Note, AMR and Metrum Acoustics rely on the NOS principle for digital/analogue converters.
Due to the principle of making the human ear part of the converter concept, misunderstandings arise again and again among some technology commentators, as the measurement results of NOS DACs are not prima facie comparable to those of oversampling concepts:
- The measurement data of NOS DACs – coming from the device and without the last filter stage (the human ear) – do not represent the final audio and are worse than those of oversampling concepts, especially signal-to-noise ratio and distortions are higher. These values would improve considerably if they were run through a reconstruction filter before measurement. But this would contradict the concept of the NOS DAC. In principle, NOS DACs can only be measured without a reconstruction filter. However, they are not heard in this way, but with the reconstruction filter of the human ear. This leads to a discrepancy between the measurement result and the listening experience compared to oversampling DACs.
- Similarly, NOS-DACs perform worse than oversampling concepts in the so-called JTests (analysis of jitter), (if the results are presented in the frequency domain, by means of spectral analysis). Although they do not exhibit higher jitter, as can be proven with alternative measuring methods (analysis in the time domain). The reason is that the Jtest is not only sensitive to time deviations, but also to amplitude deviations, so that without reconstruction filters, the JTest shows higher jitter values. Accordingly, these values would also improve considerably if they were run through a reconstruction filter before measurement, but this would again contradict the concept of the NOS DAC.
- NOS DACs are in principle less sensitive to jitter than oversampling concepts. For example, at a clock frequency of 44.1kHz, the pulse width is 1/44.1kHz = 22.6757μs and 16-bit resolution means 216 = 65,536 different voltage values. To ensure that the last bit can just be reproduced, the maximum deviation from the pulse width (frequency jitter) must not be greater than 22.7μs/217 = 173ps. However, to achieve the same accuracy with 4-fold oversampling, the frequency jitter must not be greater than (1/176.4kHz)/217 = 43.3ps and with 8-fold oversampling not greater than 21.6ps.
- The principle-related high-frequency drop of approx. 3.2 dB at 20Khz, which is compensated for by the reconstruction filter in oversampling concepts, remains without correction, so that NOS DACs exhibit a slight treble drop. Some NOS DACs correct this drop by a specially calculated analogue filter at the output, others simply leave the treble drop in place.
© Alexej C. Ogorek
