SDM versus PWM power digital-to-analogue converters (PDAC) in high-resolution digital audio applications

Sigma-delta modulation (SDM) and pulse-width modulation (PWM) are compared as a means of structuring power digital-to-analogue converters (PDAC) designed specifically for wide-band audio, low power loss and direct loudspeaker drive. Recent innovations in SDM coding and output-stage topologies using pulse shaping techniques are discussed with emphasis on achieving stable and low distortion operation especially under high-level signal excitation having a modulation index circa 0.7 necessary to process peak transients. A simplified variant of predictive SDM with step back is introduced that offers both low latency and probability of instability and structures for both analogue and digital input data reviewed. 0 Introduction There is a growing awareness of the role for highefficiency topologies in power amplifier applications and especially their strategic significance in the application to a wide range of audio products [1,2]. This is already evident in the home-theatre markets, where ever smaller size yet higher performance products are emerging. There is also the opportunity to lower overall power dissipation which when mapped into volume production is a most critical issue in terms of environmental factors. Key advantages stem from reduced size and heat loss; however there are also more fundamental philosophical reasons for adopting digital technology in the amplification process. Switching amplifiers configured specifically for use with digital signals take on the mantle of a power digital-to-analogue converter (PDAC). As such there is reduced analogue processing as the digital signals are, in a figurative sense, brought into closer proximity with the loudspeaker. Consequently, there is opportunity to maintain better signal integrity and to achieve a more transparent overall performance, commensurate with appropriate design and physical implementation. The reduction in analogue-related artifacts such as dynamic modulation of the closed loop transfer function through device non linearity including active device transconductance and internal capacitance modulation, implies less amplifier dependent signal HAWKSFORD POWER DIGITAL-TO-ANALOGUE CONVERSION coloration and should lead to more neutral and consistent sound quality. However, switching output stages offer potentially better control of a loudspeaker as the source impedance of the amplifier remains low and almost resistive even under overload; this is contrary to most analogue amplifiers that are highly dependant on negative feedback. The output impedance is determined principally by the real on-resistance of the output switching devices, moderated only by a passive low-pass filter necessary to limit extreme high frequency signal components resulting as a consequence of the type of modulation scheme selected. Also, depending upon topology, the characteristics of the power supply can be critical. Until recently most PDAC modulators were based on a paradigm of PWM that can offer a range of attractive features. However, where the source signal is digital it is prudent to maintain signals within the digital domain and not to impose additional cascaded stages of analogue-to-digital (ADC) and digital-toanalogue conversion (DAC). Because uniformlysampled PWM is inherently non linear and extra noise is problematic when output pulses are quantized in time, then to successfully implement a PDAC additional processing must be included to linearize the modulator and simultaneously noise shape the time quantization needed to constrain pulses to match the system clock frequency. Also, within PWM there are two clock rates that bound performance: First there is the sampling frequency that determines the repetition rate of pulse transition and second, there is the clock that establishes the discrete time locations of each pulse transition. In PWM the latter clock is considerably higher than the sampling rate. With the advent of the direct-stream digital (DSD) format based upon sigma-delta modulation (SDM) [4], the effective sampling rate of the system has been elevated to 2.8224 MHz where the sampling rate and pulse transition rates, unlike PWM, are the same. Also, SDM can be implemented in such a way that within the audio band the modulator is effectively linear and does not require an additional linearization processor to achieve acceptable levels of distortion. The increase in sampling rate also facilitates a simpler low-pass filter with the potential for reduced signal losses as of course such filter have to handle the full output current of the amplifier. This paper presents a comparative study of PWM and SDM as a means of implementing both a PDAC as well as non-quantized switching amplification. In particular, the output stage configuration is considered including in Section 6.2 discussion on a recently introduced topology [3] designed to lower high frequency signal components and only to allow device commutation when switching voltages are zero, thus dramatically lowering switching losses. In addition in Section 6.1, the type of SDM modulator required to implement a SDM based PDAC is considered in the light of the growing application in this technology to high-resolution audio. When practical factors are included and real-world compromises made, then SDM can be tailored to allow more robust coding and also to maximize the modulation index, an important factor in achieving the full output signal capability of a DSD-based PDAC. Discussion and circuit topologies for PWM are also included as these set a foundation for understanding the linearity requirements of this class of modulation. The study is based on theoretical observations enhanced by Matlab-based simulations. 1 SDM-PWM ANALYTICAL COMPARISON It is well known that naturally sampled, non-time domain quantized PWM implemented using a symmetrical saw-tooth waveform and binary comparator offers low intrinsic distortion providing the bandwidth of the input signal is suitably constrained to prevent reflected components about the sampling frequency from falling within the audio band [5]. On first encounter it may appear unusual for a signal that is processed by a 2-level amplitude quantizer to have low intrinsic distortion; however in this Section it is shown that the modulation process has strong fundamental similarity with the linear frequency modulation (LFM) model proposed for SDM [6,7,8,9].