Noise Minimization for Ultra-High SNR Class-D Power Amplifiers

air bearings, whose key characteristics are low friction and damping [3]–[6]. Consequently, the noise requirements for the driving amplifiers are critical in a frequency range from DC to ≈ 10 kHz, as the mechanical stages typically provide little attenuation in the transfer functions from actuator currents to positioning stage accelerations in this bandwidth. Besides very low-noise, amplifiers in lithography systems also have to provide high output powers and dynamics to enable fast accelerations of the motion stages in order to sustain high production throughput rates and large wafer diameters [7]. Due to integrated semiconductor features that continuously shrink in size and grow in complexity, actuator load current dynamic ranges in excess of 90 dB are expected, with signal-to-noise ratio (SNR) requirements in excess of 100 dB [8], [9]. Traditionally, linear amplifiers, which are commonly based on power operational amplifiers or discrete devices, are preferred for these tasks due to their inherently low noise over wide frequency ranges, combined with low output impedances [10]. Noise and linearity can be further improved with closedloop feedback systems that can be implemented in the analog or digital domain, whereas the former also features intrinsic low noise due to the absence of (digital) amplitude quantization [11], [12]. However, linear amplifiers collectively suffer from limited efficiencies and limited output power levels. Hybrid amplifiers strive to alleviate these restrictions by combining linear amplifiers with high-power, efficient switch-mode converters [13], [14]. Nonetheless, such topologies increase the complexity of the electrical circuit and, if utilized, the feedback control system, as the fundamentally different characteristics of the linear and switched conversion stages, with respect to their dynamics and input/output impedances, have to be analyzed and stabilized individually, which increases development effort and cost. Therefore, this work analyzes key influence factors on the output noise of digitally controlled, pulse-width modulated (PWM) switch-mode power amplifiers/converters. The analysis is similar to the one conducted in [15], which focuses on distortion and utilizes the same hardware demonstrator system to provide verification measurements as in this work. Fig. 1 lists important sources of noise in such converters. Due to the intended application in mechatronic positioning systems, the amplifier output current noise is considered, as the generated electromagnetic actuator forces are proportional to current. Nonetheless, the presented insights are universally applicable to amplifiers that provide either a controlled current or a controlled output voltage. Throughout this work, the term noise encompasses all undesired signal components, except for Abstract—Important noise sources affecting power output waveforms of digitally controlled switch-mode (Class-D) converters/amplifiers are investigated with a 400 V hardware demonstrator utilizing gallium nitride (GaN) power transistors. First, the influence of the open-loop gains of the cascaded feedback control system on the load current signal-to-noise ratio (SNR), which is a key metric in low-noise, nanometer-precision mechatronic positioning applications, is demonstrated. With a PWM frequency of 200 kHz, the high achievable controller gains enable unprecedented SNR values in excess of 105 dB (DC–10 kHz). Next, it is shown how a real-time Kalman filter, calculated at a rate of 100 kHz and used to attenuate sensor noise, increases the amplifier output SNR by more than 10 dB. Furthermore, digital delta-sigma (noise shaping) modulation improves the SNR by 5 dB, while not affecting distortion.