Basics of Low-Pass Delta Modulation

Abstract

Multi-bit analog-to-digital converters (ADC) have dominated digital signal processing (DSP) for the last 50 years or so. There are many ADC conventional architectures such as successive approximation register (SAR) ADC, flash ADCs, integrating, ramp-compare, Wilkinson, and others. All operate at a Nyquist sampling rate fN. Since the Nyquist rate ADC converters operate at sampling frequency fN, which is approximately two times the maximum frequency of input signal (fN > = 2fmax = 2fB), a high-order low-pass filter (LPF) is required to limit higher frequency components than fmax = fB of an input signal entering ADC. This filter is usually referred to as an anti-aliasing filter (AAF). This is a higher-order analog filter, and it is more expensive than an entire ADC. To overcome problems of an anti-aliasing filter and complexity of an n-bit ADC, linear delta modulation (LΔM) was proposed [1]. It trades off amplitude quantization of n-bit ADC for 1-bit quantization using oversampling technique. Primary use of highly oversampled LΔM is in a LΔM-to-PCM conversion. To improve signal-to-noise ratio and dynamic range, higher-order LΔM was proposed [2]. Unfortunately, LΔM systems have problems related to stability, slope overload, and accumulation of errors during transmission. To overcome these problems, Inose and Yasuda proposed an improved method of a one-bit analog-to-digital conversion of low-frequency analog signals. The paper of Inose and Yasuda can be found in the edited book of Candy and Temes [3]. Their proposed method is known as delta-sigma modulation (Δ-ΣM). This inexpensive, low-power consuming, high-resolution ADC revolutionized VLSI System-on-Chips (SoCs) design. In 1989, Schrier and Snelgrove [4] extended oversampling and noise principles of low-pass Δ-ΣM to applications at intermediate and radio frequencies (IF and RF). This method of ADC conversion is known as band-pass delta-sigma modulation (BP Δ-ΣM) [10, 11, 12, 13]. Because LP Δ-ΣM plays a very important role in many applications, such as sensor networks, hand-held mobile devices (cellular phone, GPS, etc.), wireless networks, software-defined radio, etc., we will briefly describe the principles of its operations. Both techniques are based on principles of oversampling and noise shaping. Both techniques trade off amplitude quantization of n-bit ADCs for oversampling of one-bit ADCs. This trade-off is possible under the condition of meeting a certain signal-to-noise ratio (SNR) for a specific dynamic range. In the following section, we will briefly describe operation of low-pass (LP) delta modulation.