A Different View of Sigma-Delta Modulators Under the Lens of Pulse Frequency Modulation [Feature

The parallelism between a first-order sigma-delta modulator and a VCO-based ADC allows to calculate the DFT of the sigma delta sequence using Pulse Frequency Modulation theory. This paper exploits this parallelism to propose a more general model that links continuous time sigma delta modulators of an arbitrary order with Pulse Frequency Modulators. This novel point of view also predicts the spectral contents of a sigma delta encoded sequence beyond the white quantization noise model. The quantization noise can be split in two components, a deterministic one representing the carrier harmonic sidebands of a Pulse Frequency Encoded signal and a noise shaped pseudorandom signal representing the sampling operation. We seize these findings to propose a conjecture on the stability of a sigma delta modulator.

An analytical expression for the myoelectric signal was derived using the integral pulse frequency and amplitude modulation (IPFAM) approach. The results indicate that, in the frequency domain, the general envelope of the EMG spectrum is affected primarily by the motor unit action potential (MUAP) and its interaction with the pulse amplitude modulation (PAM) and pulse frequency modulation (PFM) processes. Furthermore, the component associated with force modulation co-exists at its modulating frequency with factors related to the MUAP. Therefore, the conventional low-pass filtering is not adequate for reconstructing dynamic muscular force signals from nonstationary myoelectric signals obtained during locomotion.

The envelope pulse-width modulation (EPWM) transmitter has been studied to address the power efficiency issue on the linear amplification of OFDM signals. However, the delta- sigma (Delta-Sigma) modulator in the EPWM transmitter generates quantization noise that degrades signal quality. In this paper, OFDM in-band noise characteristics of EPWM transmitters are analyzed for first and second order Delta-Sigma modulators. Distortion noise power due to envelope clipping of OFDM signals is also analyzed. The combined effects of noise and distortion on the error vector magnitude (EVM) and adjacent channel leakage power ratio (ACLR) are examined. Simulations to validate the total performance were performed using the IEEE 802.11a OFDM signal. Results showed good agreement with analytical results considering a linear-approximation gain for the 1-bit quantizer in Delta-Sigma modulators. The first order EPWM transmitter provides slightly better EVM and ACLR values than second order EPWM transmitters, since the effective quantizer gain of second order Delta-Sigma modulators is smaller, that limits the noise- shaping capability of Delta-Sigma modulators. A 0.1% clipping probability for a first order EPWM transmitter with an oversampling ratio of 32 and a three-pole Butterworth bandpass filter gives an EVM of 1.8% and ACLR of-37.9 dB.

This paper focuses on the nature of the rate error which arises when a first-order digital differentiator is applied to the output of a uniform quantizer for the purpose of rate estimation. The quantizer input is assumed to be a constant-rate signal which is subject to a uniformly distributed noise source. New formulae are presented for the corresponding rms and spectral error characteristics. The results are applicable to the signal processing of sensor outputs, exemplified by the shaft encoder-based velocity estimation of an almost uniformly rotating mass. Both computer-generated finite data sets and experimental data derived from encoder-based shaft velocity measurements are utilized to verify the theoretical results. The results described are also applicable to a more general class of systems which involve the digital differentiation of quantized, noise-affected signals, such as first-order sigma-delta modulators with nominally constant input.

Sigma delta modulation is a popular technique for high-resolution analog-to-digital conversion and digital-to-analog conversion. We investigate chaotic phenomena in multibit first-order sigma-delta modulators. Particular attention is placed on the occurrence of periodic orbits or limit cycles. These may result in idle tones audible to the listener when sigma-delta modulation is used for audio signal processing. One suggested method of eliminating idle tones is the operation of a sigma delta modulator in the chaotic regime. Unfortunately, chaotic modulation of a first order sigma delta modulator is a poor system for signal processing. We show that minor variations on a traditional first order sigma-delta modulator, together with a multibit implementation, may be used to produce an effective, stable chaotic modulator that accurately encodes the input and helps remove the presence of idle tones. (c) 2001 American Institute of Physics.

A delta-sigma-modulated intermediate-frequency-over-fiber (IFoF) transmission system assisted by a correlative-level coding technique is proposed and experimentally demonstrated. Unlike conventional delta-sigma IFoF systems with multiple output levels to achieve higher signal quality or larger capacity, a correlative-level encoder is exploited as a second modulator preceded by the delta-sigma modulator. The encoder compresses the bandwidth of the delta-sigma modulated signal by creating a correlation between adjacent signal symbols. As a result, the sampling frequency of the delta-sigma modulator in the proposed system can be increased beyond the transmission bandwidth of the IFoF system, considerably improving the in-band signal quality and the transmission capacity over the conventional multi-level approach. This is because the quantization noise from the delta-sigma modulation in the proposed scheme is more aggressively pushed away from the signal bandwidth with the high sampling frequency. According to experimental results, the proposed link provides at least a 40% larger transmission capacity for similar in-band signal quality or 2.1% better average EVM performance for the same capacity than the conventional four-level pulse-amplitude-modulation delta-sigma IFoF systems.

Sigma-Delta modulators (SDMs) are capable of shaping the quantization noise out of a specific frequency band defined by their noise transfer function (NTF). A single-bit output SDM pose further advantages in applications that would typically require a multi-bit DAC, since then only a single-bit DAC is required, which is much easier to design and is inherently linear in comparison to a multi-bit one. Look-ahead SDMs have been proposed to enhance the signal-to-noise-and-distortion-ratio (SNDR) and the output bandwidth of conventional single-bit SDMs. Multi-Step Look-Ahead sigma-delta modulators (MSLA SDMs) further reduce the hardware complexity required for the implementation of typical look-ahead SDMs while maintaining their performance advantages. In this work the architecture and the benefits of the MSLA SDMs are showcased. Finally the advantages of the MSLA SDMs over single-bit conventional ones are demonstrated and several hardware implementation choices for design optimization are discussed.

A design of a 5.6 GHz frequency synthesizer with switched bias LIT VCO and low noise on‐chip LDO regulator for 5G applications

The spectrum of quantization noise in a dithered sigma-delta modulator and multistage sigma-delta modulator is derived under the constraint that the dithering signal does not cause overload. It is shown in the case of a simple sigma-delta modulation that no-overload dithering can smooth the noise spectrum and can make the binary quantization noise asymptotically uncorrelated with the input. It does not, however, make the noise white. In the case of multistage sigma-delta modulation with the appropriate dithering, the binary quantization noise becomes asymptotically white, even for a system with only two-stages. The signal-to-quantization-noise ratio is derived for sigma-delta and multistage sigma-delta oversampled analog-to-digital conversion with additive dithering. Simulation results are presented to support the theoretical analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This brief describes a framework for the analysis of continuous-time sigma-delta (ΣΔ) modulators (CTSDM) in the presence of a feedback digital-to-analog converter (DAC)'s clock jitter using the discrete-time Volterra series. A time-domain mixing operation between jitter and CTSDM's digital output sequence is modeled with a second-order Volterra operator. The resulting closed-form jitter-induced CTSDM's output power spectral density is simple and includes the effects of the following: 1) quantization noise power; 2) input signal power and frequency; 3) CTSDM's quantization noise transfer function; 4) DAC's pulse shape; and 5) colored jitter. A third-order CTSDM is analyzed as a test bed. Excellent agreement between theoretical predictions and behavioral simulations is observed.

The effect of certain fundamental nonidealities on the resolution of a continuous-time (CT) delta sigma modulator are examined in this paper. We start by talking about the equivalence between an ideal CT delta sigma modulator and its discrete-time (DT) counterpart, then consider the effect of quantizer/DAC propagation delay, clock jitter, and the recently-identified phenomenon of signal-dependent jitter on the ideal performance.

This paper presents a digital controller architecture oriented to IC implementation. The classical digital pulse width modulator (D-PWM), using digital analog converter (DAC), is replaced with a Sigma-Delta (/spl Sigma//spl Delta/) modulator based on pulse frequency modulator (PFM) technique. Results of an investigation from a prototype for DC-DC converter, in terms of simulated and experimental performances, are reported, together with harmonic frequency investigation. The control function design is implemented on a field programmable gate array (FPGA). As a consequence of good agreement between simulated and experimental results, the proposed architecture realizes a digital control loop with dynamic performances comparable to analog control systems.

Sinusoidal signal can be used as stimulus to test static and dynamic parameters of ADC. A sigma-delta modulation based sinusoidal signal generator for ADC testing in SOC was introduced. The generator was built on the same chip with ADC. A numerical resonator generated a sinusoidal signal which was converted to a single bitstream by a sigma-delta modulator. Due to oversampling, the quantization noise was pushed to high frequency range. A high-quality sinusoidal signal was generated by low-pass filtering the bitstream. The sigma-delta modulator was inserted into the resonator to decrease silicon area overhead and calculate time. A cascaded integrator comb decimation filter was used as the low-pass filter. The amplitude and frequency of the output sinusoidal signal could be accuratly set by digital parameter of the generator to meet the requirement of static and dynamic performances testing. DOI: http://dx.doi.org/10.11591/telkomnika.v11i7.2818

A theoretical basis is provided for multistage sigma-delta modulation (MSM), which is a cascade realization of several single-loop sigma-delta modulators with a linear combinatorial network. Equations are derived describing the output and the quantization noise of MSM for an arbitrary input signal, and the noise-shaping characteristic of MSM is investigated. The spectral characteristics of an m-stage sigma-delta modulator with both DC and sinusoidal inputs are developed. For both types of inputs the binary quantizer noise of the mth (m>or=3) quantizer, which appears at the output as an mth order difference, is asymptotically white, uniformly distributed, and uncorrelated with the input level. It is also found that for an m-stage sigma-delta quantizer with either an ideal low-pass filter or a sinc/sup m+1/ filter decoder, the average quantization noise of the system is inversely proportional to the (2m+1)th power of the oversampling ratio. This implies that the high-order systems are favourable in terms of the trade-off between the quantization noise and oversampling ratio. Simulation results are presented to support the theoretical analysis. >

In a visible light communication (VLC) system, the modulation bandwidth of light emitting diode (LED) is limited with current technology. In addition, the nonlinearity inherited in the LED prevents the application of spectral efficient modulation schemes with high peak-to-average power ratio. These characteristics limit the overall throughput of the VLC system. In this letter, a one-bit sigma-delta modulator (SDM) is introduced to the transmit signal. Such modification is compatible with the current LED lighting systems and LED drivers as the output of the one-bit SDM is equivalent to ON-OFF keying signal, thus is immune to system nonlinearities. In addition, the output of the one-bit SDM enjoys high spectral efficiency as the original input signal does. The out-of-band quantization noise can be taken care of at the receiver with analog filtering and digital signal processing. Simulation and experiment results validate that the SDM can significantly improve the VLC system performance.