A describing function study of saturated quantization and its application to the stability analysis of multi-bit sigma delta modulators

Just as their single-bit counterparts, multi-bit sigma delta modulators exhibit nonlinear behavior due to the presence of the quantizer in the loop. In the multi-bit case this is caused by the fact that any quantizer has a limited output range and hence gives an implicit saturation effect. Due to this, any multi-bit modulator is prone to modulator overloading. Unfortunately, until now, designers had to rely on extensive time-domain simulations to predict the overloading level, because there is no adequate analytical theory to model this effect. In this work, we have developed such an analytical theory based on multiple input describing function analysis. This way, we obtained expressions for the signal gain, the noise gain and the variance of the quantization noise. Here, both the case of DC as well as sinusoidal signals was considered. These results were used for the stability analysis of multi-bit Sigma Delta modulators, which allows to predict the overloading level. Code implementing the proposed expressions is available for download at http://cas1.elis.ugent. be/cas/en/download

System Design of a Wide Bandwidth Continuous-Time Sigma-Delta Modulator

Sigma-delta analog-to-digital converters are gaining in popularity in recent times because of their ability to trade-off resolutions in the time and voltage domains. In particular, continuous-time modulators are finding more acceptance at higher bandwidths due to the additional advantages they provide, such as better power efficiency and inherent anti-aliasing filtering, compared to their discrete-time counterparts. This thesis work presents the system level design of a continuous-time low-pass sigma-delta modulator targeting 11 bits of resolution over 100MHz signal bandwidth. The design considerations and tradeoffs involved at the system level are presented. The individual building blocks in the modulators are modeled with non-idealities and specifications for the various blocks are obtained in detail. Simulation results obtained from behavioral models of the system in MATLAB and Cadence environment show that a signal-to-noise-and-distortion-ratio (SNDR) of 69.6dB is achieved. A loop filter composed of passive LC sections is utilized in place of integrators or resonators used in traditional modulator implementations. Gain in the forward signal path is realized using active circuits based on simple transconductance stages. A novel method to compensate for excess delay in the loop without using an extra summing amplifier is proposed

High Performance Class-AB Output Stage Operational Amplifiers for Continuous-time Sigma-delta ADC

One of the most critical blocks in a wide-band continuous time sigma delta (CTSD) analog-to-digital converter (ADC) is the loop filter. For most loop filter topologies, the performance of the filter depends largely on the performance of the operational amplifiers (op-amps) used in the filter. The op-amps need to have high linearity, low noise and large gain over a wide bandwidth. In this work, the impact of op-amp parameters like noise and linearity on system level performance of the CTSD ADC is studied, and the design specifications are derived for the op-amps. A new class-AB bias scheme, which is more robust to process variations and has an improved high frequency response over the conventional Monticelli bias scheme, is proposed. A biquadratic filter which forms the input stage of a 5th order low pass CTSD ADC is used as a test bench to characterize the op-amp performance. The proposed class-AB output stage is compared with the class-AB output stage with Monticelli bias scheme and a class-A output stage with bias current reuse. The filter using the new op-amp architecture has lower power consumption than the other two architectures. The proposed class AB bias scheme has better process variation and mismatch tolerance compared to the op-amp that uses conventional bias scheme