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

A rigorous approach to the robust design of continuous-time ΣΔ modulators

In this paper we present a framework for robust design of continuous-time Sigma Delta modulators. The approach allows to find a modulator which maintains its performance ( stability, guaranteed peak SNR, ...) over all the foreseen parasitic effects, provided it exists. For this purpose, we have introduced the S-figure as a criterion for the robustness of a continuous-time Sigma Delta modulator. This figure, inspired by the worst-case-distance methodology, indicates how close a design is to violating one of its performance requirements. Optimal robustness is obtained by optimizing this S-figure. The approach is illustrated through various design examples and is able to find modulators that are robust to excess loop delay, clock jitter and coefficient variations. As an application of the approach, we have quantified the effect of coefficient trimming. Even with poor trim resolution, good performance can be achieved provided beneficial initial system parameters are chosen. Another example illustrates the fact that also the out-of-band peaking behavior of the signal transfer function can be controlled with our design framework

Multirate cascaded discrete-time low-pass ΔΣ modulator for GSM/Bluetooth/UMTS

This paper shows that multirate processing in a cascaded discrete-time ΔΣ modulator allows to reduce the power consumption by up to 35%. Multirate processing is possible in a discrete-time ΔΣ modulator by its adaptibility with the sampling frequency. The power reduction can be achieved by relaxing the sampling speed of the first stage and increasing it appropriately in the second stage. Furthermore, a cascaded ΔΣ modulator enables the power efficient implementation of multiple communication standards.@The advantages of multirate cascaded ΔΣ modulators are demonstrated by comparing the performance of single-rate and multirate implementations using behavioral-level and circuit-level simulations. This analysis has been further validated with the design of a multirate cascaded triple-mode discrete-time ΔΣ modulator. A 2-1 multirate low-pass cascade, with a sampling frequency of 80 MHz in the first stage and 320 MHz in the second stage, meets the requirements for UMTS. The first stage alone is suitable for digitizing Bluetooth and GSM with a sampling frequency of 90 and 50 MHz respectively. This multimode ΔΣ modulator is implemented in a 1.2 V 90 nm CMOS technology with a core area of 0.076 mm2. Measurement results show a dynamic range of 66/77/85 dB for UMTS/ Bluetooth/GSM with a power consumption of 6.8/3.7/3.4 mW. This results in an energy per conversion step of 1.2/0.74/2.86 pJ

Advanced Algorithms for Satellite Communication Signal Processing

Dizertační práce je zaměřena na softwarově definované přijímače určené k úzkopásmové družicové komunikaci. Komunikační kanály družicových spojů zahrnujících komunikaci s hlubokým vesmírem jsou zatíženy vysokými úrovněmi šumu, typicky modelovaného AWGN, a silným Dopplerovým posuvem signálu způsobeným mimořádnou rychlostí pohybu objektu. Dizertační práce představuje možné postupy řešení výpočetně efektivní digitální downkonverze úzkopásmových signálů a systému odhadu kmitočtu nosné úzkopásmových signálů zatížených Dopplerovým posuvem v řádu násobků šířky pásma signálu. Popis navrhovaných algoritmů zahrnuje analytický postup jejich vývoje a tam, kde je to možné, i analytické hodnocení jejich chování. Algoritmy jsou modelovány v prostředí MATLAB Simulink a tyto modely jsou využity pro ověření vlastností simulacemi. Modely byly také využity k experimentálním testům na reálném signálu přijatém z družice PSAT v laboratoři experimentálních družic na ústavu radioelektroniky.The dissertation is focused on software defined receivers intended for narrowband satellite communication. The satellite communication channel including deep space communication suffers from a high level of noise, typically modeled by AWGN, and from a strong Doppler shift of a signal caused by the unprecedented speed of an object in motion. The dissertation shows possible approaches to the issues of computationally efficient digital downconversion of narrowband signals and the carrier frequency estimation of narrowband signals distorted by the Doppler shift in the order of multiples of the signal bandwidth. The description of the proposed algorithms includes an analytical approach of its development and, if possible, the analytical performance assessment. The algorithms are modeled in MATLAB Simulink and the models are used for validating the performance by the simulation. The models were also used for experimental tests on the real signal received from the PSAT satellite at the laboratory of experimental satellites at the department of radio electronics.

SWIPE: a bolometric polarimeter for the Large-Scale Polarization Explorer

The balloon-borne LSPE mission is optimized to measure the linear polarization of the Cosmic Microwave Background at large angular scales. The Short Wavelength Instrument for the Polarization Explorer (SWIPE) is composed of 3 arrays of multi-mode bolometers cooled at 0.3K, with optical components and filters cryogenically cooled below 4K to reduce the background on the detectors. Polarimetry is achieved by means of large rotating half-wave plates and wire-grid polarizers in front of the arrays. The polarization modulator is the first component of the optical chain, reducing significantly the effect of instrumental polarization. In SWIPE we trade angular resolution for sensitivity. The diameter of the entrance pupil of the refractive telescope is 45 cm, while the field optics is optimized to collect tens of modes for each detector, thus boosting the absorbed power. This approach results in a FWHM resolution of 1.8, 1.5, 1.2 degrees at 95, 145, 245 GHz respectively. The expected performance of the three channels is limited by photon noise, resulting in a final sensitivity around 0.1-0.2 uK per beam, for a 13 days survey covering 25% of the sky.Comment: In press. Copyright 2012 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibite