Course Catalogue

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This course will equip the student with an understanding of sigma-delta data converters using theoretical analysis and high level macromodel simulation.

The course will briefly review the basics of discrete-time signals and systems, before looking at block diagrams and signal flow graph implementations of modulator structures. Saturation, stability and limit cycle behaviour of modulator loops will be described and related to circuit structure.

The course will be illustrated throughout with MATLAB, Simulink examples linking to laboratory sessions and a design exercise issued at the start of semester.

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PHYS5044 Fundamentals of Sensing

Coursework.

Reassessments are normally available for all courses, except those which contribute to the Honours classification. Where, exceptionally, reassessment on Honours courses is required to satisfy professional/accreditation requirements, only the overall course grade achieved at the first attempt will contribute to the Honours classification. For non-Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

The course aims to teach students the following topics:

Basics of discrete-time signals and systems, sampling, aliasing, interpolation, reconstruction, quantization modelled as noise, and the effects of sampling jitter. General block diagram of oversampled system (ADC and DAC, decimation and interpolation). Frequency domain representation of signals and noise. Fourier series, Fourier transforms and computer-based computational techniques, including the Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT), windowing and coherent sampling principles. Power spectral density (PSD). Averaging to reduce quantisation noise. The principles of delta-sigma modulation. Principle of oversampling to reduce the effects of quantization noise, followed by noise-shaping to enhance performance. Block diagram of 1st order modulator. Time-domain model using a first-order lowpass system then followed by a frequency-domain description. Z-transfer function of NTF and STF. In-band and filtered noise. Power of noise and signal, SNR formula. Quantiser gain. Simulink examples. Time domain simulation. Limit cycles, idle tones and dither. Dead zone. Simulink examples. Second-order modulator block diagrams. Z-transfer function of NTF, STF. MASH implementation. Single loop implementation. Comparison of 1st and 2nd order. Saturation. Dynamic range scaling equalisation at internal nodes. Limit cycles. Formula of SNR with modulator order and oversampling. Boser-Woolley, Silva-Steensgaard. Error feedback. Simulink examples. Higher-order block diagram. Implementation of higher order modulator as MASH or single loop. Instability. General higher order modulator. Placement of zeros in NTF. Feedback/feedforward to improve THD. NTF comparison. CIFF, CIFB, CRFF, CRFB structures. Matlab SD toolbox for design. Simulink examples. Multi-bit feedback. Multi-bit quantisers. Effects on SQNR and stability. Simulink examples.

By the end of this course students will be able to:

1. Understand the operating principles of sigma delta converters.

2. Choose the order, structure and coefficients of sigma delta modulators at a block level.

3. Employ SIMULINK and MATLAB to simulate and design the modulator coefficients.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.