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DRPS : Course Catalogue : School of Engineering : Postgrad (School of Engineering)

Postgraduate Course: Sigma Delta Data Converters (MSc) (PGEE11114)

Course Outline
SchoolSchool of Engineering CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits20 ECTS Credits10
SummaryThis course will equip the student with an understanding of sigma-delta data converters at a theoretical and practical level. The coursework makes a link between the digital signal processing concepts of sigma delta conversion and implementation in integrated circuit hardware.

The course will briefly review the basics of discrete-time signals and systems, before looking at block diagrams and circuit implementations of modulator structures. Saturation, stability and limit cycle behaviour of modulator loops will be described and related to circuit structure. Non-ideal behaviour of modulators such as noise, matching, finite gain and settling will be related to circuit level implementations.

The course will be illustrated throughout with MATLAB, Simulink and Cadence Verilog A examples linking to laboratory sessions and a design exercise issued at the start of semester.
Course description Lecture 1:
Reminder of the basics of discrete-time signals and systems.
Topics include: 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.

Lecture 2:
First order modulator continued. Time domain simulation. Limit cycles, idle tones and dither. Dead zone. Simulink examples.

Lecture 3:
Second order modulators.
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.

Lecture 4:
Higher order modulators.
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.

Lecture 5:
Multi-bit feedback. Multi-bit quantisers. Effects on SQNR and stability. Simulink examples.

Lecture 6:
DAC matching effects in multi-bit DAC. Mismatch effects on modulator linearity. Randomised selection of elements. Dynamic element matching (DEM). Data weighted averaging (DWA). Tones. Tree DEM. Multi-bit feedback in ADC. Simulink examples.

Lecture 7:
Multi-stage modulators. 1+1+1, 2+1 MASH, SMASH. Stability. Error term generation. Simulink examples.

Lecture 8:
Circuit Implementation of Modulators.
Non overlapping clock generation.
Switched capacitor implementation of delaying and non-delaying integrators. Latched comparators. 2-level DAC implementation. First and second order switched capacitor modulator. Cadence examples.

Lecture 9:
Fully differential switched-capacitor modulators. Multi-bit quantiser and DAC implementation.
Switch resistance and transmission gate sizing. Amplifier and switch settling. Synamic range scaling. Cadence examples.

Lecture 10:
Noise sources. 1/f and thermal noise. kT/C noise in switched capacitor modulators. Capacitor sizing for noise. Total modulator noise. Cadence examples.

Lecture 11:
Guest lecture.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites It is RECOMMENDED that students have passed Digital Signal Analysis 4 (ELEE10010) OR Discrete-Time Signal Analysis (PGEE11026)
It is RECOMMENDED that students have passed Analogue Electronics (Project) 4 (ELEE10021) OR Analogue Electronics (Circuits) 4 (ELEE10020) OR Analogue VLSI A (ELEE11041) OR Analogue circuit design (ELEE11045)
Prohibited Combinations Other requirements None
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. understand the operating principles of sigma delta converters
  2. choose the order, structure and coefficients of sigma delta modulars at a block level.
  3. employ SIMULINK and MATLAB to simulate and design the modulator coefficients
  4. use Cadence to study non-ideal effects in modulators
  5. propose circuit implementations of modulators and understand the range of applications of sigma-delta converters.
Reading List
Understanding Sigma-Delta Data Converters, Schreier and
Temes, IEEE Press, ISBN 978-0-471-46585-0
Additional Information
Graduate Attributes and Skills Not entered
KeywordsSigma-delta,delta-sigma,analogue to digital,digital to analogue,integrated circuits
Course organiserDr Robert Henderson
Tel: (0131 6)50 5645
Course secretaryMrs Megan Inch-Kellingray
Tel: (0131 6)51 7079
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