# HARVARD VLSI GROUP

# Sigma-Delta Systems

## Graduate Student: Phil Steiner

## Faculty Advisor: Woodward Yang

Sigma-Delta systems have been successfully utilized in high
resolution, oversampled analog-to-digital and digital-to-analog
conversion applications. Sigma-Delta (also known as Delta-Sigma)
systems are essentially clocked linear feedback systems with the
exception of a single nonlinearity due to a comparator (or more
generally a quanatization element). In the past, analysis of
Sigma-Delta systems has focussed on approximating this nonlinear
system as a linear feedback system and modeling the quanatization
element as an additive noise element. However, we have developed a
nonlinear analysis that incorporates the full nonlinear
characteristics of quanatization element. We have a closed form proof
of stability of the second order sigma-delta modulator and have
extended our analysis to higher order systems (see ISCAS94 paper in
our technical reports).
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Jeff Miller
miller@atlantis.harvard.edu