Abstract

This paper considers optimized design of
interpolative sigma delta modulators (SDMs). The first
optimization problem is to determine the denominator
coefficients. The objective of the optimization problem is to
minimize the passband energy of the denominator of the loop
filter transfer function (excluding the DC poles) subject to the
continuous constraint of this function defined in the frequency
domain. The second optimization problem is to determine the
numerator coefficients in which the cost function is to minimize
the stopband ripple energy of the loop filter subject to the
stability condition of the noise transfer function (NTF) and signal
transfer function (STF). These two optimization problems are
actually quadratic semi-infinite programming (SIP) problems.
By employing the dual parameterization method, global optimal
solutions that satisfy the corresponding continuous constraints
are guaranteed if the filter length is long enough. The advantages
of this formulation are the guarantee of the stability of the
transfer functions, applicability to design of rational IIR filters
without imposing specific filter structures, and the avoidance of
iterative design of numerator and denominator coefficients. Our
simulation results show that this design yields a significant
improvement in the signal-to-noise ratio (SNR) and have a larger
stability range, compared to the existing designs.