Stability testing of hybrid DT+CT systems

Unstable behavior of discrete-time systems cooperating with continuous-time sub-blocks is analyzed. Typical examples are the instabilities in convolution digital filters operating in feedback loops together with AD and DA converters, analog anti-aliasing and smoothing filters, and other application circuits. It is shown that the stability of such systems can, in linear cases, be tested via the location of z-domain poles of an associated transfer function, and that the poles depend not only on the algorithm of digital filter but also on the sampling frequency and the parameters of analog circuitry. A methodology of the stability analysis via the SPICE-family simulation programs is presented.