Theory and Methodology of Integrated Ladder Filter Design

This thesis presents a systematic study of integrated ladder filter design. A theoretical model of ladder structures is first established in terms of a family of symmetric matrix polynomial systems (SMPS's). It is shown that SMPS's are a natural mathematical abstraction of ladder circuits. The properties of stability, canonical (or minimal) realisation, low-sensitivity and low-noise, are proved for SMPS's under certain very simple conditions. A design methodology is then presented for active-RC, SC and digital ladders. The basic principle is that a SMPS can be decomposed by means of matrix factorisation into several linear systems, which can then be easily realised by active or digital circuits. It is shown that many existing methods, such as leapfrog or coupled biquads, result from some special decompositions. It is further shown that LU and UL factorisations drawn from numerical methods can be used to develop several novel structures (so-called LUD and ULD structures) which demonstrate significant improvments over existing ones regarding sensitivity, component area and dynamic range. This is confirmed by examples and statistical investigations. Besides the matrix methods applicable to standard lowpass and bandpass cases, further research is undertaken for bandstop, highpass and allpass filter designs. It is demonstrated that frequency transformations can be used to reduce the hardware cost in many classical filtering cases. A novel building block, the so called TWINTOR, is introduced in bandstop design to reduce the switching rate. Active-RC and SC allpass ladders are constructed and proved to have significant advantages over the existing biquad circuits. Matrix methods also provide an efficient vechicle for the development of a filter design software package called PANDDA. Its many outstanding features are described. Finally measured results from two fabricated LUD SC filters are presented. They confirm the high quality of the novel circuit structures developed by this research