Accurate decomposition of transfer matrices

An important problem in passive filter synthesis is the calculation of accurate element values. For example, in some synthesis procedures up to a decimal digit of accuracy can be lost during each element calculation. To improve accuracy, cascade synthesis can be used. This method gives two estimates of each element value, and also allows flexibility in the order of removal of elements. The cascade method was reported by Lind in 1978. The paper showed that very large variations in accuracy exist, depending on the removal order. For example, a 10 element network gave a 10⁷ variation in accuracy! This paper will describe a further accuracy improvement for the cascade synthesis method