CAD of equiripple filters

Optimisation techniques are applied to numerous engineering problems. Many algorithms are based upon finding the solution to the global minimum of a scalar function in terms of the available parameters which themselves may be constrained in value. When this technique is applied to the design of electrical filters, great difficulty occurs due to the fact that many local minima can be encountered. For passive filters with all-pole transfer functions it may be shown that a design with an equiripple passband behaviour is optimum and also has a zero first ordered sensitivity with respect to all parameters as the optimum performance is approached. These facts enable a vector optimisation technique to be used which zeros an nth degree vector producing a unique solution within the constraint of all positive element values. This technique will be applied to a high frequency printed circuit filter where the transfer characteristic has to be computed numerically using complex equivalent circuits for the elements in the filter