In this thesis a clear synthesis technique to design a power splitter based on three resonators is introduced. A new analytic synthesis method is developed to investigate a coupled resonator structure with only three resonators and three ports. The general formulae to calculate the coupling coefficients between resonators are analytically derived. This method avoids the use of the polynomial synthesis technique. The mathematical analysis is extended for the realisation of an asymmetric frequency response of a trisection filter. A simple mathematical function with a minimum number of parameters is developed which can be used as a cost function when using optimisation. These parameters are coupling coefficients and external quality factors, and are called control variables. A coupling matrix optimisation technique is used to obtain optimised values of control variables to realise an asymmetric frequency response of a trisection filter. The optimisation algorithms effectively reduce the cost function, and generate appropriate values of control variables when the function is minimised.