On the realization of voltage transfer functions by distributed active networks

It is shown that a matrix that characterizes the network can be put in a form in which its elements are dependent only on the order of the transfer function to be realized. An algorithm is presented which can generate the elements of the characteristic matrix. It is also shown that the adjoint of the characteristic matrix and the determinate of the characteristic matrix can be evaluated by means of two simple algorithms. Computer programs based on these algorithms were written. The characteristic matrices and their adjoints for transfer functions of order up to nine were obtained and tabulated. Criteria are developed which can be used to indicate whether a given transfer function of first or second order can be realized. A new method of determining realizability called the Uspensky-Descartes scheme is developed for third order functions. A design method for optimization techniques is also presented.