Realization of biquadratic impedances with at most four elements

This paper considers the realizability problem of biquadratic impedances with at most four elements. To solve the problem, the necessary and sufficient realizability condition for no more than three elements is obtained by some topological properties derived previously. Furthermore, the constraints on the possible realizations are used to find out the networks which can cover all the cases, and they are classified as several quartets. Finally, investigating one of the networks in each quartet yields the necessary and sufficient condition for a network to be realized with at most four elements.