Categorizations And Realizations Of Positive Real And Biquadratic Immittance Functions PDF Download

It is shown that a positive real immittance function F(s) is of one of eight categories. The category can be recognized by the sign polarities of three test values that are functions of the coefficients of F(s). If F(s) is of a certain category, then 1/F(s) can only be of some other categories. According to the categories of F(s) and 1/F(s) the immittance function can be realized (1) either by an RC or an RL network with positive elements, (2) by an RLC network with exclusively positive elements and an equivalent model circuit, or (3) only by model circuits. A model circuit is an RLC ladder structure with one negative branch element. The RC, RL, RLC, and model circuits have several equivalences.