Foster's realisation was limited to LC networks and was in one of two forms; either a number of series LC circuits in parallel, or a number of parallel LC circuits in series. Foster's method was to expand Z(s) into partial fractions. Cauer showed that Foster's method could be extended to RL and RC networks. Cauer also found another method; expanding Z(s) as a continued fraction which results in a ladder network, again in two possible forms.Kalman, p. 4 In general, a PRF will represent an RLC network; with all three kinds of element present the realisation is trickier. Both Cauer and Brune used ideal transformers in their realisations of RLC networks. Having to include transformers is undesirable in a practical implementation of a circuit.Hubbard, p. 3
