A method for one port and two-port RC circuit synthesis

A new method for the synthesis of RC one ports and two-ports is proposed in this paper. A new model of the human body, computed using this method, is developed. This model proves to be more accurate than the classical Cole model. The proposed synthesis method can be used to compute reduced order models (ROM), preserving the circuit passivity, unlike most known ROM computation methods. Key-Words: Synthesis of RC circuits, pole/zero , RC model of human body, reduced order models 1.Introduction The common approach to circuit synthesis is to start from a given set of frequency characteristics, to approximate them with realizable rational fractions (ratios of polynomials of the Laplace variable s), and to use a synthesis method for finding a circuit which corresponds to the above circuit functions [1]. A new approach to this problem, based on pole/zero placement of RC circuits, is presented in this paper. A new method for RC admittance synthesis is given in Section 2. Section 3 outlines a new method for the synthesis of RC two-ports. A new circuit model for body cell mass prediction, illustrating the new synthesis method, is described in Section 4. 2. Synthesis of a RC admittance The poles and zeros of a RC admittance YRC(s) alternate on the negative real axis, the closest to the origin being a zero. The shape of the curve |YRC(jω)| vs. ω is defined by the location of the poles and zeros. Sweeping the ω axis starting from the origin we remark that the occurence of a zero is associated with a slope change of decade dB 20 and the occurence of a pole is associated with a slope change of decade dB 20 − [2]. This is because the characteristic |YRC(jω)| has asymptotes whose slopes are decade dB 20 , 0, decade dB 20 , 0 a.s.o. Characteristic approximation by asymptotes has the maximum error of 3dB at the asymptote intersection (Fig.1). A natural way to approximate |YRC(jω)| is to consider fewer asymptotes with the same slopes as the original ones. Fig. 1. The frequency characteristic of a RC admittance and its asymptotes The complexity of the syntehsized circuit depends on the relative error ε with respect to the original characteristic. Obviously a greater ε leads to a simpler circuit. Our algorithm for synthesis of a RC admittance has the following steps: 1. computation of the first zero z1 2. computation of the other poles and zeros 3. computation of the circuit parameters The frequency range of interest is [ωm, ωM]. z1 is set to ωm. Sweeping the frequency axis with a step ∆ωm, the error between the asymptote of decade dB 20 and the given characteristic is checked. The first pole p1 is placed to the last value before that corresponding to an error of 2ε or greater. If this error occurs after the first step ∆ωm then p1 is placed very close to z1. The first asymptote is Proceedings of the 7th WSEAS International Conference on CIRCUITS, SYSTEMS, ELECTRONICS, CONTROL and SIGNAL PROCESSING (CSECS'08) ISSN: 1790-5117 124 ISBN: 978-960-474-035-2 translated so that a maximum error of ε is obtained. The other asymptotes are determined without translation using the condition error ≤ ε in each frequency interval corresponding to the given asymptote. Computation of the circuit parameters is performed using a Foster, a Cauer or a FosterCauer procedure. 3.Synthesis of a RC two-port admittance matrix Knowing 12 21 , 22 , 11 y y and y y = the Cauer method of synthesis [1] can be used for finding the twoport circuit. Two outstanding properties related to this synthesis method must be taken into account: • the poles of 12 21 y y = must be poles of