Extension of Bode's Constant Resistance Lattice Synthesis of Transfer Impedance Function*

Abstract

Bode developed some explicit formulas in terms of the poles and zeros of the transfer impedance function for each element of the first and second degree constant resistance lattice structures. To extend work in this area, we derive explicit formulas for two of Bode's structures using coupled coils; we give two new structures which avoid coupled coils. Illustrative examples show the usage of these formulas. Finally, we include a general procedure for synthesizing any physically realizable, rational transfer impedance function by a constant resistance lattice network. A flow chart aids in detailing this procedure. With the addition of these results, a general method for synthesizing any physically realizable, rational transfer impedance function with explicit formulas is complete. The explicit formulas method developed in this paper gives more rapid results and introduces fewer round-off errors than the step-by-step procedures used in the past.