The FEM method and program for optimizing the synthesis processes of three - phase thick-film resistors is presented. The program allows calculating the effective conductivities and temperature coefficients of resistance of matrix systems containing circular inclusions characterized by variable sizes, mutual position and conductivity. It is shown that a metal-semiconductor transition can exist in such a system and states with abnormally small TCR (temperature coefficient of resistance) can be realized. © 2023 American Institute of Physics Inc.. All rights reserved.