The cascaded steady-state lumped parameter circuits for describing resonance characteristics of transmission lines

This paper proposes a determination method for cascaded lumped parameter circuits (LPCs) to describe steady-state resonance characteristics of transmission lines, with a focus on the cascaded number. The physical simulation of long-distance transmission lines is achieved by cascaded LPCs. The existing methods for determining the cascaded number are applicable to transient-state operating conditions. The LPC with a cascaded number adequate for transient-state needs causes misjudgment in physical simulation. The number is determined by simulation and is limited by computational simulation software tools. This paper proposes a fitting participation factor (PF)-based method to determine the cascaded number. With the proposed method, the LPC and the transmission line have approximately proportional harmonic propagation distribution and harmonic voltage. Errors of resonance frequency and resonance center in the LPC are investigated based on numerical analysis and resonance mode analysis. The misjudgment in physical simulation is discussed through PF. Next, the general expression for the measuring impedance of the LPC is deducted. The applicable operating conditions and equivalent conditions for various LPCs are examined. In addition, the proposed method is independent of skin effect and suitable for lossy lines. The validity of the proposed method is verified by simulations.