Circuit Parameters of Vertical Wires Above a Lossy Ground in PEEC Models

This paper presents an investigation into circuit parameters of vertical wires over a lossy ground in partial element equivalent circuit (PEEC) models. The full-wave PEEC formulation of the vertical wires is presented, and formulas of circuit parameters for the vertical wires are derived using the Sommerfeld integral. Frequency responses of circuit parameters are discussed for both poor and good grounds, respectively. The results are validated numerically using the numerical electromagnetic code (NEC2). It is found that the lossy ground can be replaced with the weighted images in the electromagnetic analysis for the vertical wires. The lossy ground can be even replaced with the perfect conducting ground for the closely spaced vertical wires. The difference of the current and potential on the wires might not be significant if the imaginary part of ground dielectric constant is much greater than its real part. Using the perfect conducting ground can reduce computing resources significantly in the electromagnetic analysis. The complex plane method could lead to a large error if it is applied for vertical wires.