A fast method for computing current distribution on printed circuit boards and microwave integrated circuits using the method of moments

In order to determine current distribution on Printed Circuit Board (PCB) or Microwave Integrated Circuit (MIC) structure using the full-wave Method of Moments (MoM), the impedance of the structure must be computed first. A full-wave impedance matrix is frequency dependent in a non-trivial way; Green's function and consequently impedance matrix [Z] must be recomputed at each frequency separately to solve for the unknown current. A large percentage of CPU time required to solve the matrix equation [Z][I] = [V] is spent on calculating the impedance matrix, which becomes less and less efficient as the number of frequency points increases. Analysis of circuits with electrically thin substrates is even less efficient because these circuits require bigger impedance matrix in order to compute the unknown current [I] accurately.; We propose a way to speed up the computation of the impedance matrix by using a static approximation to Green's function and further simplifying the image part of the Green's function as a single term. Frequency independent inductance and capacitance elements L_nn and C_nn′ are computed using analytic expressions, which are exact, even for electrically thin substrates. We multiply L_nn′ and C_nn′ with phase shifts, which are linear functions of wave number k₀, to get quasistatic inductance and capacitance matrices [L_eq] and [C_eq]. Modified quasistatic impedance matrix [Z] is then assembled from jω[L_eq] and 1/jω[C _eq]. Impedance matrix [Z] at other frequencies is computed by multiplying L_nn′ and C_nn′ with appropriately scaled phase shifts and with jω.; Approximations made in computing impedance matrix cause error in current. We use an error bound not widely used in literature (but more accurate than better known bounds) to estimate current error. We show the improved accuracy of full-wave MoM solution when the substrate is electrically thin. CPU time needed to calculate current distribution on a MIC over frequency range using the approximate and full-wave MoM approach is compared, as well as accuracy of radiation pattern prediction.