Analytic determination of the capacitance matrix of planar or cylindrical multiconductor lines on multilayered substrates

Determination of Capacitance and Conductance Matrices of Lossy Shielded Coupled Microstrip Transmission Lines

“…As it is clear from these two examples, the results of the presented method have a little discrepancy compared to [3] and [12]. Therefore one may satisfy about the accuracy of the presented methods.…”

“…The 20 different coefficients of the capacitance matrix (normalized to ε 0 = 8.842 × 10 −12 ) obtained from the presented methods and from that proposed in [12] (reported in [13]) have been compared in Table 1. For a second example consider an M = 2 conductor lossless microstrip coupler with parameters w 1 = w 2 = w, h = 1, s = 1, a and b very large (e.g., a = b = 30h) and ε r = 2.35.…”

“…The matrix equation (12) can be solved by pseudo-inverse matrix method. Obviously, as the number of harmonics, i.e., N , increases, the accuracy of the solution is increased.…”

“…To analyze these transmission lines one has to find the capacitance and conductance matrices of the structure [1]. The capacitance matrix of lossless structures is determined using conformal mapping transformations [2,3], variational methods [4,5], spectral domain techniques [6,7], method of moments and green's function [8,9], analytically for certain particular geometries [10] and solving Laplace's equation [11][12][13]. Some ones solve Laplace's equation numerically, e.g., finite difference method [11] and some others analytically, e.g., fourier series or fourier integral method [12,13].…”

Electromagnetic Coupling to Circulant Symmetric Multi-Conductor Microstrip Line

“…in which V and I are N × 1 voltage and current vectors, respectively and C and L are capacitance and inductance matrices of the lines, respectively that can be obtained using a similar method to that of [1] or [7] for CSMSL structure. Also, V F and I F are N × 1 distributed forcing sources and regarding to [6] can be obtained as follows.…”