Alternative Phase-domain Model for Multi-conductor Transmission Lines Using Two Modal Transformation Matrices

A new model for multi-conductor transmission lines is proposed based on an alternative modal decoupling technique. The line decoupling is accomplished using two modal transformation matrices: the real and constant Clarke's matrix and a reduced frequency-dependent matrix for decoupling the remaining mutual terms in the impedance and admittance matrices (quasi-modes). This procedure results in a simple matrix formulation in the frequency domain, which time-domain results can be obtained using inverse transforms. The proposed line model provides accurate results because the phases of a multi-conductor line are decoupled into exact propagation modes from a second modal transformation, using a reduced frequency-dependent matrix. Each propagation mode is modeled in the frequency domain as three independent two-port circuits. The proposed model is evaluated in the frequency and time domains based on results obtained from the line modeling using the exact modal transformation matrix of the line. The advantage of the proposed line model is the simplified modeling based on a constant and real matrix and a reduced matrix with dimension two per two instead a frequency-dependent transformation matrix with dimension three per three.