document: Accurate modeling of lossy nonuniform transmission lines by using differential quadrature methods This paper discusses an efficient numerical approximation technique , called the differential quadrature method -LRB- DQM -RRB- , which has been adapted to model lossy uniform and nonuniform transmission lines . The DQM can quickly compute the derivative of a function at any point within its bounded domain by estimating a weighted linear sum of values of the function at a small set of points belonging to the domain . Using the DQM , the frequency-domain Telegrapher 's partial differential equations for transmission lines can be discretized into a set of easily solvable algebraic equations . DQM reduces interconnects into multiport models whose port voltages and currents are related by rational formulas in the frequency domain . Although the rationalization process in DQM is comparable with the Pade approximation of asymptotic waveform evaluation -LRB- AWE -RRB- applied to transmission lines , the derivation mechanisms in these two disparate methods are significantly different . Unlike AWE , which employs a complex moment-matching process to obtain rational approximation , the DQM requires no approximation of transcendental functions , thereby avoiding the process of moment generation and moment matching . Due to global sampling of points in the DQM approximation , it requires far fewer grid points in order to build accurate discrete models than other numerical methods do . The DQM-based time-domain model can be readily integrated in a circuit simulator like SPICE
doc_bio_tags: O O O B I I I O O O O O O O O O O B I I O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O B I O O O B O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O