Rational approximation of irrational functions by linear fractional transformations

The cascaded two-port circuit theory is generalized and applied to the approximation of the square root of a rational function by a rational function in the form of a chain of linear fractional transformations. We prove the convergence of the approximation, and derive an explicit expression of the relative error in terms of the two-port parameters and the order of approximation. Examples are given. Index Terms-RLGC transmission lines, approximation theory, irrational functions, linear fractional transformation.