Padé approximations and analog computer simulations of time delays

Abstract

The Padé approximations 1 of e- x are reviewed in con nection with their application in simulations of transpor tation delays (time delays) by analog computers. The approximation coefficients are specified in terms of the order of the approximations, and recurrence relation ships are established for the most common types. Analog computer circuits are given for general Padé approxima tions of any order and type, together with practical exam ples of both constant and variable transportation delay simulations. Special attention is paid to the zero-variable delay time constant, and circuits are given for this type of application. The performance of the Padé approximation circuits is discussed in terms of phase error and amplitude char acteristics for sinusoidal signals, together with rate-of- change measures in connection with step-response analy ses. Conclusions are drawn as to the order and type of Padé approximation to be selected to meet given per formance requirements. A table of Padé approximations up to the 12th order is included.