Envelope Transfer Function of Modulated Servo Systems

Abstract

Several procedures to calculate the envelope transfer function of modulated servo systems consideringthe behaviour in frequency and time domain have been published. However, those paperstreat the transfer function only in the form of frequency response and their relations to the Laplacetransform are not investigated. Takahashi proposed the method to calculate the transfer functionof A-C servo systems considering transient response caused by arbitrary input signal and introducingspecial series expansion.
In this paper the auther describes the general method to calculate the envelope transfer functionof the modulated servo systems which is based on the complex convolution theory and the cosniderationin subsidiary domain.Modulation and demodulation are defined as the multiplication of inputsignal and, function of time f₁ (t) or f₂ (t) .This method gives the envelope transrfer function inthe closed and refined form.Therefore frequency characteristics are easily derived by sabstitutingjca for s in the envelope transfer function.
Two examples are calculated and their results are examined using slow type electronic analogcomputer.