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On the analog simulation of a pure time delay

In the investigation of many physical systems, it becomes necessary to simulate the time-delay phenomenon on the computer. This phenomenon arises in such investigations as shock waves in mechanical systems, sound waves in acoustical systems, and more generally in connection with the flow of materials in chemical processes and heat exchangers. Since information about such systems is not available until a finite time after certain actions have been performed, it is essential to represent this time-delay phenomenon adequately. Various methods have been used to do this, depend ing on the value of the time delay involved and the frequencies contained in the variable quantity passing through the delay. This paper discusses the application of operational amplifiers to form time-delay approximations for those applications where the delay is more or less constant. A number of such approaches are discussed and the resulting approximations are brought into a common form and scale, so that comparisons between the different approximations may be easily accomplished.