A method for implementing wideband time delays on an analogue computer

A TIME delay between cause and effect is a crucial feature of many biological systems. Obvious examples are involved in the transport of blood-borne drugs between organs of the body and in the transmission of nervous impulses. The computer simulation of such systems involves the implementation of time delays and, particularly in the case of analogue computers, this requires a careful choice between alternative techniques, each of which represents a different compromise between the various factors involved. The most common techniques make use of active networks that may be implemented using standard analogue modules, and are designed to approximate as closely as possible a time delay between input and output waveforms. Despite a great deal of attention to improving the design of such networks, their performance imposes a strict limit upon the bandwidth of the input functions, and, at present, the best designs require the minimum periodic time of a significant frequency component in the input waveform to be less than about half the delay time (DAv]ES, 1972). If this requirement is taken too lightly, as has been shown by MAZANOV and TOGNETTI (1974) in a comparable case, unsuspected errors may arise in the final computation. In situations where network approximations are inappropriate, resort is usually made to special equipment, either a magnetic-tape recorder, where the spacing of write and read heads introduces the required time delay, or to a digital memory buffered by a.d. and d.a. convertors, where the time delay is introduced by appropriate write and read control. There is, however, a method of implementing time delays which imposes no bandwidth limitations, apart from that inherent in the analogue computer itself, and which does not require special equipment. The technique is not sparing in its use of analogue modules but has been found indispensable in a number of biological simulations where computational efficiency was not a prime consideration. Since no reference to the method has been found in the literature, an explanation and illustration of the method would seem to be warranted.