A Method of Generating Functions of Several Variables Using Analog Diode Logic

A diode-resistor network technique for simulating functions of any number of variables is described. The function is approximated by a polyhedron, or its N-dimensional equivalent, and this polyhedral model is generated directly by the circuit. The circuit is formed of two cascaded sections: the first, using resistive networks, generates voltages representing each of the faces of the polyhedron; the second section, using analog diode logic, selects the appropriate voltage as the output. The analog diode logic uses basic circuits similar to those used in digital logic. It is shown that the analog logic can be described by a distributive lattice, closely related to Boolean algebra. Methods of logic synthesis are developed. Circuit design is discussed, and it is shown how the effect on the logic section of the finite source impedance of the resistive networks which feed it can be turned to practical advantage. The specific example of the multiplication of two variables is studied in some detail, providing a basis of comparison with the known techniques such as the quarter-squares and log-antilog methods. Finally, test results on a simple three-variable function generator are given. The method is not incremental in nature, and differs from current techniques in this regard. Thus the setting up of a function on a generator is simplified, owing to the noninteraction between segments. Also, the area of the input space to be covered is adjustable to correspond with the input domain of the function.