A mathematical model for simulating pulse propagation in ferrite core memory arrays is described. Although specifically developed to analyze 3-dimensional arrays, the model is sufficiently general to give a satisfactory analysis of pulse propagation, waveform deterioration, and noise generation in a wide variety of memory configurations. The model treats the memory as a generalized, mutually coupled, multiconductor transmission line system. Insofar as is possible, the transmission line parameters are calculated from the array geometry, thus leaving only a small number of parameters that must be supplied empirically. Following a discussion of the equations which define the model and the methods by which they are solved, a sample array calculation is given to illustrate the kind of information that can be obtained from the model.

A method is described for the numerical inversion of Laplace transforms, in which the inverse is obtained as an expansion in terms of orthonormal Laguerre functions. In order for this to be accomplished, the given Laplace transform is expanded in terms of the Laplace transforms of the orthonormal Laguerre functions. The latter expansion is then reduced to a cosine series whose approximate expansion coefficients are obtained by means of trigonometric interpolation. The computational steps have been arranged to facilitate automatic digital computation, and numerical illustrations have been given.

The evolution of a simple mathematical model for pulse propagation in memory arrays and its implementation by computer programs is described. The development of the model is based initially on the properties of a simplified two-dimensional memory array using common bit-sense lines. The model is then generalized to include separate bit and sense lines. Finally, applications to three-dimensional arrays are considered. It is shown that for a wide variety of calculations nonlinear bit-storage devices such as ferrite cores, tunnel diodes, etc., can be replaced by linear equivalent circuits. With the aid of these equivalent circuits the array is characterized in the language of linear transmission-line theory. Two computer programs are described which solve the resulting differential equations. Applications of these computer programs to the analysis of sense-signal propagation, bit-sense noise, signal transfer between crossed wires, and propagation of pulses along bit lines are discussed. The mathematical theory is derived explicitly for ferrite-core memories but care is taken to point out the changes required to extend the model to other technologies. These changes can be effected in the supporting computer programs by a simple interchange of subroutines which characterize the properties of bit-storage devices.