Patent GB-801253-A (GB)
Title: Improvements in or relating to electric analogue computers
Inventor: MONTGOMERY WILLIAM ALAN
IPC: G06G7/46
Filed: 1955-10-20
Abstract: 801,253. Electric analogue calculating systems. STANDARD TELEPHONES & CABLES, Ltd. Oct. 20, 1955, No. 29959/55. Class 37. An electrical analogue computing network comprises a lattice of interconnected resistors arranged in rows and columns wherein the respective resistance values are such as to satisfy Bickley's finite difference approximation equations when applied to the differential operators in the Laplace equation for a field having cylindrical symmetry and an axis of symmetry lying within the field, and is utilizable for the solution of field problems governed by the Laplace equation in a system of cylindrical symmetry containing the axis of symmetry within the field of the system; the computation being performed by the application to a first selection of nodal points of the lattice of a range of electrical potentials representing parameters obtaining at corresponding points of the field under investigation and by the determination of the resultant potentials at (or currents between) individual nodal points of a further selection of nodal points of the lattice; such resultant potentials or currents representing required parameters obtaining at points of the field corresponding to the respective nodal points of said further selection. For a field of cylindrical symmetry, the Laplace equation expressed in cylindrical polar coordinates is: where r, z are the radial and axial co-ordinates respectively, and where the field under investigation contains (Fig. 1) plural points #A, #B, #C, #D and #E of which the first four are distant a from the central point #E of coordinates (r, z), it is shown that by Bickley's finite difference approximation when a is small, the following differential operators are given by: so that if r # 0: and by finite difference approximation (#a = #c) It is shown that for a junction (Fig. 4) of resistors R0, R0 and R1D at a node of row 0 of a lattice network of interconnected resistors (Fig. 3) wherein a voltage Ve appears at the junction and voltages Vb, Va and Vd appear at the ends of the respective resistors and if and that for a junction (Fig. 5) of resistors Rn, (R(n + 1)D), Rn and RnD at a node of rown of the network, wherein a voltage VE appears at the junction and voltages VB, VA, VD and VC appear at the ends of the respective resistors, analogously to the respective field equations (7) and (5), above, so that the nodal potentials satisfy the finite difference relations expressed therein. The field defined by equation (1) is thus represented by the analogue network of Fig. 3 and the system is symmetrical about row 0. It is further shown by mathematics that in this network, for row n: so that the network takes the form of that of Fig. 6 having resistance values expressible in terms of Ro and being extensible indefinitely in rows and columns to investigate any desired field problem governed by the Laplace equation; electrical voltages being applied to junctions within the area of the field under investigation to represent a first set of known physical parameters and voltages present at selected junction points or currents flowing between such points being measured to represent unknown parameters connected with the first set by the Laplace equation. The computing network is stated to be particularly applicable to problems involving magnetic and electrostatic fields governed by the Laplace equation and examples are given of its use for determination of electrostatic voltage gradients in television line transformer design (Figs. 7, 8, 9, not shown) and for the investigation of the effect of a thin screening cylinder of highly permeable material on a magnetic field (Figs. 10, 11, not shown).