Patent GB-756325-A (GB)
Title: Improvements in electrical equation-solvers
Inventor: LIEBMANN GERHARD
IPC: G06G7/34
Filed: 1952-09-23
Abstract: 756,325. Electric analogue calculating apparatus. ASSOCIATED ELECTRICAL INDUSTRIES, Ltd. Aug. 12, 1953 [Sept. 23, 1952], No. 23856/52. Class 37. An electric analogue computor for solving simultaneous equations comprises a resistance chain corresponding to each unknown in which variable alternating currents simulating the values of the appropriate unknowns flow, so that the voltages across the individual resistances represent corresponding component terms of the individual equations and a multiple primary transformer corresponding to each equation, having one primary connected across that resistance of each chain which is associated with the equation to which the transformer corresponds, so that plural voltages representing the component terms of such equation are applied in correct phase to the transformer to develop a secondary voltage representing the algebraic sum of the component terms, which may be reduced to zero by iteritively adjusting the resistance currents to represent the solution values of the unknowns. The simultaneous equations (1) may be written as (2) where x 0  is a constant, and are solved for values of x 1 /x 0  and x 2 /x 0  such that P 1 #P 2  #0. A pair of busbars are supplied with alternating voltages Œ V. 180 degrees out of phase with each other, and resistance chains (Rx 1 , Rs 1 , a 11 , a 21 ) and (Rx 2 , Rs 2 , a 12 , a 22 ) are connectible by switches C 1 , C 2  between either busbar and earthed neutral, while resistance chain (Rxo, Rs 0 , -b 1 , - b 2 ) is permanently connected between the reference busbar and neutral O. The currents I 0 , I 1 , I 2  in the chains are adjusted by variable resistances Rx 0 , Rx 1 , Rx 2  to represent the constant x 0  and unknowns x 1 , x 2  respectively and the resultant voltage drops across resistances (-b 1 , a 11 , a 12 ) and (-b 2 , a 21 , a 22 ) representing I' by analogy the coefficients in equations (2)  are respectively coupled over change-over switches So 1 , S 11 , S 21  and So 2 , S 12 , S 22  determining the signs of the coefficients, to energize equal primaries of transformers T 1 , T 2  corresponding one to each equation. The secondary outputs of the transformers represent the residuals P 1 , P 2  and by keeping I 0  constant and iteritively adjusting I 1'  I 2  the residuals P 1 , P 2  as indicated by a galvanometer or amplifier and cathode-ray tube indicator are simultaneously reduced to zero. The solution values x 1 , x 2  are determined by measuring the voltage drops across Rs 1 , Rs 2  due to the analogue currents I 1 , I 2  and if Rs 0 , Rs 1 , Rs 2  are made equal in value and the reference voltage drop across Rs 0  is taken as unity, the volatge drops across Rs 1 , Rs 2  give the solutions x 1 , x 2  directly. The residuals may be determined sequentially, by measurement on a single instrument, or simultaneously by the use of a multi-channel galvanometer or a selectively switched long-afterglow cathode-ray display as described in Specification 754,113. The variable resistances may be replaced by arrays of fixed resistances selectively switchable into circuit according to a binary code.