A method of using an electrical network to solve a determinental or secular equation has been devised (i.e., to determine the characteristic values of a real, symmetrical matrix). By plugging suitable coils and condensers into a panel board, a network is assembled which has for its description at resonance an equation identical with the secular determinant. The circuit consists of n junction points, each connected to every other through fixed reactive admittances equal to the corresponding off‐diagonal terms of the matrix, and each connected to ground through a fixed admittance equal to the negative of the sum of the constant part of the diagonal term and the off‐diagonal terms in the same row or column. In addition each junction is connected to ground through a variable admittance which represents the unknown in the equation; these latter admittances are equal for all of the junction points. While the network is excited with alternating current from a constant current source of constant frequency, the variable admittances are all altered simultaneously by the same amount until all the maxima of the electromotive forces of the junction points with respect to ground have been found. The values of the variable admittances at the several maxima constitute the desired roots. Usually an accuracy of better than one percent is obtained.
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Research Article| February 01 1947
An Electrical Network for the Solution of Secular Equations
Richard H. Hughes;
Richard H. Hughes, E. Bright Wilson; An Electrical Network for the Solution of Secular Equations. Rev. Sci. Instrum. 1 February 1947; 18 (2): 103–108. https://doi.org/10.1063/1.1740892
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