The Solution of Circuit Problems. Mathematical Methods of Investigation Resulting from the Application of Fourier's Integral
Abstract
Circuit theory; current in any network; expansion of fundamental integral in Bessel's series. This is treated quite fully, and is shown to be applicable to circuits with either lumped or distributed impedances. If the upper limit for the roots of the equation for the impedance function is known, the problem may be reduced to the expansion of a function in a Fourier series. By this method, the principal difficulties of computation are included in those processes which can be mechanically performed. This method is, therefore, a valuable addition to those commonly used in the solution of problems relating to complicated circuits. Circuit theory; current in any network; expansion of fundamental integral. Summary of treatment (I) using HeavisideCarson expansion, and (2) using Taylor's series, with a discussion of the limitations of each method. Integral of e^{in(tλ)}dnZ(in) from ∞ to +∞ expansion in Bessel's series. Treated quite fully, especially in relation to circuit theory. Telegrapher's equation; solution by expansion of an integral in Bessel's series. This is treated quite fully, with simple examples.
 Publication:

Physical Review
 Pub Date:
 August 1919
 DOI:
 10.1103/PhysRev.14.115
 Bibcode:
 1919PhRv...14..115F