Zerocrossings of periodic time functions that appear in a nonlinear equation relevant to electrical engineering

Abstract

The equation f(t)+μ L sign (f(t))v(t) , by means of which a zerocrossing representation of the time function f(t) is obtained, is analyzed. v(t) is a known T-periodic zerocrossing (i.e. without a touching of the time axes and dv/dt ≠ 0 at the zero point) function. L is a linear integral operator. The possibility of the zerocrossing representation of f(t) appears when the parameter μ is with certain limits defined by v and L . The representation reduces the finding of f(t) to the finding of the zerocrossings, which in some cases may be very simply done. The mathematical investigation is motivated by work in the theory of fluorescent lamp circuits where the zerocrossing representation of a current function appears to be useful. The equation is finally generalized which also is associated with the applications.