Algorithm development to ascertain the true characteristic impedance of a wire for wire diagnostics

Electronic wiring interconnect system (EWIS) traditionally have been treated as a commodity as apposed to a system. The EWIS, being responsible for the transfer of power and information of aircraft systems, represents a point of failure that is usually considered as a maintainer´s last resort. We attempt to develop a diagnostic capability for the detection and progression of EWIS damage of data using time domain reflectometry (TDR). TDR measures changes in EWIS characteristic impedance. Damage, such as chafe, nicks and corrosion, change the characteristic impedance of the EWIS, suggesting that detection is dependent upon as true representation of impedance as possible. Wire characteristic impedance is corrupted by: multiple reflections (an artifact resulting from the interaction of the TDR waveform and changes in impedance on the EWIS), and attenuation in the high frequency component of the TDR signal. A transmission line problem was developed using RLC circuit model. We present systems of differential equations to solve for the wire characteristic impedance. This led to a system of wave equations in terms of line voltage and current, which we solve by the method of characteristics. The inverse scattering method was then successfully implemented to remove multiple reflections. We then control environmental effects including skin effect, capacitance and wire resistance to account for attenuation in the TDR signal. Formulas based on hypothesis as well as derived from the electromagnetic field theory for the capacitance as a function of the distance of the wires were developed and tested. These solutions were then implemented in a hand held device for the prognostics of EWIS