Development and Use of the BLT Equation in the Time Domain as Applied to a Coaxial Cable

This paper discusses the use of the Baum-Liu-Tesche (BLT) equation for calculating transmission-line load responses directly in the time domain. From the frequency-domain BLT equation, its transient counterpart is first derived. For the special case of a coaxial cable, explicit expressions for the transient propagation function, the surge impedance and admittance, and the transient reflection coefficients at each end of the line are derived. These quantities, together with the transient-BLT equation, are used to compute the transient load voltages. The computed results are subsequently compared with transient responses obtained using the frequency-domain BLT equation and Fourier inversion, and the agreement is excellent for highly conducting cables. The benefit of deriving the BLT equation in the time domain is that it may be used, with slight modifications, to treat the case of nonlinear or time-varying loads. This will be described in a future paper