Using Equations and to replace and in these then gives dI/dx dV/dx and Replacing and using Eq. , and simplifying, yields Gd, Id Rd and Equations and are second order ordinary differential equations that can be solved exactly giving the I/O relationship for an exponential TL segment. Assuming that the input is at = 0, the output at = and setting x, x x and and, in to satisfy Equations and , and and solving Equations and gives the I/O relationship where , , and and In a situation where is zero, the I/O relationship is K
Using Equations and to replace dI/dx and dV/dx in these then gives and Replacing Gd, Id and Rd using Eq. , and simplifying, yields and Equations and are second order ordinary differential equations that can be solved exactly giving the I/O relationship for an exponential TL segment. Assuming that the input is at x = 0, the output at x = x, and setting and and, in to satisfy Equations and , and and solving Equations and gives the I/O relationship where , , and and In a situation where K is zero, the I/O relationship is