Before revision: After sections the voltage ratio will be, At a distance along the line, the number of sections is so that, In the limit as , The second order term will disappear in the limit , so we can write without loss of accuracy, and comparing with the mathematical identity, yields, From the definition of propagation constant, Hence, Special cases Ideal transmission line An ideal transmission line will have no loss, which implies that the resistive elements are zero.
After revision: After sections the voltage ratio will be, At a distance along the line, the number of sections is so that, In the limit as , In the limit, the second order term will be insignificant compared to the first order term , so we can write without loss of accuracy, and comparing with the mathematical identity, yields, From the definition of propagation constant, Hence, Special cases Ideal transmission line An ideal transmission line will have no loss, which implies that the resistive elements are zero.