Impulses concealed by singularities: transmission line theory

The input admittance of a loss-free short-circuited transmission line is generally said to be a cotangent function of frequency, a function that is imaginary and odd. The symmetry implies that the impulse response, which has the admittance function of frequency as its Fourier transform, is also odd. However, there can be no response at negative times preceding the applied impulse. Therefore the cotangent formula for susceptance cannot be correct. A real, even function of frequency representing a conductance term must be added to the imaginary, odd susceptance. Likewise, the familiar formula Z=iZ₀ tan(2πL/λ) is deficient