Frequency- and time-domain expressions for transfer functions and impulse responses related to the waveguide propagation

Analytic expressions for frequency dependent transfer functions and their time dependent inverse Fourier transforms, which represent the forward transmission and the multiple reflection in a waveguide section, are derived. Making use of these analytic expressions, the multiple reflection of a narrowband Gaussian pulse in a waveguide section with different load side and generator side terminations is graphically demonstrated. This shows that early reflections are in general less dispersed than later ones. For electrically long waveguide sections operating high enough above their cutoff frequency, the different reflections are temporally distinguishable. However, in both electrically short and evanescent waveguide sections, the temporal overlapping between the different reflections is so strong that their individual identification is not possible. It is also shown that recently reported superluminal propagation of pulse peaks can take place in electrically short evanescent waveguide sections only. Increasing the waveguide length beyond a certain limit destroys such a superluminality.