Transmission Line Equations Questions and Answers

Answer: D

The line should be 39 km long.

For exactly three pulses to be on the line, it must hold three pulse widths and the two gaps between them:

\[ \begin{aligned} t &= 3 \times 30 + 2 \times 20 = 130\ \mu\text{s} \\ L &= 3 \times 10^{8} \times 130 \times 10^{-6} \\ &= 39000\ \text{m} = 39\ \text{km} \end{aligned} \]

3.9 km is the same length with the power of ten slipped by one. 25 km is not a combination of three pulses, and 2.5 km would hold less than a single pulse, since one 30 μs pulse alone is 9 km long.

Answer: C

The principal mode of a coaxial line is the TEM mode.

A coaxial line has two separate conductors, so it supports the transverse electromagnetic mode, in which both electric and magnetic fields lie wholly in the transverse plane. TEM has no cut-off frequency and is the dominant mode used in normal operation.

TE and TM modes, of which TE₁₁ is the lowest in a coaxial line, appear only above their cut-off frequencies and are avoided by keeping the line's dimensions small compared with the wavelength.