A time domain reflectometer (TDR) of output impedance 50- sends a step voltage down a 50-2 transmission line that is terminated in an unknown resistive load and displays the voltage at the sending end of the line, Figure Q6a. The line's insulating material has a relative permittivity, &= 2.25. Determine: Q6 (a) (i) the source voltage of the TDR, (ii) the length of the line, and (iii) the load resistance. V(0,t) ↑ 6 V- 3 V- 12 us Figure Q6a (b) The TDR in part (a) is now connected to a metre-long 50 Q transmission line which is terminated in a load of 100 N. Calculate and sketch the voltage at the source for time t= 0 to t = 15 ns, given that the velocity of propagation on the line is 2 x 10 m/s.

(V.3) A common commercial size of rectangular hollow-conductor waveguide has (inner) dimensions a = 2.286 cm by b = 1.016 cm. (a) What is the single-mode bandwidth of this size waveguide frequency range (in gigahertz) within which the TE10 mode propagates but the next higher mode does not? [Most practical waveguide systems are operated under this single-mode condition.] that is, what is the (b) The maximum field strength that air can support without breakdown is about 50,000 V/cm (at standard atmospheric pressure). What is the maximum power that can be trans- mitted by this size waveguide at frequencies within the single-mode band?

4. Again, from the zigzag-path waveguiding model, explain why the group velocity is always slower than the phase velocity in a waveguide with a cutoff frequency.

Solve the cutoff frequency for the first mode and third mode of WR430 waveguide.