Download Test1_Spring12 - UTK-EECS

1. The voltage of an electromagnetic wave traveling on a transmission line is
v( z, t )  2ez sin( 4 108 t  2z ) V,
where z is the distance in m from the generator and t is time in s.
(a) Find the frequency, wavelength, and phase velocity of the wave. (Note: you must
get the units right to get full points.)
(b) At z = 2 m, the amplitude of the wave was measured to be 1 V. Find . (Note:
Again, you must get the unit right.)
2. With an unknown load connected to a slotted air line, a voltage standing wave ratio S
= 2 is recorded by a standing wave indicator and minima are found at 11 cm, 19 cm, ...on
the scale. When the load is replaced by a short circuit, the minima are at 16 cm, 24
cm, … If Zo = 50 , calculate the wavelength , the frequency f, and the load ZL. Hint:
what information do you get from that the slotted line is an air line?
3. A voltage generator with vg(t) = cos(2 109t) V and an internal impedance Zg = 100
 is connected to a 100- lossless air-spaced transmission line. The line length is 5 cm
and it is terminated in a load with impedance ZL = (200j200) . Find the following:
(a) Reflection coefficient  at the load,
(b) Input impedance Zin at the input end of the transmission line,
(c) The input voltage vi(t) and input current ii(t), [Hint: simple circuit. First use
phasors, then get to the time domain.]
(d) The average input power Pav, [hint: again, simple circuit]
(e) The incident voltage phasor V0 , incident current phasor I 0 , and average
incident power Pinc, and
(f) The reflected voltage phasor V0 , reflected current phasor I 0 , and average
reflected power Pref.