ECEN5533 Exam #1 30 September 2008 Name_______________________________
1) A waveform x(t) = m(t)cos2π1,000,000t, where m(t) is a 700 symbol/second random 3-ary square wave. 1/3rd of the time m(t) is a +4 v pulse, 1/3rd of the time m(t) = 0 v, and 1/3rd of the time m(t) is a -4 v pulse.
[25] Compute the average power of x(t). [Answer: 5 1/3 watts]
<<<<<>>>>>
2) A satellite antenna has a Low Noise Amplifier (LNA) with a gain of 50 dB and a noise figure of 3.0 dB directly connected to the output of the antenna. The LNA is followed by a cable with a loss of 6 dB. The signal power out of the antenna is known to be 440 pW and has a noise bandwidth of 45 MHz. The antenna is currently aimed at the Sun and has an antenna temperature of 8,000 degrees Kelvin.
[25] Compute the SNR out of the cable. [85.47 = 19.32 dB]
<<<<<>>>>>
3) A 6 watt, 500 Gbps random binary square wave s(t) is contaminated by a statistically independent additive 1 watt band-limited White Noise waveform n(t) to form x(t), i.e. x(t) = s(t) + n(t). n(t) is known to have a bandwidth of 1,000 GHz. s(t) is known to have a mean of -1 volt D.C.
3a) [15] Sketch the output power spectrum GX(f). [You should sketch a sinc2 function added to a frequency domain "pulse". The sinc2 function has nulls at integer multiples of 500 GHz. Below 1,000 GHz, the sinc2 function is riding on top of 500*10-15 watts/Hz band limited white noise, hence there is a jump discontinuity right at the 1,000 GHz null. You should also include a delta function of weight 1 at f = 0 Hz.]
3b) [10] Sketch the PDF fX(x) of the voltage distribution of x(t). [You should sketch two bell shaped curves, one centered at 51/2-1 = 1.236 volts, the other at -51/2-1 = -3.236 volts. Both have maximum heights of 0.399/2 volts.]
<<<<<>>>>>
4) A communications link using a center frequency of 41 MHz operates over a large lake. The wind is calm and the lake is perfectly flat. A 21 meter high antenna right by the water is transmitting to a receiving antenna on the edge of other side of the lake. The receiving antenna is 2 meters above the water. The two antennas are 901 meters apart. Both antennas are isotrophic. Besides the line-of-sight EM wave, the receiving antenna is also picking up a reflected signal off the water. The signal reflected off the water undergoes a 180 degree phase shift (equivalent to adding 1/2 wavelength to the distance).
4a) [10] Compute the reflection angle of the signal that bounces off the lake surface. [1.462 degrees]
4b) [10] Compute the phase angle difference between the direct path and reflected signal. [184.6 degrees]
4c) [5] Will the power out of the receive antenna be greater than or less than that predicted by the free space RF link equation? Explain. [The reflected signal is almost perfectly out of phase with the direct path signal, hence the two will at least partially cancel. The received signal power will be less than what is predicted by the RF free space link equation.]
<<<<<end>>>>>