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Exam 1 - Communications Systems

This communication systems exam is prepared to evaluate the student's comprehension of the following fundamental topics; pulse width, frequency period, waveforms, duty cycles, frequency spectrum theory, computational analysis, modulation, carrier frequency, base-band, wave propagation, radio frequency, power and loss calculations, and signal to noise ratio. For full credit, students must show all work to include calculations, assumptions, and graphs. All final answers should be circled, enclosed in a box, or properly identified as your final answer. This is a closed book and closed note exam, although students are allowed the use of one, standard college-rule paper with formulas they feel necessary and the use of a calculator. Good luck.

1. Given the following frequency spectrum in Figure 1 calculate the following parameters. Find the Period, the Pulse Width, the Peak Value of the Waveform, and the Duty Cycle. Note that the voltage level of the fundamental frequency is 0.374 volts peak. Also, sketch the waveform of the signal (as a function of time) that would produce this frequency spectrum in Figure 1.

2. For the given waveform in Figure 2, where the period T = 1second; write a formula for each of the following terms and simplify the formulas, but you do not have to solve the integrals.

a) A0 = ?
b) A3 = ?
c) B1 = ?
d) B3 = ?

3. Match the term with the appropriate descriptive text that most correctly describes or defines one of the ten terms.

1) ____ a.m.
2) ____ carrier
3) ____ multiplexing
4) ____ base band signal
5) ____ f.m.
6) ____ demodulation
7) ____ modulate
8) ____ half - duplex
9) ____ ionosphere
10) ____ simplex

a) Transmission in one direction
b) Vary, change, or regulate
c) Combining information into a composite signal
d) Vary the carrier amplitude
e) Information signal
f) RF waves bounce off this
g) High frequency RF signal
h) Vary the carrier frequency
i) Remove information from a carrier
j) Transmission in two directions not at the same time

4. In a radio receiver the antenna receives an 8 micro-volt signal into its 50 ohm input impedance. The signal flows through an amplifier (RF Amp), a mixer, and an intermediate frequency amplifier (IF Amp). These devices have the following power gains or losses associated with them depicted in Figure 3. For this problem, find what the power is at; RF Amp output, Mixer output, IF Amp output. Express your solutions in dBm.

5. Given an amplifier with a power gain of 500, a bandwidth of 50MHz, and a noise figure of 5dB. If the input signal is -80dBm, calculate the input signal to noise ratio in decibels (input S/N dB), and the output signal to noise ratio in decibels (output S/N dB).

6. For the given waveform in Figure 4, sketch the power spectrum and label as it would be displayed on a spectrum analyzer. Label the relevant spectrum components with your calculated values, the x-axis, and y-axis.

Solutions: Provided in the Exam Notes Calculations Section below.

Exam Calculations and Notes
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Engineering key words: Frequency spectrum, fundamental frequency, period, pulse width, waveform, duty cycle, magnitude, computational, integral, general form of equation, DC offset, half wave symmetry, amplitude modulation, frequency modulation, AM, FM, carrier, base band, multiplexing, simplex, mixing, half duplex, demodulation, ionosphere, modulation techniques, signal, directional, RF, radio frequency, antenna, voltage, ohms, impedance, power, gain, loss, amplifier, IF, intermediate frequency, noise figure, dBm, power gain, bandwidth, NF, signal to noise ratio, S/N ratio, spectrum waveform, spectrum analyzer, pulse width, sideband, harmonics.

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