Telecommunications – I

Homework 2
Commonly used units used to describe electrical quantities. Use the correct units you’re your answers.
Unit Scale
n
Nanometer / nanohertz / nanofarad
.000 000 001 = 10-9
µ
Micrometer / Microhertz/ microfarad / microhenry
.000 001 = 10-6
m
Millimeter / millihertz / millifarad / milliohm / milliheny
.001 = 10-3
Unit
Meter / Hertz / Farad
1
k
Kilometer/ kilohertz/ kilohm
1 000 = 103
M
Megameter / megahertz/ megaohm
1 000 000 = 106
G
Gigameter / Gigahertzg
1 000 000 000 = 109

Also helpful
AB*AC = AB+C
For example
103 * 10-6 = 10-3 = 1/103
m * k = unit (10-3 * 103 = 1)
10 kHz * 27 µF = 10 * 103 Hz * 27 * 10-6 F = 10*27*103*10-6 Hz * F= 270 * 10-3 1/Ω
= 270 * 1/103 1/Ω = 270 * 1/(103 Ω) = 270 * 1/(kΩ)
So if we were looking for a resistance (note: this is similar to finding impedance in that it is the correct unit, but wrong in that we are ignoring 2π), 1/(270 * 1/(kΩ)) = .0037 kΩ

Question #1
A sine wave generator has an output waveform v(t) = 10 cos ( 200 π t) volts

a. What is the amplitude of the sine wave?

b. What is the frequency of the sine wave?

c. What is the rms voltage of the generator output?

Question #2

A sine wave generator has an output waveform v(t) = 10 cos ( 200 π t).

a. A second sine wave generator has an output waveform v(t) = 10 cos ( 200 π t + π / 2 ).
What is the relative phase angle between the waveforms of the two generators?
Give you answer in radians and degrees.

b. The trig identity cos (A + B) = cos A cosB – sin A sin B is useful in telecommunications.
Expand the equation v(t) = 10 cos ( 200 π t + π / 2 ) using this identity, where A = 200 π t and B = π / 2.

Question #3

An FM broadcast station transmits music at a frequency of 91.7 MHz.

a. What form of modulation is transmitted?

b. Which parameter of the transmitted signal is varied by the audio signal?

c. What is the wavelength of the transmitted signal?

Question #4

a. What is the approximate range of frequencies that can be heard by the human ear?

b. What is the range of frequencies sent over a wire line telephone connection?

c. What is the bandwidth of an analog (NTSC) television video signal? (Note with the advent of digital TV broadcasting analog NTSC broadcast signals are now obsolete.)

Question #5

A square wave has amplitude 0 volts and 1.0 volts, and a period of 0.5 ms.

a. What is the frequency of the square wave?

b. What is the fundamental frequency of the spectrum of the square wave?

c. What is the magnitude of the fundamental frequency component of the spectrum of the square wave?

d. The square wave is passed through an ideal rectangular low pass filter that completely attenuates all frequencies higher than 3 kHz. What is the spectrum at the output of the filter?

Question #6

a. What is the unit of capacitance?

b. What is the unit of inductance?

c. What is impedance of a 1 mF capacitor at a frequency of 10 kHz?

d. What is the impedance of a 1 mH inductor at a frequency of 10 kHz?

Question #7

In the United States, residential mains power is nominally 120V rms at 60 Hz.

a. What is the peak voltage?

b. What is the rms current that would flow through a 100W incandescent light bulb (of happy memory!)?

c. You replace the incandescent bulb with an LED lighting fixture that creates the equivalent amount of light but consumes only 23 watts. What is its rms current of the LED fixture?

Question #8

A 1 kW resistor is in series with a 1 mF capacitor.

a. What is the RC time constant of the resistor – capacitor pair?

b. The 1 mF capacitor is charged from a 10 volt battery via the 1 kW resistor.
How long does it take for the voltage on the capacitor to reach 6.3 volts?

c. The 1 mF capacitor is charged from a 10 volt battery via the 1 kW resistor.

What is the voltage on the capacitor after one second?