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Modulation
If we want to send information (i.e. a signal) from one place to another, one way of
doing it is to superimpose the signal onto a carrier wave. This process is known as
modulation. A demodulator is needed at the receiving end to extract the signal
information.
Two commonly used types of modulation are illustrated below:
Amplitude Modulation (AM)
Note that:
 the amplitude of the carrier wave is made to vary according to the signal.
 the carrier wave has a higher frequency than the signal. For example, in AM radio
transmission the carrier wave is of radio frequency (typically ~ Mz) and the signal is
speech, music etc, which is of audio frequency (typically ~ kHz).
Advantage of AM:
 It is cheap and simple.
Disadvantages of AM:
 It is suceptible to noise (random unwanted signal) and fading.
Frequency Modulation (FM)
Note that:
 the frequency of the carrier wave is made to vary according to the signal.
 the carrier wave has a higher frequency than the signal - as for AM. (Both AM and
FM are used for radio transmission.)
Advantage of FM:
 It is less susceptible to noise than AM.
Disadvantages of FM:
 It requires more complex electronics than AM - and the signal may still be
degraded to some extent.
Pulse Code Modulation
In both AM and FM the signal is analogue. i.e. It consists of a continuously varying
voltage. The end result (the modulated carrier wave) is also an analogue signal.
In pulse code modulation (PCM) the analogue signal is converted to a digital
signal - i.e. a series of 0s and 1s (e.g. 00110001011001). This process is illustrated
below:
The main features of the process are as follows:
 The analogue signal is sampled at regular time intervals - the samples are shown
as vertical lines on the diagram above.
 The voltage range of the signal is divided up into a number of discrete levels called quantum levels. These are the horizontal bands shown above. This process
is known as quantisation.
 An analogue-to-digital converter (ADC) converts each sample to an appropriate
binary number, depending on which quantum level its voltage falls within.
 The analogue signal is thus encoded as a series of binary numbers - i.e. a digital
signal.
 At the receiving end the digital signal must be decoded - i.e. converted back to an
analogue signal (speech, music, etc). A digital-to-analogue converter (DAC) is
used.
Note that:
 The quantum levels are narrower (closer together) for the smaller values of signal
voltage. This is called companding. The purpose of companding is to encode
smaller amplitude signals more precisely than larger ones. (Smaller signals are more
important to the "ear-brain" than their amplitude would suggest - because the
response of the "ear-brain" is logarithmic.) Without companding, smaller amplitude
signals would be lost - or encoded very crudely.
The process can be improved (made more precise) by:
 Having more quantum levels. This means having more bits in the binary code.
e.g. 8 bits would give 256 levels.
 Sampling more frequently. The sampling rate must be at least twice the highest
frequency present in the signal. Audio (sound) has a maximum frequency of about
20 kHz - so the sampling rate needs to be at least 40 kHz. The reason for this is
illustrated below:
If the sampling rate is too low, as shown below, the signal will appear to have a lower
frequency than it really has. i.e. A false signal (called an alias) has been created.
Analogue and digital transmission compared:
 Digital signals are less susceptible to noise because the system merely has to
decide whether the voltage is high or low. i.e. As long as the voltage is above or
below a certain threshold value the signal is not degraded.
 Digital signals can be fed directly into computers.
 Digital signals can contain "check digits" which verify that the signal has been
correctly received.
On the other hand:
 Analogue systems are simpler.
Multiplexing
Multiplexing means sending more than one signal down a single cable etc.
2 important methods of multiplexing are described below:
Time division multiplexing (TDM)
TDM involves slicing the signals into equal time sections, and sending the sections in
turn down the single cable as shown below:
The letters in the diagram above represent sections of the signal. These sections
may not literally be letters - the letters simply stand for sequences of bits of equal
time-length. (e.g. A = 10110110, B = 11110011, etc)
A multiplexer is used to slice up and send the sections in the correct sequence. A
demultiplexer is needed at the other end to reconstruct the original signals.
Frequency division multiplexing (FDM)
FDM is used with analogue signals. Carrier waves of different frequencies are used
for the different signals. These carrier waves, when modulated, consist of a range of
frequencies - e.g. 12-16 kHz, 16-20 kHz, etc - as shown below. Thus they can be
sent down the same cable and separated out using filters at the receiving end.
Optical Fibres
Optical fibres are very thin transparent fibres down which light can be made to
pass. The light can be made to carry a signal by varying its intensity accordingly. The
light stays within the fibre because of total internal reflection, as shown below:
Coaxial cables are the electrical alternative to optical fibres. Their basic structure is
illustrated below:
 Unlike coaxial cables, optical fibres are not susceptible to electromagnetic
interference.
 Optical fibres are lighter than coaxial cables (important in aircraft).
Multipath dispersion is a potential problem with fibre optic cables. There are many
paths of different lengths that the light can take to get from one end of the fibre to the
other, as shown below:
This means that different parts of the signal take different lengths of time to reach the
receiving end, with the result that sharp pulses become smeared out and may even
overlap, as shown below:
3 possible solutions to the problem are illustrated below:
Attenuation
Attenuation means "loss of intensity". (Intensity is "power per unit area".) It affects
signals in both coaxial and fibre optic cables. In optical fibres it occurs because the
fibre is not perfectly transparent. Some of the light energy is absorbed by the
material. A typical graph of intensity against distance along an optical fibre is shown
below:
The drop in intensity is exponential and is given by the formula:
I = Ioe-x
where Io is the intensity at x = 0 and  is a constant for the material called its
absorption coefficient.
The units of  are m-1 (or km-1 etc).
If we substitute x = 1/ into the above formula we get:
I = Ioe-1 = 1o/e
Thus the intensity at x = 0 is divided by e (2.718) after 1/ metres.
Taking logs of both sides of the equation in the box above:
ln I = ln Io - x
Or:
ln I = - x + ln Io
Compare the above with:
y = mx + c
It follows that a graph of ln I against x will be a straight line of gradient -, as shown
below:
N.B. You can test whether one quantity varies exponentially with another by
plotting a log-linear graph. The relationship is exponential if the graph is a
straight line.
Energy Stored in a Capacitor
Recall that, for a capacitor:
C = Q/V
(see TRA notes)
It follows that:
V = (1/C)Q
i.e. V is proportional to Q, as shown below:
As the capacitor is charged, V and Q both increase - starting from zero and
remaining proportional to each other.
Suppose that, at some point in the charging process when the voltage is V, we add
an extra bit of charge Q. To do this we have to do work W on the charge, given
by:
W = VQ
(see SPC notes)
But VQ is also the area of the strip on the graph above.
i.e. Work done in adding Q = area of strip.
It follows that the total work that must be done to completely charge the capacitor is
the area of all such strips. i.e. It is the total area under the graph.
It therefore also follows that the energy stored in the capacitor (W) is the total area
under the V-Q graph. i.e.....
W = 1/2QV
..... since the area is a triangle (1/2 x base x height).
Substituting Q = CV into W = 1/2QV:
W = 1/2CV2
Substituting V = Q/C into W = 1/2QV:
W = 1/2(Q2/C)
Electric Fields
An electric field is a region of space where a charge Q experiences a force F.
Electric field strength E is defined by the equation:
E = F/Q
i.e. It is the force per unit charge.
Since F is in N and Q is in C, the unit of E is NC-1.
One common way of producing an electric field is to have 2 parallel plates a distance
d apart with a voltage V applied across them, as shown below:
Note that the direction of E is the direction of the force on a positive charge - i.e.
from +ve to -ve.
In the above case E is uniform (constant) - although it does tail off a bit near the
edges of the plates.
The following alternative formula for E can be used in the case of parallel plates:
E = V/d
Since V is in V and d is in m, it follows that Vm-1 is an alternative unit for E.
Moving Charges in Magnetic Fields
Free charges (e.g. electrons) moving through a magnetic field experience a force for the same reason that a current-carrying conductor in a magnetic field has a force
acting on it. The two situations are rather similar, except that there is no wire in the
case of free charges:
The direction of the force F is given by Fleming's Left Hand Rule (see TRA Notes).
The second finger (current) is pointed in the same direction as the velocity of positive
charges. However, in the case of negative charges (e.g. electrons), it must be
pointed in the opposite direction to their velocity. (The direction of conventional
current is opposite to the flow of electrons.)
The size of the force F is given by the equation:
F = Bqvsin
(Compare the above with F = BIlsin for a current-carrying wire in a magnetic field.)
[Note that magnetic field B is often also referred to as "magnetic flux density".
This is because B = flux/area = /A (see TRA Notes). i.e. B is flux per unit area
or "flux density".]
Because the force is always at right-angles to their velocity, free charges move in a
circle in a magnetic field, as shown below:
The Cathode Ray Tube (CRT)
Below is a diagram of a cathode ray tube. (The electron gun has been simplified
somewhat.)
The filament heats the metal cathode, which emits electrons. Hot metals emit
electrons because at higher temperatures the electrons have enough thermal energy
to escape the surface of the metal. This process is known as thermionic emission.
The anode is at a potential of +V volts so the negative electrons are accelerated
towards it, and carry on through the hole in the anode towards the screen. This
whole arrangement is called an electron gun. (Real electron guns are a bit more
complex. They may have 2 anodes and a grid to control the rate of flow of the
electrons.)
When a charge Q is accelerated through a voltage V it gains energy W. W is given
by the equation .....
W = QV
(see SPC notes)
In the electron gun, the energy gained (W) is the final kinetic energy of the electrons
(1/2mv2), and Q is the charge on an electron (e).
Therefore .....
1/
2mv
2
= eV
..... where m is the mass of an electron, and v is its velocity as it emerges from the
gun.
The above equation can be used to calculate the velocity v of electrons, if the
accelerating voltage V is known.
The X- and Y-deflection coils are used to deflect the electron beam in the
horizontal and vertical planes respectively. To achieve this, the X-coils produce a
magnetic field from top to bottom (or bottom to top) of the diagram and the Y-coils
produce a magnetic field into (or out of) the paper. The electron beam will follow an
arc of a circle while it is within the field, and carry on in a straight (deflected) line after
it has left the field.