Tutorial 14  Amplitude and Frequency Modulation Techniques

What is Modulation?

When a radio signal is transmitted, a high frequency electronic circuit makes electrons oscillate in an antenna.   This results in an electromagnetic wave propagating from the transmitter.  It is detected by the antenna of a receiver, and the voltage amplitude is magnified by the phenomenon of electrical resonance


A simple sine wave on its own is no good for transmitting information, whether it's analogue or digital.  The remote reception of such a wave is merely a physics curiosity.  However if we can get information to ride piggy-back on the transmitted wave, things become very much more useful.  We can do this by superposing the information that we want to broadcast to the transmitted wave.


The transmitted wave at the station frequency is the carrier wave.  The information is put onto the carrier wave using a technique called modulation.  In modulation the audio signal is added to the carrier wave.


Amplitude Modulation



In Amplitude Modulated (AM) broadcasting the amplitude of the carrier wave varies so that the envelope traces the audio signal around the modulated wave.  In the diagram above the audio signal is shown as a sine wave.  The diagram above shows the idea of amplitude modulation.  In reality the audio signal of "Rabbit, Rabbit, yap, yap, yap" would be much more complex.  The antenna of the receiver detects the changing voltage due to the variations in the amplitude.  These are demodulated and sent to the amplifier and loudspeaker.


The separation of stations is about 10 kHz. 


The graph below shows the interaction between the signal wave and the carrier wave.  The carrier wave is at a slightly higher frequency than the signal wave.


The resultant waveform looks like this:



In reality, the carrier wave is at a much higher frequency than the signal wave.



Frequency Modulation

The diagram below shows an audio signal being combined with a carrier wave.  In this case, the frequency of the carrier wave is changed by the frequency of the audio signal.  Hence it's called frequency modulation (FM)



Each station has a frequency that is separated by 200 kHz.  Each frequency quoted is the middle value of the range of frequencies.


Question 1

Classic FM has a frequency of 101.1 MHz.  Calculate the minimum and maximum frequencies that are used for Classic FM.



In reality the frequency variation is 53 kHz above and below the middle frequency.  Above and below this is a 25 kHz cushion (guard band) to prevent interference between adjacent radio stations.  The wide range of frequency allows for a high fidelity signal to be broadcast.  The audio range is limited to 15 kHz.  Although 53 kHz is much higher than this, it allows for other information such as the carrier signal (19 kHz) for stereo reception. 


In the Exam

You are NOT expected to know details of any modulation or demodulation circuit.


You are expected to know about AM and FM.  However you are NOT expected to know about any other form of modulation.  Nor are you expected to do a mathematical treatment of the modulation.


You are not expected to know about stereo reception.


Here is an animation of FM and AM:

Wikimedia Commons, Animation by Bezerkerus.


Wave Bands

This radio receiver can pick up stations from all the radio bands that are available for broadcasting.



The medium wave band has stations transmitting on AM and the frequencies are from 535 kHz to 1605 kHz.  The long wave band has frequencies from 150 to 300 kHz.  They too transmit using AM.  In the UK Radio 4 still broadcasts on long wave at 198 kHz.


Short wave radio transmits at frequencies 1.6 MHz to 30 MHz.  Mostly such stations use AM, but there are other forms of modulation available, including:



Bandwidth is a term that describes a range of frequencies.


In electronic circuit theory the bandwidth of an amplifier is the range of frequencies in which the power is greater than half the maximum power.  This is shown on the graph:


If we consider the voltage amplitude, the bandwidth is the range of frequencies in which the voltage is greater than 71 % (1/Ö2) of the maximum voltage.



AM Bandwidth

In radio communication the term bandwidth is used slightly differently.  When we quote the frequency of a radio station, we are stating the carrier frequency.  The signals that are super-imposed on the carrier wave form sidebands.  The idea is shown in the diagram below.



The range of audio frequencies (shown in the green box) is called the modulating frequency, fM.  The carrier frequency is given the code fC.  The bandwidth is simply the difference between the lowest frequency and the highest frequency.  In AM radio the bandwidth is limited.  Channel spacing in Europe is 9 kHz.  To avoid interference, the lower and upper side bands need to be about 4 KHz each.


The bandwidth for AM is summed up in this simple equation:


Question 2

The bandwidth for a radio station broadcasting on a wavelength of 247 m is 8200 Hz.

(a) Calculate the audio bandwidth.

(b) Calculate the carrier frequency to this station.

(b) Calculate the minimum and maximum frequencies of this station.



The narrow bandwidth explains why AM radio does not give high fidelity reception.  There is no technical reason why AM should not have a higher bandwidth, but that would restrict the number of radio stations that would be available.  Stations on the short-wave bands have even more restricted bandwidth.


A way round restricted bandwidth is to prevent stations with adjacent frequencies being anywhere near each other geographically.



FM Bandwidth

The bandwidth for FM transmission is not so easy to understand.  In theory the frequency range in an FM signal can be infinite.  For narrow bandwidth FM, the situation is similar to AM, with a central carrier with two sidebands.  However the lower sideband is 180o out of phase with the upper sideband.


For wide bandwidth FM, the situation is even more complex.  There are a lot of sidebands.  It is the usual practice to consider the bandwidth as that which contains 98 % of the power.  The detailed analysis of FM sideband spectra is not on the syllabus, so we will not worry about it here.


The difference between the maximum modulation frequency of the signal and the carrier frequency of the FM transmission is called the deviation frequency, which has the physics code Df.  This quantity is used in Carson Bandwidth Rule, devised by John Renshaw Carson (1886 - 1940).  This is given in the equation:



Most FM radio transmissions use a deviation frequency of 75 kHz.  The audio frequency is set at 15000 Hz.


Question 3

(a) What is the bandwidth of a radio station in the FM band?

(b) A station is transmitting on 93.5 MHz.  What is the minimum and maximum frequency that it uses?



The spacing is set at 200 kHz on the FM band (87.5 MHz to 108 MHz).  This allows for a cushion of 25 kHz above and below to prevent interference.



Aircraft radios operate on the Aircraft band frequencies, from 108 MHz to 137 MHz.  From 108 MHz to 118 MHz, the stations are set at 50 kHz intervals transmitting using narrowband FM techniques.  There are 200 channels.  These are used for navigation beacons.  The picture shows an aeroplane on a flight simulator approaching the aerodrome at Aix-les-Bains (LFLB).



The navigation radio is tuned to 115.40 MHz (Chambéry VOR, CBY) and the instrument just below the aircraft registration (F-JLCO) is the navigation display linked with this.  Since this is a physics tutorial, not a flight school, the meaning of the display is not relevant.  The VOR (VHF Omnidirectional Radio Ranger) transmits on narrow band the Morse code identifier, in this case CBY, or "-.-. -... -.--".  The pilot can hear this through the headphones.  It is repeated every fifteen seconds, and gets rather monotonous if left on.  Knowledge of Morse code is expected of all pilots.


The communications radio is set to 121.20 MHz, which is the radio frequency for the tower at Aix-les-Bains. 


In the last few years aircraft radios in Europe have to use a separation of 8.33 kHz with a frequency deviation of 2 kHz.  It used to be 25 kHz.  This has not pleased pilots who have had to replaced their radio equipment (not cheap).


Question 4

(a) How many channels does this allow?

(b) What is the bandwidth, assuming that the frequency deviation is 2 kHz and that the modulation frequency is 500 Hz?



Your answer to Question 4 will show that air-to-ground radio communication does not exactly result in High-Fidelity sound quality.



Data Capacity of a Channel

Digital data are transmitted as a series of pulses of value 1 (ON) and value 0 (OFF).  When digital signals are sent by radio waves, they are carried like this:



The higher the frequency of transmission, the more data are carried every second.  Also the bandwidth can be increased, so that even more data can be carried.  So let's have a look at some definitions:

A channel of bandwidth B Hz can be used to carry 2B symbols (or level changes) every second.  The channel capacity for binary digital signals is given by this equation:


B is the bandwidth in Hz, and M is the number of signalling values.  For a binary channel, M = 2, so log2 (2) = 1.  Therefore the capacity is twice the bandwidth.   This relationship is called the Nyquist Equation.  It is NOT on the syllabus, but it's the sort of thing that might come in an extension question.


Question 5

A transmission has a deviation frequency of 100 kHz and a modulation frequency of 50 kHz.

(a) What's the bandwidth?

(b) What is the data capacity in bytes per second?



For noisy data channels, the Shannon data capacity relationship applies, which takes into account the signal-to-noise ratio.  A weak signal is noisy and this can blot out the data.


The limiting factors for the channel's data carrying capacity are:


Bandwidths of Different Kinds of Data Channels

High speed nternet communication is, nowadays, reckoned to be as much of vital service as electricity, gas, water, sewerage, and telephone.  The world wide web was invented in 1989 to allow university computer systems to exchange data, using a language, html, devised by the Physicist Tim Berners-Lee in three hours one Christmas Day (doesn't say much for his Christmas, does it?).  The Internet was a network of military computers in the USA set up in the 1970s, so that a nuclear strike on one site would not destroy the capability of the others.  Nowadays the terms are interchangeable.


At the start of this century, more people and institutions were connected to the web using modems connected to their telephone lines.  These were used to dial-up a number given by the internet service provider.  The maximum channel carrying capacity was 56 kilobits per second.  This page would take 5 minutes and 3 seconds to load, sufficient for you to make a cup of coffee.  The bandwidth of a telephone line is 4 kHz.



This speed would be considered primitive today.  Also your phone was engaged while you were on-line.  You could neither make nor receive calls.


ADSL Broadband internet of 1 megabit per second came in about ten to fifteen years ago.  It was considered (rightly) a considerable advance on dial-up.  You were on-line all the time and your phone-line was available for use.  The photo shows an old ADSL modem.




Today, a broadband of 1 Mbps is considered unacceptable, although there are places in these islands where this is the speed.  One village in Kent has had speeds as slow as 540 kbps.  The village of Miserden in Gloucestershire has the dubious honour of being the slowest broadband in the UK, at 1.2 Mbps.  And it's not just in the most isolated villages, either.  Some parts of London have surprisingly low broadband speed.  Of the major cities, Kingston-upon-Hull has an average broadband speed of 12 Mbps, which is considered poor.  Where I live, 38 Mbps is the quoted speed.


Gigabit Ethernet has a capacity of 1000 Mbps.  You can also get ethernet adapters that use the house wiring to transmit data from the modem and router to a second computer.




This one operates at 200 Mbps.


USB 3.0 can transmit data at 5 Gbps.  Some wireless networks can operate at 54 Gbps.


Question 6

A student downloads a film which is a 1.5 Gigabyte file.  It takes 10 hours to download.  What is the rate of data transfer?