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1143 lines
53 KiB
Text
1143 lines
53 KiB
Text
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==Phrack Inc.==
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Volume 0x0b, Issue 0x3e, Phile #0x0b of 0x10
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|=---------------------=[ The basics of Radio ]=-------------------------=|
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|=-----------------------------------------------------------------------=|
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|=------------------=[ shaun2k2 <shaun at rsc dot cx> ]=----------------=|
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0 - Introduction
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0.1 - Technical Terms
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1 - Radio Basics
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1.1 - Radio Waves
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1.2 - Carrier
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1.3 - (RF) Frequency Bands
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1.4 - Wavelength
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1.5 - Transmission
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1.6 - Receiving
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2 - AM Radio
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2.1 - What is AM Radio?
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2.2 - Modulation
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2.3 - Demodulation
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2.4 - Circuits
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2.4.1 - Receivers
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2.4.2 - Transmitters
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3 - FM Radio
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3.1 - What is FM radio?
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3.2 - Modulation
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3.3 - Demodulation
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3.4 - Circuits
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4 - Misc
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4.1 - Pirate Radio
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4.2 - Wireless Telephone Tapping
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4.3 - Jamming
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5 - Conclusion
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6 - Bibliography
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--[ 0 - Introduction
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Ever since our discovery of radio, in around 1902, we have proceeded
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to utilise it for many different purposes -- from sending others short
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messages, to transmitting large and critical data sequences to other
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computer systems. As time has gone on, as useful a technology as
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radio is, it is barely noticed anymore. When most people think of
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'radio', they picture a small black device sitting in their car,
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which they will use to listen to their local radio stations during car
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journeys. On the other hand, very few people realise the true
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usefullness of radio, often forgetting that their cellphones,
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televisions, satellite TV and alarm systems all too use radio to complete
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their task on a very regular medium -- radio is not just that boring
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old thing gathering dust in the corner.
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This article is divided up into four parts. The first part describes
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the basic theory of radio, and examples to illustrate some of the
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common day uses of it. In parts two and three, AM and FM radio
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details are outlined showing various different circuits to illustrate
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how these principles can be applied to real-life, functioning
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circuits. Section four is a misc. section, presenting some
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miscellaneous interesting points. Some electronics knowledge is
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useful in radio, though not totally necessary. Most circuits
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presented here are quite rough, and can be greatly improved upon in
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many ways.
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----[ 0.1 - Technical Terms
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Below is a description of technical terms used throughout the article:
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RF -- Any frequency within the radio spectrum, which can be
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used by to transmit and receive radio signals.
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Modulation -- A technique used to package data into a radio signal
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which is of use to the destination radio receiver.
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AM -- Amplitude Modulation. This involves shifting the amplitude
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of a radio signal's carrier very slightly in sympathy with
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a modulating signal.
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FM -- Frequency Modulation. FM modulation involves shifting the
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frequency of a radio wave's carrier very slightly in
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sympathy with a modulating signal.
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Receiver -- Any device which is capable of receiving radio signals
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sent by a radio transmitter.
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Transmitter -- A device which can transmit radio waves into the
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surrounding environment.
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Aerial -- A medium to large piece of wire which is used by either a
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radio transmitter or receiver to propagate or detect an
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incoming radio signal. In a radio receiver or transmitter,
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an aerial acts as one plate of a capacitor, whilst the other
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plate is taken place by the Earth.
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Antenna -- See aerial.
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Wireless -- Refers to any technology which communicates data without the
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need for a wired connection. Most wireless devices, such as
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cell phones, televisions, and others use radio, but several
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do use technologies such as infrared, which is not covered
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here.
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Radio wave -- A radio wave is an 'electromagnetic' wave, most commonly
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containing data to be received by a remote radio receiver.
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Oscillator -- Refers to an electronic circuit which 'oscillates', or
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'vibrates', to complete a certain task. Oscillators are
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used in radio to transmit radio waves at a given
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frequency -- the rate at which the oscillator oscillates is
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the RF (see RF) at which the wave is transmitted. Common
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oscillator circuits, also used in this paper, are LC
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oscillator circuits, and crystal-controlled oscillators.
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Crystal-controlled
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oscillator -- An oscillator circuit whos oscillation frequency is
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controlled by a 'crystal'. See oscillator.
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LCoscillator -- An oscillator consisting of a capacitor and an inductor,
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whos frequency of oscillation is controlled directly by the
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capacitor, which is usually variable. See oscillator.
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Capacitor -- Device which stores current as an electrical field.
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Broadcast -- A term used to describe transmitting radio waves into the
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atmosphere.
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Wavelength -- The physical distance between two waves on the same
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frequency, transmitted successively.
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Bands -- Frequency Bands are a range of frequencies used
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interchangeably or commonly for the same type of technology.
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For example, televisions often use the VHF band.
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Frequency -- Number of cycles per seconds. Frequency can be used to
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describe how often an oscillator oscillates.
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Sidebands -- When modulation of a carrier is applied, two extra
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bands are generated, both slightly higher and lower
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than the carrier frequency, equating from the 'sum and
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difference' of the carrier and audio
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frequency. These two bands appear at either end of
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the RF carrier, hence the term 'sidebands'.
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--[ 1 - Radio Basics
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----[ 1.1 - Radio Waves
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Radio waves, otherwise referred to as 'radio signals', are simply
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electromagnetic waves. Radio waves are transmitted by devices called
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'radio transmitters' or 'transmitters' for short. Despite our wide and
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many uses for radio waves as a whole, we actually known very little about
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'radio'. We do know, however, that radio waves are a form of energy, which
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act exactly like they have been propagated as any other type of wave we
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know of. For example, an audio wave.
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Radio waves are made up of three things; an electric field, a
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direction, and a magnetic field.
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Despite our underlying ignorance of radio and its properties, we can
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predict and use its properties to our advantage to undergo a wide variety
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of different tasks -- and will probably do so for a long time to come.
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----[ 1.2 - Carrier
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An 'RF carrier' can be thought of as the part of the radio wave which
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can be modulated to 'carry' a data signal. An analogy to help with
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understanding this is to think of turning on a flashlight and pointing it
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towards a wall. The light which is seen on the wall is the 'carrier'.
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Before and without modulation, the carrier of a radio wave contains no
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data, and just contains peaks of an RF voltage.
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peak voltage
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||\\ ///\ //\\
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|| \\ // \\ // \\
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|| \\\/ \\\/ \\
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RF carrier
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Because sending radio waves with a carrier containing no data would be
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almost useless, a carrier is 'modulated' to contain data. There are various
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modulation schemes in wide use, but the two most common schemes are AM
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(Amplitude Modulation) and FM (Frequency Modulation). These are discussed
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later.
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----[ 1.3 - (RF) Frequency Bands
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As we can gather from listening to a variety of radio stations,
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different forms of technology use an entirely different 'band' of radio
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frequencies on which to send and receive their radio signals.
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The entire range in which radio signals are transmitted extends from
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around 30KHz, up to about 30GHz. This whole range of available RFs
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(Radio Frequencies) is known as the 'radio spectrum'. The radio
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spectrum's range of frequencies, and their concurrent uses are shown
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in the below table.
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+-------------------+----------------------------+---------------------+
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| Frequency | Uses | Name |
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+-------------------+----------------------------+---------------------+
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| 30KHz-300KHz | Long-wave radio, useful | Low Frequency (L.F) |
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| | for long distance | |
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| | communications | |
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+-------------------+----------------------------+---------------------+
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| 300KHz-3MHz | Medium wave, local radio | Medium Freq (M.F) |
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| | distant radio stations | |
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+-------------------+----------------------------+---------------------+
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| 3MHz-30MHz | Short wave radio | High (H.F) |
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| | Communications | |
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| | Amateur radio | |
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+-------------------+----------------------------+---------------------+
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| 30MHz-300MHz | FM Radio | Very High (V.H.F) |
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| | Police radio | |
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| | Meteorology Comms | |
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+-------------------+----------------------------+---------------------+
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| 300MHz-3GHz | Air Traffic Control | Ultra High (U.H.F) |
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| | TV | |
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+-------------------+----------------------------+---------------------+
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| 3GHz-30GHz | Radar Comms | Microwaves (S.H.F) |
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| | Satellites | |
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| | Telecommunications (TV & | |
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| | telephone) | |
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+-------------------+----------------------------+---------------------+
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Since certain frequency bands are used to accomodate important
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communications, such as the VHF band, it became illegal to transmit
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radio waves at certain frequencies without a license. It was made so
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because transmission of radio signals at important frequencies could
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interrupt critical communication, such as communication between police
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officers with their radio transmitter devices.
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All frequencies within the radio spectrum are invisible to humans.
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Light frequencies which are visible to humans, i.e frequencies which
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are present in the light spectrum, operate at *much* lower
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frequencies.
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----[ 1.4 - Wavelength
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Wavelength is the physical distance between a peak in one radio wave,
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to the peak in another radio wave transmitted successively -- on the same
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RF. As a general analogy, the wavelength can be thought of as the distance
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that the peak in a given wave will have travelled in the space of time for
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one cycle. This can be calculated using the below simple formula.
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|\ = V / F
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* |\ = lamda
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V = Velocity
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F = Frequency
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Using this formula, the wavelength for an example scenario can be
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calculated, when the RF is 27MHz. The speed of light is 300 million
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meters/second, which is therefore the velocity of the electromagnetic
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wave.
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|\ = 300,000,000 / 27,000,000
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= 11.11r
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Looking at the above calculation, what can be gained? It seems that the
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wavelength for waves transmitted in the example scenario is 11.11
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(recurring) meters, so from this, it can be gathered that a peak in a
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particular radio wave will have travelled 11.11r meters in the time it
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took for one oscillation of the transmitting oscillator. But how can we
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know how long this oscillation period takes? We can calculate this
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using the formula '1 / f'.
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1 / 27,000,000 = 0.0000000370r
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This means that within the miniscule time frame of 0.0000000370
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(recurring) seconds, the peak within the radio wave should have travelled
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approximately 11.11 (recurring) meters.
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Wavelength might seem quite a useless thing to calculate on its own,
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but it comes in very useful when it comes to calculating suitable aerial
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lengths for both radio transmitters and radio receivers. As a rule of
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thumb, an ideal length for a radio aerial is around 1/2 of the signals
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wavelength. This can be calculated very easily.
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11.11 / 2 = 5.555 (roughly)
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From this calculation, we can gain the knowledge that a near ideal
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radio transmitter/receiver aerial can be constructed to be of around 5.5
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meters. Exact precision is not generally critical to the overall operation
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of the radio transmitter/receiver. For example, where portability of
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equipment is more of a concern than great efficiency, 1/4, 1/8 or even 1/16
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of the wavelength in meters is often used for the length of the radio aerial.
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11.11 / 4 = 2.7775
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11.11 / 8 = 1.38875
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11.11 / 16 = 0.694375
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From this little experiment we can see that we can turn a length which
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is considerably out of question due to portability desires, into a length
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which is much more suitable, yet efficiency is not affected too much.
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This technique is very commonly employed to calculate sensible lengths
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for radio aerials. However, other techniques are also employed, especially
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in the case of satillite TV. Notice how TV satillite dishes house tiny
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holes in the body of the dish? These holes are specially sized to ensure
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that radio waves with wavelengths less than that associated with the
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desired RFs (3GHz-30GHz) do not create an electrical current in the aerial
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wire, as suitable radio waves do. Holes based upon the same principle can
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also be found when looking inside a microwave oven.
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----[ 1.5 - Transmission
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Perhaps one of the most difficult concepts to grasp in radio is how
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radio waves are actually broadcast into the environment. As touched upon
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previously, radio waves are transmitted using oscillators in electronic
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circuits, and the rate at which the oscillator oscillates is the frequency
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at which the radio waves are transmitted.
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As an example, we will focus on using an LC tuned oscillator circuit in
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the radio transmitter circuit. LC oscillators are made up of an inductor
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(L), and a capacitor (C). If we consider how a capacitor stores current,
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we can come up with the conclusion that it is stored as an electric field
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between two plates -- these two plates make up the capacitor. During one
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oscillation (also known as a 'cycle') of the LC tuned circuit, all
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available current is stored first in the capacitor as an electric field,
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and then as a magnetic field associated with the LC circuit's inductor.
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After a *very* short time period (1/f), the magnetic field is turned back
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into an electrical current, and begins to recharge the capacitor again.
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Because the inductor's magnetic field is beginning to change back into
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electrical charge, the inductor turns another electrical field into a
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magnetic field in order to counter-act the change. This continuous cycle of
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quick changes keeps the current in the LC circuit flowing in the same
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direction, driven by the current stored in the inductor. When the
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inductor's charge eventually becomes zero, the capacitor becomes charged
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again, but with the opposite polarity. After each oscillation (cycle),
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energy loss has occured, but not all of the energy loss can be accounted
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for as energy lost as heat from the inductor's coil. Thus, we can gather
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that some energy has been 'leaked' from between the capacitor's plates, as
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electromagnetic energy -- radio waves.
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If we consider this, we can conclude that the further apart the plates
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in the capacitor are, the more energy is broadcast ('leaked') as radio
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waves. This must mean that if we have a capacitor with plates spaced
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1 meter apart, more energy will be broadcast as radio waves than if the
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capacitor had plates spaced a very small distant apart. By thinking even
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deeper, we can conclude that to maximise 'leakage' of radio energy, a
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capacitor is needed in the LC tuned oscillator circuit with plates spaced
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at quite a distance apart. It just so happens that for this task, to
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maximise broadcast of radio waves, the world's largest plate can be used
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to take the place of one plate of the capacitor -- the Earth! The other
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capacitor plate needs just be a suitably lengthed piece of wire, which is
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an equally common sight -- this piece of wire is known as an 'aerial'!
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In real-world radio transmitters, oscillator circuits are used to make
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a small current 'oscillate' in an aerial wire. Because of the constant
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change of energy form in the oscillator circuit, the current oscillating in
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the length of the wire becomes electromagnetic and is radiated as radio energy.
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Back to the length of the aerial in relation to wavelength; this is
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where the length calculated earlier comes in handy. From the knowledge
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gained here, we can assume an adapted LC oscillator circuit as below.
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Capacitor Inductor
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________________
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| )
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| )
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--- )____________ Aerial
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--- )
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| )
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|________________)
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As a concept, using the adapted LC tuned oscillator circuit above, the
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transmission of radio waves can be thought of like this; radio waves are
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generated due to the propagation of an electric current in an aerial wire.
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It is, as we have learnt, the 'leakage' of electromagnetic energy from
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between the two plates of the capacitor which causes broadcasting of radio
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waves.
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As oscillations occur in our LC tuned circuit, all available energy is
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stored in the capacitor, followed by energy (electrical current) not leaked
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as electromagnetic waves being fed into the inductor. This whole process
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measures one oscillation, and once one oscillation is over, the whole
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process repeats itself again, and each time energy is being lost as radio
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waves from the acting 'capacitor' (aerial and Earth). Therefore, it is the
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rate at which the LC circuit is oscillating (the 'frequency') at that
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determines the frequency at which the radio waves are broadcast at -- thus
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determining the RF of the radio signals.
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----[ 1.6 - Receiving
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The concept of receiving radio signals is based upon almost the opposite
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of the concepts of transmitting radio waves. In similarity to radio
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transmitters, radio receivers also use an aerial, but for a totally
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different purpose; for detecting the radio signals in the environment. As
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described previously, radio waves are a form of energy, propagated as
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electromagnetic waves through the air. Thus, when radio signals transmitted
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by nearby radio transmitters pass the aerial of the receiver, a *tiny* RF
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alternating current is generated in the aerial wire. When a signal becomes
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present in the aerial wire, 'wanted' radio frequencies are 'selected' from
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the assortment of RF currents in the aerial, using a 'tuned circuit'.
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As an example, we'll focus on the LC tuned circuit as in the previous
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section, due to the simplicity of this circuit. RF current of the 'wanted'
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||
|
frequency can be selected from amongst the other RFs by use of an LC tuned
|
||
|
circuit, which is set to resonate at the frequency of the 'wanted' radio
|
||
|
frequency. This selection is done because the LC tuned circuit has low
|
||
|
impedance at any frequencies other than the 'wanted' frequency. Frequencies
|
||
|
other than the 'wanted' frequency are prevented from passing through the
|
||
|
circuit because they are 'shorted out' due to low impedance of the LC
|
||
|
circuit at any other frequency than the resonant frequency (the frequency
|
||
|
of the 'wanted' signals).
|
||
|
|
||
|
Following the selection of correct radio frequencies from the other RF
|
||
|
signals, the radio receiver will usually amplify the signal, ready for
|
||
|
demodulating. The technique which is adapted by the receiver for
|
||
|
demodulating the radio signal into the modulating signal is totally
|
||
|
dependant on the type of modulation being used in the received radio
|
||
|
wave. In the case of an AM radio receiver, a selected signal will be
|
||
|
'rectified' and thus demodulated, using a low-drop germanium diode. This
|
||
|
process basically turns the alternating RF current back into a direct DC
|
||
|
current, which represents the power strength of the AM signal. Next, the
|
||
|
RF component is generally removed by using a capacitor. The output product
|
||
|
of this process is a recovered modulating signal which can be fed to a pair
|
||
|
of high impedance headphones. The diagram below represents how the
|
||
|
selected RF current is rectified by the diode.
|
||
|
|
||
|
|
||
|
||\\ //\\ ----------------------|>|--------------- ||\\ //\\
|
||
|
|| \\|| \\ || \\|| \\
|
||
|
\/\/\/\/\/\/
|
||
|
|
||
|
AM Modulated Carrier diode Modulating signal
|
||
|
(RF carrier present)
|
||
|
|
||
|
|
||
|
After being rectified by the diode, the AM radio signal is still not
|
||
|
suitable to be fed to an audio output, as the RF carrier is still present.
|
||
|
The RF carrier can be removed by using a single capacitor.
|
||
|
|
||
|
| |
|
||
|
||\\ //\\ ------------------------| |--------------------- /\ /\
|
||
|
|| \\|| \\ | | / \/ \
|
||
|
|
||
|
Modulating signal capacitor Modulating signal
|
||
|
(RF carrier removed)
|
||
|
|
||
|
|
||
|
The output of the capacitor is a recovered modulating audio waveform
|
||
|
which is suitable for passing to an audio output device, such as a set
|
||
|
of headphones with a high impedance.
|
||
|
|
||
|
This technique is likely to be the simplest way to create an AM radio
|
||
|
receiver, commonly known as the 'crystal set', used by the mass in the
|
||
|
1920s. Other receivers are more often used to produce a higher quality of
|
||
|
audio output, such as TRFs (Tuned Radio Receivers) and Superhetrodyne
|
||
|
receivers.
|
||
|
|
||
|
The whole system model of a radio receiver at its most basic level can
|
||
|
be thought of as the below diagram.
|
||
|
|
||
|
|
||
|
Modulated Radio Signal
|
||
|
(electric current generated in aerial wire by radio wave)
|
||
|
|
|
||
|
\|/
|
||
|
Signal amplified
|
||
|
|
|
||
|
\|/
|
||
|
Signal demodulated
|
||
|
|
|
||
|
\|/
|
||
|
Modulating signal
|
||
|
|
||
|
|
||
|
Although the techniques and components needed to achieve each step of
|
||
|
the diagram are different, most receivers stick to this sort of system.
|
||
|
Other types of receivers and their circuits are discussed more indeph in
|
||
|
the section they are related to.
|
||
|
|
||
|
|
||
|
--[ 2 - AM Radio
|
||
|
|
||
|
----[ 2.1 - What is AM Radio?
|
||
|
|
||
|
AM Radio refers to any form of technology which makes use of Amplitude
|
||
|
Modulation to modulate the 'carrier' with information. To package a radio
|
||
|
wave with often complex signals, the carrier of a radio wave is shifted in
|
||
|
power very slightly in sympathy with a modulating audio or data signal.
|
||
|
Next to morse code, AM is one of the simplest forms of modulation, and with
|
||
|
this, comes its disadvantages.
|
||
|
|
||
|
----[ 2.2 - Modulation
|
||
|
|
||
|
AM Modulation involves nothing more than shifting the power of a radio
|
||
|
wave's carrier by tiny amounts, in sympathy with a modulating signal.
|
||
|
Amplitude, as you probably already knew, is just another word for 'power'.
|
||
|
|
||
|
The simplicity of AM modulation can be demonstrated with a simple
|
||
|
diagram like the one below.
|
||
|
|
||
|
|
||
|
||\\ ///\ //\\
|
||
|
|| \\ // \\ // \\ ---> \ /\ / ---> \\ \\
|
||
|
|| \\\/ \\\/ \\ \/ \/ \\ ///\\
|
||
|
\\// \\
|
||
|
|
||
|
RF Carrier Modulating signal AM signal
|
||
|
|
||
|
|
||
|
As you can hopefully make out from the diagrams, whenever the
|
||
|
modulating signal (the signal which we are modulating) increases in
|
||
|
voltage, the amplitude (power) of the RF carrier is increased in sympathy
|
||
|
with the modulating signal. When the voltage of the modulating signal
|
||
|
declines in voltage, the opposite of above happens. After AM modulating
|
||
|
the carrier, the signal has usually twice the 'bandwidth' of the original
|
||
|
modulating signal.
|
||
|
|
||
|
|
||
|
----[ 2.3 - Demodulation
|
||
|
|
||
|
When an AM designed radio receives a radio wave, as previously noted,
|
||
|
a small RF alternating current is generated in the aerial wire. Because of
|
||
|
the AM modulation of the carrier applied by the sending transmitter, the
|
||
|
voltages in the carrier are larger and smaller than each other, but in
|
||
|
equal and opposite amounts. As a result, to recover the modulating signal,
|
||
|
either the positive or the negative part of the modulated signal must be
|
||
|
removed. In the simplest AM radio receivers, the modulated signal can be
|
||
|
'rectified' by making use of a single germanium low-drop diode.
|
||
|
|
||
|
|
||
|
\\/\/\/\/\
|
||
|
\\ /// // ---------------------|>|----------------- \\ /// //
|
||
|
\\// \\/ \\// \\//
|
||
|
|
||
|
AM radio signal diode Modulating signal
|
||
|
|
||
|
|
||
|
|
||
|
Here, part of the carrier has been removed, resulting in recovery, or
|
||
|
'rectification' of the modulating signal.
|
||
|
|
||
|
Because the carrier frequency (the RF of the radio wave) is usually
|
||
|
significantly greater than the modulating frequency, the RF carrier can be
|
||
|
removed from the resultant modulating signal, using a simple capacitor.
|
||
|
|
||
|
|
||
|
\\ // | |
|
||
|
\\ /// // ----------------| |---------------- \ /\ /
|
||
|
\\// \\// | | \/ \/
|
||
|
|
||
|
|
||
|
Modulating signal capacitor Modulating signal
|
||
|
(with RF carrier) (without RF carrier)
|
||
|
|
||
|
|
||
|
By exposing the rectified signal to a capacitor, the audio signal (or
|
||
|
otherwise data signal) is smoothed, producing a higher quality of audible
|
||
|
output. At this point, the modulating signal is more or less recovered.
|
||
|
|
||
|
Although this technique of AM demodulation can be made to work to a
|
||
|
satisfactory level, the vast majority of commercial radio receivers now
|
||
|
adopt a design known as 'superhet', which I will explain briefly here.
|
||
|
|
||
|
Superhet receivers are based upon the principle of 'mixing' two signals
|
||
|
to produce an intermediate frequency. The diagram illustrates a superhet
|
||
|
receivers operation.
|
||
|
|
||
|
|
||
|
Carrier in ---> Tuned circuit ---> Mixer ---> IF amplifier ---> Detector
|
||
|
(selects correct RF) | |
|
||
|
| |
|
||
|
| |
|
||
|
Local oscillator Audio Amp
|
||
|
|
|
||
|
|
|
||
|
+--+
|
||
|
| |
|
||
|
+--+
|
||
|
\__/
|
||
|
|
||
|
As we can see, superhet demodulation is significantly more complex than
|
||
|
'rectification'. Superhet receiver systems, like the above system diagram,
|
||
|
works basically as follows. First, an RF alternating current becomes
|
||
|
present in the circuit, because of the electromagnetic activity around the
|
||
|
aerial. Signals of the correct radio frequency are selected via a tuned
|
||
|
circuit, and inputted into one input pin of the 'mixer'. In the meantime,
|
||
|
the other input of the mixer is occupied by the 'local oscillator', which
|
||
|
is designed to be oscillating at a frequency just lower than the inputted
|
||
|
radio frequency. The output of the mixer is known as the 'Intermediate
|
||
|
Frequency' (IF), which is the difference between the local oscillator
|
||
|
frequency, and the frequency of the received AM radio signal. Next, the
|
||
|
'IF' is amplified, and passed to an 'envelope detector'. The output of the
|
||
|
envelope detector is the modulating audio signal (an AF -- Audio Frequency),
|
||
|
which is in turn amplified, and outputted to the user via a loudspeaker or
|
||
|
other audio output device.
|
||
|
|
||
|
Since the local oscillator is almost always set to oscillate at a
|
||
|
frequency of approximately 465KHz *below* the frequency of the carrier
|
||
|
input, the output of the mixer will always be a 'carrier' of 465KHz --
|
||
|
which still carries the modulated information. After the signal is
|
||
|
amplified by the IF amplifier(s) (there can be more than one IF amplifier),
|
||
|
the signal is now demodulated by the detector -- which is often just a
|
||
|
single diode. As mentioned above, the modulating signal recovered by the
|
||
|
system can be fed to an amplifier, followed by an audio output device.
|
||
|
|
||
|
As well as producing a higher quality of audio signal, superhet
|
||
|
receivers also eliminate the need to be able to tune multiple tuned
|
||
|
circuits in a TRF (Tuned Radio Receiver). TRF designs become awkward
|
||
|
when it comes to tuning them into different radio frequencies because
|
||
|
of the many tuned circuits needed -- superhets overcome this problem
|
||
|
as they always 'know' what the collector load will be -- a 465KHz signal.
|
||
|
Superhet designs can also be adapted to work with FM radio signals, assuming
|
||
|
the 'detector' is changed to a suitable detector for FM signals (i.e phase detector).
|
||
|
|
||
|
|
||
|
----[ 2.4 - Circuits
|
||
|
|
||
|
Since radio technology is a frequently discussed topic across the
|
||
|
Internet, many radio circuit design implementations are readily available,
|
||
|
ranging from very simple circuits, to quite complex ones. Here I present
|
||
|
some radio related circuits which most people with a bit of electronics
|
||
|
knowledge and the right components can build.
|
||
|
|
||
|
|
||
|
------[ 2.4.1 - Receivers
|
||
|
|
||
|
Discussed above was the historic 'crystal set' radio receiver, which
|
||
|
allows anyone with a long enough aerial wire and a few components to
|
||
|
listen to AM radio bands. Below is the basic crystal set radio
|
||
|
receiver circuit, which is very easy to construct.
|
||
|
|
||
|
|
||
|
Aerial Wire D1 *
|
||
|
| Q1
|
||
|
| ____|>|__________________
|
||
|
|_____________|/ | |
|
||
|
| |\ | |
|
||
|
_______|_____ | | |
|
||
|
( | | | |
|
||
|
( L1 --- C1 * | C2 --- 0 high impedance
|
||
|
( --- | --- 0 headphones
|
||
|
( | | | |
|
||
|
(_____________| | | |
|
||
|
| | | |
|
||
|
|_______________^____________|__________|
|
||
|
| | (not joined)
|
||
|
|_______________|
|
||
|
|
|
||
|
GND
|
||
|
|
||
|
- C1 should be a variable capacitor to allow the station to tune into
|
||
|
other frequency bands.
|
||
|
|
||
|
- D1 should be a low-drop germanium diode -- non-germanium diodes
|
||
|
won't work.
|
||
|
|
||
|
|
||
|
From previous discussion, we can figure out that the above 'crystal
|
||
|
set' AM radio receiver works as follows; incoming radio waves generate a
|
||
|
tiny alternating current in the aerial wire, from which 'wanted' radio
|
||
|
frequencies are selected, by the tuned LC circuit. Selected current passes
|
||
|
through a diode, which 'rectifies' the signals, thus demodulating them.
|
||
|
Before the diode, there is a simple transistor, which amplifies the
|
||
|
'wanted' frequency. The only reason for this is to make the quality of
|
||
|
sound slightly better. Any remaining RF components are removed using a
|
||
|
single capacitor -- this consequently has the effect of smoothing out the
|
||
|
signal. The product audio signal is passed to a set of headphones -- these
|
||
|
*must* be high-impedance, or nothing audible sounds on the headphones.
|
||
|
|
||
|
As was noted earlier, this type of receiver was used frequently in the
|
||
|
1920s, and gave even newbie electronic enthusiasts of that time the
|
||
|
opportunity to build something that would be considered very useful at that
|
||
|
time. To make decent use of the 'crystal set' circuit, around 60-70 turns
|
||
|
of wire around a rod of ferrious metal would create a good aerial.
|
||
|
|
||
|
Designs like above are never used in commercial radio receivers anymore.
|
||
|
Excluding superhet receivers, TRFs are occasionally used to produce low
|
||
|
quality radio receivers. Below is a simple TRF receiver schematic.
|
||
|
|
||
|
|
||
|
|
||
|
Aerial
|
||
|
|
||
|
| C5* C6 +9V
|
||
|
| ________________________________________
|
||
|
| | | | ) |
|
||
|
| | --- --- ) LC2 |-|
|
||
|
| | --- --- ) __| |
|
||
|
| | |____|_______) | |_|
|
||
|
| | | | | C8
|
||
|
--- C1 | | D1 C7 | |___| |____0
|
||
|
--- _|_ Q1_____________|>|________| |_|_|/ | | 0
|
||
|
LC1 | R1 | | / | | | |\ Q2
|
||
|
_________|__ |_| __|/ | | High impedance
|
||
|
| ) | | |\_____ | | headphones
|
||
|
| ) | | | | |
|
||
|
| ) | | | | |
|
||
|
--- C2 * )___| |__|_ | | |
|
||
|
--- ) | | | | | |
|
||
|
| ) C3 | | | |
|
||
|
|___________) | | C4 | |
|
||
|
| |_____ | |
|
||
|
| | | R4 |-| R6 |-|
|
||
|
R2 |-| R3 |-| --- | | | |
|
||
|
| | | | --- |_| |_|
|
||
|
|_| |_| | | |
|
||
|
____|______|____|_________ |___________|
|
||
|
|
||
|
0V
|
||
|
|
||
|
|
||
|
- C2 should be a variable capacitor
|
||
|
- C5 and C6 should be variable capacitors
|
||
|
- Resistors of sensible values should suffice
|
||
|
- Capacitors of sensible values should suffice
|
||
|
|
||
|
|
||
|
As in the 'crystal set' receiver, when a radio signal is 'picked up'
|
||
|
by the aerial, the proper frequency is selected using the LC tuned
|
||
|
circuit. The signal is passed to a transistor amplifier. However,
|
||
|
this time, the transistor amplifier has a 'tuned collector load',
|
||
|
because of the tuned LC circuit (LC2) at the collector leg of the
|
||
|
transistor. Next, the signal is rectified, stored in a few capacitors
|
||
|
until enough current has collected, and is eventually fed to the user
|
||
|
with the high impedance headphones. The use of the tuned collector
|
||
|
load at the transistor causes for the receiver to be more precise,
|
||
|
amplifying only the signals which are at the frequency of LC2's
|
||
|
resonant frequency. As expected, this causes for a higher quality of
|
||
|
audio signal to be fed into the users headphones, making this a much
|
||
|
better radio receiver.
|
||
|
|
||
|
A few things can be done to improve the above receiver, such as adding
|
||
|
yet more tuned amplifiers, and perhaps adding a few more resistors and
|
||
|
capacitors for safety and efficiency purposes.
|
||
|
|
||
|
|
||
|
|
||
|
------[ 2.4.2 - Transmitters
|
||
|
|
||
|
All that we really need to do when designing a simple radio transmitter
|
||
|
is keep in mind that we require an oscillator -- either tuned or crystal
|
||
|
controlled -- and a series of amplifier circuits which boost our signal.
|
||
|
After these stages, all that is left is to make the signals oscillate in
|
||
|
the aerial wire.
|
||
|
|
||
|
Below is a simple radio transmitter schematic.
|
||
|
|
||
|
Aerial
|
||
|
|
||
|
|
|
||
|
|
|
||
|
___________________________________________________________________|
|
||
|
| | | | | |
|
||
|
| | | | | |
|
||
|
| L1 ) | | | L3 |
|
||
|
| ) R3 |-| C3 | |__ )
|
||
|
|-| R1 Crystal ) | | --- | | )
|
||
|
| |_________|_____________) |_| --- | | C5)
|
||
|
|_| ||| | | | | --- )
|
||
|
| |_______| |_______|_AM ___|_______|/ --- |
|
||
|
| / | | Modulator |\___|___|
|
||
|
|__________| |________|/ C2 Q2 | |
|
||
|
| | | |\ Q1 (PNP) | )
|
||
|
| C1 | --- )
|
||
|
| |-| C4 --- )
|
||
|
M | | R4 | L2 )
|
||
|
| |_| | |
|
||
|
| | | |
|
||
|
| | | |
|
||
|
|_______________________|______________________________________|____|
|
||
|
|
||
|
|
||
|
- TR2 is a PNP transistor
|
||
|
- M is a microphone
|
||
|
|
||
|
This circuit works by oscillating at the frequency controlled by the
|
||
|
crystal (27MHz would be legal in the UK), amplifying the signal with tuned
|
||
|
collector loads at the transistor (TR1), and then by radiating the signal
|
||
|
off as radio waves by oscillating the signal in the aerial wire. Amplitude
|
||
|
modulation is added to the signal by varying the gain of the transistor
|
||
|
driver, by connecting it to the output of a microphone. The above circuit
|
||
|
is quite inefficient, and is likely to produce low quality signals, but it
|
||
|
can be used as a starting point to building a simple AM radio transmitter.
|
||
|
It's probably illegal to operate the above circuit on frequencies requiring
|
||
|
a license, so some countries *require* the circuit to be crystal controlled
|
||
|
on a 'model radio' RF. One improvement to be made on the schematic is to
|
||
|
amplify the output of the microphone before feeding it to the transistor
|
||
|
driver.
|
||
|
|
||
|
Possible devices which could apply the AM modulation are audio
|
||
|
amplifiers, or even op-amps. An audio amp following the oscillator
|
||
|
would produce a higher quality, stronger signal, but would also provide
|
||
|
power gain (i.e amplitude gain), in sympathy with the audio signal produced
|
||
|
by the microphone. This gain of amplitude due to the audio amp has
|
||
|
essentially applied Amplitude Modulation of the carrier signal,
|
||
|
because the power of the signal has been altered according to the
|
||
|
inputted audio signal (at the microphone). An ordinary op-amp could
|
||
|
be used in a similar way, but by substituting the non-inverting input
|
||
|
pin with a suitable power supply. Essentially, this would cause for
|
||
|
an outputted gain from the op-amp, according to the audio signal,
|
||
|
because the two inputs to the op-amp are compared, as such.
|
||
|
|
||
|
|
||
|
|
||
|
--[ 3 - FM Radio
|
||
|
|
||
|
----[ 3.1 - What is FM radio?
|
||
|
|
||
|
FM radio just means any form of technology which makes use of radio
|
||
|
with FM modulated signals. To modulate a radio wave's carrier with
|
||
|
information, FM transmitters shift the frequency of the carrier very
|
||
|
slightly, to be in sympathy with a modulating signal.
|
||
|
|
||
|
|
||
|
----[ 3.2 - Modulation
|
||
|
|
||
|
FM modulation consists of little more than shifting a radio wave's
|
||
|
carrier frequency very slightly in sympathy with a modulating signal's
|
||
|
frequency.
|
||
|
|
||
|
Modulation of an example audio signal is shown in the figures below.
|
||
|
|
||
|
|
||
|
||\\ ///\ //\\
|
||
|
|| \\ // \\ // \\ ---> \ /\ / ---> ||\\ /\\ //
|
||
|
|| \\\/ \\\/ \\ \/ \/ ||\\ //\\ //
|
||
|
||\\// \\//
|
||
|
|
||
|
RF Carrier Modulating signal FM signal
|
||
|
|
||
|
The diagrams show that when the frequency of the modulating signal
|
||
|
increases, so does the given carrier frequency, and the opposite when
|
||
|
the modulating signal's frequency decreases. This is shown in the FM
|
||
|
signal diagram by the bands being spaced widely apart when the modulating
|
||
|
signal frequency is increasing, and more closely together when the
|
||
|
modulating signal's frequency is decreasing.
|
||
|
|
||
|
|
||
|
----[ 3.3 - Demodulation
|
||
|
|
||
|
When an FM modulated carrier signal is detected by the receiver's
|
||
|
aerial wire, in order to recover the modulating signal, the FM modulation
|
||
|
must be reversed.
|
||
|
|
||
|
Most modern FM radio receivers use a circuit called the 'phase-locked
|
||
|
loop', which is able to recover FM modulated radio signals by use of a VCO
|
||
|
(Voltage Controlled Oscillator), and a 'phase detector'. Below is the
|
||
|
system diagram of a PLL suitable for use in FM radio receivers.
|
||
|
|
||
|
|
||
|
FM signal in -------------> Phase ---------------
|
||
|
Detector |
|
||
|
| |
|
||
|
| |
|
||
|
| |
|
||
|
| |
|
||
|
VCO |
|
||
|
|__________________|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
Modulating signal
|
||
|
out
|
||
|
|
||
|
|
||
|
The above PLL is able to recover the modulating signal by having one
|
||
|
input to a phase detector as the modulated carrier, and the other input as
|
||
|
a VCO oscillating at the frequency of the RF carrier. The phase detector
|
||
|
'compares' the two frequencies, and outputs a low-power voltage relative to
|
||
|
the difference between the two 'phases', or frequencies. In essence, the
|
||
|
outputted voltage will be relative to the frequency by which the carrier's
|
||
|
frequency was shifted during modulation by the transmitter. Therefore, the
|
||
|
output of the PLL, known as the 'phase error', is the recovered modulating
|
||
|
signal. In addition to being outputted from the small system, the voltage
|
||
|
is also given to the VCO as 'feedback', which it uses to 'track' the
|
||
|
modulation. Acting upon the feedback received, the frequency of
|
||
|
oscillation is altered accordingly, and the process is repeated as
|
||
|
necessary.
|
||
|
|
||
|
In the past, less efficient and reliable circuits were used to
|
||
|
demodulate FM radio signals, such as the 'ratio detector'. Although the
|
||
|
'ratio detector' is less sophisticated than PLL methods, a functioning
|
||
|
ratio detector circuit is actually a little more complex than PLLs.
|
||
|
|
||
|
It should be noted that superhet receivers, touched upon a little
|
||
|
earlier, can also be used as FM radio receivers, but their 'detectors' are
|
||
|
different to that of an AM superhet -- for example, a PLL circuit or ratio
|
||
|
detector discussed here could be used in conjunction with a superhet
|
||
|
receiver to make an FM radio. This is the method which is actually adopted
|
||
|
by most commercial radio receiver manufacturers.
|
||
|
|
||
|
----[ 3.4 - Circuits
|
||
|
|
||
|
|
||
|
------[ 3.4.1 - Transmitters
|
||
|
|
||
|
The same general principles apply to FM radio transmitters as they do
|
||
|
to AM radio transmitters, except that information must be modulated in a
|
||
|
different way. In AM radio transmitters, the carrier frequency is more or
|
||
|
less always constant. However, in FM transmitters, the whole principle is
|
||
|
to alter the carrier frequency in small amounts. This means that a tuned
|
||
|
oscillator circuit is not appropriate, because we need to alter the
|
||
|
frequency accordingly, not transmit at one static frequency. The method
|
||
|
used to overcome this problem is discussed a little later. A simple FM
|
||
|
transmitter schematic diagram is presented below.
|
||
|
|
||
|
|
||
|
Aerial
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
____________________________________________________________________|
|
||
|
| | | | | |
|
||
|
| | | | | )
|
||
|
| ) |-| --- C3 | )
|
||
|
| R1 L1 ) R3 | | --- |_ C4 )
|
||
|
|-| ) |_| | | | )
|
||
|
| | ) | | | --- |
|
||
|
|_| | Crystal | C2 | | | --- | L2
|
||
|
|_______________|||_____________|___________| |___|____|____|/ | |
|
||
|
| / | | |\___|___|
|
||
|
|____________| |_____________|/ |
|
||
|
| | | |\ Q1 Q2 |
|
||
|
| | |
|
||
|
| C1 | |
|
||
|
M |-| |
|
||
|
| | | R2 |
|
||
|
| |_| |
|
||
|
| | |
|
||
|
|______________________________|_____________________________________|
|
||
|
|
||
|
|
||
|
When audio signals are produced by the microphone, current carrying
|
||
|
audio frequencies are amlified, and are used to modulate the radio
|
||
|
wave. Since the microphone does this all for us, there is no need to
|
||
|
use modulation modules, ICs, or other technology. In situations where
|
||
|
an elecret microphone is not available to do the modulation for us, a
|
||
|
varactor diode can be used to vary the capacitance in an oscillator
|
||
|
circuit, depending on the amplitude of a modulating signal. This
|
||
|
varies the oscillation frequency of the oscillator circuit, thus
|
||
|
producing FM modulation.
|
||
|
|
||
|
|
||
|
|
||
|
--[ 4 - Misc
|
||
|
|
||
|
----[ 4.1 - Pirate Radio
|
||
|
|
||
|
Pirate Radio stations are simply just radio stations ran by
|
||
|
individuals who are not licensed amateur radio enthusiasts. Although
|
||
|
radio is actually a natural resource, it has been illegal for a
|
||
|
significant amount of time in some countries to transmit radio waves
|
||
|
on certain frequencies. Although transmitting radio signals on
|
||
|
certain frequencies (around 27MHz) is legal in places like the UK,
|
||
|
strict FCC regulations kick in, almost limiting the threshold to
|
||
|
useless. Because of this limitation, radio enthusiasts all around the
|
||
|
globe see fit to set up pirate radio stations, which they use for
|
||
|
their enjoyment, playing their favourite music tracks to the 'public',
|
||
|
and for a breeding ground for aspiring DJs. Some 'pirate radio'
|
||
|
stations keep within the FCC terms, by transmitting at low-power.
|
||
|
These types of stations are often referred to as 'free radio', or
|
||
|
'micropower stations'.
|
||
|
|
||
|
The legality of pirate radio stations is questionable, but varies from
|
||
|
country to country. In some European Countries, you can be arrested
|
||
|
for just owning an unregistered transmitter. In Ireland, prosecution
|
||
|
rarely takes place if registered radio stations are not affected, but
|
||
|
it is still illegal. The US allows transmission of radio signals at
|
||
|
*microscopic* power, making the limitations almost useless for
|
||
|
unlicensed radio enthusiasts, thus causing them to resort to pirate
|
||
|
radio.
|
||
|
|
||
|
Contrary to popular belief, setting up a pirate radio station is not
|
||
|
necessarily a difficult task. At the minimum, someone wanting to
|
||
|
setup a pirate radio station would need the following pieces of
|
||
|
equipment:
|
||
|
|
||
|
- Stereos, CD Players, Microphones, etc.
|
||
|
- Audio Amp
|
||
|
- Audio Mixer
|
||
|
- Transmitter
|
||
|
- Aerial
|
||
|
|
||
|
Stations using only the above equipment can sometimes sound quite
|
||
|
crude, and might interfere with other legal radio stations. To avoid
|
||
|
this, a 'compressor' can be used, which also limits the noise created
|
||
|
by sudden loud noises in the background.
|
||
|
|
||
|
Although any of the example transmitters in this article probably
|
||
|
wouldn't be sufficient enough to transmit music audio signals over the
|
||
|
air, but they could be used as a starting point to building your own, more
|
||
|
efficient kit. Additionally, FM and AM radio kits can be purchased,
|
||
|
which anyone with a soldering iron can build.
|
||
|
|
||
|
The length and height of the antenna depends entirely on how far the
|
||
|
radio signals need to be transmitted. By reading the previous
|
||
|
sections, some information on getting a correctly sized aerial can be
|
||
|
gained. For example, a quick and dirty aerial for an AM pirate radio
|
||
|
station could be around 15-20 feet tall.
|
||
|
|
||
|
To avoid being busted, it is probably a good idea to stay within the
|
||
|
legal power limits. Otherwise, a Direction Finding device used by the
|
||
|
authorities could easily track down the exact location of the
|
||
|
transmitter.
|
||
|
|
||
|
|
||
|
|
||
|
----[ 4.2 - Wireless Telephone Tapping
|
||
|
|
||
|
'Beige boxing' has long been the easiest and most exploited way to tap
|
||
|
telephones, interrupt on neighbours conversations, and use enemies
|
||
|
phone lines to make long distance calls to your friend in Australia.
|
||
|
However, since beige boxing requires the phreak to lurk around like a
|
||
|
ninja, a safer method can be used, which doesn't require you to be
|
||
|
physically close to the target phone line.
|
||
|
|
||
|
As expected, audio signals on a target phone line can be transmitted as
|
||
|
radio signals at an arbitrary frequency, and be received by any phreak with
|
||
|
an FM radio receiver. Although this concept is not new, it serves as an
|
||
|
interesting and useful project for radio newbies to try out. Below is a
|
||
|
simple FM phone bug transmitter circuit.
|
||
|
|
||
|
__________________________________________________________
|
||
|
| | |
|
||
|
| | |
|
||
|
IN (green) ___.___|_______ |-| |
|
||
|
| | | | | |
|
||
|
| /\ LED | |_| |
|
||
|
| --- | | |___| | op-amp |
|
||
|
| | C1 | | | | |---|\ |
|
||
|
| | |__________|/ ____| >------- Aerial |
|
||
|
IN (red) _____|___| |\ _____|___|/ |
|
||
|
| | | | | |
|
||
|
| | | | | |
|
||
|
OUT (green) __| | ( | | |
|
||
|
/\ ( | /\ varactor |
|
||
|
--- ( | --- |
|
||
|
| ( | | |
|
||
|
OUT (red) ________|____________________|_____|___|__________________________|
|
||
|
|
||
|
|
||
|
- inductor should be about 8 turns of wire
|
||
|
- aerial should be about 5 inch long
|
||
|
|
||
|
|
||
|
By interchanging the varator with a crystal, or by using a variable
|
||
|
capacitor, the frequency band on which the bug transmits line activity
|
||
|
could be changed accordingly. The varactor making up part of the
|
||
|
oscillator circuit is intended to alter the frequency of oscillation,
|
||
|
depending on the audio signal inputted from the green wire of the
|
||
|
telephone line. The varactor diode can be thought of as an
|
||
|
electrically variable capacitor, which in this case alters its
|
||
|
capacitance in sympathy with the audio frequency on the telephone
|
||
|
line -- causing for change of oscillation frequency, and thus
|
||
|
frequency modulation.
|
||
|
The following op-amp provides additional strength to the
|
||
|
signal, in an attempt to avoid a weak, unreliable signal. For
|
||
|
user-friendly purposes, the LED connecting to the red wire of the line
|
||
|
pair should illuminate when a signal is present on the line.
|
||
|
|
||
|
The above circuit can be modified to be made more efficient, and a
|
||
|
longer aerial is an obvious way of lengthening the range of
|
||
|
transmission. If a phreak was to contruct and use a device like this,
|
||
|
all they would need is an FM radio to tune into the correct
|
||
|
frequency. There are much better designs than the minimalistic one
|
||
|
above -- if a practical FM telephone bug is required, many plans are
|
||
|
available.
|
||
|
|
||
|
|
||
|
----[ 4.3 - Jamming
|
||
|
|
||
|
Technically, all it takes to carry out 'radio jamming' is to transmit
|
||
|
noise at a desired frequency. For example, if a person in the UK were
|
||
|
to transmit RF noise at 30MHz+, police radio communications could
|
||
|
possibly disrupted. Although the principles are mostly the same,
|
||
|
there are several different types of jamming.
|
||
|
|
||
|
- modulated jamming
|
||
|
This consists of mixing different types of modulation, and
|
||
|
transmitting the results at a desired radio frequency. This is
|
||
|
designed to make receiving legimate radio signals hard or next to
|
||
|
impossible.
|
||
|
|
||
|
- CW (continuous wave)
|
||
|
CW jamming only involves transmitting a consistant carrier frequency
|
||
|
once tuned into a RF frequency/band you want to jam. This again makes
|
||
|
receiving desired radio signals particuarly hard.
|
||
|
|
||
|
- Broadband
|
||
|
Broadband jammers spread Gaussian noise across a whole band of audio
|
||
|
frequencies, blocking legimate audio signals from easy receival.
|
||
|
|
||
|
|
||
|
A basic radio transmitter is easily modifiable, by adding a noise
|
||
|
generator, to successfully jam arbitrary frequency bands. Many other
|
||
|
types of radio jammers exist, and their details are readily available
|
||
|
on the World Wide Web.
|
||
|
|
||
|
|
||
|
--[ 5 - Conclusion
|
||
|
|
||
|
Radio is an extremely useful technology, which is at least as old as
|
||
|
the atom. But we are only just beginning to exploit its full
|
||
|
usefullness in even new and up and coming technology, and probably
|
||
|
will do for the next few hundred years.
|
||
|
|
||
|
As we've discovered, contrary to popular belief, employing the use of
|
||
|
radio in electronic circuits isn't at all as complicated as one would
|
||
|
think. Because of this, the use of radio and be both used and
|
||
|
exploitfully abused -- only a few basic principles need to be
|
||
|
understood to make use of this wonderful technology. Although the
|
||
|
surface has only been scratched, and way forward is open.
|
||
|
|
||
|
|
||
|
--[ 6 - Bibliography
|
||
|
|
||
|
Phrack 60
|
||
|
Low Cost and Portable GPS Jammer
|
||
|
<http://www.phrack.org/phrack/60/p60-0x0d.txt>
|
||
|
|
||
|
|
||
|
The Art of Electronics
|
||
|
<http://www.artofelectronics.com>
|
||
|
|
||
|
Updates to the article:
|
||
|
http://nettwerked.co.uk/papers/radio.txt
|
||
|
|
||
|
|