Author: Eric Brasseur
Suppose I have a little device capable of emitting a beep sound. It's just a little box, with a loudspeaker and an on/off switch. When you turn the switch on, the device emits a continuous beep sound. When you turn the switch off, the device becomes silent. This device is an emitter.
Secondly, suppose I have another little device capable of hearing the beep sound. It is also a little box, with a microphone and a lamp. When the microphone hears a beep sound, the lamp glows. When the microphone hears no beep sound, the lamp stays dark. This device is a receiver.
You can play with those two little devices as much as you want :
When you turn the switch of the emitter on, the lamp of the receiver begins to glow. When you turn the switch of the emitter off, the lamp of the receiver darkens. And so on.
Has the receiver having been build a classic way, then the distance over which the communication works will be a few meters or a few tens of meters :
If you put the receiver, say 50 meters away of the emitter, then there will be no more communication. When you turn the switch of the emitter on, the lamp of the receiver will not begin to glow. It will remain dark.
But, if you build a long distance receiver, then the distance may be a lot more than 50 meters :
Suppose you are in a noisy city. You put the emitter somewhere, then walk away. At a few tens of meters distance your ears no more hear the sound of the emitter. But, after 1 kilometre walking away, the long distance receiver still manages to hear the sound of the emitter. Amazingly, the communication works : when the switch of the emitter is pulled to on; the lamp of the receiver begins to glow. And when the switch of the emitter is pulled to off, the lamp of the receiver darkens. At 1 kilometre distance ! That's magic.
There is only one drawback : the communication is now rather slow. When the switch of the emitter is pulled to on, you have to wait 1 minute until the lamp of the receiver begins to glow. And when you push the switch of the emitter to off, you have to wait again 1 minute till the lamp of the receiver darkens.
It is thanks to the technology of the long distance receiver that communication with space probes going outside the solar system has been possible.
Our purpose is thus now to explain how this little miracle works.
2. The signal/noise ratio
The emitter is put a few centimetres away from the microphone.
When the emitter is switched off, the oscilloscope will show a straight line, no signal :
Suppose now we put the emitter two times further from the microphone.
When the emitter is on, the signal shown by the oscilloscope will be two times weaker :
Well, in fact this is not true. Once we have put the emitter, say 5 meters away from the microphone and the amplification has become relatively important, we see the noise appear :
This is what the oscilloscope shows when the emitter is off :
Noise is something you cannot avoid. Whatever you measure, if you amplificate it enough, you always get a noise. In fact it was there since the beginning, but it was so weak that we didn't notice it. It became visible once we amplificated it enough.
Let's put the emitter again two times further. We have to increase two times the amplification. Now the noise has the same amplitude as the sine wave :
This is what appears when we put the emitter 10 meters away :
The emitter may be on or off, the oscilloscope will show exactly the same thing : a noise.
Thus, at a distance of 40 meters our system does not work any more. A deaf person can no more use the oscilloscope to tell wether the emitter is on or off.
The key is the intensity of the signal versus the intensity of the noise. That's why we use the concept of signal/noise ratio.
The signal/noise ratio is a number. You obtain this number by dividing the number of the measure of the intensity of the signal by the number of the measure of the intensity of the noise.
Examples :
When the emitter was at a distance of 5 meters, the intensity of the signal was 1 and the intensity of the noise was 0.5. The signal/noise ratio was thus 2.
When the emitter was at a distance of 10 meters, the intensity of the signal was 1 and the intensity of the noise was 1. The signal/noise ratio was thus 1.
When the emitter was at a distance of 40 meters, the intensity of the signal was 0.25 and the intensity of the noise was 1. The signal/noise ratio was thus 0.25.
When the emitter is very close to the microphone, the intensity of the signal is 1 and the intensity of the noise is certainly less than 0.01. The signal/noise ratio is thus greater than 100.
We can say this :
The question is thus : what is the trick to determine the presence of the signal when the signal/noise ratio is a lot less than 1 ?
Answer : you must cut what you receive in exact pieces and make the sum of those pieces.
Like this :
Let's use what we received when the signal/noise ratio was 1. We had 4 periods of sine wave.
We have increased our signal/noise ratio by two !
How comes ?
Here is the explanation :
When you make the sum of four sine periods, the result is a sine period four times bigger.
7 + 7 + 7 + 7 = 28 -5 + -5 + -5 + -5 = -20
8 + 3 + -5 + -10 = -6 1 + -5 + 11 + -8 = -1
The sum of n noise "periods" of amplitude a is a noise "period" of amplitude
n . a.
Thus, when we made the sum of four periods, the sine wave grew four times, but the noise grew only two times. The signal/noise ratio was thus increased by two.
When we make the sum of n periods,the signal/noise ratio is increased by a factor n.
A sum of periods is a very important object. Because it tells us if the sine wave was there or if it was not there. That allows us for example to transmit morse code. Here are the results of 27 successives results of sums calculated by a receiver :
absent absent there absent there absent there absent absent there there absent there there absent there there absent absent there absent there absent there absent absent
Transcribed with more readability, a space for absent and an underscore for there, it gives us this :
The same way, you can transmit modern digital code.
The space probe Galileo is curently in orbit around the planet Jupiter. The radio signal we receive from the probe is cut into one billion periods each tenth of a second. All those periods are carefully summed to generate an information flow of ten bits per second. That makes one text character per second. Character afther character, word afther word, sentence afther sentence, the probe transmits a description of what it sees or measures.
More refined systems do measure the intensity of the sine wave. Each time a sum is calculated, the size of the sine wave is measured and that measure is transmitted to whatever needs it. AM long wave and short wave receivers you can by in any store work that way. By calculating several thousand sums per second and transmitting the result to a loudspeaker they make that loudspeaker reproduce a certain sound, voice or music.
You may now stop reading this text if you want, the rest of it are technical details.
4. The precision of the clocks
A few periods may even be hidden by the noise, you still know where to cut just by looking at the position of the other periods near them. (That's what a PLL does.)
But what if the sine wave is completely hidden by the noise ? Where should we cut ?
There is only one solution : rely uppon a clock.
If we know that one period takes a milionth of a second, we make a clock give a tick each milionth of a second. Each time we hear a tick, we cut a period out of the received signal, blindly. And when we have accumulated enough periods, the sum of them will tell us wheter there was a sine wave hidden inside the noise or not.
OK. But that clock must have a certain accuracy. Let's take for example the following signal :
The more periods we want to cut and sum, the more accurate the clock will have to be.
If we want to sum hundred periods, we need a clock with a precision better than one hundredth. (This means that afther a time of say 100 seconds it deviates of less than a second.)
Attention : we have spoken about the precision of the clock used by the receiver. The clock of the emitter must have the same precision. It wouldn't help that the receiver cuts accurately the signal in periods, if the signal send by the emitter is unreliable. Both clocks must be accurate.
5. Bandwidth
And the radio frequency he is made to hear is 10,000,000 Hz (10 MHz). That makes 10,000 sums calculated each second.
It will hear perfectly an emitter emitting at 10,000,000 Hz. Of course.
It will also hear an emitter emitting at 10,002,000 Hz. Nearly perfectly.
But il will not hear an emitter emitting at 10,500,000 Hz. For the obvious reason given in chapter 4. (Well in fact it may hear it if it emits a very powerful signal, but let's no think about that.)
So, an emitter at 10,500,000 Hz will not disturb our receiver working at 10,000,000 Hz.
Thus we can use a second receiver, receiving at 10,500,000 Hz, to hear that emitter at 10,500,000 Hz.
That receiver at 10,500,000 Hz will not be disturbed by the emitter at 10,000,000 Hz.
That's wonderful. Each emitter receives the signal emitted by the emitter using the same frequency, but is not disturbed by the other emitter using another frequency.
If a receiver can be tuned it will be able to choose to which emitter it listens. It can be tuned to listen to the emitter emitting at 10,000,000 Hz or to listen to the emitter emitting at 10,500,000 Hz. Or any other frequency. It's just a matter of clock frequency.
We work at about 10 MHz and we do 10,000 sums per second. We have the ability to use several frequencies at the same time to allow different emitters and receivers to work at the same place without disturbing each other. But, if we use frequencies between 9 MHz and 11 MHz, how many different couples of receivers ans emitters will be able to work simultaneously ?
The answer depends on several things. Commonly a difference in frequency of ten times the transmission rate is taken. We transmit 10,000 informations per second, so we will rely upon a difference of 100,000 Hz between each emitter-receiver couple. Thus : 9,000,000 Hz, 9,100,000 Hz, 9,200,000 Hz... up to 11,000,000 Hz, that makes 20 couples of emitter and receiver talking to each other at the same time without disturbing each other.
10,000 is the bandwidth. It is the number of elementary informations elements that are transmitted each second. That is, the number of times per second you calculate the sum of the periods received.
The broader the bandwidth,
6. Accumulator atenuation
The method we described can be sumarized this way :
At the beginning of a series of periods, an accumulator is set to null. Then, each period received is added to the accumulator. Ones n periods have been received and added, the content of the accumulator is looked at. If it draws a sine period, we state the signal was on. If it draws pure noise, we state there was no signal. (Or we measure the size of the sine.)
The method that is most commonly used is this one :
The accumulator is never set to null. Each period received is added to it, then the content of the accumulator is shrinked a little bit (it is multiplicated by 0.999, say). The content of the accumulator is looked at continuously. If it draws a sine period, we state the signal is on. If it draws pure noise, or a too little sine period, we state there is no signal. (Or we measure the size of the sine.)
This second method is less mathematicaly correct, but it is more physicaly realistic, smoother, and easier to use.
The first method has three practical drawbacks :
| First method | Second method |
| It requires perfect memories, that are not disturbed afther n periods. That can only be done with digital memories or with delay lines. | It only requires simple components like a guitar string, a tuning fork or a condensator and a self. |
| When you look at how frequencies different from the perfect frequency are received, you get unregular results : a frequency slightly different will not be received at all, but another frequency further away from the perfect frequency will be heared a little bit. | You get a smooth behaviour : the further away from the perfect frequency, the less it is received. |
| You must know when a series of periods starts (for digital transmissions) and when it ends. This requires circuits or algorithms in order to allow the receiver to be phased with the emitter. | Because the accumulator is looked at continuously, you don't bother to be synchronised with the emitter. |
The first method was characterised by the number n of periods summed. Everything depends on the number n. You may wonder what characterises the second method. Answer : the number by which the content of the accumulator is multiplicated each time a period is added. That is 0.999 in our example above.
Now let's look at some practical aspects of this second method :
Simple electronic receivers that use a rudimentary LC circuit as their heart work that way naturally. The LC circuit (one capacitor and one self latched together) works as a resonator : if it receives pure noise, it will just oscillate a little bit at low amplitude. But if the noise contains a signal that has the same frequency as the resonance frequency of the circuit then the circuit will begin resonating and will thus oscillate at higher and higher amplitude. Once the amplitude reaches a given threshold, that will trigger a transistor and "make a lamp glow". The LC circuit acts as a memory that sums the oscillations.
Mechanical receivers work the same way too. Early radio command devices used little tuning forks to determine if a given beep sound was being received : if the beep sound was there the appropriate tuning fork would begin vibrating so strongly it's end would touch an electric contact.
If you want to build some mechanical device to visualize what's happening, here are two suggestions. I tried out none of them so if you do please mail me your remarks and recomendations.
The super-hetrodyne receiver is the most widespread type of radio receiver. It works on a mathematical trick :
When you multiply a sine wave by a sine wave with a slightly different frequency, you get a result that is the sum of two other sine waves :
The lowest frequency is equal to the difference between the frequencies of the two initial sine waves. If the first frequency was of 1,000,000 Hz and the second was of 999,000 Hz then the sine wave will have a frequency of 1,000 Hz.
That sine wave with the lowest frequency is the one we are going to use. The sine wave with the highest frequency is filtered away.
What is that low frequency good for ? A lot of things :
screen 1 frequency1 = .2 frequency2 = .24 FOR t = 0 TO 254 STEP .1 sine1 = SIN(t * frequency1) sine2 = SIN(t * frequency2) sinem = sine1 * sine2 PSET (t, sine1 * 10 + 10) PSET (t, sine2 * 10 + 50) PSET (t, sinem * 10 + 100) NEXT t |
8.1 Directivity of the emitter
A device is added to the emitter to make as much as possible of the signal go towards the receiver. So there is no waste in useless directions. That's what you do when you put your hands around your mouth when you whant to shout at somebody far away or in a noisy environment.
The device best known is the parabolic antenna, but there are a lot of other ways to achieve directivity. For example sets of common antennas connected together trough wires of acurately calculted length.
The bigger the antenna, the more directivity you will get.
The bigger the wavelength of the signal you transmit, the bigger the antenna you will need to achieve the same directivity.
8.2 Directivity of the receiver
A parabolic antenna acts for radio waves just like a solar oven acts for the sunlight, concentrating what it receives on one given point.
The considerations about antenna size, directivity and wavelength are the same as for point 8.1 just above.
8.3 Reduction of the internal noise of the receiver
Metalfilm resistors are prefered over carbon resistors, FET transistors are prefered over bipolar transistors, and so on.
To decrease even more the remaining amount of noise, and it can physically not be done another way, the receiver must be cooled down. It can be plunged into liquid nitrogen or even liquid helium. This is true whatever the type of communication system you are using : radio waves, light, light trough fibre optics, sound, electric signals trough wires, even interstellar gravitational waves...
Inside a simple component like a resistor, the noise is simply due to the electrons moving around inside the resistor. The hotter the resistor, the faster the electrons move thus the more noise. The higher the impedance, the higher the noise tension (this is compensated by the fact the noise is limited by the higher impedance).
If you want to hear directly such a noise, just put your ear inside an empty glass. Or both ears (inside two separate glasses, not inside the same glass).
8.4 Increase of the emitted power
Here is some data for amateur electronics. Let's talk about the basic straight antenna.
You may consider an antenna as behaving like a simple electric resistance connected to the ground (picture below). But it has two differences with a common electric resistance :
.
In other words : you may consider the signal is send trough a resistance of 75 connected to the ground.
on
it. Other common impedances are 50 and 100. The
impedance of a coaxial cable means that if you send a signal of any frequency trough a cable of infinite length it will behave for your generator like a resistance of that impedance. Symetricaly, if a signal comes trough a coaxial cable or twisted pair, it will be like if it came trough a resistance of that impedance. If one of the three impedances is not the same, then you will get ghosts and signals bouncing back partialy. Coaxial cables and twisted pairs have three main particularities : they do not distort the signal (it may weaken, but it will keep the same shape), they do not spill radio waves around (that would polute around and weaken the signal inside the cable) and they are insensible to external noise (even if your cable went trough a room with radio emitters, electric sparks or
whatever, the signal stays clean). For example, you may transmit RS/232 signals or even VGA screen signals on hundreds of meters provided you do that trough such wires.
8.5 Increase of the received power
The quality of the "hearing device" matters, but also it's surface, a bit like for the directivity. The bigger an antenna, the more powerfull will be the signal it delivers. (In the case of an omnidirectional antenna, noise and useful signal are both increased.)
The most serious reason why the received signal should be as strong as possible is to make it be stronger than the internal noise produced by the electronics of the receiver.
It is not necessary to try to make the received power as big as possible : you just have to make it be louder than the internal noise of the electronics.
In the case of a basic straight antenna, you increase the received power
by making the antenna longer. You may consider that a thick metalic antenna
with a length of one half the wavelength of the frequency received has an impedance of 75 (wavelength = 300,000,000 / frequency).
This is to say you may consider the signal is coming trough a resistance of
75. If you double the length of the antenna, you half the resistance and thus you get two times more power. (The electric tension of the signal will stay the same, but you will be able to rely on a stronger current.) Attention : once the antenna becomes longer than half the wave length you get a certain form of disturbing directivity.
A receiving antenna transforms radio waves into an electric signal just like a microphone transforms sound waves into an electric signal.
9. A practical software example
While the program is running, press the 0 or 1 key on your keyboard to switch the emitted signal on or off. Then look at the sum result that appears at the bottom of the screen (wait). If the signal was on, a sine wave period will be drawn. If it was off, just a weak noise will be drawn.
In order to run this program you need a PC running (or emulating) DOS or Windows. They contain a powerfull BASIC language interpreter capable of running this program. Just select the program with your mouse, copy it, paste it inside a simple text editor, then save it under the name you want (with the .BAS extension). Start the BASIC interpreter (QBASIC.EXE), load the program and run it.
SCREEN 1 'switch to 320 x 200 graphical output screen
LOCATE 1, 1: PRINT "Signal emitted (press 0 or 1) :"
LOCATE 8, 1: PRINT "Signal weakened, noise added :"
LOCATE 15, 1: PRINT "Result of last sum of 1000 periods :"
t = 0 'time
x = 0 'horizontal display position on screen
i = 0 'sweep inside receiver memory
p = 0 'number of periods received
s = 0 'signal to transmit
DIM r(16) 'receiver memory : 16 registers
DO
i$ = INKEY$ 'key pressed ?
IF i$ = "0" THEN s = 0 'signal to transmit
IF i$ = "1" THEN s = 1
m = s * SIN(t * 2 * 3.1415627# / 16) 'modulated signal
LINE (x, 20)-(x, 40), 0 'erase old pixel
PSET (x, m * 10 + 30) 'display modulated signal
t = t + 1
n = RND - RND 'noise
r = n * .9 + m * .1 'received signal
LINE (x, 80)-(x, 100), 0 'erase old pixel
PSET (x, r * 10 + 90) 'display received signal
x = x + 1: IF x = 320 THEN x = 0 'display sweep
r(i) = r(i) + r 'add to register
i = i + 1: IF i = 17 THEN i = 1: p = p + 1 'registers sweep
IF p = 1000 THEN '1000 periods
FOR a = 1 TO 16
LINE (a + 140, 135)-(a + 140, 165), 0 'erase old pixel
PSET (a + 140, r(a) / 10 + 150) 'display register value
r(a) = 0 'reset register
NEXT a
BEEP 'beep sound
p = 0 'start new 1000 periods
END IF
LOOP
Following program is much simpler. It works the same way as algorithms I implement inside microcontrollers. You may compare it with the program above to understand clearly how it works. Note only two registers are used and only the sign of the signal is used.
CLS
LOCATE 1, 1: PRINT "Signal emitted (press 0 or 1) : no"
LOCATE 15, 1: PRINT "Result of last sum of 1000 periods : nothing"
t = 0 'time
i = 0 'sweep inside receiver memory
p = 0 'number of periods received
s = 0 'signal to transmit
DIM r(2) 'receiver memory : 2 registers
DO
i$ = INKEY$ 'key pressed ?
IF i$ = "0" THEN 'signal to transmit
s = 0
LOCATE 1, 1: PRINT "Signal emitted (press 0 or 1) : no "
END IF
IF i$ = "1" THEN
s = 1
LOCATE 1, 1: PRINT "Signal emitted (press 0 or 1) : yes"
END IF
m = s * SIN(t * 2 * 3.1415627# / 16) 'modulated signal
t = t + 1
n = RND - RND 'noise
r = n * .9 + m * .1 'received signal
IF i = 1 OR i = 2 OR i = 3 OR i = 4 THEN r(1) = r(1) + SGN(r)
IF i = 5 OR i = 6 OR i = 7 OR i = 8 THEN r(2) = r(2) + SGN(r)
IF i = 9 OR i = 10 OR i = 11 OR i = 12 THEN r(1) = r(1) - SGN(r)
IF i = 13 OR i = 14 OR i = 15 OR i = 16 THEN r(2) = r(2) - SGN(r)
i = i + 1
IF i = 17 THEN
i = 1
p = p + 1
END IF
IF p = 1000 THEN '1000 periods
result = r(1) * r(1) + r(2) * r(2)
IF result > 100000 THEN
LOCATE 15, 1: PRINT "Result of last sum of 1000 periods : signal !"
ELSE
LOCATE 15, 1: PRINT "Result of last sum of 1000 periods : nothing "
END IF
BEEP 'beep sound
p = 0 'start new 1000 periods
r(1) = 0
r(2) = 0
END IF
LOOP
Please note two things about this second program :