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Created it, 06/09/09
Update it, 06/09/11
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1. - INFORMATION IN THE NUMERICAL SYSTEMS
1. 1. - CONCEPT OF SIGNAL
The signal is the data carrier. This information carries in itself a message.
Suppose that I say :
“The mouse eats cheese in the pantry”.
We can say that I emitted by the voice an aural signal. This signal, you heard it, but still is necessary it that you know the language in which I express myself, French : in order to be able to decode the information which it contains. When you decode this information, a message will appear to you.
The message contained in information is the active component of the signal, it will start a reaction of your share : to pose a trap or to repair the netting of the pantry following the logical consequences that you will have drawn from information.
1. 2. - THE SIGNAL IN ELECTRONICS
In the preceding example, the signal was the acoustic vibration emitted by the voice.
In electronics, one also uses signals to transport information: they are electric signals, i.e. electric variations.
Now let us suppose that I want to transport a sound on electric wire, to amplify it, then to diffuse this sound in a room (figure 1).
Which are the systems which we will have to implement?
First of all, I need a microphone (1) which will transform the acoustic vibration into electric variation, then a block box (2) which will increase the amplitude of this signal, finally a loudspeaker (3) which will retransformera the increased electric variation, in acoustic vibration, in order to restore the sound.
Generally, one will be able to say that the microphone and the loudspeaker are transducers : term which indicates all the apparatuses transforming a physical size into electric variation or carrying out the opposite operation.
It is very desirable so that the electric signal is the most exact possible image of the vibration which gave him birth, which requires that the microphone is most faithful possible. Same manner, the loudspeaker must most accurately restore possible the acoustic image of the electric signal.
One can quote among the transducers of entry :
microphones
cameras
magnetic heads for reading of band
photoelectric readers
temperature gauges
strain gauges, etc …
One can quote among the transducers of exit :
Loudspeakers
cathode ray tubes.
The transducers, which they are of entry or exit, have as a task to transpose nature of the signal but not to transform the information contained in this one.
Inside the block box, we saw that the signal was amplified : one can say in general that we made undergo a treatment this signal. Indeed, to treat a signal, that means : to amplify, attenuate it, etc …
The block box (2) can contain, either an analogical system, or a numerical system.
1. 3. - ANALOGICAL SYSTEM
An analogical system is characterized by the fact that the electric signal that it uses, has an amplitude or a frequency which is constantly proportional to the physical size that it represents. There is analogy in the evolution of the two sizes in time (example figure 2).
1. 4. - NUMERICAL SYSTEM
The digital technique as its name indicates it uses numbers.
In a numerical system, there is no more direct and permanent relationship between the physical size of departure and the representative electric variation as for its form.
The numerical signal is materialized by successive levels of tensions which can have only two different values, and which represent figures 1 and 0, only figures used in a numbering system at base 2. This electric signal, made up of 1 and 0 represents the continuation of the values which the physical size can take successively. These values are expressed by successive binary numbers.
In the electronic circuits, the numerical signal is characterized by the presence of tension or absence of tension (figure 3).
These are the two levels which interest us. The passage of a level to another will have to be carried out as soon as possible because it is regarded as a parasitic state.
Moreover, these two levels will have to be quite distinct, so that there is no possible doubt on the value of the level. One of the important characters of the digital technique, resides in the fact that the signal used does not leave the place to ambiguity.
1. 4. 1. - THE NUMERICAL PRINCIPLE
Why a numerical system ? Which are the advantages of this system compared to those traditional, which one calls analogical and, which is controlled perfectly for a long time ?
Let us take an example :
A chart of geography constitutes the representation on a certain scale of physical reality of the ground. Any place, the deferred distances are proportional to the effective distances. However, the distances measured on the chart are a function of the precision of the layout.
Taking into account the scale, one multiplies the error of measurement which one carries out on the chart. We have an analog representation.
If, for example, we measure in centimetres the distance Dijon - La Rochelle, starting from the found number and of the report/ratio of reduction or scale, one can easily find the real distance. In addition, while following the road of Dijon to the La Rochelle, it would be possible on each crossed kilometric terminal, to note the distance covered. A simple addition would then make it possible to find this value directly.
In the first method, the figure obtained, is a function of the precision of the chart and the care taken to measurement. On the other hand, by using the milestones, the exact result is obtained with a negligible error which, whatever the measured distance, cannot differ that from a terminal in more or less.
The analogical systems call upon electric signals on which can appear, during their treatment and of their transport, of the deformations called distortions which will be harmful with the faithful restitution by the final transducer.
The numerical systems handle them, only figures which are constants. As long as these numbers see their preserved integrality, they are characterized by their extreme precision. This precision is known to 1 figure or 1 digit close (digit = English figure).
Aren't the pocket calculators, watches with quartz and other computers famous for their precision, and they did not already invade our modern world ?
Generally, one can say that the digital circuits, used in electronics, present compared to the analogical circuits of many advantages :
They are not very sensitive to the disturbances,
because the parasitic variations of their amplitude is not taken into account
bus nonsignificant (figure 4).
They do not ask adjustments long and tiresome, which decreases their cost price.
However, they also use in entry and exit of the transducers whose fidelity is a condition of the quality of the system.
It is necessary, in entry, to physical / electric conversion carried out by the transducer, to make follow this one of a circuit which transforms the analogical electric signal obtained, in numerical signal. This circuit is called : analogical / numerical converter (A / N). The circuit carrying out the opposite operation, at exit, is called digitizer / analogical (N / A).
1. 4. 2. - CONVERSION ANALOGICAL / NUMERICAL AND NUMERICAL / ANALOGICAL
To convert analogical signals into numerical signals, it is to transpose the code of the signals, without modifying information which they contain. What wants to say, obviously, that a signal having undergone two successive conversions opposite will find exactly its initial form.
Analogical / numerical conversion (A / N) still called P.C. M. (Pulsate Codes Modulation) or into French M.I.C. (Pulse modulation Coded) is illustrated figure 5.
The analogical wave (a), is sampled (b), i.e. measured with sufficiently brought closer regular intervals. The sampling rate is very large compared to that of the analogical signal and particularly compared to the component of the highest frequency in the case of composite signals.
The values thus measured are then translated into a number coded into binary (c), which is appeared as a succession of impulses (d). The numerical signal thus made up can then be used in the numerical system (computer, radio operator transmitter, magnetic tape, hi-fi system, etc…).
At the end of the chain, the train of impulses is detected and restored in binary format (e). By means of a digitizer / analogical (N / A), one reconstitutes the analogical wave (f).
The angular signal crosses a low-pass filter (g) to find its form of origin.
One calls low-pass filter a well-known device in analogical electronics. This one, as its name indicates it, lets pass only the low frequencies.
This system causes to remove the stiff faces of the signal from the converter N / A to preserve only the envelope of the signal of lower frequency, and to thus reconstitute the original shape of the analogical signal by smoothing.
1. 4. 3. - CODING
We saw previously that the numerical signal was composed of a succession of impulses of level 1 or 0. These impulses 1 or 0, functions of the successive values that takes the physical size that they represent, can be coded in various ways.
Binary code
You are accustomed to counting in a numbering system at base 10 in which there are 10 signs: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
The binary system is a numbering system at base 2, i.e. a system in which one uses only 2 signs : 0 and 1.
Other codes are also used, they are forms nonnatural or derived from the binary notation. They make it possible to avoid the errors in the event of loss of a bit (contraction of English binary digit : binary digit) or to reconstitute lost information: they still add to the safety of the numerical system.
All these codes will be studied later on.
1. 4. 4. - NUMERICAL ANALOGICAL MIXED CIRCUITS
For those which do not have a great professional experience, it is difficult to physically distinguish the technique used for the design from an apparatus.
For an integrated circuit, if his destination is not known, the distinction is practically impossible.
One can understand now that a circuit must be built to accept one of the two types of numerical or analogical signals. It will interpret only the signals of the technique for which it was conceived. It can happen that an apparatus uses the two shapes of signals, but, in this case, the analogical signals are distributed to the analogical circuits, and the numerical signals with the corresponding circuits.
In addition, it may be, that a signal between in analogical form in a circuit and arises from it in form numerical or vice versa and this thanks to the converters about which we spoke.
2. - EXAMPLE OF PROBLEM SOLVED BY
THE ANALOGICAL TECHNIQUE THEN BY THE DIGITAL TECHNIQUE
Before passing being studied basic functions and Boolean algebra, we will make the comparison between two elementary assemblies, one analogical, the other numerical one.
It should however be specified, as a warning, that this example voluntarily was very simplified and reflects only in a very remote way what would be done in technical reality; but it allows an approach of this comparison. It should well be known that for a given problem, there are two techniques to solve it: one analogical, the other numerical one, but the physical sizes at the entry and the exit of the two systems are identical.
This being said, let us pose the parts of the problem to be solved in these two techniques :
You have a work table which is located close to a window, consequently, you
profit from illumination due to sunlight. Work that you carry out on this table
requires an important and constant illumination. This natural light cannot be
given to you throughout the day, either because the sun is masked by clouds, or
because it is not present any more (when it grows dark).
It will thus be necessary that you have a complementary lighting, which is not other than a desk lamp.
But you are a technician, and you are not satisfied to press on the switch to light or extinguish your lamp. You decide to make this system automatic.
You can that there exists in electronics 2 techniques to solve your problem, to extend your personal experiment, you plan to carry out 2 assemblies, one using the analogical technique, the other the digital technique.
Figure 6 represents the diagram of the assembly using an analogical signal, figure 7 also represents the diagram corresponding to a numerical signal.
We find in both cases, a common starting point, the sensor (c) or transducer which makes it possible to translate the physical size corresponding to sunlight into an analogical electric signal, image of this light.
The second common point is of course the lamp and its feeding circuit.
The signal from the transducer will inform your system about the value of solar illumination and this one will carry out the operation necessary in order to light the lamp more or less. Thus, in the course of time, luminous flow on your table will remain practically constant.
Except these two common points, the way of proceeding is appreciably different in one or the other case.
Analogical assembly (figure 6)
The sensor (c) provides a signal proportional to the illumination which it receives (figure 8 represents the variation of the light, during the day). This electric signal is amplified then applied to a small engine intended to drive the cursor of a rheostat.
This rheostat is, in fact, a variable resistor. The installation of this system will be made way such, that to any increase in sunlight an increase in the ohmic value of the rheostat corresponds.
By doing this, when the external light increases, the light intensity of the lamp (L) decreases (curve of figure 9). Between the extreme positions, lit lamp and extinct lamp, there is an infinity of values of illumination (in theory).
In this figure, one considers that the luminous flow emitted by the lamp is proportional to the current which crosses it. Figure 9 is the opposite curve of figure 8. The curve of figure 9 corresponds to the complement of curve 8. It represents the value of illumination which it is necessary to add to natural illumination to obtain the desired result.
Numerical
assembly (figure 7)
We defer on figure 7, the sensor is followed of an analogical/numerical converter which will take on the curve of figure 8 of the samples and to affect a numerical value to them or to quantify them (operation which consists in assigning to each sample a numerical value i.e. a number).
Knowing that the contact (I) opens and is closed at the rate/rhythm given by the vibrator, this number represents the relationship between the time of closing and the time of opening of contact I. the time of opening corresponds to the extinct lamp and the time of closing to the lit lamp.
Consequently, a high number corresponds to a very large time of closing compared to the time of opening, which results in a time of long illumination of the lamp compared to the time of extinction. Contrary, a small number would correspond to a long time of extinction compared to the time of illumination.
When times are equal (a number = 1), the time of illumination and the time of extinction of the lamp are identical. Figure 10 summarizes this situation.
If the quench frequency at the rate/rhythm of which the switch I vibrates is high, the retinal persistence of the observer will give to this one the illusion which the lamp is permanently lit, but with a luminosity which will vary according to the report/ratio, time of illumination over time of extinction.
According to these data, the digitizer will actuate a relay or vibrator at a given frequency (in order to avoid the phenomenon of flutter) and according to the external light intensity will act on the cyclic report/ratio of this frequency in order to have a time report/ratio of closing over time of opening corresponding to desired complementary illumination.
We obtain finally curve 2 of figure 11. It is similar to that obtained with the analogical assembly. More the number of sampled points will be large plus the curves will be superposable.
In practice, it will be enough to fix the number of points so that the passage of a luminous level to the following is not perceptible. Thus, with the observation of the result it is impossible to distinguish which is the technique employed.
In figure 11, curve 1 represents the variation of sunlight (it is curve 8 the preceding one) and the points carried above are the points of sampling.
We finish this first lesson thus, in the next one, we will thus study the concepts on the sets then on the logical algebra the variable functions with N and well of others still …
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