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Created it, 06/09/09
Update it, 06/09/30
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3. 4. - ERRORS OF CONVERTER A SUCCESSIVE APPROXIMATIONS
Converter A / D can be prone to the same errors as the converter D / A ; error of offset, error of transfer, error of linearity.
If the latter is excessive, it can happen that certain combinations “are jumped” quite simply. Figure 35 shows the effects of these various errors on the curve of transfer of the converter.
There is another possibility of error, due to the variations of the signal to convert, which until now, was regarded as fixed.
Usually, that does not occur thus. Figure 36 illustrates the process when signal Vx varies during conversion.
The tension to convert Vx master key of 3 / 8 of VR at the beginning of the first conversion, 5 / 8 of VR at the end of the second conversion and however, two conversions give the same result (011).
It is thus necessary that the signal does not vary too quickly. The maximum variation V authorized is a function of the reference voltage standard VR, the number of bits n of the converter, and the time of conversion tconv according to the formula:
For a converter A / D with 10 bits, working with a reference voltage standard VR = 10 volts and a time of conversion of 0,1 second, one will have :
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Thus the input signal will be able to vary to the maximum of approximately of 1 / 10 of volt a second.
Fortunately, the converters with successive approximations are generally faster and carry out a conversion into a few microseconds.
If the time of conversion is 10 µs, one obtains :
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Although this value seems high, it makes some is not it. Indeed, 1000 V / s is equivalent to 10 volts in a hundredth of second. Very often, the signals to be converted vary more quickly.
One must then resort to an artifice : to maintain the signal fixed for all the duration of conversion, by means of a circuit adapted, called “Sample And Hold” in English, which wants to say circuit of sampling and maintenance.
The English term of writing exactly the function of the circuit, because it means literally “Samples and preserves”. Indeed, it takes on order a value of the analogical signal and preserve during all the time necessary to conversion.
Figure 37 shows a circuit “Sample And Hold” very simple. A condenser C is connected to the entry “+” of an operational amplifier assembled out of following amplifier (profit = 1) and having an impedance of high entry.
When switch I is closed, the input signal is found, without modification, at exit of the amplifier, since the profit of this last is equal to 1.
When the switch is opened, the input signal does not have any more any influence. The condenser C preserves in the form of electric charge, the last value of tension of entry existing before the opening of the contact. At exit of the amplifier, one finds this tension throughout all opening of the switch. Indeed, the discharge of the condenser C is unimportant since the impedance of entry of the amplifier is very high.
Figure 38 illustrates the principle of operation of the circuit “Sample And Hold”.
A data processing sequence of analogical data includes/understands usually a converter A / D associated with a circuit “Sample And Hold”, except if the signal to be converted is very slow.
Figure 39 shows the example treated figure 36, but with the correction made by a circuit “Sample And Hold”.
At points A and B, one opens the switch I which before was closed. There remains open throughout all conversion. The first conversion gives value 010, but the second conversion indicates the value 011, which is closer to reality than that obtained from figure 36.
3. 5. - CONVERTER A CRAWLS
The converters of this type are very much used for the construction of the digital voltmeters and to measure sizes which vary slowly, like the temperature and the pressure.
They are not adapted to the conversion of the signals varying quickly.
The converter with the simplest possible slope is represented figure 40. It is consisted a circuit RC, a control circuit and a meter.
Before conversion, the condenser C is discharged and switch I is open.
At the beginning of conversion, the control circuit closes contact I and starts the meter which starts to count the clock pulses.
As I is closed, the condenser C starts to take care through resistance R.
If one uses a sufficiently high tension VR compared to tensions Vx to convert, one can consider that the load of C is comparable to a linear slope (figure 41).
When tension VC at the boundaries of the condenser reaches value Vx to measure, the comparator rocks and announces the equality to the control circuit which stops the comparator immediately and opens contact I.
Conversion is finished and one can read on the meter the pulse repetition frequency of clock which was counted during Dt time put by the condenser to discharge with value Vx.
The more the value of Vx is raised, the more the time put by the condenser to take care with this value will be long.
It is enough to design the meter in an adapted way, so that the added up number directly gives the value of Vx in the desired binary code.
Actually, the things are not also simple. Indeed, the precision of such a converter depends mainly on the condenser and, generally, the condensers are not very precise.
One then has recourse to a more complex method called conversion with double slope, where the precision does not depend on the condenser.
This method illustrated by graphics of figure 42 is founded on the load and the linear discharge of a condenser (let us recall that the linearity of the load or the discharge is obtained when these two operations are carried out with a constant current).
The tension to convert Vx is applied to a condenser C, during a time T fixed, independent of the value of Vx.
The load of C thus depends only on Vx and is all the more high as Vx are large.
The slope of the slope during the load of C is variable and depends on the value of Vx.
When the load is finished, the control circuit applies to the condenser the reference voltage standard VR. This last tension is of contrary sign to that applied previously and causes the discharge of the condenser C.
The discharge is done with a constant slope equal to VR / RC.
When tension VC (at the boundaries of the condenser C) reached zero value, conversion is stopped. A meter measures Dt time necessary to discharge the condenser C and provides directly in exit the result of conversion in the form of a binary number.
Dt time is directly related to the height of the charging voltage, which in its turn, depends on Vx.
Owing to the fact that the condenser C works in linear mode, we can say that the load stored by C is proportional to Vx x T, while the load that C yields during the discharge is proportional to VR x Dt. As the quantity of electricity yielded by the condenser is equal to that which it had received previously, one deduces from it that :
Vx x T = VR x Dt from where Dt = Vx x (T / VR)
T and VR are constant and known terms since the beginning of measurement. One can thus conclude that Dt is directly proportional to Vx.
Figure 43 gives the general diagram of a converter to double slope.
Entry Vx is not connected directly to network RC, but crosses before an operational amplifier of profit - 1. This stage reverser makes it possible to apply an opposite signal of sign to that of VR the condenser C and it is also used to separate the converter from the circuits which precede it.
Signal Vx is applied by the I1 switch to resistance R and the condenser C.
The condenser C is not connected any more between one of the terminals of R and the mass, but between the exit and the entry “-” of an operational amplifier. This assembly constitutes an integrating circuit which makes it possible to obtain a perfectly linear load and a discharge of the condenser.
The control circuit actuates alternatively two switches. First I1 at the beginning of conversion is placed to the bottom and transmits tension Vx to network RC, thus allowing the load of C. At the end of a fixed time T, the I1 switch is rocked upwards. Tension VR, of contrary sign with Vx, is applied to network RC and the discharge of C is carried out.
At the same time, the control circuit gives the order to the meter to begin the counting of the clock pulses.
A comparator located following the integrating circuit makes it possible to detect the passage to zero of the discharge of the condenser C. This information is sent to the control circuit which blocks the meter.
The second I2 switch is closed a short moment before the beginning of conversion in order to short-circuit the condenser C and to eliminate any residual electric charge thus.
A converter with double slope offers many advantages : The measuring accuracy is independent of the precision of the condenser, moreover, the linearity is excellent and there cannot be missing combinations like in the case of the converter with successive approximations. Lastly, the resolution is limited only by the characteristics of the analogical circuits (amplifier operational) and can be very high. Let us add to that that possible high frequency parasites are very well tolerated and do not give place, generally, with erroneous indications.
All these advantages, should be opposed a major disadvantage : it is the slowness of conversion.
The meter must indeed start from scratch and count until time T, then to total zero and to count Dt time then. If the meter operates on more than 10 bits, there are several thousands of combinations : the clock must deliver a significant number of impulses and one can obtain only a few tens of conversions a second.
The operational amplifiers and the comparators are not perfect and often introduce small errors
These errors are reduced by using converters with quadruple crawls that we will not develop here since they are founded on the same principle as the converters with double slope
At the beginning of conversion, one closes again the entry on the mass and one carries out a conversion with double slope One should obtain a binary number equal to zero, but because of the errors, the binary number obtained is not null. This binary number is stored.
In the same way, the true conversion of tension Vx is then carried out and, at the end, the first binary number is cut off from the result obtained. A binary number much more precise is obtained thus.
3. 6. - CONVERTER TENSION
/ FREQUENCY
These converters are founded on the oscillators whose frequency depends on a tension of order.
They are called V.C.O. (of English “Voltage Controlled Oscillators” what means “oscillating ordered by tension”).
There are many oscillators of this type and in the trade one finds them in the form of integrated circuits.
The synoptic diagram of an analogical / digital converter using a V.C.O. is given figure 44.
The tension to convert Vx is applied to the entry of ordering of the oscillator V.C.O. which delivers a rectangular signal whose frequency depends on tension Vx. This signal is transmitted to the entry of clock of a meter which works during a time T determined by the orders on the entries “Start” and “Stop”. At the end of counting and if time T were judiciously selected, the meter indicates a binary number corresponding to tension Vx of entry.
Converters A / D of this type are slow but very precise.
3. 7. - CONVERTER A METER
In fact devices include understand a meter, a converter D / A, a comparator and a control circuit (figure 45).
Tension Vx to convert is applied to the entry “+” comparator.
The departure of conversion is given by an impulse on the entry “Start” of the control circuit.
At this moment, the clock pulses are transmitted to the meter through the control circuit.
The meter thus will be incremented with each clock pulse.
The binary exits of the meter are connected to the entries of a digital / analogical converter which delivers an analogical tension in staircase. This tension is applied to the entry “-” comparator.
When the tension in staircase, from converter D / A, reached or exceeds value Vx, the exit of the comparator changes state what informs the control circuit that it must block the meter. At exit of the meter, one thus has a binary number corresponding to the analogical entry Vx.
This type of converter D / A is rather slow. In certain cases, in particular when one wishes to treat analogical signals varying in time, one thus uses a reversible counter, instead of a normal meter. A following converter thus is obtained.
If the exit of the converter D / A is lower than entry Vx, the meter counts while growing and thus the exit of the converter D / A increases. If on the contrary, the same exit is higher than entry Vx, the meter countdown thus decreasing the exit of the converter D / A.
An example of conversion using a reversible counter is illustrated on figure 46.
The following converter is able to react very quickly for small variations of the input signal. For abrupt and important variations, it is as slow as the meter converters of first type.
Thus these theoretical lessons devoted to digital electronics are completed and which constitute an excellent preparation to approach the examination of the microprocessors and microcomputers.
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