Analogical
Digital converter |
Digital
Analogical converter with Tension divider Bridge |
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Created it, 06/09/09
Update it, 06/09/29
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In the theoretical latter, we will examine another family of very widespread circuits : “converters”. Let us see first of all which are their roles and which can be the applications for it.
1. - CONVERSIONS OF THE ANALOGICAL AND DIGITAL SIGNALS
There are very many applications, where digital apparatuses must communicate with the external world, for example when one must control the temperature, pressure, speed, moisture, the level of a liquid, illumination, etc…
These physical sizes are analogical data which can take all the possible values.
The measurement of these sizes is carried out thanks to sensors which transform them into analogical electric signals.
Each time a digital circuit must treat an analogical data, it is necessary that the latter is translated into a comprehensible language by the circuit, i.e. in binary code.
The analogical / digital converters are intended for this use.
Let us suppose a system of temperature control controlled by a computer. First of all, it is necessary to measure the temperature by means of a sensor, for example a thermocouple. To maintain the temperature constant, it is necessary to order the flame of the boiler, while varying the mass fuel rate of flow by means of a pump.
But the pump cannot be ordered directly by a digital circuit which delivers only two levels : 1 and 0. The order must be continuous, proportional to the mass fuel rate of flow which one wishes to obtain.
It is thus necessary to transform the orders coded into binary delivered by the computer in an analogical electric signal. This operation is carried out by a digital / analogical converter (A / D).
In the same way, the analogical signal delivered by the thermocouple, is not assimilable by the computer. In this case, it is necessary to intercalate between the sensor and the computer, an analogical / digital converter (A / D), figure 1.
One meets other examples of use of the converters in all the fields and particularly in the communications (radio, television, telemetry, etc…). Let us consider the case of a telephone call. When one speaks in front of the microphone, the vibrations of the air are transformed into an electric signal of analogical type, more or less full according to the intensity of the sound.
This signal, suitably amplified, is transmitted along the telephone line and on arrival, it is transformed by the loudspeaker, in audible vibrations (figure 2).
Along the line, the signals are often deteriorated by spurious electromagnetic signals, causing grésillement and a background noise very awkward.
In an entirely analogical system of transmission, as that which has been just described, it is rather difficult to avoid or eliminate these parasites.
With a digital system of transmission, it is much easier to solve this problem (figure 3).
Between the microphone and the telephone line, one intercalates an analogical/digital converter. One thus obtains on the line a series of number binary indicating the amplitude of the signal at every moment to be transmitted. In this manner, it is much easier to fight the noise since one must only distinguish two levels (0 and 1).
Circuits CMOS have an immunity with the noise equal to 0,45 times Vcc. Under these conditions, by feeding the circuits with a tension Vcc of 10 volts, parasites of an amplitude lower than 4,5 volts are not able to influence the behavior of the converters and are easily eliminated. To restore the sound with the other end of the line, should obviously be used a digital/analogical converter.
There exists, moreover, other methods which make it possible to treat the digital signals in order to eliminate the parasites which would have possibly infiltrated in the transmission.
Another example of use of the converters is met in the modern planes manually-controlled by a computer of edge.
All data necessary (altitude, pressure, speed, outside temperature, etc…) are measured by sensors. These data are converted into number binary and are transmitted to the computer of edge which carries out all calculations according to the indications of the pilot (figure 4).
The computer of edge delivers binary continuations of numbers which must be converted into analogical data by means of suitable converters.
It is obvious that the converters are not only useful, but that in very many cases, they are essential. The use of the converters tends to spread since the digital circuits are more stable, less expensive and in general creates less problems than the analogical circuits.
2. - THE ANALOGICAL
DIGITAL CONVERTER
The operation of a digital/analogical converter (D / A) can be compared with that of a potentiometric circuit of the type presented figure 5.
The converter receives a numerical signal on as many terminals of entry than there are bits in the binary number.
In bottom, there are the least significant bits (LSB = Least Significant Bit) and in top (figure 5), arrive the most significant bits (MSB = Most Significant Bit).
The binary digit of entry determines at exit a tension VA proportional to the numerical value which the input signal represents, just like in the potentiometric circuit, VA depends on the position of the cursor.
The converter also receives a reference voltage standard VR. In the comparison, this tension corresponds to existing VR between the extreme terminals of the potentiometer. In both cases, VR represents a level by report/ratio to which the output voltages are referred VA.
In the potentiometric system, VA can take all the values ranging between 0 volt and VR.
In the converter, one observes a similar behavior, but at exit, VA progresses by jumps or in “staircase”. Each rise in a walk corresponds to a unit increase in the numerical value of entry.
One can thus say that the tension VA from converter is still of the numerical type, but compared to the binary digits on the terminals of entry, it acquires already an analogical pace.
Will determine the value of the tension VA delivered by the converter, one uses the formula : VA = D x VR.
D represents a fractional coefficient corresponding to the numerical value present at the terminals of entry.
A converter comprising four terminals of entry, can receive sixteen bit configurations different energy from number 0000 with the number 1111.
Each unit increase in the binary number of entry corresponds to a progression of 1 / 16 of VR on the exit VA.
The table of figure 6 gives the value of the coefficient D for a converter to four bits of entry.
| Row
4
MSB |
Row
3
3rd bit |
Row
2
2nd bit |
Row
1
LSB |
Coefficient D |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 / 16 |
| 0 | 0 | 1 | 0 | 2 / 16 = 1/8 |
| 0 | 0 | 1 | 1 | 3 / 16 = 1 / 8 + 1 / 16 |
| 0 | 1 | 0 | 0 | 4 / 16 = 1 / 4 |
| 0 | 1 | 0 | 1 | 5 / 16 = 1 / 4 + 1 / 16 |
| 0 | 1 | 1 | 0 | 6 / 16 = 1 / 4 + 1 / 8 |
| 0 | 1 | 1 | 1 | 7 / 16 = 1 / 4 + 1 / 8 + 1 / 16 |
| 1 | 0 | 0 | 0 | 8 / 16 = 1 / 2 |
| 1 | 0 | 0 | 1 | 9 / 16 = 1 / 2 + 1 / 16 |
| 1 | 0 | 1 | 0 | 10 / 16 = 1 / 2 + 1 / 8 |
| 1 | 0 | 1 | 1 | 11 / 16 = 1 / 2 + 1 / 8 + 1 / 16 |
| 1 | 1 | 0 | 0 | 12 / 16 = 1 / 2 + 1 / 4 |
| 1 | 1 | 0 | 1 | 13 / 16 = 1 / 2 + 1 / 4 + 1 / 16 |
| 1 | 1 | 1 | 0 | 14 / 16 = 1 / 2 + 1 / 4 + 1 / 8 |
| 1 | 1 | 1 | 1 | 15 / 16 = 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 |
The bit of row 1 (LSB), when it takes value 1, determines a value VA equal to 1 / 16 of VR.
Under the same conditions (bit = 1), the bit of row 2 corresponds to 1 / 8 of VR, the bit of row 3 to 1 / 4 of VR and the bit of row 4 (MSB) to 1 / 2 of VR.
To find the value of the coefficient D corresponding to an unspecified binary number, it is enough to add the coefficients assigned to the rows in which one finds value 1.
Example : 1001 correspond to the coefficient D = 1 / 2 + 1 / 16 = 9 / 16.
In practice, it is advisable to represent the pace of report/ratio VA / VR according to the binary number of entry. Figure 7 represents the characteristic of transfer of a converter to 3 bits of entry.
It should be noted that maximum value VR (8 / 8) is not reached. The highest combination that one can have is 111. The coefficient D which one obtains in this case is :
1 / 2 for the MSB
1 / 4 for the 2nd bit
1 / 8 for the LSB.
The sum D for the highest combination is consequently equal to : 1 / 2 + 1 / 4 + 1 / 8 = 7 / 8, value beyond which one cannot go, or rather beyond which one can be only adding other bits, therefore other levels of entry.
For example with 4 bits, one obtains 16 levels from 0000 to 1111 and, as we saw previously, each level or walk is distant precedent of 1 / 16 of VR.
Figure 8 gives the characteristic of transfer for a converter D / A to 4 entries. In this way, one succeeds in reaching the 15 / 16 the top of scale. In the cases of this kind, one usually says that one increased the nominal resolution of the circuit.
The nominal resolution is the amplitude of the steps and coincides with the weight of the least significant bit (LSB) : 1 / 16 in the case of entry with 4 bits.
NOTE : One should not confuse the resolution with the precision of the converter which will be examined a little further.
2. 1. - DIGITAL
CONVERTER ANALOGICAL A TENSION DIVIDER BRIDGE
Figure 9 shows the principle of a digital / analogical converter with tension divider bridge.
The numerical entry is consisted a number of switches equal to the number of possible combinations with three bits, less one i.e. :
23 - 1 = 8 - 1 = 7
It is supposed that, in this circuit, one can close one switch at the same time.
Thus, to each closed switch, corresponds an analogical tension VA proportional to the binary number represented by the switch.
Let us note that the affected binary value with each switch is equal to the number of resistances connected between the switch considered and masses it.
This circuit presents two disadvantages. The first lies in the fact that it is necessary to have as many switches minus one than there are possible configurations bit (you point out that for only 8 bits, there are already 256 combinations what would require 255 switches). In addition, the resistance of load RL, of noninfinite value, imbalance all the dividing bridge and the output voltages are not exactly any more proportional to the numerical values of entry.
For these reasons, one is useful oneself in practice of a more complex circuit using an operational amplifier. Let us make a digression to give some essential precise details on this type of circuit.
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