How Do I Convert Analog to Digital?

Digital-to-analog conversion (D / A converter) is a bridge between the computer acquisition control system and the analog control object. The role of the D / A converter is to convert discrete digital signals into continuously changing analog signals; ^[1]

Digital quantity is composed of digits one by one, and each digit represents a certain right. For example, for a binary number 1001, the weight of the most significant bit is 2 ³ = 8, and the code 1 on this bit represents the value 1 * 2 ³ = 8; the weight of the least significant bit is 2 ⁰ = 1, and on this bit, the code 1 represents the value 1 * 2 ⁰ = 1; the other digits are 0, so the binary number 1001 is equal to the decimal number 9. ^[1]

There are many types of integrated D / A converters, and there are multiple classification methods:

1) According to its conversion method, it can be divided into two categories: parallel and serial;

2) According to the production process, it can be divided into bipolar type (TTL type) and CMOS type, etc., their accuracy and speed are different;

3) According to the resolution, it can be divided into 8 bits, 10 bits, 12 bits, 16 bits, etc .;

4) According to the output mode, it can be divided into voltage output type and current output type. ^[1]

T Digital-to-analog conversion T-type resistor network

Figure 9-3 is a schematic diagram of a 4-bit D / A converter with a T-type resistor network. The resistor decoding network in the figure is a T-type resistor network composed of two resistances of R and 2R. The operational amplifier forms a voltage follower. The data latch is omitted in the figure. The electronic switches S ₃ , S ₂ , S ₁ , S ₀ is controlled by the corresponding bit of the binary number D or connected to the reference voltage V _R (the corresponding bit is 1) or grounded (the corresponding bit is 0). When the electronic switches S ₃ , S ₂ , S ₁ , and S _{0 are} all grounded, the equivalent resistance viewed from any node a, b, c, and d toward the lower left is equal to R. ^[3]

The following uses the superposition principle and Thevenin's theorem to find the output U _{0 of the} converter.

When D ₀ acts alone, the T-type resistor network is shown in Figure 9-4 (a). The lower left of point a is equivalent to Thevenin power supply, as shown in Figure 9-4 (b); then the lower left circuits of points b, c, and d are equivalent to Thevenin power supply, respectively, as shown in Figure 9-4 (c ), (D), (e). Because the input resistance of the voltage follower is very large, much larger than R, so when D ₀ acts alone, the potential at point d is almost the open circuit voltage D ₀ V _R / 16 of the Thevenin power supply.

When D ₁ acts alone, the T-type resistor network is shown in Figure 9-5 (a), and the Thevenin equivalent of the lower left circuit at point d is shown in Figure 9-5 (b). Similarly, the Thevenin equivalent power of the lower left circuit at point d when D ₂ is acting alone is shown in Figure 9-5 (c); As shown. Therefore, the output of the converter when D ₁ , D ₂ , and D ₃ act separately are ^[4]

Using the superposition principle, the total output of the converter can be obtained as

It can be seen that the output analog voltage is proportional to the digital input. Generalized to n bits, the output of the D / A converter is

Because the T-type resistor network uses only two resistors, R and 2R, its accuracy is easy to improve and it is also convenient to manufacture integrated circuits. However, the T-type resistance network also has the following disadvantages: In the working process, the T-type network is equivalent to a transmission line. It takes a certain transmission time from the beginning of the resistance to the establishment of a stable current and voltage at the input of the op amp. When there are many digits, it will affect the working speed of the D / A converter. In addition, the load resistance of the resistor network as the reference voltage V _R of the converter will fluctuate with different binary numbers D, and the stability of the reference voltage may be affected as a result. So in practice, the following inverted T-type D / A converter is commonly used. ^[4]

T Digital-to-analog conversion inverted T-shaped resistor network

Figure 9-6 is a schematic diagram of an inverted T-type resistor network D / A converter. Because point P is grounded and point N is a virtual ground, the electronic switches S ₀ , S ₁ , S ₂ , and S ₃ are equivalent to ground regardless of whether the numbers D ₀ , D ₁ , D ₂ , D ₃ are 0 or 1. Therefore, the magnitudes of the branch currents I ₀ , I ₁ , I ₂ , I ₃ and I _R in the figure will not change due to the difference in binary numbers. In addition, the equivalent resistance viewed from any node a, b, C, and d to the left is equal to R, so the total current flowing out of V _R is ^[4]

The current flowing into each 2R branch is

The current flowing into the inverting side of the op amp is

The output voltage of the operational amplifier is

If R _f = R and I _R = V _R / R is substituted into the above formula, then

It can be seen that the output analog voltage is proportional to the digital input. Generalized to n bits, the output of the D / A converter is

Inverted T-type resistor networks also use only R and 2R resistors. However, compared to T-type resistor networks, the current of each branch is always present and constant. There is no transmission time at the phase input, so it has a high conversion speed. ^[4]