What are DAC and ADC? Types of analog-to-digital converters (ADC) 8 bit analog-to-digital converter
Analog-to-digital converters (ADCs) – this is a device with the help of which the process of converting an input physical quantity into a numerical representation occurs. The input quantity can be current, voltage, resistance, capacitance.
The ADC is closely related to the concept of measurement, which refers to the process of comparison with a standard of the measured input quantity. That is, analog-to-digital conversion is considered as a measurement of the value of the input signal and, accordingly, the concepts of measurement error can be applied to it.
The ADC has a number of characteristics, the main ones being the bit depth and conversion frequency. The bit depth is expressed in bits, and the conversion frequency is expressed in samples per second. The higher the bit capacity and speed, the more difficult it is to acquire the necessary characteristics and the more complex and expensive the converter.
The ADC principle, composition and structural diagrams largely depend on the conversion method.
Classification
Currently, a large number of voltage-code conversion methods are known. These methods differ significantly from each other in terms of potential accuracy, conversion speed, and complexity of hardware implementation. In Fig. 2 presents the classification of ADCs by conversion methods.
Among the types of analog-to-digital converters, the most popular are:
1. Parallel conversion ADC. They have low bit depth and high performance. The principle of operation is that the input signal is supplied to the “positive” inputs of the comparators, and a number of voltages are supplied to the “negative” ones. The comparators operate in parallel; the delay time of the circuit is the sum of the delay time in one comparator and the delay time in the encoder. Based on this, the encoder and comparator can be made fast and the circuit will achieve high performance.
2. Successive approximation ADC. Measures the magnitude of the input signal by performing a series of “weightings” or comparisons of the input voltage values and a number of values. Characterized by high conversion speed and limited by the accuracy of the internal DAC.
3. ADC with charge balancing. The principle of operation is to compare the input voltage with the voltage value accumulated by the integrator. Pulses are supplied to the input of the integrator of negative or positive polarity, based on the comparison result. As a result, the output voltage “tracks” the input voltage. Characterized by high accuracy and low noise levels.
Analog-to-digital conversion is used wherever an analog signal needs to be received and processed in digital form.
- The ADC is an integral part of a digital voltmeter and multimeter.
- Special video ADCs are used in computer TV tuners, video input cards, and video cameras for digitizing video signals. Microphone and line audio inputs of computers are connected to an audio ADC.
- ADCs are an integral part of data acquisition systems.
- Successive approximation ADCs with a capacity of 8-12 bits and sigma-delta ADCs with a capacity of 16-24 bits are built into single-chip microcontrollers.
- Very fast ADCs are needed in digital oscilloscopes (parallel and pipeline ADCs are used)
- Modern scales use ADCs with a resolution of up to 24 bits, which convert the signal directly from the strain gauge sensor (sigma-delta ADC).
- ADCs are part of radio modems and other radio data transmission devices, where they are used together with a DSP processor as a demodulator.
- Ultra-fast ADCs are used in base station antenna systems (in so-called SMART antennas) and in radar antenna arrays.
34. Digital-to-analog converters, purpose, structure, principle of operation.
Digital-to-analog converter (DAC) - a device for converting a digital (usually binary) code into an analog signal (current, voltage or charge). Digital-to-analog converters are the interface between the discrete digital world and analog signals.
An analog-to-digital converter (ADC) performs the reverse operation.
An audio DAC usually receives a pulse code modulated digital signal as its input. The task of converting various compressed formats to PCM is performed by the respective codecs.
DAC applied whenever it is necessary to convert a signal from a digital representation to an analogue one, for example, in CD players (Audio CD).
Digital-to-analog converters (DACs) and analog-to-digital converters (ADCs) are primarily used to interface digital devices and systems with external analog signals to the real world. In this case, the ADC converts analog signals into digital input signals that are fed to digital devices for further processing or storage, and the DAC converts the digital output signals of digital devices into analog signals.
Specialized microcircuits produced by many domestic and foreign companies are usually used as DACs and ADCs.
DAC chip can be represented as a block (Fig. 13), which has several digital inputs and one analog input, as well as an analog output.
Rice. 13. DAC chip
The n-bit code N is supplied to the digital inputs of the DAC, and the reference voltage U op is supplied to the analog input (another common designation is U REF). The output signal is voltage U out (another designation is U O) or current I out (another designation is I O). In this case, the output current or output voltage is proportional to the input code and the reference voltage. For some microcircuits, the reference voltage must have a strictly specified level; for others, it is possible to change its value within wide limits, including changing its polarity (positive to negative and vice versa). A DAC with a large reference voltage range is called a multiplying DAC because it can be easily used to multiply the input code by any reference voltage.
The essence of converting an input digital code into an output analog signal is quite simple. It consists of summing several currents (according to the number of bits of the input code), each subsequent one is twice as large as the previous one. To obtain these currents, either transistor current sources or resistive matrices switched by transistor switches are used.
As an example, Fig. 14 shows a 4-bit (n = 4) digital-to-analog conversion based on an R–2R resistive matrix and switches (in reality, transistor-based switches are used). The right position of the key corresponds to one in this bit of the input code N (bits D0...D3). The operational amplifier can be either built-in (in the case of a voltage-output DAC) or external (in the case of a current-output DAC).
Rice. 14. 4-bit digital-to-analog conversion
The first (left in the figure) switch switches a current of value U REF /2R, the second switch - current U REF /4R, the third - current U REF /8R, the fourth - current U REF /16R. That is, the currents switched by neighboring keys differ by half, as do the weights of the bits of the binary code. The currents switched by all switches are summed up and converted into an output voltage using an operational amplifier with resistance R OS = R in the negative feedback circuit.
When each switch is in the right position (one in the corresponding bit of the DAC input code), the current switched by this key is supplied for summation. When the switch is in the left position (zero in the corresponding bit of the DAC input code), the current switched by this key is not supplied for summation.
The total current I O from all switches creates a voltage at the output of the operational amplifier U O =I O R OS =I OR. That is, the contribution of the first key (most significant bit of the code) to the output voltage is U REF /2, the second - U REF /4, the third - U REF /8, the fourth - U REF /16. Thus, with input code N = 0000, the output voltage of the circuit will be zero, and with input code N = 1111 it will be equal to –15U REF /16.
In general, the output voltage of the DAC at R OS = R will be related to the input code N and the reference voltage U REF by a simple formula
U OUT = –N U REF 2 -n
where n is the number of bits of the input code. Some DAC chips provide the ability to operate in bipolar mode, in which the output voltage changes not from zero to U REF, but from –U REF to +U REF. In this case, the output signal of the DAC U OUT is multiplied by 2 and shifted by the value U REF. The relationship between the input code N and the output voltage U OUT will be as follows:
U OUT =U REF (1–N 2 1–n)
ADC chips perform a function directly opposite to that of a DAC - they convert the input analog signal into a sequence of digital codes. In general, an ADC chip can be represented as a block that has one analog input, one or two inputs for supplying a reference (reference) voltage, as well as digital outputs for issuing a code corresponding to the current value of the analog signal (Fig. 15).
Often the ADC chip also has an input for supplying a clock signal CLK, an enable signal CS and a signal indicating the readiness of the output digital code RDY. The microcircuit is supplied with one or two supply voltages and a common wire.
Rice. 15. ADC chip
Currently, many different methods of analog-to-digital conversion have been developed, for example, methods of sequential counting, bitwise balancing, double integration; with voltage to frequency conversion, parallel conversion. Converter circuits built on the basis of the listed methods may or may not contain a DAC.
Scheme Serial counting ADC is shown in Fig.16, a. As can be seen from the graph, the conversion time of this type is variable and depends on the input analog signal, however, the operating cycle of the entire device is constant and equal to,, where T0- period of the reference pulse generator, n-bit capacity of the counter and the ADC itself. The operation of such an ADC does not require synchronization, which greatly simplifies the construction of a control circuit. From the moment the “Start” signal arrives at the ADC output with a frequency of 1/ Tp digital codes of the conversion result change (frequency 1/ Tp- parameter that determines the maximum permissible tracking frequency of the input signal).
The most important characteristics of ADCs are their accuracy, speed and cost. Accuracy is related to the ADC bit depth. The fact is that the analog signal at the ADC input turns into a binary digital code at the output, i.e. An ADC is an analog signal magnitude meter accurate to half the least significant digit. Therefore, say, an 8-bit ADC provides conversion accuracy no higher than the maximum possible value. A 10-bit ADC provides a conversion accuracy no higher than , a 14-bit ADC provides an accuracy no higher than , and a 16-bit ADC provides no higher accuracy 
from the maximum possible value.
The performance of an ADC is characterized by the period of time required to perform one conversion, or the number of possible conversions per unit of time (conversion frequency).
Typically, the higher the accuracy (bit capacity) of an ADC, the lower its performance, and the higher the accuracy and performance, the higher the cost of the ADC. Therefore, when designing a smart sensor, it is necessary to select its parameters correctly.
ADCs are now built according to different circuit principles and are produced in the form of both individual integrated circuits and as units of more complex circuits (for example, microcontrollers).
Digital-to-analog converter. .
These devices are “conductors” between analog And digital worlds of electricity.
The bottom line is that sensors, motors, lights and many other devices use analog signal, that is, for example, a voltage with a level from 0V to 12V, while digital FPGAs, microcontrollers and chips require constant voltage levels, for example 0V and 5V, representing logical 0 and 1 respectively.
Example 1. DAC
Let's imagine that we are given the task of controlling the brightness of an LED:
- 10 levels (gradations) LED brightness
- maximum voltage via LED 9V
- controlled using a microcontroller and two buttons “+1 brightness level”, “-1 brightness level”
So, the LED operates at a voltage from 0 to 9V. It’s not hard to guess that 10 gradations of brightness are 10 voltage levels that we apply to the LED - 0V, 1V, ..., 9V
The microcontroller outputs voltage either 0V or 5V. But not 1B, 3B, 4B or 9B. But the microcontroller has a lot logical pins that we can connect to DAC y and convert logic in analog signal.
U digital-to-analog converter there are, for example, 4 input pins for connecting logic signals and 2 pins for output analog voltage from 0 to 15V - terminals “+” and “-“.
Here's your job DAC a: when we feed on all 4 legs logical 1, then the voltage level analog output signal is maximum( 15V in our case), when we supply 0 - minimal, that is 0V
Now comes the fun part. At each input pin DAC and there is a “weight” for the output signal. For example, the top pin “weighs” 8V (that is, if we apply logical 1 only to the 1st pin, then we will get 8V at the output), the next one below is 4B, the next one is 2B, and the last one below is 1B. Now add these numbers and you get 15V.
We need to get levels 0B, 1B, 2B, 3B, 4B, 5B, 6B, 7B, 8B and 9B.
This means that the inputs DAC you need to submit codes in accordance with the following table
| Voltage at analog exit | 0V | 1B | 2B | 3B | 4B | 5V | 6V | 7V | 8V | 9V |
| Input 1, weight 8V | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| Input 1, weight 4V | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 |
| Input 1, weight 2V | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| Input 1, weight 1V | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
Buttons “+1 brightness level”, “-1 brightness level” will add or subtract 1 unit from the output digital microcontroller signal. This signal will be sent to the inputs DAC. Exit DAC will be connected to the LED. Mission accomplished!
Example 2. ADC
Analog-to-digital converterworks on the reverse principle. We apply a changing voltage level to the input, and at the output we get logic (bits) +5V and 0V, or logical 1 and 0
Let's set the task of taking readings from the temperature sensor:
- the sensor shows the temperature from 0C to 30C
- at 0C the sensor outputs 0V, at 30C it outputs 15V
- the signal must be received by the microcontroller in digital form (logical 1 and 0, voltage +5V and 0V)
ADC has two input pins for receiving an analog voltage signal, for example, from 0 to 15V and, in our case, 4 pins for output digital logic signal. That is, a four-bit parallel code signal.
We connect the output from our sensor to the analog input ADC, and the digital four-bit output from ADC connect to the microcontroller. And we already receive readings from the sensor in digital form on the microphone. The data in the process will correspond to the table below.
APC- This A tax C digital P converter In English ADC (A tax-to- D digital C onverter). That is, a special device that converts it to digital.
ADC is used in digital technology. In particular, almost all modern ones have a built-in ADC.
As you probably already know, microprocessors (like computer processors) understand nothing more than binary numbers. It follows that the microprocessor (which is the basis of any microcontroller) cannot directly process an analog signal.
A microcontroller's ADC typically only measures voltage in the range from 0 to the microcontroller's supply voltage.
ADC characteristics
There are different ADCs with different characteristics. The main characteristic is the bit depth. However, there are others. For example, the type of analog signal that can be connected to the ADC input.
All these characteristics are described in the documentation for the ADC (if it is designed as a separate chip) or in the documentation for the microcontroller (if the ADC is built into the microcontroller).
In addition to the bit capacity, which we have already discussed, we can name several more basic characteristics.
Least significant bit (LSB). This is the smallest input voltage that can be measured by the ADC. Determined by the formula:
1 LSB = Uop / 2 R
Where Uop is the reference voltage (indicated in the ADC specifications). For example, with a reference voltage of 1 V and a bit width of 8 bits, we get:
1 LSB = 1 / 2 8 = 1 / 256 = 0.004 V
Integral Non-linearity - integral non-linearity of the ADC output code. It is clear that any transformation introduces distortions. And this characteristic determines the nonlinearity of the output value, that is, the deviation of the ADC output value from the ideal linear value. This characteristic is measured in LSB.
In other words, this characteristic determines how “curve” a line on the output signal graph can be, which ideally should be straight (see figure).
Absolute precision. Also measured in LSB. In other words, this is measurement error. For example, if this characteristic is +/- 2 LSB, and LSB = 0.05 V, then this means that the measurement error can reach +/- 2 * 0.05 = +/- 0.1 V.
The ADC also has other characteristics. But for starters, this is more than enough.
ADC connection
Let me remind you that there are basically two types: current and voltage. In addition, signals can have a standard range of values, and a non-standard one. Standard ranges of analog signal values are described in GOSTs (for example, GOST 26.011-80 and GOST R 51841-2001). But, if your device uses some kind of homemade sensor, then the signal may differ from the standard one (although I advise you to choose some standard signal in any case - for compatibility with standard sensors and other devices).
ADCs primarily measure voltage.
I’ll try to talk about (in general terms) how to connect an analog sensor to an ADC and then how to understand the values that the ADC will produce.
So, let's say that we want to measure temperature in the range of -40...+50 degrees using a special sensor with a standard output of 0...1V. Let's say that we have a sensor that can measure temperature in the range -50...+150 degrees.
If a temperature sensor has a standard output, then, as a rule, the voltage (or current) at the sensor output varies linearly. That is, we can easily determine what voltage will be at the output of the sensor at a given temperature.
What is linear law? This is when the range of values on the graph looks like a straight line (see figure). Knowing that a temperature from -50 to +150 gives a voltage at the output of the sensor that varies according to a linear law, we, as I already said, can calculate this voltage for any temperature value in a given range.
In general, in order to convert a temperature range into a voltage range in our case, we need to somehow compare two scales, one of which is a temperature range, and the other is a voltage range.
You can determine the voltage by temperature visually using the graph (see figure above). But the microcontroller doesn’t have eyes (although, of course, you can have fun and create a device on a microcontroller that can recognize images and determine the temperature value from the voltage on the graph, but let’s leave this entertainment to fans of robotics)))
First of all, we determine the temperature range. We have it from -50 to 150, that is, 201 degrees (don’t forget about zero).
And the range of measured voltages is from 0 to 1 V.
That is, we need to squeeze the range from 0 to 200 (201 in total) into the scale from 0 to 1.
Finding the conversion factor:
K = U / Td = 1 / 200 = 0.005 (1)
That is, when the temperature changes by 1 degree, the voltage at the sensor output will change by 0.005 V. Here Td is the temperature range. Not the temperature values, but the number of units of measurement (in our case, degrees) on the temperature scale, compared with the voltage scale (we do not take zero into account for simplicity, since there is also a zero in the voltage range).
We check the characteristics of the ADC of the microcontroller that we plan to use. The LSB value should not be more than K (more than 0.005 in our case, more precisely, this is acceptable if you are satisfied with an error of more than 1 unit of measurement - more than 1 degree in our case).
Essentially, K is volts per degree, that is, this is how we found out by what value the voltage changes when the temperature changes by 1 degree.
Now we have all the necessary data to convert the ADC output value into a temperature value in the microcontroller program.
We remember that we shifted the temperature range by 50 degrees. This must be taken into account when converting the ADC output value into temperature.
And the formula will be like this:
T = (U / K) - 50 (2)
For example, if the ADC output is 0.5 V, then
T = (U / K) - 50 = (0.5 / 0.005) - 50 = 100 - 50 = 50 degrees
Now we need to determine the discreteness, that is, the desired measurement accuracy.
As you remember, the absolute error can be several LSB. In addition, there is also nonlinear distortion, which is usually equal to 0.5 LSB. That is, the total error of the ADC can reach 2-3 LSB.
In our case it is:
Up = 3 LSB * 0.005 = 0.015 V
Or 3 degrees.
If in your case everything is not so smooth, then again we use the formula derived from (1):
Td = Up / K = 0.015 / 0.005 = 3
If an error of 3 degrees suits you, then you don’t have to change anything. Well, if not, then you will have to select an ADC with a higher bit capacity or find another sensor (with a different temperature range or with a different output voltage).
For example, if you manage to find a sensor with a range of -40...+50, as we wanted, and with the same output 0...1V, then
K = 1 / 90 = 0.01
Then the absolute error will be:
Td = Up / K = 0.015 / 0.01 = 1.5 degrees.
This is already more or less acceptable. Well, if you have a sensor with an output of 0...5V (this is also a standard signal), then
K = 5 / 90 = 0.05
And the absolute error will be:
Td = Up / K = 0.015 / 0.05 = 0.3 degrees.
This is no good at all.
But! Remember that we are only looking at ADC error here. But the sensor itself also has an error that must also be taken into account.
But all this is already from the field of electronics and metrology, so I will finish this article here.
And at the end, just in case, I will give the formula for converting temperature back into voltage:
U = K * (Tv + 50) = 0.005 * (150 + 50) = 1
P.S. I wrote this article after a hard day at work, so if I made a mistake somewhere, I apologize)))
This article discusses the main issues regarding the operating principle of various types of ADCs. At the same time, some important theoretical calculations regarding the mathematical description of analog-to-digital conversion were left outside the scope of the article, but links are provided where the interested reader can find a more in-depth consideration of the theoretical aspects of the operation of the ADC. Thus, the article concerns itself more with understanding the general principles of operation of ADCs than with a theoretical analysis of their operation.
Introduction
As a starting point, let's define analog-to-digital conversion. Analog-to-digital conversion is the process of converting an input physical quantity into its numerical representation. An analog-to-digital converter is a device that performs such a conversion. Formally, the input value of the ADC can be any physical quantity - voltage, current, resistance, capacitance, pulse repetition rate, shaft rotation angle, etc. However, for definiteness, in what follows, by ADC we will understand exclusively voltage-to-code converters.
The concept of analog-to-digital conversion is closely related to the concept of measurement. By measurement we mean the process of comparing the measured value with some standard; with analog-to-digital conversion, the input value is compared with some reference value (usually a reference voltage). Thus, analog-to-digital conversion can be considered as a measurement of the value of the input signal, and all the concepts of metrology, such as measurement errors, apply to it.
Main characteristics of the ADC
The ADC has many characteristics, the main ones being conversion frequency and bit depth. The conversion frequency is usually expressed in samples per second (SPS), and the bit depth is in bits. Modern ADCs can have a bit width of up to 24 bits and a conversion speed of up to GSPS units (of course, not at the same time). The higher the speed and bit capacity, the more difficult it is to obtain the required characteristics, the more expensive and complex the converter. Conversion speed and bit depth are related to each other in a certain way, and we can increase the effective conversion bit depth by sacrificing speed.
Types of ADCs
There are many types of ADCs, but for the purposes of this article we will limit ourselves to considering only the following types:
- Parallel conversion ADC (direct conversion, flash ADC)
- Successive approximation ADC (SAR ADC)
- delta-sigma ADC (charge-balanced ADC)
ADCs of direct (parallel) conversion have the highest speed and lowest bit depth. For example, the TLC5540 parallel ADC from Texas Instruments has a speed of 40MSPS with only 8 bits. ADCs of this type can have a conversion speed of up to 1 GSPS. It can be noted here that pipelined ADCs have even greater speed, but they are a combination of several ADCs with lower speed and their consideration is beyond the scope of this article.
The middle niche in the bit-rate-speed series is occupied by successive approximation ADCs. Typical values are 12-18 bits with a conversion frequency of 100KSPS-1MSPS.
The highest accuracy is achieved by sigma-delta ADCs with a bit width of up to 24 bits inclusive and a speed from SPS units to KSPS units.
Another type of ADC that has found use in the recent past is the integrating ADC. Integrating ADCs have now been almost completely replaced by other types of ADCs, but can be found in older measuring instruments.
Direct conversion ADC
Direct conversion ADCs became widespread in the 1960s and 1970s, and began to be produced as integrated circuits in the 1980s. They are often used as part of “pipeline” ADCs (not discussed in this article), and have a capacity of 6-8 bits at a speed of up to 1 GSPS.
The direct conversion ADC architecture is shown in Fig. 1
Rice. 1. Block diagram of direct conversion ADC
The principle of operation of the ADC is extremely simple: the input signal is supplied simultaneously to all “positive” inputs of the comparators, and a series of voltages are supplied to the “negative” ones, obtained from the reference voltage by dividing them with resistors R. For the circuit in Fig. 1 this row will be like this: (1/16, 3/16, 5/16, 7/16, 9/16, 11/16, 13/16) Uref, where Uref is the ADC reference voltage.
Let a voltage equal to 1/2 Uref be applied to the ADC input. Then the first 4 comparators will work (if you count from below), and logical ones will appear at their outputs. The priority encoder will form a binary code from a “column” of ones, which is captured in the output register.
Now the advantages and disadvantages of such a converter become clear. All comparators operate in parallel, the delay time of the circuit is equal to the delay time in one comparator plus the delay time in the encoder. The comparator and encoder can be made very fast, as a result the whole circuit has very high performance.
But to obtain N bits, 2^N comparators are needed (and the complexity of the encoder also grows as 2^N). Scheme in Fig. 1. contains 8 comparators and has 3 bits, to obtain 8 bits you need 256 comparators, for 10 bits - 1024 comparators, for a 24-bit ADC they would need over 16 million. However, the technology has not yet reached such heights.
successive approximation ADC
A successive approximation register (SAR) analog-to-digital converter measures the magnitude of the input signal by performing a series of sequential “weightings,” that is, comparisons of the input voltage value with a series of values generated as follows:
1. in the first step, the output of the built-in digital-to-analog converter is set to a value equal to 1/2Uref (hereinafter we assume that the signal is in the interval (0 – Uref).
2. if the signal is greater than this value, then it is compared with the voltage lying in the middle of the remaining interval, i.e., in this case, 3/4Uref. If the signal is less than the set level, then the next comparison will be made with less than half of the remaining interval (i.e. with a level of 1/4Uref).
3. Step 2 is repeated N times. Thus, N comparisons (“weightings”) produce N bits of the result.
Rice. 2. Block diagram of a successive approximation ADC.
Thus, the successive approximation ADC consists of the following nodes:
1. Comparator. It compares the input value and the current value of the “weighting” voltage (in Fig. 2, indicated by a triangle).
2. Digital to Analog Converter (DAC). It generates a voltage “weight” based on the digital code received at the input.
3. Successive Approximation Register (SAR). It implements a successive approximation algorithm, generating the current value of the code fed to the DAC input. The entire ADC architecture is named after it.
4. Sample/Hold scheme (Sample/Hold, S/H). For the operation of this ADC, it is fundamentally important that the input voltage remains constant throughout the conversion cycle. However, “real” signals tend to change over time. The sample-and-hold circuit “remembers” the current value of the analog signal and keeps it unchanged throughout the entire operating cycle of the device.
The advantage of the device is the relatively high conversion speed: the conversion time of an N-bit ADC is N clock cycles. The conversion accuracy is limited by the accuracy of the internal DAC and can be 16-18 bits (24-bit SAR ADCs have now begun to appear, for example, AD7766 and AD7767).
Delta-Sigma ADC
Finally, the most interesting type of ADC is the sigma-delta ADC, sometimes called charge-balanced ADC in the literature. The block diagram of the sigma-delta ADC is shown in Fig. 3.
Fig.3. Block diagram of a sigma-delta ADC.
The operating principle of this ADC is somewhat more complex than that of other types of ADC. Its essence is that the input voltage is compared with the voltage value accumulated by the integrator. Pulses of positive or negative polarity are supplied to the integrator input, depending on the result of the comparison. Thus, this ADC is a simple tracking system: the voltage at the integrator output “tracks” the input voltage (Fig. 4). The result of this circuit is a stream of zeros and ones at the output of the comparator, which is then passed through a digital low-pass filter, resulting in an N-bit result. LPF in Fig. 3. Combined with a “decimator”, a device that reduces the frequency of readings by “decimating” them.
Rice. 4. Sigma-delta ADC as a tracking system
For the sake of rigor of presentation, it must be said that in Fig. Figure 3 shows a block diagram of a first order sigma-delta ADC. The second order sigma-delta ADC has two integrators and two feedback loops, but will not be discussed here. Those interested in this topic can refer to.
In Fig. Figure 5 shows the signals in the ADC at zero input level (top) and at Vref/2 level (bottom).
Rice. 5. Signals in the ADC at different input signal levels.
Now, without delving into complex mathematical analysis, let's try to understand why sigma-delta ADCs have a very low noise floor.
Let's consider the block diagram of the sigma-delta modulator shown in Fig. 3, and present it in this form (Fig. 6):
Rice. 6. Block diagram of a sigma-delta modulator
Here the comparator is represented as an adder that adds the continuous wanted signal and the quantization noise.
Let the integrator have a transfer function 1/s. Then, representing the useful signal as X(s), the output of the sigma-delta modulator as Y(s), and the quantization noise as E(s), we obtain the ADC transfer function:
Y(s) = X(s)/(s+1) + E(s)s/(s+1)
That is, in fact, the sigma-delta modulator is a low-pass filter (1/(s+1)) for the useful signal, and a high-pass filter (s/(s+1)) for noise, both filters having the same cutoff frequency. Noise concentrated in the high-frequency region of the spectrum is easily removed by a digital low-pass filter, which is located after the modulator.
Rice. 7. The phenomenon of “displacement” of noise into the high-frequency part of the spectrum
However, it should be understood that this is an extremely simplified explanation of the phenomenon of noise shaping in a sigma-delta ADC.
So, the main advantage of the sigma-delta ADC is its high accuracy, due to the extremely low level of its own noise. However, to achieve high accuracy, it is necessary that the cutoff frequency of the digital filter be as low as possible, many times less than the operating frequency of the sigma-delta modulator. Therefore, sigma-delta ADCs have low conversion speed.
They can be used in audio engineering, but their main use is in industrial automation for converting sensor signals, in measuring instruments, and in other applications where high accuracy is required. but high speed is not required.
A little history
The oldest mention of an ADC in history is probably the Paul M. Rainey patent, "Facsimile Telegraph System," U.S. Patent 1,608,527, Filed July 20, 1921, Issued November 30, 1926. The device depicted in the patent is actually a 5-bit direct conversion ADC.
Rice. 8. First patent for ADC
Rice. 9. Direct conversion ADC (1975)
The device shown in the figure is a direct conversion ADC MOD-4100 manufactured by Computer Labs, manufactured in 1975, assembled using discrete comparators. There are 16 comparators (they are located in a semicircle in order to equalize the signal propagation delay to each comparator), therefore, the ADC has a width of only 4 bits. Conversion speed 100 MSPS, power consumption 14 watts.
The following figure shows an advanced version of the direct conversion ADC.
Rice. 10. Direct conversion ADC (1970)
The 1970 VHS-630, manufactured by Computer Labs, contained 64 comparators, was 6-bit, 30MSPS, and consumed 100 watts (the 1975 version VHS-675 had 75 MSPS and consumed 130 watts).
Literature
W. Kester. ADC Architectures I: The Flash Converter. Analog Devices, MT-020 Tutorial.
