► Image source: Pixabay.com
Written by | Wu Jinyuan (National Accelerator Laboratory of Fermi, United States)
Editor | Chen Xiaoxue
Intellectual For a better intellectual life ID: The-Intellectual
●●●
"The digitalization of analog quantities sounds very high-end, but the related concepts have existed for a long time." I just said half of this sentence, a young classmate raised his hand: "Teacher, I don't care about this now. You should talk about something practical. I'm going to propose to my girlfriend soon and want to buy a diamond ring. I want to know how many carats to buy, and what's going on with carats."
carats are derived from beans from beans. They weigh very evenly, so they are used by merchants to measure the weight of gems. You see, weight is originally an analog quantity, but it can be changed to a digital quantity by comparing it with beans, and a spiritual element in analog-to-digital conversion is comparison. Of course, you must not compare with others when buying a ring. You should do whatever you can. As long as both of you like it, it doesn’t matter how big or small it is. Don't worry, isn't there a saying that children who learn piano will not become bad? Similarly, students who read "Intellectuals" every day are not vulgar.
is just yourself, don’t pull out the word “pul” of “carat”. One carat is 200 mg, with less "pul" and a 5-fold increase in weight, which is difficult for ordinary people to afford. Okay, go buy a diamond ring. Students who don’t propose marriage will continue to attend classes today.
What we are going to talk about today is the digitization of physical quantity .
Scientific research cannot be separated from scientific observation. The goal of scientific observation can be a natural phenomenon or a controlled experimental phenomenon.
In the era when computers did not appear, people used instruments to measure the physical quantity presented by observations and recorded it on the work log book. Sometimes, some photos will be taken, printed out, and posted in the book. Now, most of these tasks can be done by computers.
If you want to transmit the values of physical quantities and their changes to a computer, an indispensable "artifact" is a digital device.
In fact, it is not only scientific research work, but also digital devices that we usually call and take photos. Voice or light intensity information is originally analog quantity, and they must be turned into digital quantity through digital devices, so that they can be processed and stored and transmitted into the mobile phone.
digital devices include two major categories. The first category is analog to digital converter (ADC), and the other category is time to digital converter (TDC).
ADC's function is to convert the input voltage amplitude or the amount of charge accumulated over a period of time into digital quantities. Figure 1 is a schematic diagram of the working principle of ADC.
► Figure 1: Schematic diagram of ADC working principle
The conversion process of modern mainstream ADC devices includes two main steps: sampling and digitization.
First, the ADC device records the instantaneous amplitude of the continuously changing input voltage onto a capacitor through the analog switching device, so that it maintains the voltage value obtained at the instantaneous sampling in a short time. Then, the ADC device uses circuits such as comparator array to convert the amplitude of the sampled voltage into binary numbers composed of two logical levels: 0 and 1, and finally outputs it to the later stage microprocessor and other logic circuits for further processing. This type of ADC is usually driven by a clock pulse signal, and every once in a while, new samples are taken and new data is produced. The function of
TDC is to convert the arrival time of the input signal into a digital quantity, and its working principle is shown in Figure 2.
► Figure 2: Schematic diagram of TDC working principle
In many cases, TDC is used in conjunction with a comparator circuit. The comparator compares the input voltage to a fixed threshold voltage, and outputs two different logic levels, high or low, when the input voltage is higher or lower than the threshold voltage. Such a logic pulse is sent to the TDC device, in which the arrival time of the logic pulse is measured through a timer and turned into a set of digital signals to output it.
Of course, time is also an analog quantity, so strictly speaking, TDC is also an ADC.However, due to the particularity of time measurement, we summarize these two digital devices into two different types.
Since most physical quantities, such as force, pressure, temperature, brightness, etc., can be simulated by converting the device to voltage, the first part of the article will focus on the properties of the ADC. TDC also has many special applications in various physics experiments, and it is easier to implement through logical electronic circuits. We will also introduce it in the second part of the article.
01 Analog-to-digital conversion
analog-to-digital conversion digitization, the main parameters are reflected in both horizontal and vertical directions.
in the vertical direction refers to dividing the full-scale voltage (usually 1V or 2V) into many parts. If an ADC is 8 bits, this means that the input voltage will eventually be converted into an 8 bit number. That is to say, the full-scale voltage will be divided into about 256 parts. Similarly, 9 bits are divided into 512 parts, 10 bits are divided into 1024 parts, etc. The bit number of the ADC directly affects its measurement accuracy.
In the horizontal direction, the sampling rate of the ADC is an important indicator.
For some physical quantities that change slowly, such as the temperature, humidity, pressure, etc. of the air in the room, one sampling point per second or even one sampling point ten minutes is enough.
Our mobile phones are usually equipped with sensors such as acceleration, angular velocity, magnetic field strength, etc. Due to the acceleration sensor, when we turn the phone over, the mobile phone will automatically turn the displayed photos or text over. Thanks to the angular velocity sensor, our phones can easily transform into virtual reality displays. With the magnetic field sensor, we can install a compass on our mobile phones, so that we can find the North when we go out. The sampling rate of these sensors is about 10 to 100 points per second, as shown in Figure 3.
► Figure 3: Some sensors in the mobile phone and the corresponding sampling rate
digital cameras When shooting videos, the sampling rate of each pixel is usually 30 points per second. When shooting slow motion lenses, 120 or 240 points per second are sampled.
In mobile phones or other digital voice transmission systems, the sampling speed is at least 8000 points per second.
. In many scientific experiments, we need faster sampling speeds. For example, in a free electron laser imaging system, the sampling speed of each pixel needs to reach the order of 5 MSPS (MSPS means 1 million sampling points per second).
The digital oscilloscope , which is commonly used in the laboratory, has a sampling rate of mostly in the range of 1-10 GSPS (GSPS means 1 billion sampling points per second).
here is a special reminder that the amount of raw data generated by ADC is very large. For example, when our oscilloscope uses 1 GSPS to sample and each sampling point generates 8 bits of data, 1 GB of data can be generated per second. If the data is not compressed, it only takes 8 seconds to fill an 8 GB memory card. (Of course, most memory cards are not so fast at all.) Therefore, in most applications, the data generated by the ADC often requires the use of additional trigger circuits to intercept only useful data. Another more commonly used solution is to compress the ADC data, which can be lossy or lossless. After compression, the changes in all signals are relatively slow, and the data containing less information in the time period can be expressed only by a relatively small number of bits, so the storage space occupied will be reduced accordingly.
02 Time conversion
Time conversion (TDC) function is to convert the arrival time of an pulse signal or the time interval between two pulse signals into numbers.
Let’s give an example here to illustrate the application of time conversion. As shown in Figure 4, when a high-energy particle flies through several detector units HA, HB, HC and HD in turn, these detector units generate a set of pulses. The time interval between these pulse signals reflects the speed of the particles' flight.
► Figure 4: Schematic diagram of different detection units of charged particles flying through the detector
For example, the moment when the particle hits HA is TA, and the moment when the HD is hit is TD. Based on the position of the particle hit on the detection unit, we can calculate the length of the particle track.With the length and time difference, we can calculate the velocity of the particles.
When the momentum of the particle is fixed, the larger the mass, the slower the speed of the particle flying. The momentum of a particle can be calculated based on the radius of curvature when the particle deflects over the magnet M. In the case of known momentum, its static mass can be calculated based on the velocity of the charged particles. After obtaining the static mass and comparing it with the static mass of known particles, we can know what charged particles are flying. This is a bit similar to Archimedes' determination of the specific gravity of the crown and then compared with the specific gravity of the known materials, you can know whether the crown is made of pure gold.
hour conversion is suitable for use with pure high-speed digital logic circuit devices, especially with field programmable gate circuit arrays (FPGAs), and can be integrated into one chip with other functions of data acquisition and transmission, making it very convenient to use. Since
TDC is very convenient to implement, it can often be used to replace ADCs with low sampling rates. For example, in Figure 5, VIN is the input signal to be digitized, the required sampling frequency is 2MSPS, and VR is a sawtooth wave reference signal we generate, and its period is 500 nanoseconds long.
► Figure 5: Schematic diagram of the principle of measuring voltage amplitude with TDC
When VR passes through VIN, a comparator circuit can obtain a jump of logic level. In a stable operating state, the rising slope or slope of the reference voltage is known, for example (2V/400 ns). As long as we use TDC to measure the time T1, T2, etc. of the comparator output jump, we can know the height V1, V2, etc. of VIN at this moment. For example, when we measure T1=150ns, we can calculate that V1 = 150* (2/400) = 0.75 (V).
03 Traps and misunderstandings that are easy to fall into
When we design experimental devices, we often focus on the ADC device itself. However, a place that must not be ignored is before the ADC. In other words, what kind of signal we need to send to the ADC is an important prerequisite for designing a good system. The signal sent to the ADC by
is usually amplified by an amplifier . For amplifier circuits, we intuitively hope that they will be faster and have lower noise. However, in practical applications, the faster the speed, the lower the noise, the better. This requires us to process the input signal from the horizontal and vertical directions of the time axis and the voltage axis.
is on the timeline, as mentioned earlier, the ADC is sampled every once in a while. Therefore, it is impossible for us to know the overall change of voltage. Fortunately, according to the sampling law, if the input signal bandwidth is limited, assuming that there is no frequency component exceeding f, as long as the sampling frequency is higher than 2f, we can completely reconstruct the original signal based on the discrete values obtained by sampling.
In turn, when the sampling frequency of the ADC is selected as f, the preamplifier circuit must limit the bandwidth of the signal to within f/2. If the bandwidth of the predecessor is too wide, it will increase the noise contained in the data. The limitation of the bandwidth of the preamplifier by the
sampling law can be reflected in the parameters of our commonly used digital oscilloscopes. We can often see two data shown in Figure 6 on the panel of the oscilloscope. In these two data, 5GS/s is the sampling rate, and the other is 500 MHz is the bandwidth of the amplifier. Apparently the bandwidth is less than half of the sampling rate.
► Figure 6: The annotation of the oscilloscope panel
is on the voltage axis. In contrast to our usual intuition, there must be a certain amount of noise in the input signal so that the ADC can achieve the best operating characteristics. This pre-processing is called dithering, which the author believes can be translated as "adding tremor" (when this pre-processing is used in two-dimensional images, it is often called "jitter display").
In many instruments containing mechanical transmission mechanisms, such as the air pressure gauge shown in Figure 7, the transmission mechanism will be "stricken" when the input physical quantity changes slowly. To get the correct reading, you can tap it gently and add a little tremor to the steady input change. This example shows that external noise can sometimes help us obtain more accurate measurement results.
► Figure 7: Schematic diagram of mechanical tremor
For electrical measurements, we discuss the tremor of the ADC input signal through an example. Consider a high-performance ADC, if the digital quantity 52 is output when the input voltage is between 51.5 and 52.5 millivolts, and when the input voltage is between 52.5 and 53.5 millivolts, the digital quantity 53 is output. When an input voltage changes steadily and slowly, we get two digital outputs 52 and 53, and the output digital quantity is shown in the light blue curve in Figure 8.
► Figure 8: ADC response to slow changing input voltage
According to these two numbers, we can only get a rough impression of the original input waveform, that is, the middle is higher and the surrounding is lower, but we cannot know its exact shape.
Now we add a very small random noise to the input signal, and the superimposed signal is shown in the yellow curve in Figure 9. This superimposed signal constantly skips the threshold of 52.5 millivolts up and down, causing the output numbers to change back and forth between 52 and 53.
► Figure 9: The ADC response after the input signal is superimposed with appropriate noise
, which jumps back and forth in this way, obviously carries more information. We can imagine that the higher the input voltage, the probability of the output number being 53 will be higher. When we add and average each sample point with the data of several surrounding sample points, we obtain a sliding average value. It can be seen that this sliding average value better reflects the original input waveform, as shown in the thick line in the figure above.
In a system, adding noise can help us get more accurate results, which sounds a bit counterintuitive, but it is absolutely true. This method has been used in digital audio technology for many years.
Generally, most of the input circuits of the ADC are shown in Figure 10.
► Figure 10: ADC input circuit
As mentioned earlier, when designing the input preprocessing circuit of the ADC, remember to check: (1) band should not be too wide, that is, the amplifier driving the ADC should be a low-pass filter. (2) There must be appropriate noise.
In modern scientific experiments, most of our experimental observation data are generated by digital systems. The quality of a digital system directly affects the quality of the data we obtain, and even affects the success or failure of the experiment. Therefore, every experimental scientist should pay enough attention to this.
plate-making editor: Huang Yuying |
Reprinting and use of this page without written permission is prohibited and reprinting is prohibited without written permission. Please contact the authorization
Intellectual For a better intellectual life ID: The-Intellectual
