How to understand the half digit of a 5.5-digit multimeter

How do you understand the half-digit principle of the multimeter? Which article has a good explanation of this? I asked some people before, but the explanations still confused me. I can only ask a master like you:-) I hope you can give me some advice!

Master Qian:

Regarding the number of digits of a multimeter, especially the half-digit, the following is a page from a training document. You will understand it after reading it. In short, if the highest digit of the reading cannot reach the full scale of 0~9, the highest digit can only be considered a fractional digit. If it is collectively called, it can be called a half digit. If it is more specific, there are 1/2 digit, 2/3 digit, 4/5 digit,... 8/9 digit. For example, the 4 1/2 digit F87V in the figure, 4 4/5 digit F187, F189, can all be collectively called 4 and a half digits, but in fact, there is still a distinction in accuracy. There is actually a count number to describe the number of digits of a multimeter more accurately, which is the indicator in the reading column in the figure below. For example, the count number of F187 is 50000, and the count number of F87V is 20000. The count number of our multimeter is 240000, that is, from 000000 to 239999.

In addition, the number of digits of a multimeter is a benchmark indicator of the multimeter, just like the bandwidth of an oscilloscope. Whether it is a 5.5-digit or 6.5-digit multimeter does not depend on how many digits it displays, but on whether the actual effective digits can be achieved. It is a comprehensive indicator that combines the ADC effective resolution implemented in the multimeter, the machine's body noise, linearity, various temperature drifts, various calibration methods, and even the traceability benchmark. Generally, the easiest way to intuitively judge is that when the input is short-circuited, the panel display must only allow the last digit to jump. If the last two digits jump, then it is obvious that there is no point in displaying the last digit.

In terms of application, multimeter measurement belongs to low-frequency and precision measurement. The frequency range of the measured signal is generally much lower than that of an oscilloscope, mainly DC measurement, and the AC measurement frequency range is generally below 1Mhz. However, the accuracy is several orders of magnitude higher than that of an oscilloscope. In terms of core components, general desktop multimeters use 24-bit ADC, which is much higher than the number of bits of an oscilloscope, but the sampling rate is much lower.

      

 

Wang Jinjin:

Sorry, I am a bit stupid and like to ask some low-level questions. I have just started to learn about multimeters and I have a lot of questions.

   1. What is the relationship between the counts you mentioned and the number of ADC bits?   

   2. Is the ADC bit count 24 bits, regardless of whether it is a multimeter with a bit count of 24 and a half? What is the specific sampling rate of the ADC?  

   3. 0.0000004% accuracy, this traceability process is terrifying? Is there any basic knowledge about calibration?

   4. There is an uncertain digit, which should be the last digit after the decimal point, just like a millimeter ruler. Why is the highest integer digit uncertain, half a digit? How is this related to the concept of LSB of ADC?   

   5. How to calculate whether it is 1/2 or 4/5? 

Master Qian:

Haha, your question is not simple at all. It may seem "low-level", but it is actually the crux and essence of the problem. If you understand it thoroughly, it will not be difficult to understand how to make the product. I will try to answer it and see if I can explain it clearly. (See the blue reply)

1. What is the relationship between the counts you mentioned and the number of ADC bits?

The count number is an indicator of the entire device. For example, our 5.5-digit count is 240,000, which basically means an effective resolution. That is to say, for a typical voltage range, such as the 2V range, considering the over-range, the range can actually be measured up to 2.39999V, that is, each count corresponds to 0.00001V, or 10uV. That is to say, the count number is how many parts a full range can be divided into. It is also 5.5 digits. If it is 120,000 counts, the range is still 0~2.4V. Obviously, each part is 20uV, which means that the effective resolution can only reach 20uV. It is also 5.5 digits. There are specific differences in the specifications of these two multimeters, so the count is more precise than the number of digits.

The number of ADC bits refers to the effective bit width of the ADC, the core device of the multimeter. However, the ADC is only one link in the product signal chain. The entire signal chain also includes the amplification and attenuation of the previous stage, multi-way switches and other conditioning links. These links will introduce noise, which greatly reduces the overall effective number of bits of the entire product measurement chain. For example, a 5.5-digit multimeter actually corresponds to 18.9 effective binary bits, but even a 24-bit ADC may not be able to achieve a 5.5-digit effect if the noise in other parts is very large. But obviously, if you use a general oscilloscope's 8-bit ADC to do it, it is theoretically impossible to make a 5.5-digit multimeter. This is the relationship between the whole and the part, and the relationship between system indicators and device indicators.

 

2. Is the ADC bit count 24 bits, regardless of whether it is a multimeter with a bit count of 24 and a half? What is the specific sampling rate of the ADC?  

There is something wrong with my statement. I am mainly talking about 5.5-digit or 6.5-digit desktop meters, not handheld multimeters, because handheld meters are usually 3.5-digit or 4.5-digit at most. A 14-digit or 16-digit meter is usually enough, and it is usually not a discrete device solution, and it can be done with a soc. The ADC of a general multimeter uses a sigma-delta ADC. This ADC is different from the general SAR high-speed ADC. It uses the so-called oversampling principle. The sampling rate and data generation rate are very different. The sampling rate of this ADC is generally referred to as the data rate, which is usually only a few K at the fastest. For example, AD7190 has a rate of 4.8Khz when it has 19 effective bits, and a maximum of 7~8hz when it has 24 bits.

 

3. 0.0000004% accuracy, this traceability process is terrifying? Is there any basic knowledge about calibration?

This precision is too high, maybe not this %, 7.5 or 8.5 digits of precision. Currently, the highest in the industry should be the 8.5 digit multimeter, which is generally used by those metrology departments or laboratories. The traceability may be based on the national standard. For our 5 or 6 digit products, we can use the calibrator of F company, because its products are theoretically calibrated to higher standards.

4. There is an uncertain digit, which should be the last digit after the decimal point, just like a millimeter ruler. Why is the highest integer digit uncertain, half a digit? How is this related to the concept of LSB of ADC?   

This does not mean that the highest bit is uncertain. It can be understood that the measurement range has been expanded. A 1000-count multimeter with a resolution of 1mV can measure up to 0.999V, while a 2000-count multimeter can measure up to 1.999V. The LSB of the ADC is equivalent to the effective resolution of the device, while the count or effective bit is an overall indicator, as described in 1.

5. How to calculate whether it is 1/2 or 4/5? 

This is to specify the count number, for example, 60000 count is 4 5/6 digits, and 20000 count is 4 1/2 digits.

Wang Jinjin:

We use a 24-bit ADC, and theoretically the count can reach 16777216, but in reality, due to the noise introduced by factors such as amplification attenuation and multiplexer, the final ENOB is only 17 or 18 bits, so the count is 240000. Can I understand it this way?  

Master Qian:

That's what I mean.

Wang Jinjin:

In addition, our Dingyang 5.5-digit desktop multimeter SDM3055 has slow, medium and fast modes. What are the differences in the algorithms of these different modes? Is it just that the number of samples of the average algorithm is different, or is there something else? Are these fast and slow modes uniformly defined on every multimeter? 

Master Qian:

The three modes mainly have different ADC configurations, which are reflected in the sampling rate, settling time, filter selection, etc., resulting in different ADC effective bits. The specific reading rates of the fast and slow modes are not completely unified by each company, but the general definition is that slow is several times, at this time the accuracy and effective bits are the highest, medium is dozens of times, the accuracy and effective bits are slightly lower, and high speed is the highest reading rate that the machine can reach, from hundreds to tens of k, but the effective bits are the lowest, for example, a 6.5-digit machine only has 4.5 or 5.5 digits.