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Fundamentals of Digital Measurement

In our previous discussion on power semiconductors, we highlighted the importance of precise numerical measurement for performance improvement. This requirement extends beyond semiconductors; digital measurement technology has become a cornerstone of modern industry, particularly with the rise of the IoT (Internet of Things).

Since the 1950s, the industry has shifted from analog to digital instrumentation. Traditional analog meters, familiar from basic educational settings, require users to visually estimate values between scale markings. While sufficient for simple checks, this method lacks the precision required for modern semiconductor design and performance evaluation.
Consequently, digital measuring instruments--which digitize data via A/D conversion--have become the standard in development environments. Today, a vast array of parameters, including voltage, current, temperature, and pressure, are captured and processed digitally.

This picture shows A/D conversion by the thermocouple, pH and ORP sensor.

As pictured in the figure, the analog value acquired by each sensor is output as a voltage. After that, the signal (voltage) is amplified by an amplifier and A/D converted and then taken into a computer. The above figure gives an example of a sensor that is output as voltage. Image sensors used in Programmable Logic Controller (PLC) and digital cameras etc. A/D converts the (integrated) current value as the input value.

Recently, communication between sensors and computers, in some cases, tablets and smartphones, has often been performed via USB or wireless. Because it is difficult to lay cables for communication in the case of outdoor installation type sensors, such as digital instrument screens, especially, uploading of data by wireless is the mainstream. There are also cases where data is uploaded directly to the system built on the Internet.

Advancements in SoC (System on a Chip) technology have dramatically reduced the size and power consumption of computing modules. High-performance wireless communication chips are now available at a very low cost. This affordability allows for the deployment of sensor nodes in locations where cable installation is difficult, enabling data collection via wireless networks or direct cloud uploads.

With the establishment of LPWA (Low Power Wide Area) standards such as SIGFOX and LoRa, as well as 4G/5G cellular networks, it is now feasible to monitor hundreds of data points--such as temperature and humidity--with minimal power consumption. This collected "Big Data" is essential for applications ranging from infrastructure monitoring to agricultural automation.

The collected data is treated as big data, and the information processing according to the field such as social infrastructure monitoring, disaster prevention, and labor-saving of agriculture is performed and applied. IoT has been attracting attention in recent years as the use of such data has progressed.

Now, let's look at the change in the data value until such data is passed from the sensor to the computer. Here, the pH sensor is taken as an example.

This picture is digitalization of pH.

The value measured by the pH sensor converts a value between 0 and 14 when passed to the pH meter. The values at this time are still in analog form. There, it is once converted to a voltage in the range of -1 V to 1 V and sent to a signal isolation converter (amplifier). In the amplifier, it is amplified to -10V to 10V as the analog value. Then, A/D conversion is performed. As a result, the analog value of -10 V to 10 V is converted to a digital value of -2048 to 2047, which may be larger if it is a Power of 2, and then sent to a computer. Of course, you may convert it back to a digital value of 0-14 again before sending it to a computer. In any case, analog values are converted to voltages and then converted to digital values.

If the input is current, for example, in the programmable logic controller (PLC), the input value is often set to 0 to 20 mA of direct current, and this is often used by A/D conversion.

Measurement Resolution

When converting analog signals to digital values, "resolution" is a critical factor. Digital systems process information in binary (0 or 1), meaning resolution is expressed as a power of 2. For example, a 12-bit resolution provides 212 or 4096 discrete steps.
In a signed 12-bit system, this range is typically represented from -2048 to +2047. A higher bit count means the analog signal (e.g., -10 V to +10 V) is divided into finer steps, resulting in more precise measurements.
The table below illustrates the relationship between bit depth, integer range, and voltage resolution (LSB) for a 10 V full-scale range.

bit Range in decimal notation
Signed Unsigned Resolution Voltage value per stage
(for 10VFS)
%FS dBFS
2 -2 to 1 0 to 3 4 2.5V 25 -12
3 -4 to 3 0 to 7 8 1.25V 12.5 -18
4 -8 to 7 0 to 15 16 0.625V(625mV) 6.25 -24
5 -16 to 15 0 to 31 32 0.313V(625mV) 3.12 -30
6 -32 to 31 0 to 63 64 0.156V(156mV) 1.56 -36
7 -64 to 63 0 to 127 128 0.0781V(78.1mV) 0.78 -42
8 -128 to 127 0 to 255 256 0.0391V(39.1mV) 0.39 -48
9 -256 to 255 0 to 511 512 0.020V(20mV) 0.2 -54
10 -512 to 511 0 to 1023 1024 0.00977V(9.77mV) 0.098 -60
11 -1024 to 1023 0 to 2047 2048 0.00488V(4.88mv) 0.049 -66
12 -2048 to 2047 0 to 4095 4096 0.00244V(2.44mV) 0.024 -72
13 -4096 to 4095 0 to 8191 8192 0.00122V(1.22mV) 0.012 -78
14 -8192 to 8191 0 to 16383 16384 0.000610V(610μV) 0.0061 -84
15 -16384 to 16383 0 to 32767 32768 0.000305V(305μV) 0.003 -90
16 -32768 to 32767 0 to 65535 65536 0.000153V(153μV) 0.0015 -96
17 -65536 to 65535 0 to 131072 131071 0.000076V(76μV) 0.0008 -102
18 -131072 to 131071 0 to 262143 262144 0.000038V(38μV) 0.0004 -108
19 -262144 to 262143 0 to 524287 524288 0.000019V(19μV) 0.0002 -114
20 -524288 to 524287 0 to 1048575 1048576 0.00000954V(9.54μV) 0.0001 -120
21 -1048576 to 1048575 0 to 2097151 2097152 0.00000476V(4.76μV) 0.000048 -126
22 -2097152 to 2097151 0 to 4194303 4194304 0.00000238V(2.38μV) 0.000024 -132
23 -4194304 to 4194303 0 to 8388607 8388608 0.00000119V(1.19μV) 0.000012 -138
24 -8388608 to 8388607 0 to 16777215 16777216 0.000000596V(596nV) 0.000006 -144
25 -16777216 to 16777215 0 to 33554431 33554432 0.000000298V(298nV) 0.000003 -151
26 -33554432 to 33554431 0 to 67108863 67108864 0.000000149V(149nV) 0.000002 -157
27 -67108864 to 67108863 0 to 134217727 134217728 0.0000000745V(74.5nV) 0.0000007 -163
28 -134217728 to 134217727 0 to 268435455 268435456 0.0000000373V(37.3nV) 0.0000004 -169
29 -268435456 to 268435455 0 to 536870911 536870912 0.0000000186V(18.6nV) 0.00000002 -175
30 -536870912 to 536870911 0 to 1073741823 1073741824 0.0000000093V(9.3nV) 0.000000009 -181
31 -1073741824 to 1073741823 0 to 2147483647 2147483648 0.0000000047V(4.7nV) 0.000000004 -187
32 -2147483648 to 2147483647 0 to 4294967295 4294967296 0.0000000023V(2.3nV) 0.000000002 -193

The fact that this number is large means that the value of -10 V to 10 V can be finely resolved. This fineness is called "resolution".

Recently, measuring instruments have increasingly been required to obtain more accurate measurement values and errors. For this reason, higher resolutions enable more precise measurement, so it is an important development requirement to decide how much resolution to aim for in production. Also, the setting of resolution is very important because the testing side cannot select the correct measurement equipment unless the required resolution is set firmly.

The figure below is a comparison of low and high resolution.

This graph explains it takes time to stabilize due to resolution in A/D conversion.
This graph is low resolution.
This graph shows high resolution.

This is a graph of analog value over time. As can be seen, when the fluctuation of the leftmost analog value is converted to a digital value, the graph at the right end, high resolution, produces a value closer to the analog value than the graph in the middle, low resolution. Therefore, the higher the resolution, the more accurate measurement results can be displayed.

Also, the time on the horizontal axis is the same. By outputting data in as short a time as possible, time changes can be measured in detail. In this case, the processing speed of the computer and A/D conversion board has been improved, so it is possible to measure in a much shorter time compared to 10 years ago and 20 years ago.

High-speed measurement is not always synonymous with high accuracy. Simply increasing the sampling rate can introduce noise, especially when measuring small signals. This is analogous to photography in low light: a faster shutter speed results in a grainy (noisy) image, while a longer exposure accumulates more light for a clearer picture.

In electronic measurement, extending the integration time or averaging multiple samples can significantly reduce random noise and improve measurement stability. For instance, a fluctuation of 1 count is significant in a 10-count sample but negligible in a 10,000-count sample. Therefore, selecting the appropriate integration time and sampling rate is essential based on the target application--whether measuring static voltage, transient switching timing, or environmental temperature.

Therefore, it is necessary to carefully consider the measurement timing and the integration (accumulation) time used for measurement. It is important to consider what design is required and what pattern of measurement may be possible when measuring voltage and current values, measuring switching timing, measuring resistance, measuring the operating environment temperature, etc.

Reference (Japanese site)