On the Measurement Speed and Accuracy of Six and a Half Digit DMM
Author: Sean Chen
Product Marketing Department
With respect to the six and a half digit DMM measurement applications, many factors will affect the accuracy of DMM measurement. This article will briefly discuss three main factors, namely speed, Power Line Cycle and temperature coefficient.
1. Speed
Measurement speed and resolution are the two keys to DMM measurement, but these two factors are mutually compromised. When we need high measurement speed, we will inevitably sacrifice resolution. When the measurement speed is reduced, the resolution can be increased. When the measurement speed is low, you can have a good signal resolution and the readings are more accurate. On the other hand, when the measurement speed is high, the test throughput can be improved. But at this time, the resolution and accuracy will decrease.
The following is a brief elaboration of the quantization error occurred in the ADC (Analog-to-Digital Converter) process. Quantization error refers to the error introduced when quantizing continuous values into discrete values. In digital signal processing, quantization is the process of converting an analog signal into a digital signal. The quantization process reduces the vertical resolution of the signal and introduces quantization errors.
Next, for the elaboration of LSB (Least significant bit) voltage. When continuous voltage signals are input, they will be converted into discrete points after being quantized by the ADC. We will further explain it with a diagram. Figure A below is 2-bit digital quantization (four levels). When the input signal is greater than 0.75V and less than 1.25V, it will be judged as 1.0V. In other words, the maximum error at this time can reach positive 0.25V (overestimate) and negative 0.25V (underestimate). At this time, the LSB of is 0.5V. From the LSB range diagram at the bottom of Figure A, we can see the range and periodic changes of the quantization error.
Figure A
Next, let’s take a look at Figure B. 3-bit digital quantization (eight levels) is utilized, when the input signal is greater than 0.875V and less than 1.125V, it will be judged as 1.0V. Put differently, the maximum error at this time is reduced to positive 0.125V (overestimated), and negative 0.125V (underestimated), the LSB at this time is reduced to 0.25V.
Figure B
Through the demonstrations in Figure A and Figure B, we now understand that 2-bit quantization will bring relatively large errors, while 3-bit quantization will have relatively small errors. The higher the number of quantization bits, the smaller the relative error of quantization. For example, 8-bit digital quantization can achieve a resolution of 256 levels, and 12-bit digital quantization can achieve a resolution of 4096 levels. The ADC of a six-and-a-half-digit meter uses 22-bit, so it can provide very high resolution.
Table 1 is the actual specification of GDM-9061 dual measurement DMM for your reference:
It can be noticed in the table that when the update rate setting is gradually increased, the resolution of the DMM will gradually decrease from six and a half digits to five and a half digits and four and a half digits. Among them, you can see that five and a half digits corresponding to three update rates of 400/ s 1.2k/s 2.4k/s/ Although 2.4k/s has a high speed, it will have a large interference error compared with 400/s and 1.2k/s. Therefore, this effect cannot be neglected in the selection of update rate. The interference caused by the increase of update rate is mainly related to PLC (Power Line Cycle), which will be explained later.
Table 1
We can use Figure C to see the relationship between resolution and measurement speed. The vertical axis is the resolution, respectively marked six and a half digits/five and a half digits/four and a half digits, and the horizontal axis is the choice of measurement speed.
Figure C
Based on the above elaboration, speed affects resolution, and resolution affects accuracy. Therefore, the choice of measurement speed should be judged according to the items to be measured, in order to have the best and meaningful results.
2. PLC
PLC (Power Line Cycle) refers to the AC power cycle used by the test and measurement instruments (60Hz power is 16.67ms, 50Hz is 20ms). Because the noise interference of the AC power will have a significant impact on the measurement of DC voltage, current and resistance. One of the methods to reduce AC power noise interference is to set the measurement cycle to 1 PLC, so that the interference can be offset by positive and negative.
As shown in Figure D below, when the measurement period is set to one PLC length, after signal summing and averaging, the AC noise interference within one period can be positively and negatively offset (the areas of red and blue remain equal), which is conducive to eliminating AC filter noise while measuring DC signals.
Figure D
In the setting parameters of the DMM, there is NPLC (Number of Power Line Cycles), which can directly set the measurement cycle as a relative multiple of the PLC, so there is no need to calculate the mathematical conversion of AC power cycle for 16.67ms (60Hz) or 20ms (50Hz). Table 2 below is the NPLC setting range of the GDM-9061 dual measurement DMM for your reference:
Table 2
When NPLC is set to 12, that is, the measurement period is set to 16.6ms x 12 = 200ms, which is equivalent to 5 samples per second.
When NPLC is set to 0.006, that is, the measurement period is set to 16.6ms x 0.006 = 0.01ms, which is equivalent to 10k samples per second.
When the NPLC is larger, the effect of suppressing the noise of the AC power supply is better and the accuracy is higher after signal summing and averaging. However, the measurement speed will be reduced.
The smaller the NPLC, the higher the measurement speed. This smaller NPLC will reduce the signal resolution, and there will be more AC power noise interference when measuring DC signals.
In GW Instek’s DMM product line, GDM-906x and GDM-8261A both provide the NPLC setting function. Please visit the links below for more product information:
https://www.gwinstek.com/en-global/products/detail/GDM-906x
https://www.gwinstek.com/en-global/products/detail/GDM-8261A
3. Temperature coefficient
In the physical world, all substances will change with temperature, and the resistance value will also change with temperature. The ratio of temperature to resistance value change is called TCR (temperature coefficient of resistance), and the unit is ppm/°C.
R(T): Resistance value at any temperature
R0: Resistance value at reference temperature
α: Temperature coefficient of resistance
T: Any temperature
T0: Reference temperature
Let's take copper as an example. The temperature coefficient of resistance of copper is 0.393% (reference temperature 20°C). Assume that a set of copper wires has a resistance of 100 ohms. At 40°C, the resistance value is calculated as follows:
R(T) = 100 (1 + 0.00393(40-20)) = 100 ( 1+ 0.0786 ) = 107.86 ohms
From the above calculation, a temperature increase of 20 degrees Celsius will bring a 7% difference in resistance value to the copper component. DMM is composed of various components, and the temperature will affect the performance of each component in the instrument extending from the simplest resistors to the most sophisticated integrated circuits. Of course, the instrument itself will have a calibration and compensation function. In order to minimize the impact of temperature on accuracy, the specification sheet of DMM will indicate precautions for instrument warm-up and operating temperature.
Table 3 is the DC measurement specifications of the GDM-8261A dual-measurement DMM for your reference:
At the very beginning, the one-hour warm-up requirement is mentioned for the DMM components to reach a stable operating temperature to ensure that the test and measurement meets the accuracy of the specifications.
Table 3
The temperature range is also mentioned in the table, 0°C~55°C is the temperature range that can ensure the accuracy meets the specifications.
It can be noticed from the table, temperatures are subdivided into three ranges: 23°C ± 1°C, 23°C ± 5°C and 0°~18°C / 28°C~55°C. In Figure E below, we use orange, blue and gray arrow lines to show ranges respectively. The optimum operating temperature range is 22°-24°C.
Figure E
Furthermore, 24 Hours / 90 Days / 1 year in the table refer to the time elapsed after the instrument is calibrated. As time increases, the error will gradually increase. To ensure that the accuracy of the specification is maintained, the instrument must be tested/calibrated on a regular basis.
Contact us:
Overseas Sales Department
Good Will Instrument Co., Ltd
No. 7-1, Jhongsing Road, Tucheng Dist.,
New Taipei City 23678, Taiwan R.O.C
Email: marketing@goodwill.com.tw