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How to make ultra-high-precision resistors? Understand the resistance trimming techniques of Kelvin-Varley voltage divider!
In the field of precision measurement, Kelvin-Varley voltage dividers have attracted widespread attention for their ultra-high accuracy.The purpose of this circuit is to generate output voltages, as an exact ratio of the input voltage, and to provide decades of analytical capabilities.The Kelvin-Varley voltage divider can be actually considered an electromechanical precision digital-analog converter, especially for precision voltage measurements in calibration and metrology laboratories.Its resolution, accuracy and linear error can reach 0.1 ppm (one in a tens of millions).
The Kelvin-Varley voltage divider is designed with unique advantages to significantly reduce the number of precision resistors required.
Circuit Structure
A traditional voltage divider (Kelvin divider) is composed of multiple resistors connected in series.However, the main disadvantage of this structure is that to achieve a resolution of 1 in 1,000, 1,000 precision resistors are required.To overcome this limitation, the Kelvin-Varley voltage divider adopts an iterative design scheme. Through multi-stage series connection, each stage consists of 11 precision resistors, which can achieve a tenfold resolution per stage.For example, in series three stages, any partial pressure ratio from 0 to 1 can be obtained, with each change of 0.001.
Each stage of Kelvin-Varley voltage divider consists of a set of equivalent resistors.If each resistor of the first stage is set to Ri, there are 11 resistors per stage.Since the input impedance of each subsequent stage is designed to be 2Ri, the effective resistance of the bridge portion is kept at Ri.In this way, the input impedance of each stage can be designed to be 10Ri.As a basic Kelvin-Varley design, the secondary resistance will decrease by five times the factor.For example, the first stage may use a 10kΩ resistor, the second stage uses 2kΩ, the third stage is 400Ω, until the fifth stage uses 16Ω.
Application Fields
The full accuracy of such a circuit can only be achieved without the output current flowing, because the effective source impedance of the output varies due to the current flowing.Kelvin-Varley voltage dividers usually need to be used with zero point detectors in order to compare their output voltage to known voltage standards, such as Weston cells, and must also be sure not to draw current from them when used. .The final stage of the Kelvin-Varley voltage divider is actually a Kelvin voltage divider, where there are ten equal resistance values, each resistor can be set to Rn Ohms.
High accuracy requirements can be achieved only by ensuring that the resistor has equal resistance in the same ten-digit number.
Resistance trimming skills
High-quality resistor selection is essential to achieve the desired accuracy, especially for first-stage resistors, where matching accuracy must be the highest.These resistors need to have strict tolerances and may need to be individually trimmed to equal values.This process can be accomplished using a Wesden bridge circuit and a sensitive zero-point detector, traditionally an 19th-century galvanometer, and today it can be performed using electronic amplification instruments.During the trimming process, the ratio of adjacent resistors is not particularly sensitive. You can slightly increase the value of Ri+1 resistor and connect an adjustable trimming resistor in parallel to the resistor of the previous stage to ensure that the effective resistance reaches the Requires value.
Potential Source of Error
Temperature coefficient
Ideally, the resistor should have a constant resistance value, but in fact, the resistance will change with time and external environment.In particular, changes in temperature will affect the stability of the resistance.For example, the temperature coefficient of carbon film resistance can reach hundreds of ppm/K, while the coefficient of some winding resistors is about 10 ppm/K.The best metal foil resistance can be as low as 0.2 ppm/K.
Self-heating effect
The power loss in the resistive element is converted into heat, which may cause the temperature of the element to rise.Under high voltage testing, the self-heating effect may have an impact on the accuracy of several voltage stages.To reduce this effect, the temperature rise caused by self-heating must be limited, which requires the use of a resistance with a low temperature coefficient and reduces the thermal resistance.Commercial Kelvin-Varley voltage dividers typically employ winding resistors and may be immersed in an oil bath to reduce temperature.
Thermoelectric force
The thermoelectric effect of different metal contacts may generate tiny voltages at different temperatures.This unnecessary voltage may cause considerable errors in such high-precision environments.This error can be reduced by keeping all contacts at the same temperature and using metal combinations with low thermoelectric coefficients to improve the design, such as the plug and socket combination of low thermoelectric EMF, which can significantly reduce the error.
The advancement of this technology has made the Kelvin-Varley voltage divider play a key role in the laboratory of electrical measurement and calibration, providing an accurate basis for subsequent technology development.While we are pursuing accuracy, should we also think about how to further improve the stability and reliability of these devices?
