On the Error Sources and Measurement Techniques of Resistance Measurement
In 2023, the first room temperature and ambient-pressure superconductor LK-99 has generated heated discussions. The superconductor has zero resistance and has the diamagnetic Meissner effect. Because the resistance is zero, there is no voltage drop and no energy loss when the current flows through.
Resistor is also the first component for electrical and electronic engineers to understand the world of circuits. Hence, how to measure resistance is not only the first lesson in learning circuits, furthermore, the measurement of tiny resistance requires understanding the measurement principle and eliminating system errors to obtain correct result.
Measured with close to zero resistance, the thermal electromotive force generated by the test lead, the contact point of the lead and the DUT due to the Seebeck Effect are sources of system error.
Because the principle of resistance measurement is by applying Ohm's law, via two test probes contacting both ends of the DUT, the current source circuit in the ammeter outputs a known current flowing through the resistance under test (DUT) and the voltage drop generated on the resistor is measured by a voltmeter, and then the voltage value obtained is divided by the current to obtain the resistance value under test (DUT).
Now, we clearly encounter a problem. That is, how to deal with the influence of the equivalent resistance of the test probe? Let’s discuss this problem separately based on the resistance value of the DUT:
When DUT resistance value > 1K ohms:
For example, if the DUT has the resistance of 5M ohms, the error caused by the test lead can be ignored, because the resistance value of the test lead is about 0.1-0.2 ohms, which is like a drop in the bucket compared to that of the DUT, and the difference is 10 to the seventh power. The impact of the test lead can be neglected.
When DUT resistance value < 1K ohms:
For example, if the DUT has the resistance of 10 ohms, the resistance value of the test lead will bring an error of more than 1%. At this time, this error has to be taken into consideration, and further explanations and solutions will be provided later.
When DUT resistance value < 1 ohm:
For example, if the DUT has the resistance of 0.05 ohms, in addition to the resistance value of the test lead, there will be another interference source, which is the contact thermal electromotive force (EMF). Further explanations and solutions will be provided later.
1. Error form test lead pressure drop
When we measure a small resistance value, the impedance of the test lead will be a factor that cannot be ignored. The conventional two-wire measurement is as shown below:
A current is output through the current source (blue arrow), and the current flows through the red test lead, through the DUT, and then flows back through the black test lead, and then the voltage is measured by a voltmeter. Finally, the formula R = V / I is used to obtain the resistance value. It is obvious that this method will include the resistance value of the red and black test leads.
Assuming that the red test lead R1 and the black test lead R2 both have a resistance value of 0.1 ohms, and the DUT itself has only 1.0 ohms. The conventional two-wire measurement will also measure the resistance values of R1 and R2. Now, you will get a result close to 1.2 ohms, and there will be a 20% error with the original 1.0 ohms.
Now, you can use the four-wire method to conduct measurement as shown in the following figure:
We divide the current source and the voltage measurement into two groups, the first group R1a/R2a is responsible for the main current transmission, and the second group R1/R2 is responsible for the voltage measurement. Now, it should be noted that the voltmeter will only measure the two ends of the DUT without including the voltage difference of R1a/R2a. In theory, it is possible to measure the pure DUT across voltage, and then using the formula of R = V / I, you can obtain closer to the real DUT resistance value.
2. Error from contact thermal electromotive force
A contact thermal electromotive force error comes from the thermoelectric effect, which is a direct conversion of voltage from temperature difference, and vice versa. Thermal electromotive force is generated from the contact of different metals at different temperatures. In measuring circuit, the thermal electromotive force generates a voltage, which causes a measurement error.
Thermal voltages can be generated within the resistor, or when different metals are used to form a circuit at different temperatures. Each metal contact forms a thermocouple, which produces a voltage proportional to the temperature of the contact. This thermal electromotive force produces unnecessary interference in resistance measurements, especially when measuring very small resistances.
Among the ways to eliminate thermal electromotive force error, the most effective way is to use the offset method. For example, the GOM-805 DC Milli-Ohm Meter, which uses a bidirectional pulse wave method to offset the contact thermal electromotive force error:
The left figure below shows that the R to be measured will be accompanied by the thermal electromotive force error of the Vemf contact, so you can use a positive pulse and a negative pulse to make a measurement first. The right figure below, the red dotted line indicates the existing Vemf error. Assuming that the correct cross-voltage of R to be measured is Vx, the positive pulse will actually get the voltage from Vx+Vemf =V1, and the negative pulse will actually get the voltage from Vx-Vemf =V2
Then Vemf is eliminated by the following formula:
(V1 + V2) / 2 = (Vx + Vemf + Vx - Vemf) = (2Vx)/2 = Vx
Finally, use the basic formula V = IR. Divide Vx by the current I to get the correct resistance value that is not interfered by the thermal electromotive force error!
GW Instek's GOM-805 DC milli-ohm meter provides bidirectional pulse measurement function, please visit the following link for more product information:
www.gwinstek.com/en-global/products/detail/GOM-804_GOM-805
3. Measurement error of resistance equivalent circuit of PCBA
Finally, let's discuss another situation. When we need to measure the resistors that have been soldered on the PCB, the only way is to remove the resistors for measurement. This method is not so practical and relatively troublesome. Hence, there is a six-wire measurement can be applied to this requirement. The resistance value can be measured without removing the resistor.
If the general four-wire method is used, as shown in the simple schematic diagram below, we directly measure the resistance value of the DUT on the PCB with an ammeter, and the current will be dispersed due to the equivalent resistance network composed of various series and parallel components such as Rx and Ry. So it is impossible to measure the resistance value of DUT by this method.
At this time, the six-wire method can be used, as shown in the simple schematic diagram below. The main thing is to add Guard Output and Guard Sense, and then collocating with an operational amplifier to generate a "Guard" voltage Vg to allow this voltage to be equal to the V1 voltage. The purpose is equivalent to a guard. Through the equipotential method, block all paths, which are not going from power circuit to the DUT, forcing the current to only pass through the DUT, so that a closer to the real DUT resistance value can be obtained.
GW Instek's GSM-20H10 Source Measure Unit provides the six-wire measurement function. Please visit the link below for more product information:
www.gwinstek.com/en-global/products/detail/GSM-20H10
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