# Resistance Measurement with a DMM

Digital Multimeters allow the measurement of resistance in a variety of ways. The measurement method chosen can affect the measurement accuracy. This application note explains how the three different modes of measurement operate and their limitations.

## Two Wire Measurements

Many resistance measurements can be made using the simple 2-wire Ohms method. To perform a measurement with a DMM simply connect V+ to one end of the resistor and V - to the other end and set the DMM to measure resistance. The DMM supplies a constant current source to the resistor and the meter measures the voltage across it, the voltage being proportional to the resistance.

As shown by the simplified diagram in above the lead resistance can introduce a significant error since the measured voltage is across both the load and resistance of the leads. The error is most significant on low resistance measurements and usually needs to be considered only for resistances below 30 kOhms - but the exact value at which you need to be concerned is dependent on the accuracy required.

The impact of the lead resistance on the measurement can be corrected by using the Relative function on the DMM.

To make the correction you should null out any lead resistance errors by first by connecting the V, + and V, - test leads together and then performing a Relative function. The reading will be changed from that of the test leads to 0 ohms.

Any resistor now placed between the ends of the test leads will now be measured relative to that the new test reference plane at the end of the two leads.

If the user is making measurements above (say) 300 k ohms shielded or twisted leads may have to be used to avoid unstable readings due to signal pick up on the leads. The problem of noise pick up becomes worse as the resistance to be measured is increased.

## Four Wire Measurements

Four Wire resistance measurements are ideal for making measurements of lower value resistance since the DMM is able to remove the effects of the leads without resorting to the use of the Relative Function. The correction is entirely automatic. In Four Wire measurements the V+ and V- terminals still supply the current to the resistor via the test leads. The voltage drop across V+ and V- is determined by the sum of the lead resistance and the resistor being tested.

The sense lines are connected to the terminals of the resistors and measure the voltage across the resistor, it does not include the voltage across the test leads (or a switching system used to connect the DMM to the UUT) and the input impedance of the voltmeter is sufficiently high that is does not divert any current or create error voltages from Rlead.

The reading is therefore dependent on just the resistor and is virtually independent of the test lead resistance.

Four wire measurements produce very accurate, repeatable and stable measurement of resistance and are particularly suited to the measurement of low values, even down to 10 mohms. It is less suited to the measurement of high value resistance since the input impedance and leakage current to the voltmeter may effect the reading. In general four wire measurements are not recommended.

## Six Wire Measurements.

Six wire measurements are used where the resistor to be measured is shunted by other resistors, a common problem in ATE systems where the resistor is to be measured in situ on a PCB. The technique isolates the resistor under test by maintaining a guard voltage at a user-defined node, the guard voltage being driven by a voltage buffer from the V+ terminal. The guard voltage ensures the constant current source from the DMM does not have current diverted into the alternate path.

###### The following is an example of how it works:

Assume a 30 kohm resistor is in parallel with two series resistors (510 ohms and 220 ohms (as in Figure 3). In a normal resistance measurement, the 510 ohms and 220 ohms would shunt most of the DMM Ohms source current, causing a very inaccurate reading. By sensing the voltage at the top of the 30 kohm resistor, and then applying this same voltage to the junction of the 510 ohms and 220 ohms, there is no current fl ow through the shunt path. The guard has forced the junction to be the same as the voltage at V+ and current required through the 220 ohm resistor is supplied by the Guard Source. The DMM accurately measures the 30 kohm resistor since the current Is flows through the 30kOhm resistor.

The current capability of the Guard Force terminal is limited on a typical DMM (and is short circuit protected), so there are limitations on the amount of driving that can be achieve.

The resistor connected between the low of the four wire terminals and the guard point is the burden resistor, or Rb. Due to the limited guard source current, this resistor can not be lower than Rbmin where:

Rbmin = Io * Rx / 0.02,
where Io is the ohms source current for the selected range
Rx is the resistance being measured.

For example, selecting the 330 ohm range and measuring a 300 ohm resistor imposes a limit on Rb of at least 15 ohm or greater.
Since the top burden resistor, Ra, does not have this limit imposed on it, choosing the measurement polarity can help since Ra can become Rb and vice versa. It is best to set the measurement polarity such that Ra is the higher of the two burden resistors. The six wire method is specified for measurement of resistors to 330 kohms, for resistors above this range the six wire configuration can be maintained but the DMM should be set to two wire measurement mode (with its lower source current).

## Thermoelectric Errors

Voltages created be thermoelectric effects in switching systems can lead to resistance measurement errors since they introduce an error in the voltage drop across the resistor being measured. The voltage may cause the observed value to be higher or lower than the actual value, in general users should use enough excitation current to ensure that the voltage measured is large enough to neglect the thermal voltage in the switches. Some DMM's may also include a function to measure the thermoelectric voltage and compensate for its effect. The impact on the accuracy of the measurement is dependent on the ratio of the thermo-electric EMF in connection (particularly the relays) and the voltage across the resistor when it is being measured.

## Summary

Two wire ohms measurement are commonly used when the resistance of the test leads is much less than the resistance being measured. The results are generally good enough for most functional test measurements. To eliminate errors associated with test lead resistance in two wire ohms measurements a “Relative” operation is available or alternatively the test system can provide the function.

Four wire measurements substantially eliminate the test lead resistance from the system, and are very useful when measuring lower value resistors. The four wire system is particularly useful when the lead resistor varies because, for example, the DMM is switched through a multiplexer or matrix that does not have the same lead resistance for each path. The 4 wire method should be avoided for measuring high resistor values.

Six wire measurements can allow resistors to be measured in situ where they may be shunted by other components. It requires the switching system that connects the DMM to the device under test to provide 6 connections, so can add complexity to the switching system.

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