Start • Basic Principle • What's Measured? • How to Measure • Measurement Technique • Complete the Circuit • Complete Application • Proven Reliability • Sources and PDF

MEASUREMENT TECHNIQUE

Resistance measurements are simple in principle. In fact, it’s the same method you remember from your first physics class on electricity. You let a constant current flow through the resistor, and the voltage drop across it will be directly proportional to the resistance. However, this basic principle can’t be applied directly because of the need for high accuracy. Eliminating the resistance of wiring and connectors would require employing the Kelvin method and four leads in the connecting cable. The resistance only changes by less than 6%, and evaluating such a small voltage change superimposed on a relatively high DC component with the required accuracy wouldn’t be simple.

Fortunately, you can use a simple method developed in 1833 by Samuel Hunter Christie to overcome these problems. Sir Charles Wheatstone described the solution in 1843 in a paper on electrical measurements. It has been known as Wheatstone’s bridge ever since then despite the fact that Wheatstone acknowledged that the invention wasn’t his. What an injustice!

Figure 1a depicts the bridge configuration with one variable-resistive element. It’s easy to see that the differential between V1 and V2 is going to be zero when R1/R2 equals R3/R4. This is satisfied, for example, when R1 equals R3 and R2 equals R4. After the variable resistance of R2 starts to differ from R4, the bridge becomes unbalanced. You can detect this by observing that V1 is no longer equal to V2.

(Click here to enlarge)

Figure 1a—Here the bridge circuit has one variable element. b—In this instance, all four bridge components are found in the soldering pen. It’s the most obvious way of adding a cable to the circuit. c—The new circuit topology involves a cable with only three conductors to complete the bridge circuit.

By going through a lengthy and fairly boring calculation, you would discover that the voltage differential V1 to V2 has nonlinear dependency on the variation of R2. The exact transfer function depends on the properties of the power supply used to power the bridge. An even longer and more boring calculation would reveal that the nonlinearity could be reduced by half by using a current source instead of a voltage source.

Using a current source to power the bridge has an additional benefit. You can reasonably expect that the voltage source supplying power to the entire application will be noisy to a greater (if you decide to use a switch-mode power supply to save space and weight) or lesser degree and not necessarily stable (mainly if an unregulated 50/60 Hz transformer supply is used). The current source will act as an additional filter blocking the noise and ripples from entering the sensitive analog portion of the circuit. Because the current source will provide DC current to the bridge, the inductances and capacitances in the circuit won’t influence the result. You can therefore tick off the first condition from your list.

Figure 1b depicts a situation where all four bridge components are located inside the soldering pen. RC1 through RC4 represent the resistances of the cable wires and connector pins. RC1 and RC4 are connected in series with the current source. Therefore, they don’t influence the result of the measurement because the current through the bridge always remains the same. RC2 and RC3 are connected in series with the voltage differential detection circuit.

You must try to design the circuit so that its input impedance is significantly higher than the cable/connector resistance. Then the current flowing through RC2 and RC3 will be small and have little dependence on RC2/RC3 variance. Thus, the solution satisfies the second condition. It requires four conductors in the cable, however.

You can improve the situation by assuming that the cable conductors and connector pins all have the same properties. (This will be true in the majority of cases with the exception of coaxial and other special cables.) The new circuit topology is depicted in Figure 1c. Only half of the bridge is located in the soldering pen; it’s separated from the other half of the circuit by the cable. RC2 and RC3 simply add to R2 and R4. If RC2 and RC3 are the same and also vary in the same way, the balance of the bridge won’t be influenced by their presence. RC4 is connected in series with the current source, and therefore doesn’t influence the measurement.

To satisfy the last requirement, design the current source to provide the optimum current for powering the bridge. You need to compromise between a high current, which would heat up the bridge elements too much, and a low current, which would make the voltage difference between V1 and V2 too low for accurate measurement.