Lead loss errors in resistive sensors

This technical brief discusses alternative circuit topologies used in resistance measurement systems, and a characteristic common to all such circuits known as "lead loss error."

Overview
Several techniques are commonly used for measuring resistive sensors. Precision bridges are useful for measuring very large and small resistance, as well as small changes in resistance. Use of such bridges, however, is generally restricted to laboratory environments. Extremely nonlinear sensors, such as thermistors, are often connected in series with a "linearizing" resistor--a resistance that tends to correct non-linearities over a narrow operating range. Such schemes require careful selection of the "linearizing" resistor based on the anticipated temperature measurement range. Unfortunately, neither of these approaches is easily applied in a versatile, multichannel sensor measurement system.

Sensoray Smart Sensor Processors employ a method for resistance measurement that is universally applicable to a wide range of resistance values and sensor types. All supported resistive sensors, including RTDs and thermistors, are acquired by forcing a constant current through the target sensor and then measuring the resulting voltage. The sensor resistance is determined by simple application of Ohm's Law: Rs=Vs/I, where Rs is the target sensor resistance, Vs is the voltage across the sensor, and I is the excitation current.

As with any other resistance measurement technique, constant-current excitation has potential pitfalls. This article examines a side-effect of constant current excitation known as lead loss error, and how to avoid it.

What is Lead Loss ?
It is well known that all electrical conductors (excepting superconductors) have finite electrical resistance. The magnitude of this resistance is a function of the conductor's material, diameter and length. For purposes of this discussion, it is important to note that a conductor's resistance increases proportionally with its length

R = MaterialResistivity * Length / CrossSectionArea

When current passes through a conductor, the electrical resistance of the conducting material will produce a voltage difference across the conductor, according to Ohm's law. This resulting voltage is called lead loss. Note that lead loss increases with increasing conductor length.

Lead Loss Error

If the distance separating a sensor and its excitation source is small, a single conductor pair may be shared by both excitation source and measurement system without compromising measurement accuracy. As this separation--and hence, conductor length--increases, measurement accuracy may be degraded due to voltage drops across the conductors. Such measurement error is classified as lead loss error.

The diagram below illustrates lead loss in a "two-wire" circuit. In this case, conductor T produces a loss of magnitude Vt=V1-V2=I*Rt, while conductor B produces a loss of Vb=V3-V4=I*Rb. The target resistance, shown at the left, produces the voltage we are interested in acquiring: Vs=I*Rs=V2-V3.

Two-Wire Circuit:  +---+(V2)------------T------------- (V1) <--I  | . |  | R |  | E |  | S |  | . |  +---+(V3)------------B------------- (V4) I-->

 Lead loss error occurs when lead loss is sufficiently large to impact the accuracy of a resistance measurement. Such errors are a consequence of attempting to measure a target resistance located at the far end of a conductor, when in reality, it is thesum of the target resistance plus the conductor resistance that is being measured. Referring to the above example again,

Rmeasured = Vs/I + Vt/I + Vb/I = Rs + Rt + Rb
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It can be seen that measured resistance increases as conductor lengths--and corresponding Rt and Rb values--increase, reducing the accuracy of the target resistance measurement. Such errors can become unacceptably large when measuring small target resistances such as RTDs.

Avoiding Lead Loss Errors

Two classic methods are available for preventing lead loss errors. In some cases, lead loss can be limited to an acceptable level by keeping conductor lengths sufficiently short or by using large diameter conductors. If this is not practical, one or two sense conductors can be added to reduce or eliminate losses, resulting in what is commonly referred to as a three-wire or four-wire circuit. In such circuits, the objective is to separate excitation and voltage sensing functions into different conductors.

Three-Wire Circuits

A "three-wire" circuit, shown below, will reduce lead losses by 50 percent. Although the third wire is shown connected at the top of the target resistance, it could just as easily be connected at the bottom. The advantage provided by the third conductor is this: since no current flows through conductor P (assuming high input impedance at the sense terminals) it experiences no lead loss.

Three-Wire Circuit:  +---+(V2)------------T------------- (V1) <--I  | . |\  | R | ---------------P------------- (V2) V+  | E |  | S |  | . |  +---+(V3)------------B------------- (V4) I-->

 If one assumes that conductors T and B have identical resistance, lead loss errors can be eliminated by making two measurements and performing a simple calculation. First, measure the loss due to conductor T: Vt=V1-V2. Next, measure the resistance as seen by the sense terminals: Vs=V2-V4. Since all conductors are assumed to have the same resistance, the loss in conductor T will be the same loss experienced by conductor B. Compute the target resistance: R=(Vs-Vt)/I.

Although this technique works in theory, in practice it can yield less than satisfactory performance for a number of reasons. Two measurements must be made every time the target resistance is to be acquired, resulting in 50 percent throughput reduction. An additional measurement channel is consumed (or an architectural compromise must be made) to make possible the second measurement. Also, any measurement noise or non-linearity is compounded because acquired data is a result of two measurements.

Four-Wire Circuits
A "four-wire" circuit is shown below. This circuit topology completely eliminates lead losses by virtue of having two sense leads and two excitation leads. Since no current flows through either of the sense leads, the measurement system is able to directly access the voltage at the target resistance.

Four-Wire Circuit:  +---+(V2)------------T------------- (V1) <--I  | . |\  | R | ---------------P------------- (V2) V+  | E |  | S | ---------------N------------- (V2) V-  | . |/  +---+(V3)------------B------------- (V4) I-->

 In a four-wire circuit, only one measurement must be made: Vs=V2-V3. It is then a simple matter to compute the target resistance value: Rs=Vs/I. Clearly, the four-wire circuit is optimal from a number of standpoints. First and foremost, all lead loss errors are completely eliminated. Only one measurement is required to acquire the voltage across the target resistance, making possible the maximum throughput rate. Only one measurement channel is required. Errors due to measurement noise and non-linearity is minimized.

Because of the significant advantages offered by the four-wire circuit topology, all Sensoray Smart Sensor Processors provide a complete four-wire circuit for each measurement channel.