**Measuring points**, e.g. at bridges or aircraft wings, are often located at greater **distances** from the **measuring instruments**. With measuring points that are not directly accessible, measuring instruments need to be connected using **long cables**. The **disadvantage**: The **lead resistance** in the cable can amount to several ohms and **negatively affect the measurement**. Particularly **electrical resistance changes** in the cable during measurement, e.g. due to temperature variations, have negative effects.

With leads that are in series with the strain gauges (SG) in the same bridge arm, the **temperature response** due to heating of the cable is calculated as follows:

Q = Conductivity of the conductor material

A copper lead of 1 m length (0.5 m each for feed and return lead) and 0.15 mm^{2 }cross-section in series with a 120-ohm strain gauge causes 20 µm/m temperature response with 10 K temperature variation. All other conditions being equal, the temperature response with a 350-ohm strain gauge is only 7 µm/m.

Various types of **strain gauge circuits** enable** lead resistances to be compensated for**. This article presents** three types of circuits** based on the Wheatstone bridge circuit explaining their advantages and disadvantages.

With the 2-wire circuit, the strain gauges and the amplifier are connected via two wires (see fig. 1). The circuit diagram shows that the **cable resistance is added twice** (feed and return) to the strain gauge resistance.

This affects both the **bridge's zero point** and its **sensitivity**. Even with cables with lengths of few centimeters it is essential to allow for the cable resistance. The 2-wire circuit is particularly **sensitive to temperature variation** during measurement, since the change in resistance immediately affects the measured value.

The 2-wire circuit's** temperature stability** has been tested using installed strain gauges and the QuantumX MX1615 strain gauge bridge amplifier.

The test result: The measurement result obtained using a 2-wire circuit has no significance. The resistance change in the cable, e.g. due to temperature variation, fully impacts on the measurement result.

Asymmetric resistance changes to the strain gauge circuit too result in measurement errors. Changes in resistance are not corrected.

With the 3-wire circuit, an **additional lead** is connected to one connecting point of the measuring resistance, which results in a **second measuring circuit** that is used as a reference. The regulated 3-wire circuit measures the **voltage **across the **upper cable resistance** and **increases the excitation voltage **by double the amount measured. As a result the **voltage** across the strain gauge is** identical with and without a cable** and the cable has **no influence on sensitivity**.

The regulated 3-wire circuit requires that the **two current-carrying leads** have **identical resistance**, since the **voltage is measured only at one lead**, however, **double the value is applied for correction**. Hence, with a cable with four leads, it would be completely wrong to connect two leads in parallel to reduce the cable resistance. This would result in a significant zero point error. On the other hand, with strain gauge rosettes and strain gauge chains, it is essential to make sure that resistor R_{Kab1} corresponds to all R_{Kab2} resistors connected in parallel.

**Our test too shows:** **Changes in resistance are corrected in one cable lead only.** **Asymmetric changes** in resistance, e.g. interference at the points of contact, **fully impact** on the measurement result. **Symmetric changes** in resistance, e.g. temperature variation during the measurement, are **compensated **for by the sense lead.

Only the 4-wire circuit, or **HBM's patented Kreuzer circuit, **enables **different cable resistances to be compensated for**. A known electric **current** flows through the** resistor** via two of the leads. The **voltage** drop at resistor R_{Kab1} is **corrected** (at high impedance) via two additional leads.

The Kreuzer circuit measures the **voltage** across resistor R_{Kab2} and **adds it to the excitation**. The **voltage** and thus the **current** through completion resistor R_{erg} are **independent of the cable resistance**. **Zero point and sensitivity errors **resulting from cable effects are electronically **compensated** for.

**Note:** the three graphs show a stain gauge measurement using **2-, 3- and 4-wire circuits**. Here it seems that all three techniques offer identical stability. Ideally, we see steps in the graphs for 2- and 3-wire; with 4-wire, the graph remains stable.

**Our test proves:** The patented Kreuzer circuit allows for **precise measurement results** through

- high
**temperature stability** - and
**correction of changes**in resistance in both cable leads.

**Asymmetric changes** in resistance, e.g. at connectors, and **symmetric changes **in resistance, e.g. through temperature variation, are **corrected** and do not affect the measurement result.