1 Bridge Overview

A Wheatstone bridge is a circuit used to measure a change in resistance among a set of resistive elements. The circuit has two parallel resistive branches that act as voltage dividers for the excitation voltage, V_EXCITATION. The output of each resistor divider is nominally at V_EXCITATION divided by two. With no applied load, the change in the resistance of the elements, ΔR, is equal to zero. Assuming an ideal system where the nominal resistance of each element is R, each voltage divider is at the same potential and the differential bridge output voltage, V_OUT, is zero. When a load is applied, one or more of the elements changes resistance such that ΔR ≠ 0 Ω. This causes a change in V_OUT that can be calculated very precisely by making a differential measurement across the bridge. Figure 1-1 shows the basic configuration of a simple bridge circuit using resistive elements.

Figure 1-1 Basic Configuration of a Simple Bridge Circuit

The basic bridge circuit is constructed using resistive elements with a single variable element in the bridge. This element is a resistive transducer that translates some physical parameter into a change in resistance. If this change in resistance is proportional to a change in the physical parameter, measuring ΔR yields an accurate representation of the physical property being sensed. While this document focuses on bridges using resistive elements, it is possible to construct a bridge using inductive or capacitive elements as well.

Bridge operation can be better understood by analyzing each side of the bridge in more detail. For example, the right side of the bridge in Figure 1-1 looks like the voltage divider circuit shown in Figure 1-2:

Figure 1-2 A Resistive Element Measured as a Voltage Divider

Equation 1 calculates V_OUT with respect to ground for the system in Figure 1-2:

Assuming V_EXCITATION = 6 V, R = 3000 Ω, and ΔR = 3 Ω, Equation 1 can be used to calculate that V_OUT = 3.0015 V. Then, the voltage across R is calculated to be V_R = V_EXCITATION - V_OUT = 2.9985 V. This yields a voltage across ΔR of V_ΔR = V_OUT - V_R = 0.003 V. While Equation 1 works in theory to calculate V_OUT, V_R, and V_ΔR, a real system must measure V_OUT and V_R to be able to derive V_ΔR. This can introduce additional challenges due to the limitations of standard measurement equipment.

For example, a simple 4-digit multimeter used to measure V_OUT and V_R could produce rounding errors that affect the calculation of V_ΔR: if the multimeter rounds V_OUT = 3.0015 V up to 3.002 V and V_R = 2.9985 V down to 2.998 V, then V_ΔR = 0.004 V; or, if V_OUT is rounded down to 3.001 V and V_R is rounded up to 2.999 V, then V_ΔR = 0.002 V. Both of these cases yield a measurement error of 1 mV relative to a 3-mV signal, or ±33% error. Ultimately, the 4-digit multimeter does not have enough resolution to consistently determine the precise value of ΔR by measuring across either resistive element in the divider.

For better results, the single-ended measurement shown in Figure 1-2 is changed to a differential measurement by placing the resistive transducer in a bridge configuration. In Figure 1-3, the bridge uses a second resistive path in parallel with the transducer path. With no applied load, ΔR = 0 Ω and V_OUT = 0 V.

Figure 1-3 A Simple Bridge Using a Differential Measurement Across Two Resistive Paths

Equation 2 calculates the differential output voltage for the system shown in Figure 1-3 assuming R1 = R2 = R3 = R and R4 = R + ΔR.

Using the same values from the single-ended example where V_EXCITATION = 6 V, R = 3000 Ω, and ΔR = 3Ω, V_OUT is now calculated to be 1.49925 mV. Importantly, the same 4-digit multimeter can measure V_OUT much more precisely and on a millivolt scale as either 1.499 mV (rounded down) or 1.500 mV (rounded up). Measuring V_OUT differentially in a bridge configuration yields a measurement error of <1 μV relative to a 1.5-mV signal, or 0.067%. This result occurs because a bridge configuration enables direct measurement of ΔR instead of a comparative measurement between ΔR and R. A direct measurement also enables V_OUT to be amplified to get a larger input signal to the ADC. This amplification enables higher-resolution measurements of smaller values of ΔR.

One challenge with a single active resistive element bridge is that it has an inherent non-linearity in the measurement. Different bridge constructions have different non-linearities, and some topologies eliminate this inherent non-linearity. This is discussed in more detail in the next section.