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Bridge circuits are widely used for the measurement of resistance, capacitance, and inductance. The resistive bridge, also known as Wheatstone bridge, is discussed in this section. |
Basic Wheatstone Bridge Circuit |
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A basic Wheatstone bridge circuit contains four resistances, a constant voltage input, and a voltage gage, as illustrated below.
For a given voltage input Vin, the currents flowing through ABC and ADC depend on the resistances, i.e., ![]() The voltage drops from A to B and from A to D are given by, ![]() The voltage gage reading Vg can then be obtained from, ![]() Now suppose that all resistances can change during the measurement. The corresponding change in voltage reading will be, ![]() |
Balanced Wheatstone Bridge Circuit |
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If the bridge is initially balanced, the initial voltage reading Vg should be zero. This yields the following relationship between the four resistances, ![]() We can use this result to simplify the previous equation that includes the changes in the resistances. Doing so results in the solution for the change in Vg, ![]() where h is defined by, ![]() Moreover, when the resistance changes are small (< 5%), the second order term h is approximately zero and can be ignored. We then have, ![]() which is the basic equation governing the Wheatstone bridge voltage in strain measurement. The coefficient |
Equal-Resistance Wheatstone Bridge Circuit |
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In practice, one often uses the same resistance value for all four resistors, R1 = R2 = R3 = R4 = R. Noting that r = 1 in this case, the change in voltage can be further simplified to, ![]() By thoughtfully selecting the target and reference resistances, the Wheatstone bridge circuit can amplify small changes in resistance and/or compensate for changes in temperature. |