Strain gauges · Measurement

Wheatstone Bridge Output Voltage Calculator

Calculate the exact output voltage and ratio U_M/U_B of an unbalanced Wheatstone bridge from the four arm resistances and the excitation.

DMSKeil 2017

Inputs

Resistance R₁ [Ω]Resistance R₂ [Ω]Resistance R₃ [Ω]Resistance R₄ [Ω]Excitation U_B [V]

Constant-voltage excitation and an unloaded measuring diagonal (high-impedance amplifier input). Constant-current excitation or a low-impedance load require different relations.

Results

Enter values and run the calculation.

Method

What is calculated?

The bridge is two voltage dividers on the same excitation; the output is the difference of the two divider voltages. Hence equal-sign resistance changes in adjacent arms cancel while those in opposite arms add. For small changes eq. 4.1 reduces to the linearised basic equation 4.6.

Equations

U_M/U_B = R₁/(R₁+R₂) − R₄/(R₃+R₄) (Keil Gl. 4.1)

Abgleich: R₁/R₂ = R₃/R₄

R_in = (R₁+R₂)‖(R₃+R₄)

Limits

Assumptions and typical mistake

Constant-voltage excitation and an unloaded measuring diagonal (high-impedance amplifier input). Constant-current excitation or a low-impedance load require different relations.

Assigning the arms incorrectly: R₂ and R₄ are adjacent to R₁, R₃ is opposite; swapping flips the sign.

Inputs

What you enter – and where the values come from

Resistance R₁ [Ω]: Resistance of the first bridge arm. In strain-gauge measurements this is usually the active gauge at its actual loaded value: unloaded nominal resistance plus resistance change. Source: precision-ohmmeter measurement or the resistance-change-from-strain calculator.
Resistance R₂ [Ω]: Resistance of the arm forming the first voltage divider with R₁ (‘adjacent’ to R₁). In a half bridge the second gauge or compensation gauge, in a quarter bridge a fixed resistor in the instrument. Source: nominal value or measurement.
Resistance R₃ [Ω]: Resistance of the arm diagonally opposite R₁. Changes here act in the same direction as at R₁. Source: nominal value or measurement; in the instrument a precision resistor for quarter/half bridges.
Resistance R₄ [Ω]: Resistance of the fourth arm (forms the second divider with R₃, ‘adjacent’ to R₁); in a quarter bridge a fixed resistor in the instrument. Source: nominal value or measurement.
Excitation U_B [V]: The bridge excitation is the DC or AC voltage with which the amplifier supplies the bridge circuit. The signal is proportional to it – which is why signals are usually stated as a ratio in mV/V and the excitation is only needed for the absolute signal voltage. Source: amplifier setting, usually 2.5 V, 5 V or 10 V; the upper limit is set by gauge self-heating (see the excitation calculator).

Context

What this calculator is for

Checking zero errors caused by resistance tolerances, sizing balancing resistors and verifying the signal a resistance standard produces in one arm.

What comes next

Enter all four arm resistances including lead contributions.
Enter the excitation and read the output voltage.
Vary one resistance to reproduce balance or a defined unbalance.

Results

How to read the results

0 mV/V means balance; the sign shows which divider sits higher.
Use the calculator to check what zero signal resistor tolerances produce: a 0.1 % deviation of one arm already gives 0.25 mV/V.

Result quantities

What each value means

Voltage ratio U_M/U_B [mV/V]: Bridge output per volt of excitation. 0 = balanced. Positive when the divider R₁/R₂ delivers more voltage than R₄/R₃ – i.e. R₁ or R₃ grew or R₂ or R₄ shrank.
Output voltage U_M [mV]: Absolute voltage between the two measuring points of the bridge at the entered excitation – what a voltmeter across the measuring diagonal shows.
Bridge resistance at the supply [Ω]: Resistance seen by the excitation source (both arm pairs in parallel). Relevant for the excitation load and for the lead-wire calculator.
Supply current [mA]: Total current drawn by the complete bridge from the excitation source. Use it to check that the amplifier can supply enough current and that cables or excitation are not unusually loaded.

Source

Technical basis

Keil, Dehnungsmessstreifen, 2nd ed. 2017, secs. 4.1–4.2, eqs. (4.1)–(4.6).

The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.

FAQ

Frequently asked questions

How does this differ from the balanced-bridge calculator?

There an unknown resistance is found from balance; here the output of the deliberately unbalanced bridge is computed, as used in strain-gauge measurement.

Why is the signal given in mV/V?

Because U_M is proportional to U_B; the ratio characterises the bridge independently of the excitation.

Is the output linear in ΔR?

Only approximately; with one active arm eq. 4.7 gives an error equal in size to the strain itself.

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