Wheatstone Bridge Calculator

This calculator can be used to either design a Wheatstone bridge or to interpret the output of a sensor within a Wheatstone bridge. As shown in Figure 1, the Wheatstone bridge is a simple circuit consisting of two sets of series resistors connected in parallel. 

 

Figure 1. A Wheatstone bridge circuit

 

The Wheatstone bridge configuration allows for high accuracy measurements of unknown resistance. 

 

Balancing a Wheatstone Bridge Circuit

This type of circuit is balanced when:

 

$$ V_{out} = 0 $$

 

To achieve this balance, the resistance ratios in the circuit must be balanced:

 

$$ \frac{R_1}{R_3} = \frac{R_2}{R_x} $$

 

Even a small change in resistance (R_x) causes the bridge to become unbalanced. These changes result in a non-zero voltage at V_out with the polarity indicating if R_x is smaller or larger than the balanced value. Utilizing a differential amplifier across the V_out terminals to extract the differential signal while rejecting common-mode noise makes precise detection of very small changes possible. 

This calculator with either solve for V_out in the figure above given the R_x resistance or solve for the R_x resistance given V_out.

 

Wheatstone Bridge Equation—Using KVL and KCL

To solve for output voltage, V_out, given the R_x resistance, we use Kirchoff's Voltage Law (KVL) and Kirchoff's Current Law (KCL) to arrive at the following equation:

 

$$ V_{out} = V_{in} \centerdot (\frac{R_x}{R_3+R_x} - \frac{R_2}{R_1+R_2}) $$

 

Where:

• V_out = differential voltage across the Wheatstone bridge, in volts
• V_in = input voltage to the Wheatstone bridge, in volts
• R_n = resistor values, expressed in ohms

 

Similarly, to solve for R_x given the output voltage V_out, we'll use KVL and KCL to arrive at the following equation:

 

$$ R_{x} = \frac{R_2 R_3 + R_3 \centerdot(R_1+R_2) \centerdot \frac{V_{out}}{V_{in}}}{R_1 - (R_1+R_2) \centerdot \frac{V_{out}}{V_{in}}} $$

 

Further Reading on the Wheatstone Bridge

• Textbook—Bridge Circuits
• Textbook—Mesh Current Method and Analysis
• Worksheets—Bridge Circuits