The Wheatstone Bridge.

Fundamental Series FS03 - January, 2006

The Wheatstone Bridge

Though not actually invented by Charles Wheatstone, the circuit element arrangement named after him, the "Wheatstone Bridge," is a staple in instrumentation and sensor designs. The Wheatstone bridge can be used to measure an unknown resistance, inductance or capacitance, and is widely used for strain gage measurements

Notes:

Biography and Backgound

Charles Wheatstone was born on February 6th, 1802, at Barnwood Manor House, near Gloucester, England. His father and uncle were music dealers and manufacturers.

Charles was a genius, excelling in anything he attempted. He invented several musical instruments, developed and made the use of the telegraph practical, and made several discoveries such as the measurement of the velocity of electricity in a wire, and the spectrum analysis, which lead to the discovery of many new elements and observations of heavenly bodies.

In 1843 Wheatstone presented a paper on what he is most famous for: The Wheatstone Bridge. Though it was first described by Samuel Hunter Christie (1784-1865) it was Wheatstone that made it practical. It is a device for measuring the electrical resistance of an unknown resistance, and still goes by the name of “Wheatstone's Bridge or Balance”.

His paper was full of simple and practical formulas for the calculation of currents and resistances by Ohms's Law. He introduced the concept of a unit of resistance, such as a foot of copper wire weighing one hundred grains, and showed how it might be applied to measure the length of wire by its resistance. He was awarded a medal for his paper by the Royal Society.

Wheatstone was knighted January 30, 1868, after he completed the automatic telegraph. He was awarded over 34 distinctions and diplomas by England and foreign societies ---a testament to his scientific achievements.

While on a trip to Paris in 1875 to perfect his receiving instrument for submarine cables, he caught a cold and inflammation of the lungs which led to his death in Paris on October 19, 1875 at the age of 73.

He left his writings, books and instruments to King’s College in England where they are preserved in the Wheatstone Laboratory.

Charles Wheatstone
(1802-1875)

An Example.

A Wheatstone Bridge consists of two parallel potential dividers connected between a voltage source and ground.

A resistive Wheatstone bridge circuit is shown in Figure 1.
The voltage between the junction of R1/R2 and R3/R4, which is:

Vb1-Vb2

is called the "bridge voltage", or V-bridge. When the voltage values match at both junctions, V-bridge is 0V, and the Wheatstone bridge is said to be balanced. This point is also sometimes referred to as the "Null" point.

Using the voltage divider application of Kirchoff's Laws we can calculate the junction values for the parallel dividers:

Vb1 = V1 × R2 ÷ (R1+R2)

Vb2 = V1 × x R4 ÷ (R3+R4)

at the balance point:

Vb1 = Vb2

Stating Vb1 and Vb2 in terms of V1, we get:

V1 × R2 ÷ (R1+R2) = V1 × R4 ÷ (R3+R4)

R2 ÷ (R1+R2) = R4 ÷ (R3+R4)

At the balance point, the ratios - not the absolute values of the resistance of each divider match. This is really cool - First, the ratios are voltage source independent, and second, it means that if three of the resistances are known at the balance point, it is possible to calculate the fourth unknown resistance.

A typical application of the Wheatstone bridge is to measure an unknown resistance. One of the "known" resistors in the "known" potential divider is a variable resistor. The variable resistor is adjusted until the bridge voltage goes to zero. At that point the unknown resistance can be calculated from above.

Suppose for example that R4 was a resistive element which varies proportionally with applied force as in the case of a strain gage where applied force:

F = k × Resistance,

where k is a linear (hopefully!) constant. To determine the force applied, we need to know the value of R4. We make R1 a variable resistor with a marked resistance indicator dial so we can read its value as we adjust it. We adjust R1 until the bridge voltage balances, or "Nulls". Solving for R4, at the balance point, R4 will be equal to:

R4 = (R2 × R3) ÷ R1

and knowing R4 we can calculate applied force:

Force = k × R4.

Modern transducers such as pressure transducers typically implement the complete bridge internally.

There are more than one configuation of the basic bridge circuit. If the resistive element occupies a single leg of the bridge, it is called a "quarter bridge." If two of the four legs are occupied, it is call a "half bridge." If all four of the legs are occupied, it is called a "full bridge." The descriptive equations vary for each topology, but the underlying principle still applies.

The Wheatstone bridge works equally well for capacitive and and inductive elements, the only difference is that an AC excitation voltage is required.

A quarter bridge has one element in one leg

A half bridge has two elements in two legs

A full bridge has four elements in four legs

In conclusion

Introduced by Charles Wheatstone in 1843, The "Wheatstone Bridge," is still widely used in instrumentation and sensor designs. The Wheatstone bridge can be used to measure an unknown resistance, inductance or capacitance. It is widely used for strain gage measurements, and with the advent of Micro-Electro-Mechanical Systems (MEMS) devices, it is finding even more and wider ranging applications in modern instrumentation.