# 102-wheatstone-measurement-bridge-simulation

Wheatstone bridge or Wheatstone measurement bridge is electric circuit for very precise resistance or impedance measurement. It has simple construction and generally looks like it is shown in picture bellow.

It can operate in balanced and non-balanced regime. Wheatstone bridge consists of two balancing legs, that are in fact two voltage dividers connected in parallel. Now, if voltage dividers are purely resistive, i.e. Z1=R1, Z2=R2, Z3=R3, Z4=R4, input voltage is divided and in terminal A it is

and in terminal B it is

If null-balance meter is positioned between points A and B, it will show zero if VAVB=0, i.e. if

So, if Wheatstone bridge is well balanced, i.e.

showing of null-balance meter is independent from input voltage, and depends only if resistors are balanced. If impedances Z1, Z2, Z3 and Z4 are made of some combination of pure resistor, capacitor and inductor then balancing legs are complex voltage dividers. In that case, voltage source should produce AC signal, and unknown impedance Z4 can be calculated as

when null-balance meter shows zero. However, if bridge is not balanced, voltage between A and B is

For non balanced Wheatstone bridge, voltage that comes from voltage source must be known (measured).
Balanced Wheatstone bridge can be used for extremely accurate measurement of resistance, capacitance or inductance. It is very accurate method because measurement with balanced Wheatstone bridge is based on difference measurement. By measuring difference of two magnitudes on the same place, measurement error caused by temperature drift of given impedances and other bad influences mutually cancel each other, including imperfectness in power supply such as noise or offset.

Since, there are resistive sensors for temperature or mechanical load measurements, Wheatstone bridge as difference measurement instrument can be also used for measurement of whole set of physical magnitudes.

Simulation model for Wheatstone bridge for AC signals is given in link bellow.