It can be shown that . . .

The output voltage, eo, is the difference between the voltage across arm BC and DC, which is:

(1")     

eo is the bridge output voltage,

ei is the bridge excitation voltage,

R1 is the active arm resistance, and

R2, R3, and R4 are the resistances of the other arms.

After algebraic manipulation becomes:

(2")     

Recalling that eo fluctuates about zero and Rx fluctuates about its initial value (Rx = Rx + [[Delta]]Rx) yields:

(3")     

Dividing Equation 3" by RxR4 yields:

(4")     

We can assume that all bridge resistances are nominally equal and have a value R. This reduces Equation 4" to

(5")     

Equation 5" can be linearized under the (common) conditions of small transducer resistance fluctuations:

(6")     

Substituting Equation 6" into Equation 5" yields a relationship between the output voltage and change in resistance for a single active arm bridge:

(1)