Data Acquisition

30 Practical Data Acquisition for Instrumentation and Control SystemsIt can be shown that if any one of the bridge resistances is an active element whosenominal resistance (R 0 ) is precisely matched to each of the other completion resistors (i.e.R 0 = R 2 = R 3 = R 4 ), then for a small change in the active element resistance (∆R), the ratioof the output voltage to the input voltage is given by:V 0 ∆ R=V EX 4 R0This equation holds true irrespective of which arm of the bridge contains the activeelement.Further to this, it can be shown that if there are (N) arms of the bridge which contain anactive element, then for a small and equal change in the active element resistances ∆R, theratio of the output voltage to the input voltage is given by:V 0 N ∆ R= ×V EX 4 R0This equation is true only if the sensitivity, of adjacent active elements of the bridge(i.e. R 1 & R 2 , R 3 & R 4 , R 1 & R 3 or R 2 & R 4 ) to changes in the physical parameter beingmeasured, is of opposite polarity. This means that if R 1 and R 2 are active elements, thenfor an incremental change in the physical parameter being measured, the resistance of R 1increases by ∆R and the resistance of R 2 decreases by ∆R. If the values in resistance of theactive elements increase by the same amount, then the resistance in both arms wouldtheoretically remain the same, the ratio of their resistances would remain the same, andtheir effects would cancel.The above equation shows that the Wheatstone bridge is a ratiometric circuit whoseoutput voltage sensitivity is proportional to the excitation voltage and the number ofactive elements in the bridge. The more closely matched the completion resistances are tothe active resistive element(s), the smaller will be the unbalanced output voltagecompared to the input excitation voltage. In addition, the output voltage polarity isdependent on where the active elements are positioned in the bridge, and whether theseactive elements increase or decrease resistance to an increase in the physical parameterbeing measured.The quarter bridge, half bridge and full bridge configurations, in which strain gaugesform the active elements, are discussed in the following sections.2.8.2 Quarter bridge configurationWhere only one of the four resistors in the Wheatstone bridge is active, as shown inFigure 2.17, the circuit is known as a quarter bridge.Figure 2.17Quarter bridge circuit