16. UNBALANCED WHEATSTONE BRIDGE EVALUATION OF RESISTANCE CHANGES OF A RESISTIVE SENSOR 16.1. Task of the measurement 16.1.1. Connect the R U converter using an operational amplifier according to the schematic diagram in Fig. 16.1 (U r = 10 V, R N1 = 10 k and measure dependence f C of the resistance of converter on its angular deflection in the range = 0 to 180° with the increments 15° (basic position of the converter slider = 90° corresponds to the resistance R 0 , i.e. R = 0). 16.1.2. Connect the resistive sensor into the Wheatstone bridge supplied from the voltage source supplying voltage U AC = 5 V (Fig. 16.2). Before starting measurement balance the bridge using the resistance decade box R D for the value = 90°. Measure the dependence f BV of the bridge output voltage U BD on the change of angular position of the sensor slider , which corresponds to the change of the sensor resistance R (for the same values of as in point 16.1.1). Find theoretical relation for this voltage, that is U BD R U R0 f BV ( R ) AC R 4 1 2 R0 (16.1) 16.1.3. Connect the resistive sensor into the Wheatstone bridge supplied from the current source supplying current I = 3,6 mA. Realize the current source by means of an operational amplifier according to Fig. 16.3. Before starting measurement balance again the bridge using the resistance decade box R D for the value = 90°. Measure the dependence f BC of the bridge output voltage U BD on the change of angular position of the sensor slider , that is on the change of the sensor resistance R (for the same values of as in point 16.1.1). Find theoretical relation for this voltage, that is U BD f BC (R) I 4 R R 1 4 R0 (16.2) 16.1.4. Connect the so-called „linearized bridge“ according to the Fig. 16.4. Set the supply voltage U Z = 2,5 V. Before starting measurement balance again the bridge using the resistance decade box R D for the value = 90°. Measure the dependence f LB of the output voltage U 2 on the change of angular position of the sensor slider , that is on the change of the sensor resistance R (for the same values of as in point 16.1.1). Find theoretical relation for this voltage, that is U 2 f LB (R) R UZ 2 R0 (16.3) Page 1 of 4 16.1.5. Plot in a common graph deviations of the measured values according to points 16.1.2, 16.1.3 and 16.1.4 from the linear function. The slope of the straight line from which you will calculate deviations from the linearity find from the end points of the measured dependence f LB (R) (that means for = 0 and = 180°). If the absolute values of output voltage in the both end points are not identical, replace them by / arithmetic mean value of these two absolute values (straight line U 2/ f LM (R ) connecting these two points intersects the origin of coordinates [R, U 2 ]). Deviations of the functions f BV (R), f BC (R) and f LB (R) from the linearity find (approximately) / as deviation of these functions from the straight line U 2/ f LM (R ) . This can be done, since values of supply voltage or current in measurements in points 16.1.2, 16.1.3 and 16.1.4 are in the instruction given so, that the slopes of all these functions in the origin be approximately the same. 16.2. Schematic diagrams RX C RN1 R4 = R0 - UAC 10 k B + Ur = 10 V RD = R0 UBD U2 D RX = R 3 = R0 R0 R A Fig. 16.1 Schematic diagram of R U converter Fig. 16.2 Wheatstone bridge supplied from a voltage source I + C R0 RD = R0 UBD D B UZ R0 R R0 A RN2 = 1 k Fig. 16.3 Wheatstone bridge supplied from a current source Page 2 of 4 RD = R0 R 0 R R0 - UZ + U2 R0 Fig. 16.4 Schematic diagram of the „linearized bridge“ 16.3. List of the equipment used PS 1 - power supply for operational amplifier, type ...; PS 2 - digitally controlled DC voltage source, type …; DV - digital voltmeter, type ..., error specification …; R N1 - resistor with resistance 10000 , tolerance ... %; R N2 - resistor with resistance 1000 , tolerance ... %; - resistance decade box 0 to 99999.9 , tolerance 0,2 % RD a box simulating the resistance sensor R 0 R (resistance potentiometer, position of its slider is indicated by a pointer over an angular scale), operational amplifier in a box provided with terminals, two identical resistors R 0 in a box. 16.4. Theoretical background For the ideal operational amplifier, there is for the circuit in Fig. 16.1 (R U converter) U2 Ur RX RN1 (16.4) and therefore the measured resistance can be found using the relation RX R N1 U2 Ur (16.5) Unbalanced Wheatstone bridge is in practice used most by evaluation of the changes of resistance of resistive sensors used for measurement of the non-electrical quantities. This solution has an advantage that zero output voltage corresponds to the basic value of the measured non-electrical quantity (e.g. 0 °C by resistance thermometer). The output voltage is proportional to the change of the resistance, and therefore also to the change of the measured quantity. Page 3 of 4 The same concerns the polarity - e.g. positive voltage corresponds to positive temperature and negative voltage corresponds to negative temperature. This cannot be achieved by the classical RU converter according to Fig. 16.1. The disadvantage of that solution is that the output voltage of the unbalanced Wheastone bridge is nonlinear function of the sensor resistance changes. The magnitude of the nonlinearity depends on the way of supplying the bridge (voltage source or current source). In the circuit shown in Fig. 16.4 the dependence of the output voltage on the resistance changes R is theoretically linear. Because of the difficulties in preparation other resistive sensors (resistance thermometer, resistance strain gauge), the measured model of the general resistive sensor in this task is realized as a series connection of resistors with constant value of resistance and a resistor, the value of resistance of which is changed with the change of the angular position of a pointer connected to the slider of the resistor. Basic value of the sensor resistance R 0 corresponds in this model to the angular deflection = 90°, and its angular deflection can be changed in the range of 90°. Notes to the measurement 1. Ground terminal on the box with the operational amplifier should be connected to the negative pole of the input voltage (see points 16.1.3 and 16.1.4). 2. Bridges should be balanced every time before starting measurement of the dependences (16.2), (16.3) and (16.4) for the angular deflection of the sensor slider = 90°. This balance is achieved by changing resistance of the resistive decade box. Calculate deviations of these three dependences from the linearity (see point. 16.1.5). Plot these deviations in common graph and evaluate the circuits from the point of linearity in the conclusion of your report. 3. Set the chosen values of angular deflections as accurately as possible, otherwise the non-linearity of the bridge corresponding to theoretical functions (16.1) and (16.2) could be masked by the non-linearity caused by the inaccurate setting the values of . 4. One of the tasks in points 16.1.2 to 16.1.4 is to derive the relations (16.1) to (16.3). When deriving relations (16.1) and (16.2) express the voltage U BD as the difference of voltages across neighboring resistors in the low arms of the bridge. To find these voltages, use in case (16.1) relation for the voltage divider and in case (16.2) relation for the current divider. The derivation is shown in [1], chap. 6.1. Evaluate in the conclusion of your report, if the non-linearity of the unbalanced Wheatstone bridge is according to results of your measurement better for bridge powered from voltage source or from the current source. If result of you measurement does not comply with comparison of theoretical relations (16.1) and (16.2), state what is probably the cause of this disagreement. When deriving the relation (16.3), do not forget to take into account that in this circuit there is not the non-inverting amplifier input connected to ground. This has to be taken into account when writing relations for currents flowing through resistors R D and R 0 R. For more details see [1], chap. 6.1. Page 4 of 4