ECE3281 Electronics Laboratory Experiment #9 TITLE: OPERATIONAL AMPLIFIER: Bridge Configurations OBJECTIVE: Test and analyze bridge configurations in which the opamp is the drive circuit Commentary: The operational amplifier is a differential amplifier. As such is designed to sample difference between input signals and amplify them. When used in combination with bridge circuits, which are strongly associated with different voltages across two nodes, the result is simple, direct, and highly effective as a circuit application. The simple resistive bridge, also known as the Wheatstone bridge, is shown by figure 9-1. It determines small changes in one branch of the bridge by assessing the voltage VAB across the bridge points. R VR R A B r V AB = ------------------------ V R 2 ( r + 2R ) VAB R+r R Figure 9-1: Wheatstone bridge The bridge is mildly non-linear with respect to its incremental resistance r. But as long as r << R, this mild non-linearity is not a problem and we can expect VAB to be proportional to r/R. If we apply an opamp across the bridge, as represented by figure 9-2, the result is still non-linear, but with amplification as defined by the ratio Rf/R. RF R R VR VO R Rx = R+r r⁄R 2 V o = α ------------------------------------------------------------------ V R [ ( 1 + 2α ) + ( 1 + α ) ( r ⁄ R ) ] where RF Figure 9-2: Wheatstone bridge with opamp differential amplifier boost RF α = -----R The non-linearities of the Wheatstone bridge circuit can be overcome by a circuit which uses the bridge itself as a feedback network. This circuit is shown by figure 9-3. R+r R R VR VO r V o = – ---V R R R Figure 9-3: Wheatstone bridge with opamp: Linear configuration and any amplification boost stages can be added after the fact to this configuration. As in other experiments using the opamp, we will use the 741C. The package and pin-out are represented in appendix 9A. This part and the resistances needed for the experiment will be in the parts/wires drawer of your workstation. PROCEDURE: A-1: Construct the circuit of figure 9A-1 (same as figure (-2) on the prototyping motheroard. Suggestions about wiring layout are indicated by figure 9A-2. Choose all resistances = 10 kΩ, including RF. Theses parts should be in your parts/wires drawer as residual parts from previous experiments. Let VR be the 5V supply of the MFJ box. RF R R VB VO Rx R RF Resistance box Figure 9-2: Wheatstone bridge with opamp differential amplifier boost Note, as in other experiments using the opamp, that it requires three voltage rails: +VS, -VS, and GND. Connect these power rails first, but do not turn on the power until the inputs and network is connected. Power rails should be +VS = +12, and -VS = -12, taken from the internal voltage supplies of the MFJ prototyping platform. A-2: Measure DC output as a function of r starting with Rx = 7.999 kΩ and through 12.999 kΩ. Use the DMM to monitor DC output. You should make approximately 20 measurements, evenly spaced. A-3: Change both resistances used for RF to 100kΩ in the above circuit and repeat part A-2. BNC SWITCH FREQUEBCY OUTPUT INDICATORS 10KΩ MULTIPLIER (To DMM) WAVEFORM VOLTAGE +VS +12V RF 5V RF -12V AMPLITUDE GND -VS (To R box) DC OFFSET 1KΩ POWER CLOCK PULSE MFJ Figure 9A-2: Recommendations for set-up of opamp bridge circuits. LOGIC SWITCHS B-1: Set up the circuit of figure 9B-1 (same as figure 9-3), with all resistances = 10 kΩ except for Rx, which will be the resistance box. Resistance box Rx R R VR VO R Figure 9B-1: Wheatstone bridge with opamp: Linear configuration B-2: Measure DC output as a function of r starting with Rx = 1.999 kΩ and through 19.999 kΩ. Use the DMM to monitor DC output. You should make approximately 20 measurements, evenly spaced. C-1: Modify the circuit to the form of a Wein Bridge, as represented by figure 9C-1. Note that the source VR is now the function generator instead of the 5V source. VR should be set to 1kHz at amplitude 1.0V. All resistances should be 10kΩ, and the capacitances should be .001µF. Monitor Vo using CH1 of your Oscope. Figure 9C-2 will give you some suggestions about setup on the prototyping motherboard. The parts that you need should be in the Ziploc bag or the parts box in the parts/wires drawer of your workstation. C function generator VR R1 R C R VO (sinusoidal) R Figure 9B-1: Wein bridge with opamp: Linear configuration C-2: Vary the input frequency from 1kHz to 100 kHz, in increment factors of 2, 3, 5,7 per decade and record the amplitude of Vo. At some point within the plot, you should notice that there is a noticeable dip in the amplitude. Take extra measurements about this point. C-3: Replace R1 with a resistance of value 20kΩ, and repeat part C-2: C-4: Replace R1 with a resistance of value 30kΩ, and repeat part C-2: (To function generator) BNC SWITCH FREQUEBCY OUTPUT INDICATORS 10KΩ MULTIPLIER (To CH1 - Oscope) WAVEFORM VOLTAGE +VS +12V R1 -12V AMPLITUDE GND -VS DC OFFSET 1KΩ POWER CLOCK PULSE LOGIC SWITCHS MFJ Figure 9C-2: Recommendations for set-up of opamp-driven Wein bridge tests s D-1: When you have completed all of the required measurements, remove the parts from the prototyping motherboard and return them to the Ziploc bag or parts box in the parts/wires drawer for use by the next person down the line. ANALYSIS: 1. Plot the measured data of parts A-2 and A-3 on the same plot with data as defined by the equation given for figure 9-2. Data should be entered as small circles. Equation data should be a continuous line (since the equation defines all points). Comment on the comparisons between the measurements and the analytical equation results, if any. 2. Plot the measured data of part B-2 on the same plot with data as defined by the equation given for figure 9-3. Data should be entered as small circles. Equation data should be a continuous line (since the equation defines all points). Comment on the comparisons between the measurements and the analytical equation results, if any. 3. How would you create a circuit that has the linearity of circuit 9-3 but has the sensitivity (transfer gain) of circuit 9-2? 4. Plot Vo vs frequency for both sets of measurements taken under parts C-2, C-3 and C-4. Determine the resonant frequency 1 2π 1 RC (where Vo = minimum) for both cases and compare to f = ------ × -------- . Comment on the three plots and the relationship of the output minimum to the ratio R1/R. REPORT: This is an informal report. APPENDIX A: Pinout for 741C opamp non-inverting input +VS +VS Vo V+ Vo V- -VS inverting input Figure A9-1a: Operational amplifier symbol V- V+ -VS Figure A9-1b: 741C Opamp: 8-pin DIP