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