Experiment 1: Index of refraction

Indiana U, Physics Dept (H.O. Meyer 7/06)
Lab #3: Operational Amplifiers
Goal: Learn how to use operational amplifiers (op-amps) with various types of feedback
gain control.
Equipment: OP-07 op-amp, bread board, assorted resistors and capacitors, DMM,
Operational amplifiers (short: op-amps) are voltage amplifiers with very high gain. An
op-amp has two inputs: one called ‘non-inverting’ (label +), and the other ‘inverting’
(label –). Normally, an op-amp is used with ‘feedback’, i.e., the output signal is fed back
in some way to affect the input. The function of an op-amp circuit is determined by how
this feedback is arranged. The function of a circuit with an op-amp can be understood
easily by remembering just two ‘golden’ rules:
No charge flows into or out of either of the two inputs.
The output (in whatever feedback scenario) strives to make the voltage difference
between the two input zero.
Our op-amp is an OP-07, actually an integrated circuit with
dozens of transistors, packaged in a mini-DIP (Dual InLine Package) with eight pins. You will find a data sheet
for the OP07, including the pin assignments, at the end of
this document. The circuit is energized by the supply
voltages ±V which we choose as ±15 V. If the output wants
to exceed the supply voltage, the signal is ‘clipped’ (see
Inverting Amplifier
In this application (see figure on the right) the feedback
resistor, R2, is connected to the inverting input. The
input signal is applied through the series input resistor
R1 to the inverting input. The resistor R3 (equal to the
parallel resistance of R1 and R2) in the non-inverting
input minimizes the output-offset voltage caused by the
input bias current, but the circuit works quite well with
R3 = 0.
The op-amp gain is given by
=− 2
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Refer to the pin assignments in the data sheet and build an inverting amplifier as shown
in fig.3. Pick R1 and R2 to yield a gain of −10. Calculate the offset minimizing resistor R3
and choose a value close to the calculated one. Use a DMM to measure the true values of
the resistors. For the input, use a signal generator to produce a 1 kHz sine wave of 1 V
peak-to-peak amplitude with no DC offset. Use the oscilloscope to measure Vin and Vout
simultaneously. From Vin and Vout determine the gain and compare to the theoretical value
Next, leaving R1 unchanged, calculate the value of R2 needed to yield a gain of 100.
Select a resistor for this new value of R2 and measure the true value. Replace R2 in the
circuit with the new value and input the same signal as before. Measure again Vin and
Vout, determine the gain and compare to theoretical value. Adjust the DC offset of the
signal generator until you can observe clipping.
The ‘slew rate’ measures how quickly the op-amp reacts to a sudden change at the input.
Determine the slew rate by applying a rectangular wave to the input and measuring with
the scope the slope of the output. The slew rate is usually quoted in V/μs. Compare to the
value for the slew rate in the dada sheet.
The largest frequency fmax for a sine wave that can be amplified without distortion is
determined by the requirement that no part of it exceeds the slew rate. Predict fmax and
verify your prediction by a measurement.
Non-inverting Amplifier
The circuit on the right represents a non-inverting
linear amplifier. Here the input goes to the noninverting input and a voltage divider returns a
fraction of the output voltage to the inverting input.
Pick the same resistors that you used in sect.2, and
construct the circuit. Measure Vin and Vout,
determine the gain and compare to the theoretical
value for the gain of this circuit,
= 1+ 2
Op-amps can be used to construct a circuit that integrates
an electrical signal over time. The circuit on the right
represents such an integrator circuit. The capacitor serves
as the memory of the integrator. To clear the memory, we
simply short circuit the capacitor. Since you have to do
this often, it is best to provide a switch or a push button
(S) to do this. When the switch is opened, the integration
starts (t = 0).
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Use the 2μF capacitor from lab #2 and build the circuit. For R, try R = 1 kΩ. Note, that
the smaller R, the larger the output signal.
Making use of the two golden rules, we obtain for the time-dependent output voltage
(t ) dt
t =0
Connect the input to ground, and start the integrator. Since the integrand is now zero, Vout
should also remain zero. Usually, however, there is a small drift of the output (because
the golden rules are not exactly true). To cure this, the OP-07 provides an offset trim that
allows you to adjust the balancing of the two inputs. Install the offset trim by connecting
a 20 kΩ potentiometer between pins 1 and 8. The moving contact of the potentiometer
connects to the +15V supply. Test if this feature allows you to adjust the drift of the
integrator to (near) zero.
Next, we want to convince ourselves that this circuit actually integrates. To this aim, we
apply a constant voltage V0 to the input. Eq.3 tells us that in this case the output is a
linear function of the time. Use a voltage divider to generate V0. We want a small V0
(order of mV) such that Vout takes about 30s to increase from 0 to 15V. Select the divider
resistors (and thus V0) accordingly. Measure the rate of increase of Vout . Compare with
the rate calculated from the values of the resistors and the capacitor in the circuit.
The Magnetic Field of the Earth
A large many-turn coil is an excellent transducer for B field measurements. This is
because of Faradays law, which states that an electromotive force ε is induced in the coil
when the magnetic field flux changes. When the coil is flipped by 180°, the flux changes
by twice the starting value. Thus, integrating this change is sufficient to determine the
flux, and we have
Vout = −
2 ANBs
ε ⋅ dt = −
Here, Bs is the component of the magnetic field in the direction of the coil axis, N is the
number of turns of the coil and A its effective area. The average area of a multi-layer coil,
whose mean radius is r and whose maximum and minimum radii are r ± δ, is given by
A = π r 2 + 13 δ 2
Choose input resistor R such that a single flip causes a Vout that can be measured with at
least 10% accuracy with the DMM. Note that the drift is faster when R is smaller. It is not
necessary to completely eliminate the drift; it only has to be small compared to the final
value for Vout. Make a series of measurements flipping back and forth.
Carry out three sets of measurements: Bz with the coil axis vertical, Bx with N-S
horizontal coil axis (along the lab room), and By with horizontal E-W axis (perpendicular
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to both). Combine the three components to get the magnitude of the B vector. Compare
with the accepted value: http://ngdc.noaa.gov/seg/geomag/jsp/struts/calcPointIGRF.
The S.I. unit for B (appropriate for eq.4) is 1 T (Tesla), and 1 T = 104 G.
List possible sources for uncertainties. Evaluate the error of the three individual field
measurements. Combine the errors to get the uncertainty of the magnitude B of the field.
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