INDIANA UNIVERSITY, DEPARTMENT OF PHYSICS, P309 LABORATORY
Laboratory #3: Operational Amplifiers
Goal:
Learn how to use operational amplifiers (op-amps) with various types of
feedback gain control.
Equipment:
oscilloscope.
OP-07 op-amp, bread board, assorted resistors and capacitors, DMM,
(A) Introduction:
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.
(B) The op-amp chip
Our op-amp is an OP-07, actually an
integrated circuit with dozens of transistors,
packaged in a mini-DIP (Dual In-Line Package)
with eight pins. Fig.1 shows the pin
assignement of the OP-07. Pins 2 and 3 are
the inverting and non-inverting inputs,
respectively, pin 6 is the output, and pins 4 and
7 must be connected to power supplies to
energize the circuit.
Fig.1: Pin configuration of the
OP-07, viewed from the top
The supply voltages (in our case +15V and –15V)
determine the limits of the output. If the output
wants to exceed the supply voltage, it is ‘clipped’.
Fig.2: Clipping.
3-1
(C) Inverting Amplifier
In this application (see fig.3) 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 op-amp gain is given by
Vout
R
=− 2
Vin
R1
(1)
Fig.3
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 if one simply connects the non-inverting input to ground.
Refer to the pin assignments of fig.1 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 (eq.1).
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. From this, calculate the largest frequency fmax for a sine wave that can be
amplified without distortion. Check if your prediction for fmax is correct.
(D) Non-inverting Amplifier
Fig.4 shows a non-inverting linear op-amp circuit. Here
the input goes to the non-inverting input and a voltage
divider returns a fraction of the output voltage to the
inverting input. The gain for this circuit is
Vout
R
= 1+ 2
Vin
R1
(2)
Pick the same resistors from part (C) that gave a gain
of −10 and construct the circuit. Use as input a 1 Vp-p 1
Fig.4: The non-inverting
kHz sine wave with no DC offset from the signal
amplifier.
generator. Measure Vin and Vout, determine the gain
and compare to the theoretical value.
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(E) Integrator
Op-amps can be used to construct a simple
circuit that integrates an electrical signal over
time. Fig.5 shows the circuit for the integrator.
Using only the two golden rules, we obtain
Vout =
1
RC
t
∫ Vin (t) dt
(3)
t =0
The capacitor serves as the memory of the
integrator. To clear the memory, we just short
out the capacitor. Since you have to do this
often, it is best to provide a switch or a push button (S) to short out the capacitor. The
moment you open the switch corresponds to t=0, and starts the integration.
Use the 2µF capacitor from lab no.2 and build the circuit in fig.5. The smaller R, the
larger the output signal (try R=1kΩ).
Connect the input to ground, and start the integrator. Since the integrand is 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 sliding contact of the
potentiometer goes to the +15V supply. Test if this feature allows you to adjust the drift
of the integrator to zero.
Now, 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.
fig.5: Integrator
(F) 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 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 in the direction of the coil axis. Thus, integrating
these changes is sufficient to determine the flux.
Connect the coil between the input of the integrator and ground, and flip the coil by
180°.
Vout = −
ANB
1
ε
⋅
dt
=
−
RC ∫
RC
3-3
(4)
Here, B 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 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
)
(5)
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
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
to both). Combine the three components to get the magnitude of the B vector. A rough
check: the magnitude of the earth’s magnetic field is about 0.5 Gauss (1×104 Gauss = 1
Tesla).
List possible sources for uncertainties. Evaluate the error of the three individual field
measurements. Combine the errors to get the uncertainty of the magnitude of the field.
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