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Lab 3
Operational Amplifiers (Op Amps)
Goals for Lab 3
- Learn how to build op-amp circuits on a breadboard.
- Experimentally measure the saturation voltage of a typical op-amp.
- Measure how the resistance of a photoresistor changes with light intensity.
- Be able to use a potentiometer as a variable voltage divider.
- Build a light sensor circuit using photoresistors, op-amps, and LEDs.
Background
1) Op-Amps
The operational amplified (op-amp) is a commonly used device in many circuit applications. It can
perform many functions including amplification, summing, subtraction, integration, differentiation,
and many others. The op-amp is an active device, which means it must be provided with a power
supply in order to function. Passive devices such as resistors, capacitors and inductors do not need a
power supply to work. The op-amp is also a non-linear device.
A typical op-amp has five connections as shown in Figure 1 : Two inputs, two power supplies, and one
output. In the lab, we will use the LM741N op-amp which comes in an eight pin DIP (dual in-line
package) integrated circuit (IC). The pin connections for this particular op-amp are also shown in
Figure 1 – Schematic diagram and pin configuration for the LM741N Op-Amp.
Figure 1. Note that there is a small semi-circular notch on one end of the IC so that you can tell which
end is pins 1-4 and which end is pins 5-8. The size and spacing of the pins on the IC have been carefully
constructed so that the IC will plug nicely into your breadboard as shown in Figures 2 and 3. Note that
the op-amp IC should straddle the “trench” on the breadboard so that each of the pins is plugged into
a different row of the breadboard.
Figure 2 – An op-amp wired on a breadboard in an inverting amplifier configuration.
The input/output behavior of an ideal op-amp is then given by
𝑜
𝐶𝐶
𝑝
𝑛
𝐶𝐶
𝑝
𝑛
𝑝
𝑛
𝐶𝐶
𝐶𝐶
𝑝
𝑛
𝐶𝐶
This equation is illustrated graphically in Figure 4. You can think of this as a three-state model.
There is a linear region where the output is proportional to the input difference voltage, 𝑣 𝑜
𝑝
𝑛
), there is a positive saturation region where the output is constant and equal to the
positive supply voltage, and there is a negative saturation region where the output is constant and
equal to the negative supply voltage.
Note that in order for the op-amp to be operating in its linear region, the difference between the
two input voltages must satisfy,
𝑝
𝑛
𝐶𝐶
With the supply voltages typically being no more than a few 10s of volts and the gain factor 𝐴
being on the order of a million, then the op-amp will be in the linear region only if the two inputs
𝑜
𝑝
𝑛
𝐶𝐶
𝐶𝐶
𝐶𝐶
𝐶𝐶
linear
region
positive
saturation
region
negative
saturation
region
Figure 4 – Output voltage vs. input difference voltage for an ideal op-amp.
are within a few 10s of micro-volts of each other. With much of the equipment we use, this voltage
level is too small to measure. So, for practical purposes we say that if the op-amp is in its linear
region then the two input voltages must be essentially the same. This is referred to as the virtual
short condition.
Virtual Short Condition: 𝑣
𝑝
𝑛
(the voltage on the two inputs will be essentially equal)
The internal circuitry of the op-amp is such that the resistance between the two input terminals is
very high (maybe in the 100s of kilo-ohms to mega-ohms range). So, when the op-amp is in its
linear range with a voltage difference on the order of micro-volts between the input terminals and
a resistance on the order of mega-ohms between the same terminals, the current flowing into (or
out of) the input terminals would be exceedingly small (pico-amps). Again, for practical purposes,
we call this zero, which leads to the infinite input resistance condition.
Infinite Input Resistance: 𝑖
𝑝
𝑛
= 0 (current into input terminals is essentially zero).
Most op-amp configurations are designed for the op-amp to operate in its linear region. In which
case, analysis of op-amp circuits generally starts from the assumption that the op-amp is operating
in its linear region leading to the virtual short and infinite input resistance equations. From there
we use Ohm’s Law, KVLs, KCLs, etc. until we have determined the currents/voltages we are
interested in. We then verify that the initial assumption of being in the linear region is valid. That
is, we check if
𝑜
𝐶𝐶
. If that checks out, then our initial assumption is valid, and we have
correctly analyzed the circuit. If it doesn’t then we must re-analyze the circuit under the
assumption that it is operating in one of the saturation regions.
We will use two different op-amp configurations in this lab (one where the op-amp operates in the
linear region and one where it operates in saturation). In later labs the op-amp will be used in other
configurations. For now, we will show how to analyze the op-amp circuit in the two configurations
that will be used in this lab.
The Comparator
The op-amp configuration shown in Figure 6 is called a comparator. Here, we are placing two
different voltages on the two input terminals of the op-amp, thereby forcing the virtual short
condition to be violated. As such we expect that this configuration operates in saturation mode.
If 𝑣
𝑠
𝑟
, then the output will saturate at the positive supply voltage while if 𝑣
𝑠
𝑟
, the output
will saturate at the negative supply voltage. Mathematically, the comparator behaves according to
𝑜
𝑐𝑐
, if 𝑣
𝑠
𝑟
𝑐𝑐
, if 𝑣
𝑠
𝑟
In words, this configuration is functioning as a binary logic device that answers the question is the
source voltage, 𝑣 𝑠
, bigger or smaller than the reference voltage, 𝑣
𝑟
2) Photoresistors
In this lab you are going to use a photoresistor. This is a resistor whose resistance varies according
to the intensity of light incident on the resistor. They are typically used for detecting the
presence/absence of light or measuring light intensity in applications such as nightlights,
streetlights that turn on at dusk, or various smart home devices. A photograph of a typical
Figure 6 – The comparator op-amp configuration.
_
𝑜
_
𝑠
_
𝑟
_
photoresistor is shown in Figure 7 along with a schematic representation we will use in this lab
manual.
For the photoresistor you are using in this lab, the resistance will be higher when it is in a dark
environment and will be lower in a bright environment. In this lab, you will experimentally
quantify how the resistance of the photoresistor changes with light intensity.
3) Potentiometers
In a previous lab, you used a potentiometer as a variable resistor. In this lab you will use a
potentiometer as a variable voltage divider. In this case, all three terminals (shown in Figure 8 )
will be connected to your circuit. As shown in Figure 9 , terminal 1 of the pot will be connected to
the + end of the voltage source, while terminal 3 of the pot will be connected to the – end (ground).
Figure 7 – A photograph of a typical photoresistor
and its schematic representation.
Figure 8 – (a) A typical potentiometer, (b) its schematic, and (c) an equivalent circuit.
3
2
𝑏
𝑎
1
2
3
(a)
(b) (c)
Lab Measurements
Task 1 – Measuring the saturation voltage of an op-amp.
A practical op-amp does not always behave exactly as the ideal equations predict. In particular,
the saturation voltage of an op-amp is usually a little smaller than the supply voltages. In this task
you will measure the actual saturation voltage of the “741” op-amp in your parts kit.
- Construct the inverting op-amp circuit of Figure 10 on your breadboard.
- Use two 9V batteries to provide the +9V and - 9V supply voltages for the op-amp (or use
the power supply in the lab to provide ± 9 𝑉).
- Use a 1.5V (AA) battery as the source voltage, 𝑉
𝑠
, (or the power supply set to 1.5V).
- Use 1 𝑘Ω resistors for both 𝑅
𝑠
and 𝑅
𝑓
in the circuit.
- Measure the actual voltage of the two supply voltages (nominally ± 9 𝑉).
- Measure the output voltage of the op-amp.
- Now replace the feedback resistor, 𝑅 𝑓
, with a 10 𝑘Ω resistor. Remeasure the output voltage.
- Now reverse the polarity of the source voltage so that it now provides - 1.5V. Remeasure the
output voltage.
- Things to include in your report:
- Provide a table of your measured results.
- Do your measured saturation voltages match what you expected? Discuss anything notable
about your measured saturation voltages.
Figure 10 – Inverting Amplifier Circuit for Task 1
- 9V
_
+9V
𝑠
𝑓
𝑠
_
𝑜𝑢𝑡
_
Task 2 – Measuring the resistive characteristics of a photoresistor.
- Take the photoresistor from your parts kit and plug it into two different nodes of your
breadboard with nothing else connected to the breadboard (or at least to that section of the
breadboard). If you do not have a photoresistor in your parts kit, your TA will provide one for
you.
- Measure the resistance of the photoresistor with the DMM in the lab under each of the
following lighting conditions:
- Normal lighting in the lab.
- With your cell phone flashlight shining on the photoresistor at distances of
(approximately): 1 inch, 3inches, 6 inches, 1 foot, 3 feet, and 6 feet. If you want to be
precise about these distances, bring a tape measure with you to the lab. Otherwise, just
make your best guesses on the distances (or find some other creative way to estimate
distances).
- In the darkest possible environment you can create in the lab. Be clever about how you
might shield the photoresistor from any ambient room light.
- Things to include in your report:
- Describe how you measured distances and also describe how you darkened the
photoresistor.
- Provide a table of your measured results. Make note of the highest and lowest resistances
you were able to measure.
- Provide a plot of resistance vs. lighting level. You may have to get creative here about
how to quantify lighting level. That is, what units will you use for the x-axis in your plot.
You are encouraged to do some research here to see how lighting intensity is quantified in
practice.
Task 3 – Using the op-amp as a comparator – Building a daylight sensor.
- Construct the circuit shown in Figure 11 on your breadboard. Note: Since this circuit is a
bit involved it may take you a few minutes to assemble. If you want to use your lab time
more efficiently, you can build the circuit on your breadboard ahead of time and bring it to
to 9V). The +9V and the - 9V supply voltages for the op-amp should be provided by two
separate batteries (or use the + and – outputs of the power supply).
- Note that there are several elements in the circuit connected to ground. They can all be
connected to the same ground strip on the breadboard.
- The resistor in the upper left (with the circle around it) will be a photoresistor. If you do
not have a photoresistor in your parts kit, your TA will provide one for you.
- The diode in the lower right (with the circle around it) should be your green LED.
- Once the circuit is hooked up correctly on the breadboard, turn the adjustment
screw/knob on the potentiometer. You should see the LED switch on and off as you
adjust the pot. Adjust the pot so that it is as close as possible to the dividing line between
the on/off state of the LED but with the LED still on. Then measure the reference
voltage, 𝑉
𝑟
, and the input voltage, 𝑉
𝑖
. Also measure the output current of the op amp.
You can either measure this with the ammeter on your DMM or you can use a voltmeter
and measure the voltage across 𝑅
𝑜
and then calculate the current using Ohm’s law.
- Now, adjust the pot so that it is as close as possible to the dividing line between the
on/off state of the LED but with the LED off. Again, measure the reference voltage, 𝑉
𝑟
the input voltage, 𝑉
𝑖
, and the output current.
- With the pot adjusted as in item 3 above, turn on the flashlight from your cell phone and
shine it in the direction of the photoresistor. If your phone is close enough to the
photoresistor, you should see the LED switch back to the on state. Slowly back your
flashlight away from the photoresistor. How far do you have to move the flashlight away
from the photoresistor before the LED switches back off?
- Demonstrate to your TA that your circuit displays the correct functionality.
- Things to include in your lab report:
- Explain how/why this circuit works.
- Compare the output current you measured with the value(s) you calculated in the prelab.
- Discuss what changes you could make to the circuit that would cause the LED to shine
brighter when it is in the on state.
- Discuss how you would calibrate the circuit to work as a daylight sensor. That is, how
could we set up the circuit so that the LED would switch on at dusk (and off at dawn) in
an outdoor environment?
- What changes would we need to make to the circuit so that the LED would turn on in
high light environments and off in low light environments?
