Lab
6: Limitations of Operational Amplifiers
Abstract:
Characteristics and limitations of operational amplifiers as are explored in this experiment using simple resistive networks. These include the gain bandwidth product, slew rate, and saturation properties.
Introduction:
The operational amplifier is a highly versatile component which is why it is widely used in various applications. However, the operational amplifier also has some limitations. It is important to be aware of these limitations so as not to be faced by unexpected surprises when using this component in circuits. In this lab we will look at two limitations on the performance of operational amplifiers. The first is characterized by the gain-bandwidth product and the second appears when the amplifier is overloaded.
Gain-Bandwidth Product
Figure 6-1: Inverting amplifier circuit
When we calculate the gain of an operational amplifier
configuration there is an implicit assumption that the gain is independent of
the frequency of the input signal.
However, if we construct an amplifier, such as the inverting amplifier
shown in Figure 6-1, and look at the gain at different frequencies we will find
that the gain decreases with increase in frequency. In order to quantify this change we find the bandwidth of the amplifier. Let’s define the gain of the amplifier for an
input sinusoid at 100 Hz as the low frequency gain. As we increase the frequency the gain will
drop until at some frequency the gain is 
of the low frequency gain.
This frequency is called the cutoff frequency of the amplifier and the
range of frequencies is called the bandwidth of the amplifier.
To illustrate the concept of bandwidth consider the two frequency responses shown in Figure 6-2. The frequency response on the left is called a low pass response with a single cutoff frequency at 600 Hz. The bandwidth of a circuit with this response is 600 Hz. The frequency response on the left is called a bandpass response. There are two cutoff frequencies, a lower cutoff at about 700 Hz, and an upper cutoff at about 1900 Hz. The bandwidth of a circuit with this response is 1200 Hz.
Figure 6-2: Frequency response of a) a 600 Hz Low-Pass system, b) a
1200 Hz Band-Pass system.
In an operational amplifier circuit, such as the one shown in Figure 6-1, if we change the resistance values so that the gain changes we will find that the bandwidth changes as well. That is, the bandwidth is not simply a property of the amplifier but depends on the components connected to it. However, the product of the gain of the amplifier and the bandwidth of the operational amplifier, know appropriately enough, as the gain-bandwidth product is a function specifically of the operational amplifier and remains constant. In this lab you will determine the gain bandwidth product of an operational amplifier and examine the value of the gain bandwidth product for several different values of gain.
The fact that the gain bandwidth product of an amplifier is constant is very helpful. If we design an amplifier with a particular gain, knowing the gain-bandwidth product automatically tells us over what range of frequencies we can operate the amplifier and expect to get a gain close to the gain that the amplifier was designed for. The gain bandwidth product for a given operational amplifier can be found on the data sheet for the amplifier.
Overloading the Operational Amplifier
When we analyze operational amplifiers we generally ignore the load. In practice, however, the load cannot be ignored. This is actually true for any voltage source. Recall that a practical voltage source can be represented by its Thevenin equivalent consisting of an ideal voltage source and a Thevenin resistance as shown in Figure 6-3.
Figure 6-3: Thevenin Equivalent for a practical voltage source.
The open circuit voltage of this circuit is clearly 
. However, when we
attach a load resistor to this the voltage appearing across the load resistor
will be minus the voltage
dropped across 
. The amount of
voltage dropped across will depend on the
amount of current flowing through it.
This in turn will depend on the load resistance. The lower the resistance value of the load
resistor, the more current will flow through the resistor and the more voltage
will be dropped across resulting in a lower
voltage across the load[1]. In an operational amplifier another mechanism
also comes into play when the resistance is lowered. The operational amplifier has protective
circuitry in it which limits the amount of current it provides to a maximum
value. When this maximum is reached
increasing the loading (decreasing the resistance) will not result in an
increase in current flow. Instead the
current flow will remain constant resulting in a decrease in voltage. We also see this effect in a different way. If the resistor is small the output might
follow the shape of the input for smaller inputs. However, when the input voltage reaches the
point where the output voltage is resulting in the maximum current flow, any
increase in the input voltage will not be reflected at the output. The
voltage across the resistor will remain constant regardless of any increase in
the magnitude of the input voltage. This
characteristic of the operational amplifier means that we have to be aware of
the loading when we decide to use an operational amplifier in a circuit. For example, it is not a good idea to use a
741 operational amplifier to drive an 
speaker.
Figure 6-4: Inverting operational amplifier with load resistor.
Experiment:
When working with electronic devices ALWAYS assemble and verify the
circuit with the power OFF. Once the circuit
has been checked, then apply the power.
ICs can be damaged by incorrect voltage connections. Work carefully and methodically.
(1) Assemble
the inverting amplifier circuit of Figure 6-1 with 
and
. Measure and record
the actual value of the resistors.
Remember the power supply connections:
use V+ = +12 volts to IC pin 7 and use V- = -12 volts to IC pin 4. Include 0.01μF bypass capacitors between
the +12V and ground and between the -12V and ground, placing the capacitors as
close the IC as possible. Use the bench
power supply for the supply connections.
Use the signal generator for Vin. with frequency set to about
100 Hz and peak-to peak voltage about 1V. Display the input voltage on channel 1 and
the output voltage on channel 2. Make
sure all of the grounds are connected and that the output remains sinusoidal
without distortion. If you see any distortion, adjust the amplitude of the
input. Record 
, 
, and 
. Increase the frequency of the input until
the magnitude of the output sinusoid is 0.707 times the output magnitude at 100
Hz. This is the 3dB cutoff frequency for
your amplifier. Note this frequency. Now measure and note the magnitude of the
input and output sinusoids at 1 KHz, 10 KHz, 100 KHz, and 1 MHz. You might want to take some extra
measurements near the 3 dB cutoff frequency.
You will be plotting the behavior of your amplifier as a function of
frequency.
(2) Repeat
this experiment using 
and. Adjust the output of
the signal generator so that the output of the amplifier is a distortion free
sinusoid.
(3) Repeat
the experiment using 
and. Adjust the output of
the signal generator so that the output of the amplifier is a distortion free
sinusoid.
(4) Assemble
the inverting amplifier circuit of Figure 6-4 with and. Use the 1K potentiometer as a load on the output. Use the signal generator with a sinusoidal
output at 500 Hz as your input. Display
the input voltage on channel 1 and the output voltage on channel 2. Make sure all of the grounds are connected
and adjust the potentiometer so that the output remains sinusoidal without
distortion. Note the magnitude of the
input voltage and the output voltage.
Disconnect the potentiometer and measure and note the resistance. Now decrease the resistance of the
potentiometer (increase the loading) until you see the output sinusoid getting
clipped. Note the magnitude of the input
and output voltage. Disconnect the
potentiometer and measure and note the resistance.
Results:
(a)
Present your measurements from parts (1) (2) and (3) of
the experiment in the form of a graph with the log of the frequency as
the abscissa (x-axis) and as the ordinate (y-axis). Label your plot. How do the three plots line up? How does the result compare to your
prediction using the ideal op amp model?
(b) Make a table with columns for low-frequency gain, the cutoff frequency, and the gain-bandwidth product. Compute the average gain-bandwidth product for your three measurements and compare this with the value in the datasheet specification.
(c) By increasing the loading (reducing the load resistance) in part (4) of the experiments we in effect were asking the operational amplifier for more current. The operational amplifier can only source a limited amount of current at which point you start to see clipping. Compute the value of this current and compare your answer with that in the data sheet.
(d) What can be done to improve this experiment?