EXPERIMENT #7
APPLICATIONS OF OPERATIONAL AMPLIFIERS
As preparation for the laboratory, you are expected to produce a design for the phase shift oscillator that will oscillate at a frequency close to 400 Hz. You will also need to produce a design for a phase shift oscillator that uses op-amp integrators to produce the necessary phase shift.
1.Phase Shift Oscillator and Positive Feedback
The OpAmp circuits that you have studied thus far have employed negative feedback to produce stable output signals. Negative feedback typically involves feeding some fraction of the output signal back into the negative input of the OpAmp, which tends to stabilize the output of the amplifier. This is actually a much broader concept used in a wide range of control systems. For instance, the thermostat in your home provides a form of negative feedback; if the temperature drops the heating is increased and if the temperature increases the heating is decreased. With the right amount of feedback this leads to a stable temperature.
Positive feedback, where the output is added onto the input, leads to an unstable output, typically breaking into wild oscillations. A familiar example is an audio amplifier system breaking into a high frequency whine if a microphone is too close to a speaker. This kind of feedback is often undesirable, but on the other hand can be used to make an oscillator.
There are many ways to make an oscillator using positive feedback, one example being the phase shift oscillator shown in Fig. 7.1. At first it appears to involve negative feedback, since it involves an op-amp that is used in a manner similar to the inverting amplifier of Expt. 4. However, the network of resistors and capacitors acts to shift the phase of the output by 180o, yielding positive feedback at a particular frequency. With sufficient gain, (set by the variable resistor and feedback resistor R') this leads to oscillations.
Design and construct the circuit shown in Fig. 7.1 with components chosen to give oscillation at about 400 Hz. This involves two issues; choosing values of R and C that produce a 180o phase shift in the ladder network, and then designing the gain of the amplifier such that it compensates the attenuation through this RC ladder network. An easy first estimate can be made by considering just a single leg of the ladder and picking a value of R and C that give a 60o phase shift at 400 Hz.
2.Active Filters
Another important use of OpAmps is in the design of filters. You have already encountered the simple RC low pass filter and have studied its ac characteristics and transient response in detail. More sophisticated filters with sharper rolloffs can be designed if one uses active elements like the OpAmp, in addition to the passive devices R, L, and C. Such filters constitute a huge topic on their own and you will study just one example here, the low pass Sallen-Key filter shown in Fig. 7.2.
Construct the filter circuit shown in Fig. 7.2 and apply a sinusoidal signal to the input using the function generator. At various frequencies, measure the amplitude ratio V0/Vi. Pay particular attention to determining the cutoff frequency, which is the frequency at which the output voltage falls to of its value at low frequencies. Make several measurements at high frequencies in order to determine how rapidly the filter rolls-off compared to the RC filter that you studied in Expt. 2.
What advantages does this active filter have over a passive RC filter designed to have a similar cutoff frequency?
Try varying the values of the capacitors in order to show that this circuit can exhibit resonant behaviour (the design shown above is at critical damping). Select values that produce underdamped resonant behaviour and measure the frequency dependent gain of the circuit in this case.
3.A Comparator
The circuit shown below in Fig. 7.3 is a comparator. Without any feedback present, the huge open-loop gain (about 106) of the OpAmp is being applied to the voltage difference between the two inputs. Thus, any small voltage difference between the inputs will be amplified enormously, causing the output to saturate. The sign of the saturated output voltage V0 will depend on which input voltage is largest, so the circuit provides a sensitive comparison of the input voltages. In the circuit of Fig. 6.3 a +2.5 V reference voltage is connected to the non-inverting input and is compared to the variable voltage connected to the inverting input. Assemble the circuit as shown and observe the behaviour as you vary the voltage provided by the potentiometer. What are the positive and negative saturation voltages? What are the input voltages when the sign of the output voltage switches?
4.The Schmitt Trigger
If you connect a 10 k resistor between the output and the noninverting input of the comparator circuit, then the circuit exhibits hysteresis. You can observe this characteristic by measuring both the input and the output voltage as you vary the potentiometer first in one direction and then in the other. Explain the cause of the hysteretic behaviour.
The switching between two distinct output states and the use of hysteresis are two key features that bring us to the topic of the next experiments - digital electronics.
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