Operational Amplifier Applications Unit 2 – Integration and Differentiation
Exercise 1 – The Integrator
EXERCISE OBJECTIVE
When you have completed this exercise, you will be able to determine the effects of an active
integrator on an input waveform. You will verify your results with an oscilloscope.
DISCUSSION
- This is an active integrator circuit. The op amp (U1) is the active component.
- The integrating network is formed by R 1 and C 1.
- No feedback resistor is needed in an ideal active integrator. In practice the feedback resistor
(R 3 in this circuit) establishes the dc and low frequency gain of the op amp. The feedback
resistor, also, prevents saturation due to input offset voltages. - The op amp acts like an inverting amplifier.
- R 2 reduces the effects of input offset currents.
- The load resistor is R 4.
- The integrator has a low frequency phase shift of 180°. At higher frequencies the phase shift
decreases from 180° because of the reactance of the feedback capacitor. - This active integrator, within a certain range of frequencies, has the basic characteristics of a
low pass filter which are: Low frequencies are passed to the output with high gain and high
frequencies are attenuated. - The cutoff frequency (fC) is the frequency at which attenuation begins.
- The breakpoint frequency is the frequency at which the feedback capacitor’s reactance equals
the feedback resistance (RF = XCF). - Integration occurs above the breakpoint frequencies. Below the breakpoint frequencies, high
capacitive reactance causes the circuit to act like a simple inverting amplifier. - Breakpoint frequency (fC) is calculated using this equation:
fC = 1/(2π x R3 x C1)