4.8 DIFFERENTIATOR AND INTEGRATOR

The output of a differentiator, or differentiating amplifier, is the differentiated version of input given.

In an ideal op-amp, the voltage difference between the input terminals is zero. Since the voltage at the non-inverting input terminal is zero, the voltage at the inverting input terminal should also be zero.

(4.38)

The currents entering the op-amp input terminals are zero.

(4.39)

Figure 4.14: Basic differentiator.

Writing Kirchhoff's Current Law at node ' N' yields

Substitute equation (4.39):

or

(4.40)

Write the current through the capacitor in terms of voltage:

Substitute equation (4.38):

(4.41)

Write the current through the feedback resistor in terms of voltage:

Substitute equation (4.38):

Substitute equation (4.40):

Substitute equation (4.41):

(4.42)

Equation (4.42) shows output voltage is proportional to derivative of input voltage

To have stability and to reduce noise, a resistor R ₁ is placed in series with C ₁ and a capacitor C _f is placed in parallel with R _f in a practical differentiator circuit.

The output of an integrator, or integrating amplifier, is the integrated version of the input.

The circuit for an integrator is the same as that of a differentiator, except the positions of the capacitor and resistor are switched.

Figure 4.15: Basic integrator.

In an ideal op-amp, the voltage difference between the input terminals is zero. Since the voltage at the non-inverting input terminal is zero, the voltage at the inverting input terminal is zero.

(4.43)

The currents entering the op-amp input...