computation in differential analysers and as components of instruments such as naval gun directors, flow totalizers and others. A planimeter is a mechanical device used for calculating the definite integral of a curve given in graphical form, or more generally finding the area of a closed curve. An integraph is used to plot the indefinite integral of a function given in graphical form. Drawbacks of ideal integrator Bandwidth is very small and used for only small range of input frequencies. For dc input (f = 0), the reactance of the capacitance, X, is infinite. Because of this op-amp goes into open loop configuration. In open loop configuration the gain is infinite and hence the small input offset voltages are also amplified and appears at output as error. This is referred as false triggering and must be avoided. Due to all such limitations, an ideal integrator needs to be modified. Some additional components are used along with ideal integrator circuit to reduce the effect of an error voltage in practice. This modified integrator is referred as practical integrator. Practical integrator (lossy integrator) The gain of an integrator at low frequency can be limited to avoid the saturation problem, therefore to avoid saturation of the op amp the feedback capacitor is shunted by a resistor Rf. The parallel combination of Rf and C behaves like a practical capacitor which dissipates power, unlike an ideal capacitor. For this reason this circuit is also called a lossy integrator. The resistor Rf limits the low frequency gain to (-Rf/R), generally [Rf=10*R1] and thus provides DC stabilisation. Applications Op-amp integrating amplifiers are used to perform calculus operations in analogue computers. Integrating circuits are most commonly used in analogue-to-digital converters, ramp generators and also in wave shaping applications. Another application would be to integrate a signal representing water flow, producing a signal representing the total quantity of water that has passed by the flow meter. This application of an integrator is sometimes called a totalizer in the industrial instrumentation trade. See also Differentiator Digital differential analyzer Fractional-order integrator Integrating ADC Lowpass filter Operational amplifier Signal processing References External links Wolfram Online Integrator Calc.Matthen Online Integrator, can do definite integrals Further reading Mathematical tools