In electronics, a differentiator is a circuit that is designed such that the output of the circuit is approximately directly proportional to the rate of change (the time derivative) of the input. A true differentiator cannot be physically realized, because it has infinite gain at infinite frequency. A similar effect can be achieved, however, by limiting the gain above some frequency. The differentiator circuit is essentially a high-pass filter. An active differentiator includes some form of amplifier, while a passive differentiator is made only of resistors, capacitors and inductors. Passive differentiator The simple four-terminal passive circuits depicted in figure, consisting of a resistor and a capacitor, or alternatively a resistor and an inductor, behave as differentiators. Indeed, according to Ohm's law, the voltages at the two ends of the capacitive differentiator are related by a transfer function that has a zero in the origin and a pole in −1/RC and that is consequently a good approximation of an ideal differentiator at frequencies below the natural frequency of the pole: Similarly, the transfer function of the inductive differentiator has a zero in the origin and a pole in −R/L. Active differentiator Ideal differentiator A differentiator circuit (also known as a differentiating amplifier or inverting differentiator) consists of an operational amplifier in which a resistor R provides negative feedback and a capacitor is used at the input side. The circuit is based on the capacitor's current to voltage relationship where I is the current through the capacitor, C is the capacitance of the capacitor, and V is the voltage across the capacitor. The current flowing through the capacitor is then proportional to the derivative of the voltage across the capacitor. This current can then be connected to a resistor, which has the current to voltage relationship where R is the resistance of the resistor. Note that the op-amp input has a very high input impedance (it also forms a virtual ground due to the presence of negative feedback), so the entire input current has to flow through R. If Vout is the voltage across the resistor and Vin is the voltage across the capacitor, we can rearrange these two equations to obtain the following equation: From the above equation following conclusions can be made: Output is proportional to the time derivative of the input. Hence, the op amp acts as a differentiator. Above equation is true for any frequency signal. The negative