In electronics, a differentiator is a circuit that outputs a signal approximately proportional to the rate of change (i.e. the derivative with respect to time) of its input signal. Because the derivative of a sinusoid is another sinusoid whose amplitude is multiplied by its frequency, a true differentiator that works across all frequencies can't be realized (as its gain would have to increase indefinitely as frequency increase).^{[citation needed]} Real circuits such as a 1^st-order high-pass filter are able to approximate differentiation at lower frequencies by limiting the gain above its cutoff frequency.^{[citation needed]} An active differentiator includes an amplifier, while a passive differentiator is made only of resistors, capacitors and inductors.^{[citation needed]}

The four-terminal 1^st-order passive high-pass filter circuits depicted in figure, consisting of a resistor and a capacitor, or alternatively a resistor and an inductor,^{[citation needed]} approximate differentiation at frequencies well-below each filter's cutoff frequency.^{[citation needed]}

According to Ohm's law, the voltages at the two ends of the capacitive differentiator are related by the following transfer function (which has a zero in the origin and a pole at ${\displaystyle s{=}{\tfrac {{\text{-}}1}{RC}}}$):

which is a good approximation of an ideal differentiator at frequencies well below the filter's cutoff frequency of ${\displaystyle {\tfrac {1}{2\pi RC}}}$ in hertz or ${\displaystyle {\tfrac {1}{RC}}}$ in radians.

Similarly, the transfer function of the inductive differentiator has a zero in the origin and a pole in ${\displaystyle s{=}{\tfrac {{\text{-}}R}{L}}}$, corresponding to a cutoff frequency of ${\displaystyle {\tfrac {R}{2\pi L}}}$ in hertz or ${\displaystyle {\tfrac {R}{L}}}$ in radians.

A differentiator circuit (also known as a differentiating amplifier or inverting differentiator) consists of an ideal operational amplifier with a resistor R providing negative feedback and a capacitor C at the input, such that:

According to the capacitor's current–voltage relation, this current ${\displaystyle I}$ as it flows from the input through the capacitor to the virtual ground will be proportional to the derivative of the input voltage:

This same current ${\displaystyle I}$ is converted into a voltage when it travels from the virtual ground through the resistor to the output, according to ohm's law: