Differentiator

Differentiators are systems that output the derivative of an input signal. Circuits that achieve this function rely on the properties of operational amplifiers and capacitors.

The most common type of analogue differentiator is the inverting differentiator below.

i_{c} (t) = C \frac{d}{d t} (v_{s} - v_{n}) = C \frac{d v _{s}}{d t}

Then taking $i_{c} (t) = - i_{r} (t) = - v_{o} (t) / R$ :

v_{o} (t) = - RC \frac{d v _{s}}{d t}

Non-inverting differentiator

Non-inverting differentiators don’t seem to be that common. Prof. Najm had to dig around for an example of this.¹ We assume:

\frac{R _{1}}{R _{2}} = \frac{R _{3}}{R _{4}} = α

Then after some complicated arithmetic we get:

v_{2} = RC \frac{d v _{1}}{d t}

From this 1974 paper by D.H. Horrocks in the International Journal of Electronics. ↩