Operational Amplifiers are fundamental to modern electronics

Properties of an ideal Op-Amp:

  • Slew rate
    • Output can change as fast as we want
  • Common Mode Rejection Ratio (CMRR)
    • Signals where are rejected and not amplified
  • Power supply rejection ratio
  • Bandwith

A large gain drives the differential input to zero , as the op-amp always tries to keep the two inputs the same.


A buffer provides unity gain while acting as a signal buffer.

As is high and is low, no current flows in and there is no impedance to current flowing out, meaning the buffer acts to isolate stages of a circuit.

Active Filters

(they aren't really active, according to Ryan.)

and are generalised impedances and can take any value. If , for example, then:

A limits test shows that this would make a low pass filter:

  • As ,
  • As ,
  • The mid-band is where

Cutoff frequency is where , which is Hz

The other way round, where and is a high pass filter:

This gives a cutoff frequency of f_c = \frac{1}{2 \pi R_1 C, where the max gain as is