# Op-Amp Filters

## Abstract

Operational amplifiers—as the name suggests—amplify most commonly difference in voltage between two input nodes. An ideal amp has infinite gain and has zero output impedance; in essence it acts as voltage-controlled voltage source (similar to controlled sources we dealt with in the Feedback chapter). Most often op-amp circuits employ feedback. Feedback can be partial or total, and most often is frequency dependent (depending on the feedback loop). Op-amp circuits pose as classic examples for spectral (and convolution) techniques. We can construct for example inverting amps, differentiators, integrators, and the list goes on. For each case we get the performance in the frequency domain and we can go back to the time domain via inverse transform. We next covered the small signal model of the differential amp where we employed the small signal of transistors (as studied in the MOSFET chapter). Next we covered some aspect of the nonideal amp, mostly the finite gain and finite output impedance. We examined output impedance open loop, with full feedback, partial feedback, and with low-pass feedback filter. We then examined impact of load cap on output impedance. Finally we made some notes on the underlying principles behind feedback and ran a simple intuitive example demonstrating the mechanism of feedback.