Oscillators With the addition of a capacitor and resistor, the Schmitt trigger can be turned into a simple oscillator. Technically, it’s known as an astable multivibrator. Before looking at the circuit, it is worth reviewing the transient response of a first order RC network.

Transient Response and

is a separable first order differential equation. These are the easiest kind to solve! First, rearrange: and integrate each side: The constant, , is the value of VR when time=0, so:

VC t VS VC(0) > VS VC(0) < VS NB. In either case, VC ® VS as t ® ¥. VC(¥) is known as the aiming potential.

Oscillator Circuit The op-amp, R1 and R2 form an inverting Schmitt trigger As R1 = R2, threshold levels are ±VSAT/2 The output is fed-back to the inverting input via an RC network The aiming potential of the capacitor voltage will be either +VSAT or –VSAT

Waveforms V VSAT t -VSAT

Analysis To calculate the time-period, consider just one half-cycle of the oscillation. V VSAT t -VSAT

Analysis (cont) V t Half-cycle ends when VC reaches VSAT/2 VSAT -VSAT t -VSAT Full period of oscillation is 2 half cycles,

Oscillator Summary Using only a couple of extra components, the Schmitt trigger can be converted into a simple oscillator R & C set the period of oscillation independently of VSAT Many square wave oscillators work using the same basic principles

Active Feedback Components There are two broad categories of non-linear op-amp circuits Those that exploit saturation Those that use active components in the feedback network We will concentrate on one example of the latter genre – the precision rectifier

Simple Half-Wave Rectifier IN OUT Ideal Output 1 1 0.5 0.5 Actual Output t t - 0.5 - 0.5 - 1 - 1

Precision rectifier Note that: The current through the diode (and therefore also through RL) can only flow in one direction The load voltage, VOUT, cannot, therefore, go below 0 V When the diode conducts, VOUT » V1 - ½

Analysis – Negative Input

Analysis – Positive Input

Waveforms V V IN V 1 V OUT t t - V SAT

Other Non-Linear Applications Circuits that effectively change the saturation level(s) of the op-amp. Precision rectifier Limiters Circuits that use the exponential V-I curve of PN junctions. Log and antilog amplifiers Multipliers, squarers and dividers

Summary Non-Linear applications of op-amps Essentials Comparator Schmitt Trigger Precision Rectifier Additions for interest Limiters Log/antilog amps Multipliers etc.