1. 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.

2. Transient Response
and

3. 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:

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

5. 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

6. Waveforms V
VSAT t
-VSAT

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

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

9. 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

10. 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

11. Simple Half-Wave RectifierIN
OUT
Ideal Output 1 1
0.5
0.5
Actual Output t t -
0.5 -
0.5 - 1 - 1

12. 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

13. Analysis – Negative Input

14. Analysis – Positive Input

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

16. 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

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