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Imagine that you are driving a car and a temperature fault develops.
Two main different detection methods come to mind (there are others, but not for now).
1: Have a detector which notifies you the instant anything different occurs (instant Volt change indicating that the sensor is too hot/cold).
2: Have a detector which notifies you only if there seems to be a gradual alteration from the usual expected Voltage.
Both of the above two detectors have their advantages and disadvantages:
In the first case, you are notified before further damage occurs, but it could be annoying if minor/one-off small volt changes keep bleeping at you or shutting the car down.
In the second case, you are only notified if a fault (volt change) is on-going for a period of time, not at every instant. The trouble with this method is that damage may occur before it notifies you.
An instant detection as in 1 here can be done by the mathematical process of calculus differentiation ... and that can be performed by an opamp which is set up as a Differentiator.
A cumulative detection as in 2 here can be done by the mathematical process of calculus integration ... and that can be performed by an opamp which is set up as an Integrator.
In the schematic above:
The normal red wave (sine, before the fault introduction) at the far left supply is as expected.
The orange wave from the differentiator opamp at top left is showing instant fault changes (introduced here by pulses at the left) and so flashing an LED.
The green wave from the integrator opamp at top right is showing cumulative time (being different from the normal red expected), and so flashes its LED warning ... but not like the instant response of the differentiator.
You can jab the button at the bottom left and introduce your own extra pulse faults if you wish....
Or hold that button closed, and watch the scope.
This article introduces the basis of PID control, where the
I is the Integrator
D is the Differentiator
(Please ignore the Mosfet settings etc for this article description... it is not for a board setup).
You don't need to know calculus to set up the opamps described, but those who like that maths aspect may wish to read here: Integrator http://everycircuit.com/circuit/5780143762309120
This article is just a very basic introduction to the concept of PID (without the P ... proportional control).
Not an authority !
The opamp error LED notifications can be adjusted as desired (resistor/cap) and forwarded to amplifier or permanent state / peak detector etc as reqd.
Key points:
Using a differentiator will give you an "Instant" rate of change of volts readout... see orange trace.
Using an Integrator will give you a sum of all instants throughout your chosen period...see green trace.
...They are the reverse of each other.
Here is the same setup (squashed in to fit in EC) but with peak output detection and selection. http://everycircuit.com/circuit/5351429400428544
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