An example of the flow of abstraction would be as follows:
Designing at the circuit level
↓
Creating digital gates/ analyzing digital signals
↓
Building systems of digital gates
↓
Creating modules
↓
Creating microprocessors and operating in assembly languages
↓
Programming with high level languages to create programs
When we work at a higher level, we do not need to fully understand the levels below us (or in my particular chart, above us) to successfully work at our particular level. For example, it it not necessary for me to understand logic gates in order to program in C++. I can skip over the lower level information, by using abstraction, thereby allowing me to work only with the information needed for my target level.
Next we reviewed resistors, which are used to measure current. The voltage in a resistor can be measured by V=Ri and the current flowing over a resistor is i=V/R. Current in circuits does not accumulate and just because you put force on something, doesn't mean you are necessarily doing work.
In our experiments, the OP Amp operates so that the voltage only exists at either of two extremes: -12V or +12V. This means, turning the nob on the potentiometer creates no change in the oscilloscope until it is turned the maximum way in either direction. We understand the voltage using this formula and drawing these conclusions:
Next Oscar explained hysteresis, using the analogy of bending a credit card. In the following diagram we see the card can bend right when positive force is applied and can bend left when negative force is applied.
In this following picture, we see the effect of adding positive or negative force on the card depending on the card's starting position. This experiment explains that the card can only exist as either bending left or right, and although there is a range of force that can be applied, change only occurs when enough force is applied and the card suddenly snaps to the other position. Weak force in either direction will not change the position of the card.
We graph a hysteretic comparator like this:
The straight green line is the hysteretic comparator, and the blue squiggly line is the potentiometer being turned to adjust the voltage. What we see here is that the voltage can fluctuate freely until it reaches +6V or -6V, which triggers the hysteretic comparator to jump from +12V to -12V depending on its previous position. Once the voltage hits +6V or -6V, it doesn't matter if it hit that value again or surpasses it; the only way to change the voltage of the hysteretic comparator, if the voltage hit +6V, for example, would be for the voltage to drop down to -6V.
We can prove this by measuring the voltage as (V+-V- ). This hysteretic comparator is an example of the Schmitt Trigger, which is illustrated like this:
Our circuit looks like this:
And here we understand how hysteresis changes our circuit:
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