Abstraction and Hysteresis 2/6

    In class on Monday we talked about abstraction, which means that I don’t have to worry about physics! Our professor outlined some concepts that he hoped we understood by now and said that we did not have to understand them on any deeper level than he had explained them. I was pretty comfortable with the material that he expected us to know. But, ignorance really is bliss. Right now I am perfectly content with not knowing everything.
    After our discussion we built a circuit with potentiometers in it. Potentiometers are resistors that you can change the resistance of by turning a knob on top of them.  We connected two of them to a op-amp. Our op-amp always had an output voltage of either +12 volts or -12 volts, depending on which resistor had a higher voltage coming out of it, because the equation of our op-amp was:

Vout = A (V+ - V-)

A was a large, positive number, so the output depended on whether V+ - V- was positive or negative. 

The output was always either -12 V or +12 V because that was  what we had connected to our power rails. If V+ > V- the output was positive. If V->V+ the output was negative.

    Then we talked about hysteresis, which I understand when I’m looking at the graph but find difficult to explain in words. Our professor also explained it using a bent playing card, which made sense to me. Wikipedia defines hysteresis as the dependence of a system not only on its current environment but also on its past environment. What I do understand is that systems with hysteresis are useful for switches.
The graph below illustrates the voltage coming out of an op-amp with positive feedback.

 Positive feedback means that the output of the op-amp is fed back into the positive part of the op-amp. Because this op-amp has has positive feedback, it displays hysteresis. What we built was a was a Schmitt trigger. Wikipedia says "The circuit is named "trigger" because the output retains its value until the input changes sufficiently to trigger a change: in the non-inverting configuration, when the input is higher than a certain chosen threshold, the output is high; when the input is below a different (lower) chosen threshold, the output is low; when the input is between the two, the output retains its value." In our case the description is just a little different. When the input (V-) is lower than -6V the output is high, or +12V. When the When the input is higher than 6V the output is low, -12V. When the input is between the two values, the output is whatever it was before, and it does not change until it reaches either -6V or 6V. This is why systems with hysteresis are systems with memory, because when the input voltage is between -6V and 6V, the output voltage depends entirely on what the it was before.