Comparator with hysteresis calculation

Question

I'm trying to calculate the hysteresis of the comparator using currents but something isn't right. I'd like a little help to find the hysteresis thresholds without the simplified equations.

schematic

^{simulate this circuit – Schematic created using CircuitLab}

The voltage at inverting input is:

\$ V_{(-)} = \dfrac{V_{IN}}{2} = 0V ...6V \$

The reference voltage is:

\$ V_{REF} = 8.2V \$

So, when the output of the Op-Amp is low we have a voltage divider as follows:

schematic

^{simulate this circuit}

Then the current \$I_{1}\$ will be \$\dfrac{V_{REF}}{R_{4} + R_{5}} = 0.112 mA\$

So the upper threshold is \$ V_{th(H)} = 0.112mA * 72kΩ = 8.064V\$

When the output of the Op-Amp is high we have the following circuit. That I think is analyzed with the Superposition Theorem.

schematic

^{simulate this circuit}

And the lower threshold is \$ V_{th(L)} = 8.252V\$. Is this correct?

Would it be different if it was a non-inverting comparator?

Yes, your answer is correct. Which means that you need Vin > 2 * 8.2V (due to voltage divider at the inverting input) to be able to see the circuit at work — G36, Feb 10 '20 at 19:23
Although the Zener diode will clamp at 8.2V in your case, you cannot **simply assume** \$V_{ref} = 8.2 V\$. Check https://electronics.stackexchange.com/questions/478471/zener-voltage-clamping/478473#478473 — Huisman, Feb 10 '20 at 19:49
@G36 would it be different if it was non-inverting comparator? — MrBit, Feb 10 '20 at 20:14
@DKNguyen I mean, Input at Vref point (variable input voltage) and a stable reference voltage at V(-) — MrBit, Feb 10 '20 at 20:47
@MrBit Define what you mean by non-inverting comparator because from what I see, that doesn't hold any meaning. Comparators don't invert, and work on positive feedback and the hysteresis also needs positive feedback. That means no matter what you do, the hysteresis feedback loop must always go from the output to the non-inverting input. — DKNguyen, Feb 10 '20 at 20:51
Yes, it changes it because if you swap the input signals then the equivalent circuits will be different since the hysteresis resistor must always sit between the output and the non-inverting input. — DKNguyen, Feb 10 '20 at 20:53
@DKNguyen I was talking about this schematic: https://www.daycounter.com/Calculators/Comparator-Hysteresis-Calculator.phtml It looks like the Vp is stable and the input feeds the non inverting input. Positive feedback still exists on the circuit. — MrBit, Feb 11 '20 at 07:32

Comparator with hysteresis calculation

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