Hi.
I'm just reading about how to use op-amps as comparators, and in particular how to use hysteresis to reduce noise effects. My book uses this circuit as an example:
If I understand correctly, the basic idea behind positive feedback is that Vin is inverted at the output and passed back to the noninverting input, increasing the voltage difference between the inputs, which pushes Vout even higher/lower, etc, etc, until Vout is saturated either positive/negative?
Say, for instance, Vout is saturated positive, then this sets an upper 'trigger' voltage at the noninverting input. When the voltage at the inverting input exceeds this trigger the output voltage will quickly saturate negative. This sets a lower trigger voltage, and when the voltage at the inverting input is less than this, the output will saturate positive again. And so it continues.
That seemed to make sense to me, but when I tried to write down some equations I got confused. We can write
\(V_{out} = A_{ol}V_d = A_{ol}(BV_{out} - V_{in})\)
where \(A_{ol}\) is the open-loop voltage gain and \(B = \frac{R_2}{R_1+R_2}\). Therefore
\( \frac{V_{out}}{V_{in}} = \frac{A_{ol}}{BA_{ol}-1} = \frac{1}{B-\frac{1}{A_{ol}}} \approx \frac{1}{B} = 1+\frac{R_1}{R_2}\)
which is the same as for the noninverting amplifier. No indication of the trigger voltages, and the output would only become saturated if I chose R1>>R2 so as to get enough gain. What have I done wrong in that analysis?
Thanks for any help
I'm just reading about how to use op-amps as comparators, and in particular how to use hysteresis to reduce noise effects. My book uses this circuit as an example:
If I understand correctly, the basic idea behind positive feedback is that Vin is inverted at the output and passed back to the noninverting input, increasing the voltage difference between the inputs, which pushes Vout even higher/lower, etc, etc, until Vout is saturated either positive/negative?
Say, for instance, Vout is saturated positive, then this sets an upper 'trigger' voltage at the noninverting input. When the voltage at the inverting input exceeds this trigger the output voltage will quickly saturate negative. This sets a lower trigger voltage, and when the voltage at the inverting input is less than this, the output will saturate positive again. And so it continues.
That seemed to make sense to me, but when I tried to write down some equations I got confused. We can write
\(V_{out} = A_{ol}V_d = A_{ol}(BV_{out} - V_{in})\)
where \(A_{ol}\) is the open-loop voltage gain and \(B = \frac{R_2}{R_1+R_2}\). Therefore
\( \frac{V_{out}}{V_{in}} = \frac{A_{ol}}{BA_{ol}-1} = \frac{1}{B-\frac{1}{A_{ol}}} \approx \frac{1}{B} = 1+\frac{R_1}{R_2}\)
which is the same as for the noninverting amplifier. No indication of the trigger voltages, and the output would only become saturated if I chose R1>>R2 so as to get enough gain. What have I done wrong in that analysis?
Thanks for any help
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