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What happens when the output voltage of an op-amp (say in a voltage follower/inverting configuration) should be higher than a certain amount (say 10V) and on the output I place a 5V zener diode in reverse, followed by GND?

schematic

simulate this circuit – Schematic created using CircuitLab

On the one side, it should be Vin, right? But I think it must also be less or equal than 5V because of the Diode

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If the inverting input is low, the op amp it will try raising the output voltage, so via the feedback it will try to match the +15V from the noninverting. As hard as possible. However, at the same time the zener sinks as hard as possible. In the end you get the equivalent of a short circuit and either the opamp, or the zener, will eventually become very hot and might get destroyed.

Realistically, the TL081 is short-circuit protected and the output current capability is not incredibly high, so both parts will just get hot and the output voltage will be somewhere in-between 5 and 15 volts, probably close to 5, because, as said, the current capability is not incredibly high.

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This is a impossible situation for a ideal opamp and a ideal zener diode. The opamp will source or sink whatever current is required to maintain its desired output voltage. The zener will sink whatever current is required to limit the voltage across it to 5 V. For ideal components, the current goes infinite and the voltage underterminable.

Real components, however, have some maximum current they can source or sink and still adhere to the other specs they promise. If the opamp can only put out 10 mA and the zener can sink 20, then the zener wins and the voltage stays at 5 V. If the opamp can source more current than the zener can handle, then the zener is destroyed and the voltage goes to 15 V.

Once you run parts past one spec, you can no longer rely on operation within any of the other specs. In addition, permanent damage can occur.

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  • \$\begingroup\$ Are you sure about that Olin in my experience dead diodes (including zener) usually fail short circuit so both zenner and op-amp would die \$\endgroup\$ – Warren Hill Nov 6 '17 at 20:40
  • \$\begingroup\$ @Warren: Diodes can fail both short and open, so what you say can happen too. The point, however, is that after you violate specs, you can't rely on any remaining spec. \$\endgroup\$ – Olin Lathrop Nov 6 '17 at 21:09
  • \$\begingroup\$ Agreed @Olin when you use parts out of spec they often die, my experience is usually diodes fail short unless in something with lots of energy like a SMPS. \$\endgroup\$ – Warren Hill Nov 6 '17 at 21:21
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The op-amp will current-limit trying to drive the output voltage to 15V (assuming the power supply voltage on the op-amp is greater than about 18V, otherwise it may not be able to drive the output that high).

The TL081 has a maximum 60mA short-circuit output current. A small axial-lead Zener (eg. the 500mW 1N751A) is rated for 70mA maximum current, so it will survive- the output voltage is going to be higher than 5.1V most likely, but not a lot higher (probably less than 6V). This is outside of even the typical curves and the zener impedance listed is only valid near the test current so it's a guess, not something you can hang your hat on, and therefore not good engineering to depend upon.

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