Electronic – Positive feedback and virtual short in Operational Amplifiers


Can anyone please explain, with sufficient mathematics, why the virtual short concept is not applicable to an operational amplifier in positive feedback.

Best Answer

At first, I assume that you speak about operational amplifiers and the virtual short across the opamps input terminals, right? In this case, your statement - in this general form - is not correct. Let me explain:

The term "virtual short" applies to amplifier units with a very large open-loop gain which may be set to infinity (during mathematical manipulations/calculations). However, this assumption is true if the opamp is dynamically stable and operated in its linear region only. Normally, this is the case for negative feedback. However, there are some other applications which use negative and positive feedback at the same time. As long as the negative feedback is dominating (negative feedback factor larger than the pos. feedback factor) the circuit remains stable - and the "virtual short" principle continues to apply.

More than that, there are active filter circuits - Sallen-Key topologies, for example - which need positive feedback for Q enhancement. These circuits have negative feedback for DC (stable operating point) and in addition positive feedback for some specific frequencies (pole frequency region). Of course, in case of large Q values the circuit operates closer to the stability limit than simple amplifiers - but as long as negative feedback dominates the active filter circuit is stable and working as desired (and the virtual short principle applies).

In summary, the "virtual short" scenario does not apply for opamps with a feedback arrangement that causes dynamic instability. This is the case - for example - if we have a pure resistive feedback to the non-inv. terminal with a loop gain larger than unity (however, slight positive feedback leading to a loop gain below unity is stable!).

However, there may be an exception to this rule during switching: The classical Schmitt trigger is such a circuit with resistive positive feedback. When this circuit is used to build a squarewave oscillator, the opamp output is switched between both supply voltage limits - and during the switching phase the circuit crosses the region where we have a linear relationship between input and output. During this very short time period, the voltage between both opamp input nodes is negligible snmall (virtual short circuit).