The Sedra book says that it's a Schmitt trigger, so there is positive feedback, but why doesn't it have negative feedback as well?
Best Answer
Why doesn't the following circuit have negative feedback?
It does have negative feedback and, once the positive feedback (R1 and R2) has done its job, that dominant positive feedback is gradually eroded by the slower negative feedback caused by R and C. After a short while (determined by R and C), the op-amp inputs are equal in value and a very, very short time later, the op-amp output will change from being end-stopped against one power rail to rapidly changing in a direction towards the other power rail. And, at this point, positive feedback will kick in once more and, once again, it will be gradually eroded by the slower negative feedback. Cycling and repeating.
Sedra book says that it's a Schimitt Trigger
It uses a Schmitt trigger, but, in its entirety, it isn't just a Schmitt trigger.
"So why do we only assume negative feedback takes place"
It is not correct that "we assume negative feedback" only. Who say this?
The shown two-opamp circuit (introduced by A. Antoniou) can be interpreted as a combination of two "Negative Impedance Converter (NIC)" circuits.
There are two basic NIC types (current-inversion - INIC, and voltage-inversion - VNIC) and both exhibit a negative input impedance. However, a stable combination results if we replace the grounded output resistor of the first NIC unit (INIC) with the negative input impedance of the second NIC unit (VNIC).
This forms already a circuit called "Generalized Impedance Converter GIC". However, this form has some disadvantages - and therefore a modification is used which is known as Antonious GIC circuit (as shown in the question). It is easy to show that this alternative has the best properties of all possible modifications - as far as influence of real opamp parameters is concerned. This form can be derived from the simple NIC combination exchanging some opamp input nodes which are (for ideal opamps) at the same potential.
This GIC is extensively used in active filter realizations as an "active inductor" and/or as a "Frequency-Dependent Negative Resistor (FDNR)".
They differ in the level of the signal that is required to change their state.
In a Schmidt trigger, a relatively small, well-controlled change of signal level is needed. The input is designed to accomodate this signal, and the input current will be relatively low. In the case of an HC14 supplied with 5v, the hysteresis, the difference in switching levels, is about 1 volt, and the current peaks up to about 400uA when switching.
When two inverters connected together, they can be forced from one state to the other and back again by driving one of the inputs high or low. However, to do this, the input voltage must be taken to the logic thresholds of the gate, and the input current must 'fight' the short-circuit output current of the other gate.
You can make two inverters into a 'tamer' schmidt, by using a resistor to feedback the logic state from the second gate back to the input. This reduces the input current as it only has to supply the current through the resistor.
Best Answer
It does have negative feedback and, once the positive feedback (R1 and R2) has done its job, that dominant positive feedback is gradually eroded by the slower negative feedback caused by R and C. After a short while (determined by R and C), the op-amp inputs are equal in value and a very, very short time later, the op-amp output will change from being end-stopped against one power rail to rapidly changing in a direction towards the other power rail. And, at this point, positive feedback will kick in once more and, once again, it will be gradually eroded by the slower negative feedback. Cycling and repeating.
It uses a Schmitt trigger, but, in its entirety, it isn't just a Schmitt trigger.