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I think, speaking about two loops really will confuse the OP.rude man said:The second loop is the feedback resistor around the op amp. It's a loop inside the major loop which you cite.
For my opinion, it makes not much sense to arbitrarily define an internal loop consisting of an opamp and a feedback resistor only.
Such a "loop" would have a loop gain of infinity (ideal opamp).
Remember: The oscillation condition for all 4-pole oscillators involves one single loop only.
Obviously - a simple visual inspection confirms that the phase shift oscillator topology consists of a single closed loop which contains a frequency-determining RC block in series with a finite gain inverting amplifier. This view reflects the principle of this oscillator type.
Comment: Even in case of the WIEN oscillator (where the combination of positive and negative feedback formally would allow a definition of 2 loops) it makes no sense to define two loops because the common approach using an ideal opamp would give infinite loop gain. Instead, the opamp with negative feedback is, of course, considered as a fixed-gain block.
Hence, we have again the classical single-loop oscillatory system.