# Can I use the EET T for stability analysis?

As the T that results from an EET is a return ratio (see EET paper), can I use it for stability analysis?

It is true that T is a return ratio with respect to the extra element EE. Hence $$F=1+T=\frac{\Delta}{\Delta_0}$$ is a return difference, with $$\Delta$$ the circuit determinant and $$\Delta_0$$ the circuit determinant with the EE removed. However, in general, you gain nothing by applying the Nyquist criterion to $$F$$. Indeed, the number of clockwise encirclements around the critical point equals the difference between the number of roots of $$\Delta$$ (circuit poles) in the RHP and the number of roots of $$\Delta_0$$ in the RHP (poles of the circuit with the EE removed). As long as the circuit corresponding to $$\Delta_0$$  can not be assumed stable, no useful stability information can be gained from the Nyquist plot.

References:

1. R D Middlebrook. Null double injection and the extra element theorem. IEEE Transactions on Education 32(3):167–180, 1989. URL, DOI

2. HW Bode. Network analysis and feedback amplifier design. D. Van Nostrand Co., Inc., 1945. URL