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.


  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