Comments and remarks over classic linear loop-gain method for oscillator design and analysis. New proposed method based on NDF/RRT

Abstract. This paper describes a new and original method for designing oscillators based on the Normalized Determinant Function (NDF) and Return Relations (RRT)- Firstly, a review of the loop-gain method will be performed. The loop-gain method pros, cons and some examples for exploring wrong solutions provided by this method will be shown. This method produces in some cases wrong solutions because some necessary conditions have not been fulfilled. The required necessary conditions to assure a right solution will be described. The necessity of using the NDF or the Transpose Return Relations (RRT), which are related with the True Loop-Gain, to test the additional conditions will be demonstrated. To conclude this paper, the steps for oscillator design and analysis, using the proposed NDF/RRj method, will be presented. The loop-gain wrong solutions will be compared with the NDF/RRj and the accuracy of this method to estimate the oscillation frequency and QL will be demonstrated. Some additional examples of plane reference oscillators (Z/Y/T), will be added and they will be analyzed with the new NDF/RRj proposed method, even these oscillators cannot be analyzed using the classic loop gain method.