Classic Linear Methods Provisos Verification for Oscillator Design Using NDF and Its Use as Oscillators Design Tool

The purpose of this paper is to show the conditions that must be verified before use any of the classic linear analysis methods for oscillator design. If the required conditions are not verified, the classic methods can provide wrong solutions, and even when the conditions are verified each classic method can provide a different solution. It is necessary to use the Normalized Determinant Function (NDF) in order to perform the verification of the required conditions of the classic methods. The direct use of the NDF as a direct and stand-alone tool for linear oscillator design is proposed. The NDF method has the main advantages of not require any additional condition, be suitable for any topology and provide a unique solution for a circuit with independence of the representation and virtual ground position. The Transpose Return Relations (RRT) can be used to calculate the NDF of any circuit and this is the approach used to calculate the NDF on this paper. Several classic topologies of microwave oscillators are used to illustrate the problems that the classic methods present when their required conditions are not verified. Finally, these oscillators are used to illustrate the use and advantages of the NDF method.

[1]  M. Randall,et al.  General oscillator characterization using linear open-loop S-parameters , 2001 .

[2]  M. J. Howes,et al.  A Reflection Coefficient Approach to the Design of One-Port Negative Impedance Oscillators , 1981 .

[3]  R. W. Jackson,et al.  Criteria for the onset of oscillation in microwave circuits , 1992 .

[4]  M. Ohtomo,et al.  Proviso on the unconditional stability criteria for linear twoport , 1995 .

[5]  A. Platzker,et al.  Rigorous determination of the stability of linear n-node circuits from network determinants and the appropriate role of the stability factor K of their reduced two-ports , 1994, Third International Workshop on Integrated Nonlinear Microwave and Millimeterwave Circuits.

[6]  D. Segovia-Vargas,et al.  TRANSPOSE RETURN RELATION METHOD FOR DESIGNING LOW NOISE OSCILLATORS J. L. Jimenez-Mart¶‡n 1 , V. Gonzalez-Posadas 1 , , 2012 .

[7]  Robert G. Meyer,et al.  Start-up and frequency stability in high-frequency oscillators , 1992 .

[8]  The Virtual Ground in Oscillator Analysis — A Practical Example This analysis technique helps us understand oscillator behavior for the design of reliable circuits , 1999 .

[9]  Luis Enrique Garcia-Munoz,et al.  Comments and remarks over classic linear loop-gain method for oscillator design and analysis. New proposed method based on NDF/RRT , 2012 .

[10]  Vicente González Posadas,et al.  Provisos for classic linear oscillator design methods. New linear oscillator design based on the NDF/RRT , 2012 .

[11]  Luis Enrique Garcia-Munoz,et al.  Oscillator Accurate Linear Analysis and Design. Classic Linear Methods Review and Comments , 2011 .

[12]  R. Jackson,et al.  Rollett Proviso in the Stability of Linear Microwave Circuits—A Tutorial , 2006, IEEE Transactions on Microwave Theory and Techniques.

[13]  Vicente González Posadas,et al.  Transpose return relation method for designing low noise oscillators , 2012 .