International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

Gourary M.M.   Русаков С.Г.   Stempkovsky A.L.   Ulyanov S.L.   Zharov M.M.  

Numerical Techniques for Oscillator Analysis in Circuit Simulators

Reporter: Русаков С.Г.

     Oscillators are essential components found in almost any electronic system. There are as many different kinds of oscillators as there are applications. The design of an oscillator, a nonlinear circuit, requires a large signal steady state analysis. Finding of periodic steady-state solution for oscillator circuits is more complicated in comparison with forced nonlinear circuits due to unknown frequency of oscillation. For this reason the development of robust computational schemes for oscillator analysis is a key problem of radio frequency (RF) IC simulation and is the object of extensive research.
      In this report the main problems are discussed from the point of view of implementation of new numerical procedures in a circuit simulator. The frequency domain numerical techniques of oscillator simulation are of primary interest.
      To improve oscillator simulation using Harmonic Balance (HB) method the concept of voltage probe has been successfully applied. This allows to reformulate the autonomous model with unknown frequency to non-autonomous model with additional conditions. The continuation trajectory can be specified by artificially embedding a fictitious forcing source, that is, a probe. The concept of the probe was extended by setting free the probe frequency. This type of probe is called the "probe with frequency adjusting" (FA). This concept is directed to expand the convergence region and improve robustness properties for high-Q free oscillators and also to provide automatic guess of starting frequency point for the continuation process. The suggested special-purpose numerical continuation procedure based on frequency adjusting probe allows to extend the application sphere of HB techniques in comparison with other known HB algorithms of oscillator simulation.
      Injection locking is a phenomenon observed in oscillators perturbed by an external signal with frequency that is close to the frequency of free-running oscillations. The oscillators perturbed by these external signals are widely used in different applications. We present a new approach to determine locking conditions of arbitrary oscillator at arbitrary periodic excitations. Unlike known methods the analysis of injection locking phenomenon is not based on the phase differential equation. In our approach it is based on the condition of the existence of solution of HB linear system with degenerate matrix.
      The actual practical problem of nanoscale design is connected with necessity to take into account the interdependence of one-chip oscillators and to predict the degree of parasitic mutual injection locking. But the analysis of coupled oscillators by standard simulation requires too high computational efforts. The new method to analyze the mutual injection locking of weakly coupled arbitrary oscillators is given. The couplings are defined by frequency-dependent admittance matrices. The algebraic system with respect to phases and common locking frequency is derived. For two oscillators the system is transformed to a single phase equation and explicit expression for the locking frequency.

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