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New Mathematical Methods for Oscillation and Nnoise Spectrum Analysis in Microwave Oscillators in the Time and Frequency Domains

Jahanbakht, Sajad | 2010

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 42073 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s):
  7. Abstract:
  8. New mathematical approaches for noise and oscillation analysis of oscillators are presented. First a new approach for computing the phase noise spectrum of microwave oscillators at every offset frequency from the carrier is introduced. This method uses the harmonic balance formulation to obtain time domain functions used in the existing time domain phase noise analysis methods to compute the phase noise spectrum. In spite of the large signal nature of the phase noise in oscillators, it is analytically proved that for the purpose of phase noise calculations for moderate offset frequencies, the phase noise process can be considered as a small signal stationary process. By this consideration, a simplified approach for the purpose of the phase and amplitude noise spectrum calculations, at far enough from the carrier offset frequencies is presented. The theoretically verified results have been observed in a P-HEMT oscillator at 10.2 GHz, which has been presented in a reference as a benchmark for noise analysis verification. This approach is general regarding the circuit topology and the circuit elements. Floquet eigenfunctions and Floquet exponents are encountered in the stability and noise analysis of circuits operating at large signal periodic regime. A new method for computing all the Floquet eigenfunctions and Floquet exponents using the harmonic balance eigenvectors and eigenvalues is presented. The new approach has been applied to a PHEMT oscillator at 10.2 GHz and very good agreement between the Floquet eigenpairs computed through the new approach and the ones computed through the time-domain integration is observed. It is seen that in addition to the ability of testing the local stability of the oscillations, this method can predict the possible spurious frequencies in the case of synchronous instabilities. After introducing the mathematical tools from stochastic differential equations theory, specially the so called Ito calculus, it is shown that the results of the existing time domain noise analysis methods can be extracted in a simpler manner using Ito calculus theory. New approaches for solving the phase noise characteristic equation in presence of white and colored noise sources are introduced which are based on the Ito calculus for stochastic differential equations. In these methods, two systems of time domain ordinary differential equations (ODE) governing the mean values and the second order correlations of the phase noise exponential terms are derived which are solved using a fast technique based on the eigenvalue decomposition of the coefficient matrices. Using these parameters the computation of the autocorrelation and the power spectral density of any circuit variable are completely addressed. The validity of the new approach is verified by comparing its results against extensive Monte-Carlo simulations for the case of white noise sources. For the colored noise sources the validity of these approaches has been verified by comparing the stationary power spectral density of the output variables of these methods and those from the previous frequency domain methods, presented in this work, for an oscillator with dielectric resonator at 4.1GHz. The advantage of this approach is that it can calculate the transient, the non-stationary as well as the stationary components of the noisy variables. Furthermore it can theoretically give the noise power spectral density at every offset frequency from the carrier
  9. Keywords:
  10. Noise Spectra ; Stochastic Differential Equation ; Microwave Oscillator ; Harmonic Balance Method ; Floquet Eigenfunctions ; Ito Calculus

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