responding HTM elements A.4 Conclusions B The Sherman-Morisson-Woodbury formula C HTM elements of the linear downconversion mixer D Oscillator dynamics: analysis of the deviation from the attracting mani- D.1 Components of the deviation Ax(t) Behavior of Ax2 (T) An expression for Ax2 (T) Boundedness of Ax2(T) The behavior of Ax3(T) D.4 Conclusions E Analysis of a harmonic oscillator Determining the oscillator's averaged dynamics Phase behavior near operating point Conclusions Bibliography Symbols and Abbreviations Conventions We use the following notations for the scalars, vectors and matrices: scalar, slanted lower- and upper-case letters vector, bold lower-case letters matrix, bold upper-case letters. Sometimes, this is also used to denote a vector in its interpretation of a matrix with a single column. matrix element located at the i-th row and the j-th column harmonic transfer matrix, bold upper-case letters with a tilde on top averaged scalar- or vector-quantity corresponding to X, X x*,**,*** complex conjugate of a scalar, vector or matrix Operators Absolute value of a real number or modulus of a complex number 11.11p p-norm of a vector or matrix II - II Shorthand notation for the two-norm of a vector or matrix Fourier-transform operator Laplace-transform operator Im{.} Imaginary part of a complex number Re{.} Real part of a complex number Symbols [a,b] interval of real numbers located between a and b. oscillating signal's amplitude symbol for a capacitance frequency in [Hz] symbol for a conductance unity matrix unity matrix belonging to RNxN complex number that equals V-1 symbol for an inductance O(en) the Landau symbol also called big-O. A function f(e) is said to be O(en) if EK>0:f(e) <AEn state vector of an oscillator's core system xviii SYMBOLS AND ABBREVIATIONS symbol for a resistance Laplace transform variable (complex frequency variable) perturbation variable P(t,T) autocorrelation function of a non-stationary stochastic process n(t) E R R. It is defined as P(T) = E{n(t)n(t-t)} If n(t) is stationary