Systematic Modeling and Analysis of Telecom Frontends and their Building Blocks

representations. 3.5 LPTV system analysis using HTMs. 3.5.1 Multi-tone analysis. 3.5.2 Stability analysis. 3.5.3 Noise analysis. 3.6 Conclusions and directions for further research. 4 Applications of LPTV system analysis using harmonic transfer matrices. 4.1 HTMs in a nutshell. 4.2 Phase-Locked Loop analysis. 4.2.1 PLL architectures and PLL building blocks. 4.2.2 Prior art. 4.2.3 Signal phases and phase-modulated signal models. 4.2.4 HTM-based PLL building block models. 4.2.5 PLL closed-loop input-output HTM. 4.2.6 Example 1: PLL with sampling PFD. 4.2.7 Example 2: PLL with mixing PFD. 4.2.8 Conclusions. 4.3 Automated symbolic LPTV system analysis. 4.3.1 Prior art. 4.3.2 Symbolic LPTV system analysis: outlining the flow. 4.3.3 Input model construction. 4.3.4 Data structures. 4.3.5 Computational flow of the SymbolicHTM algorithm. 4.3.6 SymbolicHTM: advantages and limitations. 4.3.7 Application 1: linear downconversion mixer. 4.3.8 Application 2: Receiver stage with feedback across the mixing element. 4.4 Conclusions and directions for further research. 5 Modeling oscillator dynamic behavior. 5.1 The story behind the math. 5.1.1 Earth: a big oscillator. 5.1.2 Unperturbed system behavior: neglecting small forces. 5.1.3 Perturbed system behavior: changes in the earth's orbit. 5.1.4 Averaging: focusing on what's important. 5.1.5 How does electronic oscillator dynamics fit in?. 5.1.6 Modeling oscillator behavior. 5.2 Prior art. 5.2.1 General theory. 5.2.2 Phase noise analysis. 5.2.3 Numerical simulation. 5.2.4 Contributions of this work. 5.3 Oscillator circuit equations. 5.3.1 Normalizing the oscillator circuit equations. 5.3.2 Partitioning the normalized circuit equations. 5.4 Characterizing the oscillator's unperturbed core. 5.5 Oscillator perturbation analysis. 5.5.1 Components of an oscillator's perturbed behavior. 5.5.2 Motion xs _ t_ p_ t_ _over the manifold M . 5.5.3 In summary. 5.6 Averaging. 5.7 Oscillator phase (noise) analysis. 5.7.1 Capturing oscillator phase behavior. 5.7.2 Practical application: oscillator injection locking. 5.7.3 Averaging in the presence of random perturbations. 5.7.4 Practical application: computing oscillator phase noise spectra. 5.8 Harmonic oscillator behavioral modeling. 5.8.1 Model extraction theory. 5.8.2 Numerical computations. 5.8.3 Experimental results. 5.9 Conclusions and directions for further research. 6 Conclusions. 6.1 Main achievements. 6.1.1 HTM-based LPTV system analysis. 6.1.2 Modeling oscillator dynamic behavior. 6.2 Leads for further work. A HTM norms and the comparison of HTMs. A.1 Operator norms and the comparison of operators. A.2 Selecting the set of test inputs. A.3 Expressing LPTV operator norms in terms of the corresponding 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 manifold. D.1 Components of the deviation Dx_ t_ . D.2 Behavior of Dx2 _ t_ . An expression for Dx2 _ t_ . Boundedness of Dx2 _ t_ . D.3 The behavior of Dx3 _ t_ . D.4 Conclusions. E Analysis of a harmonic oscillator. E.1 Determining the oscillator's averaged dynamics. E.2 Phase behavior near operating point. E.3 Conclusions. Bibliography.