Q factor measurements using Matlab Machine generated contents note: 1.Theoretical Foundations 1.1.Fosters Theorem 1.1.1.Lumped Element Lossless Circuits 1.1.2.Microwave Lossless Circuits 1.1.3.Reflection Coefficient of a Lossless Circuit 1.2.LCR Resonant Circuits 1.2.1.Series Resonant Circuit 1.2.2.Parallel Resonant Circuit 1.2.3.Augmented Parallel Resonant Circuit 1.3.Lossy Microwave One Port 1.4.Q Factor Definitions 1.4.1.Q in Terms of Energy Ratio 1.4.2.Q in Terms of Reactance (or Susceptance) Slope 1.4.3.Coupling Coefficient 1.4.4.Partial Qs 1.5.Q Circles 1.6.Fractional Linear Curve Fitting 1.6.1.De Embedding Problem 1.6.2.Scalar Products 1.6.3.Overdetermined System of Equations 1.6.4.Weighting 1.6.5.Error Estimates 1.7.Lossless Coupling 1.7.1.High Q Approximations 1.7.2.Input Reflection Coefficient 1.7.3.Repeated Curve Fitting 1.7.4.Computation of Q1 and k from a1 to a3 1.8.Correction for Coupling Losses References 2.Reflection Measurement Method 2.1.Program Q0REFL 2.1.1.Selecting MATLAB Properties 2.1.2.Using Q0REFL on Measured Data 2.2.Using Q0REFL on Validation Data 2.2.1.Generating the Validation Data 2.2.2.Influence of X5 and R5 2.2.3.Influence of the Line Length 2.2.4.Influence of Random Errors References 3.Reaction Measurement Method 3.1.Equivalent Circuit and the Corresponding Q Circles 3.2.Program Q0REAC 3.3.Generating the Validation Data 3.3.1.Influence of Capacitances in Microstrip to Coaxial Launchers 3.3.2.Influence of the Microstrip Line 3.4.De Embedding Resonators S Matrix 3.4.1.Equivalent Network Matrix Transformations 3.4.2.Evaluating the Element Values of the Fixture by Optimization 3.5.Program DEREAC 3.6.Program DEREACPL References 4.Transmission Measurement Method 4.1.Equivalent Network for Transmission Type Measurement 4.1.1.Q Circle for Scattering Coefficient S21 4.1.2.Q Circles for Scattering Coefficients S11 and S22 4.1.3.Generating the Validation Data 4.2.Program Q0TRAN 4.2.1.Recovering Resonator Characteristics from the S Parameter Data 4.2.2.Processing Failure 4.2.3.Uncertainty Estimates 4.2.4.Use of Q0TRAN on the Measured Data 4.2.5.Use of Q0TRAN on the Simulated Data References