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Basics of microwave network analysis

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Solving Maxwell's equations to analyze a given electromagnetic (EM) problem yields an accurate solution with a plethora of spatiotemporal electric and magnetic fields information that may not be needed. It is also evident that quantities resulting from solving Maxwell's equations are interrelated and reconciled to the transmission line (TL) and circuit theory. Practically, port analysis techniques are more prevalent as a simple and effective method in analyzing microwave and mixed radio frequency (RF) digital circuits. Integrating additional components to the original problem has become an easy task by applying port analysis, where network loss, impedance transformation, and other effects are preserved. While most port parameters are valid to represent the device linear behavior due to small signal stimulus, other parameters are also available to cope with the nonlinear characteristics of circuits due to large signal excitation. Some network parameters are convenient to use than others depending on the circuit topology; therefore, conversions between the different port network parameters are also possible. Circuit analysis techniques can be classified into two categories based on their frequency of operation: low frequency based on quasi-static approximations of Maxwell's equations and high frequency (microwave) circuits based on full-wave EM analysis. At low frequencies, circuit physical dimensions are relatively small when compared to the operating wavelength and phase variation at any point in the circuit is considered negligible. There are several techniques used to analyze low-frequency circuits; however, they are not applicable for circuits operating at high (gigahertz) frequencies due to the domination of parasitic effects. Circuit synthesis techniques greatly benefit from applying port analysis methods to simplify the mathematical representation of the network transfer function and thereby the subsequent steps required to realize the circuit parameters.

Chapter Contents:

• 3.1 Introduction
• 3.2 Microwave port analysis
• 3.2.1 Voltage–current-based parameters
• 3.2.1.1 Impedance (Z-) parameters
• 3.2.1.3 Transmission (ABCD) parameters
• 3.2.1.4 Hybrid (h-) parameters
• 3.2.2 Traveling wave-based parameters
• 3.2.2.1 Scattering (S-) parameters
• 3.2.2.2 Generalized S-parameters
• 3.2.2.3 Scattering transfer (T-) parameters
• 3.2.2.4 Hybrid scattering (HS-) parameters
• 3.2.2.5 X-parameters
• 3.3 Microwave network basic properties
• 3.3.1 Linearity
• 3.3.2 Time invariance
• 3.3.3 Reciprocity
• 3.3.4 Symmetry
• 3.3.5 Passivity
• 3.3.6 Lossless
• 3.4 Signal flow graph
• 3.5 De-embedding and embedding S-parameters
• 3.6 Two-port equivalent circuits
• 3.7 Passive and lossless circuit synthesis
• 3.7.1 Singly and doubly terminated networks
• 3.7.2 One-port circuit synthesis
• 3.7.2.1 Foster synthesis
• 3.7.2.2 Cauer synthesis
• 3.7.3 Two-port circuit synthesis
• References

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