1. topics Basic Transmission Line Equations
Nine Power Gains of Amplifiers
Linear and Nonlinear Synthesis/Analysis
Full-Wave Analysis for Microstrip
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2. basic transmission line equations
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3. basic transmission line equations
Important Conclusions from the above equations :
When ZL =ZO, ΓL = 0 and Zin = ZO
For an open transmission line ΓL = 1, Zin = -jZocotθ. Under the condition θ < π/2, the behavior of the input impedance is like that of a capacitance. Hence a short open-circuit transmission line can be used as a capacitance element.
For a shorted transmission line ΓL = -1, Zin = -jZotanθ. Under the condition θ < π/2, the behavior of the input impedance is like that of an inductance. Hence a short short-circuit transmission line can be used as an inductive element.
When an electrical length θ = π/2 (of physical length l = λ/4), the transmission line is called a quarter-wave transformer. The quarter-wave transformer has the following important property:
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4. basic transmission line equations
For a Matched Lossless two-port Transmission Line with electrical length θ :
S matrix
ABCD matrix
VSWR is the ratio of Vmax to Vmin. The relationship between VSWR and reflection coefficient is as follows:
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5. basic transmission line equations
Shift in Reference Planes
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6. basic transmission line equations
Shift in Reference Planes
The S-matrices of the 50Ω transmission lines are represented by S1 and S2 :
The S-matrix of the device can be represented by S1 and S2 and the measured matrix S’ as follows :
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7. nine power gains of amplifiers
Power Gains of different amplifiers are determined using S- parameters to get the following results :
Transducer power gain in 50-Ω system
Transducer power gain for arbitrary ΓG and ΓL
Unilateral transducer power gain
Power gain with input conjugate matched
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8. nine power gains of amplifiers
Available power gain with output conjugate matched
Maximum available power gain
Maximum unilateral transducer power gain
Maximum stable power gain
Unilateral power gain
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9. full wave analysis for microstrip
METHOD FEATURES DISADVANTAGES
Spectral Domain Method
One of the most popular methods for infinitesimally thin conductors on multilayer structures
Closed-form expressions for Fourier-transformed Green’s functions
Numerical efficiency
Cannot handle thick conductor structures
For tight coupling the number of basic functions becomes large; would involve convergent problems
Finite Difference Method
Mathematical preprocessing is minimal
Can be applied to a wide range of structures
Numerically inefficient
Precautions must be taken when the method is applied to an open-region problem
Need layer computer storage for accurate solution
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10. full wave analysis for microstrip
METHOD FEATURES DISADVANTAGES
Finite Element Method
Similar to the finite difference method
Has variational features in the algorithm and is more flexible in the application
Developed to solve very large matrix equations
Numerically inefficient
Existence of so-called spurious (unphysical) zeros
Mode- Matching Method
Typically applied to the problem of scattering at the waveguide discontinuity
Often used to solve enclosed planar structures, including metal thickness effects
Several different formulations possible, all theoretically equivalent; however, they may be different numerically
Precautions must be taken on relative convergence for some problems
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11. full wave analysis for microstrip
METHOD FEATURES DISADVANTAGES
Equivalent Waveguide Model
Very useful method for analysis of microstrip discontinuity problem
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12. linear and nonlinear synthesis
Matching networks for single-frequency and wide-frequency bands (e.g., a 4:1 for complex loads and termination).
Narrowband/wideband lumped and distributed filter synthesis.
Oscillator synthesis from small- and large-signal S parameters. Parallel-series design, determination of all components, determination of efficiency, output power, phase noise, and other relevant data.
Open and closed loop, PLL design, phase nosie determination, nonlinear switching, frequency lock phase lock.
System analysis and optimization for noise figure IMD performance.
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13. linear and nonlinear analysis
When load impedance ZL equals ZO, the characteristic impedance of the transmission line, the load reflection coefficient ΓL = 0, and the input impedance equals the characteristic impedance of the transmission line, namely Zin = ZO.
For an open transmission line ΓL = 1, Zin = -jZOcotθ. Under the condition θ < π/2, the behavior of the input impedance is like that of a capacitance. Hence a short open-circuit transmission line can be used as a capacitance element.
For a shorted transmission line ΓL = -1, Zin = -jZOtanθ. Under the condition θ < π/2, the behavior of the input impedance is like that of an inductance. Hence a short short-circuit transmission line can be used as an inductive element.
When an electrical length θ = π/2 (of physical length l = λ/4), the transmission line is called a quarter-wave transformer. The quarter-wave transformer has the following important property: Zin = ZO2 /ZL.
11/27/2018