D. M. Pozar, Microwave Engineering, 4th ed., Ch. 2 and network analysis chapters
Forward/backward line waves, load reflection and RF port waves.
RF-04
Course overview
Scattering parameters: waves, references and energy
Build RF scattering theory from physically defined waves on transmission lines. Derive the incident/reflected decomposition before selecting reference impedances, constructing S-matrices and testing reciprocity and energy conservation.
5/5available
Prerequisites
- RF-00 — transmission lines
- RF-01 — reflections and Smith chart
- RF-03 — two-port matrices and power
Learning goals
- Derive incident and reflected waves from line equations.
- Separate physical line impedance and measurement reference.
- Build S-parameters from normalized waves.
- Test reciprocity, passivity and scattering power.
Syllabus
Scattering parameters: waves, references and energy
Build RF scattering theory from physically defined waves on transmission lines. Derive the incident/reflected decomposition before selecting reference impedances, constructing S-matrices and testing reciprocity and energy conservation.
- 01→
Incident and reflected waves on a transmission line
Derive forward and reverse voltage/current solutions, load reflection, open/short conditions, standing waves, power and reference-plane rotation without changing the current sign convention.
200–260 min · Intermediate → advanced · available - 02→
Reference impedance and wave renormalization
Distinguish line Zc, input Zin and measurement Rref, derive real-reference wave power, unequal-port S conversion, complex Kurokawa and pseudo waves, and compare reported matching and VNA planes.
230–290 min · Advanced · available - 03→
Definition and extraction of S-parameters
Derive the scattering matrix from matched-wave experiments, convert from Z/Y/ABCD under fixed inward current signs, and test reflection, transmission, power and reference-plane shifts.
210–270 min · Intermediate → advanced · available - 04→
Reciprocity, passivity and scattering energy
Derive S†S passivity and lossless unitarity, test reciprocal symmetry, coherent eigenchannels, a dissipative series resistor, an ideal gyrator and an isolator, with hidden physical power channels.
220–280 min · Advanced · available - 05→
From V/I ports to normalized power waves
Synthesize equal and unequal real/complex reference impedances, derive Z↔S and Kurokawa transforms, quantify passive power and plan calibrated VNA renormalization.
250–310 min · Advanced · available
Scientific references
References
Derivations follow a declared exp(+jωt) convention, with the load at z=0 and the generator toward negative z.
R. E. Collin, Foundations for Microwave Engineering, 2nd ed.
Wave and modal impedances, reference planes, complex representations.