D. M. Pozar, Microwave Engineering, 4th ed., Ch. 2
Load reflection coefficient, standing waves, input impedance, VSWR and transmission-line transformations.
RF-01
Course overview
Reflection, standing waves & Smith chart
Turn the forward/backward waves of RF-00 into boundary-value reasoning: first derive reflection from a load, then understand standing waves, input impedance, quarter-wave transformations and finally the Smith chart as a map of those equations rather than a collection of graphical tricks.
5/5available
Prerequisites
- RF-00 — distributed transmission lines
- Complex numbers and phasors
- Sinusoidal power
By the end of this course
- Derive reflection directly from a load boundary condition.
- Connect reflection to standing waves and local impedance.
- Use line transformations without losing sign conventions.
- Build the Smith chart as a map of reflection coefficient rather than a graphical recipe.
Syllabus
Reflection, standing waves & Smith chart
Turn the forward/backward waves of RF-00 into boundary-value reasoning: first derive reflection from a load, then understand standing waves, input impedance, quarter-wave transformations and finally the Smith chart as a map of those equations rather than a collection of graphical tricks.
- 01→
Reflection coefficient from the load boundary
Start from the RF-00 forward/backward transmission-line solution, impose the load relation at z=0, derive ΓL=(ZL−Z₀)/(ZL+Z₀), preserve the fixed +z current reference, interpret magnitude and phase, audit matched/open/short/reactive limits and connect |Γ|² to reflected power only under the stated real-Z₀ lossless assumptions.
190–245 min · Advanced · available - 02→
Standing waves and VSWR
Build the spatial voltage/current envelopes from the same incident/reflected phasors, derive extrema and their λg/2 periodicity, obtain VSWR=(1+|Γ|)/(1−|Γ|), locate maxima from reflection phase, audit open/short patterns and separate standing-wave contrast from net transported power.
190–245 min · Advanced · available - 03→
Input impedance along a transmission line
Turn the local reflection coefficient into Z_in(d)=Z₀(1+Γ)/(1−Γ), derive the exact lossy tanh form and the lossless tangent form, audit matched/open/short limits, half-wave repetition and quarter-wave inversion, and explain why a sufficiently long lossy line approaches Z₀.
200–255 min · Advanced · available - 04→
Quarter-wave transformations
Derive the λg/4 impedance inversion from the general line law, obtain the geometric-mean single-section match between positive real impedances, calculate detuning and ideal bandwidth, and state clearly why complex loads, loss, dispersion and fabrication require more than the memorized square-root rule.
200–255 min · Advanced · available - 05→
Smith chart from the impedance–reflection map
Derive the Smith chart from z=(1+Γ)/(1−Γ): special points, passive unit disk, constant-resistance circles, constant-reactance arcs, clockwise reference-plane motion under the course coordinate convention, impedance/admittance duality and physically identified matching trajectories.
200–255 min · Advanced · available
Reference backbone
References
The course follows standard microwave transmission-line theory while keeping AoN's voltage/current references and peak-phasor normalization explicit.
R. E. Collin, Foundations for Microwave Engineering, 2nd ed., Ch. 3
Rigorous forward/backward modal solution, reflection and line transformations.
P. H. Smith, Electronic Applications of the Smith Chart, 2nd ed.
Later graphical impedance/reflection mapping and Smith-chart construction.