D. M. Pozar, Microwave Engineering, 4th ed., Ch. 2
Transmission-line model, telegrapher equations, propagation constant, characteristic impedance and line power.
RF-00
Course overview
Distributed circuits & transmission lines from Maxwell
Build transmission-line theory as a controlled reduction of electromagnetic propagation: first local voltage/current and distributed storage/loss, then telegrapher equations, characteristic impedance, propagation constant and line power.
5/5available
Prerequisites
- EM-04 — electromagnetic waves & power
- AC-02 — frequency response
- Basic differential calculus
By the end of this course
- Decide when an interconnect must be modeled as a transmission line.
- Derive distributed equations from an infinitesimal line element.
- Connect R′,L′,G′,C′ to fields, loss and stored energy.
- Obtain γ and Z₀ and interpret propagation, attenuation and power.
Syllabus
Distributed circuits & transmission lines from Maxwell
Build transmission-line theory as a controlled reduction of electromagnetic propagation: first local voltage/current and distributed storage/loss, then telegrapher equations, characteristic impedance, propagation constant and line power.
- 01→
From lumped circuits to distributed lines
Decide when propagation delay matters, define voltage and current on a two-conductor line, connect fields to per-unit-length R′, L′, G′ and C′, derive the infinitesimal line element and obtain the time-domain telegrapher equations from local KVL/KCL without treating them as memorized RF formulas.
180–230 min · Advanced · available - 02→
Solve the telegrapher equations
Move the time-domain line equations into AoN phasor form, define the series impedance and shunt admittance per unit length, decouple the system, derive γ²=Z′Y′, interpret γ=α+jβ, and obtain forward/backward voltage and current waves with the correct reverse-current sign.
180–230 min · Advanced · available - 03→
Characteristic impedance
Promote the forward-wave voltage/current ratio to the exact lossy characteristic impedance Z₀=√(Z′/Y′), tie its branch to passive γ, recover the lossless limit, connect Z₀ to geometry through a TEM coax example, derive the low-loss approximation and use the backward-current sign to audit transported power.
190–245 min · Advanced · available - 04→
Propagation constant, loss & distortion
Open γ=α+jβ into exact attenuation and phase, derive the low-loss conductor/dielectric contributions, convert nepers to decibels, distinguish phase and group delay, prove the Heaviside distortionless condition and delimit the frequency-independent RLGC model.
190–245 min · Advanced · available - 05→
Transmission-line power flow
Derive instantaneous and harmonic line power from the fixed voltage/current references, preserve the peak-phasor factor 1/2, distinguish forward/backward signed power, obtain the exact local RLGC loss balance, recover the Poynting-flux identity for a TEM line, connect power to stored energy and introduce a safe real-Z₀ normalization before later scattering theory.
200–255 min · Advanced · available
Reference backbone
References
The course uses field theory and microwave texts together so that line quantities retain their electromagnetic meaning.
R. E. Collin, Foundations for Microwave Engineering, 2nd ed., Ch. 3
Distributed-line theory, field interpretation and rigorous transmission-line limits.
S. Ramo, J. Whinnery & T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed.
Connection between electromagnetic fields, two-conductor lines, stored energy and distributed parameters.