Electromagnetics
Electromagnetics tests Maxwell's equations, wave propagation, transmission-line behaviour and boundary conditions. Expect a numerical reflection or line-impedance question with a physical interpretation.
Core rules
- Maxwell: ∇×E = −∂B/∂t; ∇×H = J + ∂D/∂t; ∇·D = ρ; ∇·B = 0.
- In a lossless medium, vp = 1/sqrt(με), η = sqrt(μ/ε); for free space η0 ≈ 377 Ω.
- Poynting vector S = E×H gives power density; average power = ½Re(E×H*).
- Boundary conditions: tangential E continuous; tangential H jumps by surface current; normal D jumps by surface charge; normal B continuous.
- Transmission line: Γ = (ZL−Z0)/(ZL+Z0); VSWR = (1+|Γ|)/(1−|Γ|); input impedance repeats every λ/2.
- Skin depth δ = sqrt(2/(ωμσ)); conductors become lossier at high frequency.
Worked example
A 50 Ω line feeds a 100 Ω load. Γ = (100−50)/(100+50) = 50/150 = 1/3. VSWR = (1+1/3)/(1−1/3) = (4/3)/(2/3) = 2. Reflected power fraction = |Γ|² = 1/9 ≈ 11.1%. A quarter-wave transformer would need Z0' = sqrt(50×100) ≈ 70.7 Ω to match this load at one frequency.
Traps
- Reversing the sign of Γ.
- Using VSWR = 1+|Γ| instead of the ratio.
- Forgetting that a short circuit has Γ=−1.
- Treating phase velocity as c in a dielectric.
- Mixing peak and RMS in power calculations.