Electromagnetic Fields and Waves
Electromagnetic Fields and Waves tests Maxwell's equations, transmission-line behavior, impedance matching, wave propagation, and boundary conditions. Expect reflection coefficients, VSWR, and skin depth.
Core rules
- For a transmission line, Γ=(ZL-Z0)/(ZL+Z0); VSWR=(1+|Γ|)/(1-|Γ|).
- Power reflected is |Γ|²; a matched load has Γ=0 and VSWR=1.
- A quarter-wave transformer matches real impedances: Z0=√(Zin ZL).
- Wave velocity is c/√εr in a dielectric; skin depth decreases as √f.
- Boundary conditions: tangential E and normal B are continuous without surface sources.
Worked example
A 50 Ω line feeds a 75 Ω load. Γ=(75-50)/(75+50)=25/125=0.2. VSWR=(1+0.2)/(1-0.2)=1.5. Reflected power fraction is 0.2²=0.04, or 4%, so 96% is delivered. A quarter-wave transformer would need Z0=√(50×75)=√3750≈61.2 Ω. This is a real, positive impedance, so the match is physically realizable with a quarter-wave line section.
Traps
Reversing the sign of Γ; using VSWR as a power ratio; forgetting velocity factor when converting electrical length to physical length; applying quarter-wave matching to complex loads without cancellation; and mixing peak and RMS amplitudes in power calculations.