Expert-level applied electromagnetics covering transmission lines, waveguides, antennas, microwave circuits, EMC, and computational EM methods.
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Characteristic impedance: Z0 = sqrt of L over C per unit length. Reflection coefficient: Gamma = ZL minus Z0 over ZL plus Z0. Standing wave ratio: SWR = 1 plus magnitude of Gamma over 1 minus magnitude of Gamma. Input impedance: varies with line length and load impedance. Quarter wave transformer: matches impedance by choosing Z1 = sqrt of ZS times ZL.
TE modes: transverse electric, no E field in propagation direction. TM modes: transverse magnetic, no H field in propagation direction. Cutoff frequency: below cutoff, mode is evanescent not propagating. Rectangular waveguide: dominant TE10 mode, used at microwave frequencies. Coaxial line: TEM mode, no cutoff, used from DC to microwave.
Radiation resistance: equivalent resistance that dissipates radiated power. Gain: directional amplification of radiated power versus isotropic. Half-wave dipole: 2.15 dBi gain, 73 ohm input impedance. Patch antenna: low profile, used in mobile devices, PCB-integrated. Phased array: electronically steerable beam, phase shift per element.
Emissions: conducted and radiated, limits set by FCC and CE standards. Immunity: susceptibility to external interference, ESD, EFT, surge. Shielding: conductive enclosure reduces radiated emissions and susceptibility. Filtering: ferrite beads and bypass capacitors reduce conducted emissions.
| Pitfall | Fix |
|---|---|
| Impedance mismatch causing reflections | Match impedances at all interfaces |
| Ground plane discontinuities | Route return currents directly under signal traces |
| Antenna detuning near ground plane | Simulate with actual PCB environment |
| Ignoring skin effect at high frequency | Use correct AC resistance in analysis |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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