7–9 Marks • Formula Heavy

Electromagnetics (EMT) — Complete Revision Notes

Maxwell's Laws, Uniform Plane Waves, Transmission Lines, Smith Chart & Waveguides • Curated by Akshat

1. Maxwell's Equations (Time-Harmonic)

Gauss's Law for Electrostatics: $\nabla \cdot \vec{D} = \rho_v \iff \oint_S \vec{D}\cdot d\vec{S} = Q_{enc}$
Gauss's Law for Magnetism: $\nabla \cdot \vec{B} = 0 \iff \oint_S \vec{B}\cdot d\vec{S} = 0$ (No magnetic monopoles)
Faraday's Law of Induction: $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} \iff \oint_C \vec{E}\cdot d\vec{l} = -\frac{d\Phi_B}{dt}$
Ampere-Maxwell Law: $\nabla \times \vec{H} = \vec{J} + \frac{\partial \vec{D}}{\partial t}$ (where $\frac{\partial \vec{D}}{\partial t}$ is Displacement Current Density)

Intrinsic Impedance: $\eta = \sqrt{\frac{\mu}{\varepsilon}}$. In vacuum: $\eta_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} \approx 120\pi \approx 377\ \Omega$.
Poynting Vector: $\vec{S} = \vec{E} \times \vec{H}$, Time-average power density $\vec{P}_{avg} = \frac{1}{2}\text{Re}\{\vec{E}\times \vec{H}^*\} = \frac{|E_0|^2}{2\eta}\hat{a}_k$.
Skin Depth (Good Conductor): $\delta = \sqrt{\frac{1}{\pi f \mu \sigma}}$, phase velocity $v = \omega \delta = \sqrt{\frac{2\omega}{\mu \sigma}}$.

Voltage Reflection Coefficient: $\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}$. (Short: $\Gamma = -1$; Open: $\Gamma = +1$; Matched: $\Gamma = 0$).
Voltage Standing Wave Ratio (VSWR): $S = \frac{1 + |\Gamma|}{1 - |\Gamma|} \ge 1$.
Input Impedance at distance $l$: $Z_{in}(l) = Z_0 \left(\frac{Z_L + j Z_0 \tan(\beta l)}{Z_0 + j Z_L \tan(\beta l)}\right)$.
Quarter-Wave Transformer ($l = \lambda/4$): $Z_{in} = \frac{Z_0^2}{Z_L} \implies Z_0 = \sqrt{Z_{in} Z_L}$.

Cutoff Frequency for $\text{TE}_{mn}$ or $\text{TM}_{mn}$: $f_c = \frac{c}{2}\sqrt{\left(\frac{m}{a}\right)^2 + \left(\frac{n}{b}\right)^2}$ (where $a > b$). Dominant mode: $\text{TE}_{10}$ with $f_c = \frac{c}{2a}$.
Phase Velocity: $v_p = \frac{c}{\sqrt{1-(f_c/f)^2}} > c$.
Group Velocity: $v_g = c\sqrt{1-(f_c/f)^2} < c$. Golden Relation: $v_p \cdot v_g = c^2$.
Guide Wavelength: $\lambda_g = \frac{\lambda_0}{\sqrt{1-(f_c/f)^2}} > \lambda_0$.

Linear Algebra, Calculus, Euler-Cauchy ODEs, Complex Variables, Probability & Statistics

LTI Convolution, CTFT, DTFT, Laplace ROC, Z-Transform, Nyquist Sampling

Thevenin, Norton, Max Power, Transient Step Response, AC Resonance, Two-Port Matrices

AM, FM, Carson's Rule, PCM Quantization SNR, BPSK, QPSK, Shannon Channel Capacity

Diodes, Small-Signal BJT & MOSFET, Op-Amp Virtual Ground, Active Filters, Oscillators

Mason's Gain, 2nd Order Transient Specs, Routh-Hurwitz, Root Locus, Bode & Nyquist

K-Maps, MUX, Decoders, Flip-Flops, Synchronous Counters, FSM Mealy/Moore, ADC/DAC

Numerical Reasoning, Spatial Reasoning, Speed-Distance, Permutations, Probability