Op-Amp Inverting Gain
Analog Circuits
Av = -(Rf / Rin)
The input node is a virtual ground (0 V) for an ideal op-amp; input impedance is Rin itself, so source impedance adds directly to Rin.
Core Engineering
Placement Formula Book
High-yield, printable formula sheets company technical rounds actually test. Search, copy the LaTeX or plain form, and export a one-page cheat sheet per branch.
12 formulas in ECE — Electronics
Op-Amp Non-Inverting Gain
Analog Circuits
Av = 1 + Rf/R1
Unity-gain follower is the limit Rf = 0; the non-inverting input impedance stays near-infinite, unlike the inverting topology.
Nyquist Sampling Criterion
Signals & Sampling
fs >= 2 * fmax
Sampling below 2fmax causes aliasing; an anti-aliasing filter must cut everything above fs/2 BEFORE the sampler, not after.
Reflection Coefficient & VSWR
Transmission Lines
Gamma = (ZL - Z0)/(ZL + Z0); VSWR = (1 + |Gamma|)/(1 - |Gamma|)
VSWR = 1 means a perfectly matched line; VSWR is always >= 1 and infinite for an open/short with |Gamma| = 1.
CMOS Propagation Delay
Digital / VLSI
tp ≈ 0.69 * Req * CL
Delay scales with fanout because CL includes gate capacitance of every load; shortening the longest path beats blind upsizing.
Fourier Transform Pair
Signals & Systems
X(w) = ∫ x(t) e^(-jwt) dt; x(t) = (1/2π) ∫ X(w) e^(jwt) dw
Multiplication in time = convolution in frequency — this is why convolution coding questions almost always start from a transform pair.
Laplace Transform Definition
Signals & Systems
X(s) = ∫ x(t) e^(-st) dt from 0- to ∞
All poles strictly left of the imaginary axis ⇒ a causal, BIBO-stable system; repeated poles on the axis are unstable even if simple poles would be marginally OK.
Friis Free-Space Path Loss
Communication
Pr = Pt * Gt * Gr * (λ / (4πd))^2
Halving the distance gains 6 dB; doubling the frequency costs 6 dB at the same distance — a classic link-budget numerical.
Shannon Channel Capacity
Communication
C = B * log2(1 + S/N)
Capacity grows linearly with bandwidth but only logarithmically with SNR — the reason spread-spectrum trades bandwidth for robustness.
RC Low-Pass Cutoff Frequency
Networks
fc = 1 / (2πRC); gain at fc = 1/√2 ≈ -3 dB
The -3 dB point is where the output drops to 70.7% of the passband gain — quote it that way in interviews, not just as a formula.
AM Power & Efficiency
Communication
Pt = Pc * (1 + μ²/2); η = μ²/(2 + μ²)
Maximum efficiency is only 33.3% at μ = 1 — the standard follow-up to 'why is AM wasteful?'.
Rectifier Ripple Voltage
Analog Circuits
Vr ≈ Iload / (f * C)
A full-wave rectifier doubles f, halving ripple for the same C — the practical reason full-wave beats half-wave supplies.