AMIE Section B EEE Exam cheat sheet

Three-phase balanced power: P = √3·V_L·I_L·cosφ, where V_L and I_L are line quantities and φ is the impedance angle.

Per-unit conversion: Z_pu = Z_actual / Z_base, with Z_base = V_base² / S_base for a single-phase base; use the line-to-line voltage and three-phase power consistently.

Thevenin equivalent: open-circuit voltage V_oc in series with R_th = V_oc / I_sc; maximum power transfer occurs when load resistance equals R_th.

Transformer EMF equation: E = 4.44·f·N·Φ_max; core loss is constant with load while copper loss varies as I².

DC machine torque: T = k·Φ·I_a; back EMF E_b = k·Φ·ω, and for a shunt motor speed falls as load increases because armature drop reduces E_b.

Induction motor slip: s = (N_s − N_r)/N_s with N_s = 120f/P; rotor frequency f_r = s·f and rotor copper loss equals s times air-gap power.

Symmetrical components: positive, negative, and zero sequence sets; a single line-to-ground fault current equals 3·V_phase / (Z_1 + Z_2 + Z_0).

Cable and line insulation coordination uses the basic impulse level (BIL) and protective margin = (BIL − residual voltage)/residual voltage × 100%.

BJT active-region bias: V_BE ≈ 0.7 V for silicon; I_C = β·I_B and I_E = (β+1)·I_B; saturation occurs when V_CE drops below about 0.2 V.

MOSFET saturation condition: V_DS ≥ V_GS − V_TH; drain current I_D = ½·k·(V_GS − V_TH)² in saturation and is linear in V_DS in triode.

Op-amp ideal assumptions: infinite open-loop gain, infinite input impedance, zero output impedance; virtual short V+ = V− holds only with negative feedback.

Nyquist sampling theorem: sample at f_s > 2·f_max to avoid aliasing; an anti-alias low-pass filter precedes the sampler.

Shannon capacity: C = B·log₂(1 + S/N); doubling bandwidth does not double capacity when noise also scales with bandwidth.

Friis noise figure: F_total = F_1 + (F_2 − 1)/G_1 + (F_3 − 1)/(G_1·G_2) + …; the first stage dominates receiver noise.

Digital modulation: BPSK and QPSK have the same energy per bit versus noise performance in AWGN; QPSK doubles spectral efficiency for the same bit error rate.

Antenna link budget: received power P_r = P_t·G_t·G_r·(λ/(4πd))²; free-space path loss increases 6 dB per doubling of distance or frequency.

CPU time = instruction count × cycles per instruction × clock period; reducing CPI and clock period both lower execution time.

Amdahl's law: speedup = 1 / ((1 − p) + p/s), where p is the fraction enhanced and s is the enhancement factor; serial fraction caps gain.

Cache average access time = hit time + miss rate × miss penalty; a two-level hierarchy uses local miss rates for the second level.

Virtual memory: TLB hit avoids a page-table walk; effective access time includes TLB lookup plus memory access on a miss.

TCP congestion control: slow start doubles the congestion window per RTT until ssthresh, then additive increase and multiplicative decrease after loss.

Binary search runs in O(log n) time and requires a sorted array; hash-table lookup averages O(1) but degrades with collisions.

RISC versus CISC: RISC uses fixed-length instructions and load/store architecture; CISC allows memory operands and variable-length encoding.

Relational normal forms: 2NF removes partial dependencies on a composite key; 3NF removes transitive dependencies on non-key attributes.

First law for a steady-flow open system: q − w = Δh + ΔKE + ΔPE per unit mass; for a nozzle with no work, enthalpy drop converts to kinetic energy.

Carnot efficiency: η = 1 − T_L/T_H with absolute temperatures; no real cycle between the same reservoirs exceeds it.

Otto cycle efficiency: η = 1 − 1/r^(γ−1), where r is compression ratio and γ = c_p/c_v; Diesel cycle efficiency also depends on cut-off ratio.

Beam bending: σ = M·y/I and deflection relates to EI; maximum bending stress occurs at the farthest fiber from the neutral axis.

Shaft torsion: τ = T·r/J; for a solid circular shaft J = π·d⁴/32, so τ_max = 16T/(π·d³).

Fatigue failure occurs below the ultimate strength; the S-N curve and endurance limit guide infinite-life design, with stress concentration reducing life.

Bernoulli equation along a streamline: p/ρ + V²/2 + g·z = constant for steady, incompressible, frictionless flow.

Heat exchanger effectiveness: ε = actual heat transfer / maximum possible heat transfer; NTU = U·A/C_min and effectiveness rises with NTU.

Concrete mix design: water-cement ratio controls strength and durability; lower w/c increases strength but reduces workability.

Reinforced concrete beam design: balanced section occurs when tension steel yields simultaneously with concrete crushing at ε_cu = 0.003.

Slope deflection and moment distribution methods solve indeterminate frames; stiffness is proportional to EI/L and carry-over factor is 0.5 for prismatic members.

Soil bearing capacity by Terzaghi: q_u = c·N_c + q·N_q + 0.5·γ·B·N_γ; the water table reduces effective unit weight.

Effective stress principle: σ' = σ − u; consolidation settlement depends on the compression index and the change in effective stress.

Open-channel flow: Manning's equation V = (1/n)·R^(2/3)·S^(1/2); hydraulic radius R = A/P.

Surveying: a closed traverse adjusts angular error by distributing it equally among angles; latitude = L·cos(bearing) and departure = L·sin(bearing).

Structural steel tension member design uses gross-section yielding and net-section fracture; block shear failure must also be checked.