Math, Prob, Ethics, Econ
21-33%of exam
CalculusLaplaceLinear AlgebraProbabilityEthics + Econ
Circuits + Materials
14-21%of exam
KCL/KVLThevenin/NortonAC PhasorsRLC ResonanceMaterials
Electronics
6-10%of exam
DiodesBJT/MOSFETOp-AmpsRectifiersBiasing
Signals, Systems, Comms
14-22%of exam
Transfer FunctionConvolutionSamplingFiltersModulation
Power + Electromagnetics
12-18%of exam
Three-PhaseTransformersMachinesMaxwellTransmission Lines
Digital, Computers, Controls
21-32%of exam
BooleanFlip-FlopsArchitectureNetworksRoot Locus
Quick Facts
- Exam
- FE Electrical & Computer
- Body
- NCEES (Pearson VUE)
- Questions
- 110 items
- Time
- 5h 20m total
- Fee
- $175
- Pass
- Scaled cut score
- Reference
- FE Handbook only
- Knowledge areas
- 18 areas
Exam-Day Flow
- Know formula location→Search Handbook(On-screen)
- Stuck >3 min→Flag and skip(Return later)
- Ethics question→Public safety first(Easy points)
- Unit mismatch→Convert to SI(Check prefixes)
- Multiple-select item→Read all options(Alt-item type)
Math Core
- d/dx sin x
- cos x
- d/dx e^x
- e^x
- ∫ 1/x dx
- ln|x| + C
- Euler
- e^{jθ}=cosθ+jsinθ
- Determinant 2×2
- ad − bc
- Eigenvalue
- det(A − λI)=0
- Dot product
- |A||B|cosθ
- Cross product
- |A||B|sinθ
Laplace Transforms
- L{1}
- 1/s
- L{t}
- 1/s²
- L{e^{-at}}
- 1/(s+a)
- L{sin ωt}
- ω/(s²+ω²)
- L{cos ωt}
- s/(s²+ω²)
- L{f'}
- sF(s) − f(0)
- Final value
- lim sF(s), s→0
- Initial value
- lim sF(s), s→∞
Probability + Econ
- Mean
- Σx/n
- Variance
- E[X²] − (E[X])²
- Std dev σ
- √variance
- Binomial mean
- np
- Future worth
- P(1+i)^n
- Present worth
- F/(1+i)^n
- Straight-line dep
- (C − S)/n
- Breakeven
- Cost = revenue
Power Wheel
V = IR | P = VI = I²R = V²/R
V voltsI ampsR ohmsP watts
Thevenin vs Norton
Thevenin
- Voltage source
- Series resistance
- Vth, Rth
Norton
- Current source
- Parallel resistance
- In = Vth/Rth
Voltage vs current source
Circuit Method Picker
- Many node voltages→Nodal analysis(KCL)
- Many mesh currents→Mesh analysis(KVL)
- One load varies→Thevenin(Vth, Rth)
- Need source current→Norton(In, Rn)
- Multiple sources→Superposition(One at a time)
- Steady-state AC→Phasors(Use impedance)
- Transient RC/RL→Time constant(τ)
DC Circuits
- Ohm
- V = IR
- Power
- P = VI = I²R
- KCL
- Σ currents = 0
- KVL
- Σ voltages = 0
- Series R
- R1 + R2 + …
- Parallel R
- 1/(1/R1 + 1/R2)
- Vdivider
- V·R2/(R1+R2)
- RC tau
- τ = RC
Reactance Memory
ELI the ICE man
ELI: L, V leads IICE: C, I leads V
Series vs Parallel Resonance
Series
- Min impedance
- Max current
- Z = R only
Parallel
- Max impedance
- Min current
- Tank circuit
Same f0, opposite Z
AC + Impedance
- Xl
- 2πfL = ωL
- Xc
- 1/(2πfC)
- Z
- R + jX
- Resonance
- f = 1/(2π√LC)
- Quality Q
- f0/bandwidth
- Real power
- P = VI cosθ
- Apparent S
- VI = √(P²+Q²)
- Power factor
- cosθ = P/S
Op-Amp Rules
Inputs equal, no input current
V+ = V−Iin = 0Virtual short
BJT vs MOSFET
BJT
- Current driven
- Base current
- Ic = β·Ib
MOSFET
- Voltage driven
- Gate voltage
- High input Z
Current vs voltage control
Electronics
- Diode drop
- ~0.7 V silicon
- Thermal Vt
- 26 mV at 300K
- BJT region
- Active amplifies
- Ideal op-amp
- V+ = V−, Iin=0
- Inverting gain
- −Rf/Rin
- Noninvert gain
- 1 + Rf/Rin
- Half-wave
- Vavg = Vp/π
- Full-wave
- Vavg = 2Vp/π
Laplace vs Fourier
Laplace
- s = σ + jω
- Transients + ICs
- Stability
Fourier
- s = jω only
- Steady-state spectrum
- Frequency content
Transient vs steady-state
Transform Picker
- Transient ODE→Laplace(s-domain)
- Steady-state spectrum→Fourier(jω)
- Discrete sequence→z-transform(Digital)
- Sampled spectrum→DFT(FFT)
- System output→Convolution(x ∗ h)
- Stability check→Pole location(LHP)
Signals + Systems
- Transfer fn
- H(s) = Y/X
- Convolution
- y = x ∗ h
- Nyquist rate
- fs > 2·fmax
- FIR
- No feedback, stable
- IIR
- Feedback, poles
- Cutoff
- −3 dB point
- Decibel
- 20 log(Vo/Vi)
- DFT bins
- N points, fs/N
Communications
- AM BW
- 2·fm
- FM BW
- 2(Δf + fm)
- Shannon C
- B log2(1+SNR)
- Nyquist rate
- 2B symbols/s
- Friis loss
- ∝ (4πd/λ)²
- FDM
- Split by frequency
- TDM
- Split by time
- Bit rate
- Baud × bits/symbol
Three-Phase Y
Y voltage up, Δ current up √3
Y: VL = √3 VpΔ: IL = √3 Ip
Power Systems
- Y line voltage
- √3·Vphase
- Δ line current
- √3·Iphase
- 3-phase power
- √3·VL·IL·cosθ
- Transformer
- V1/V2 = N1/N2
- Slip
- (ns − n)/ns
- Sync speed
- 120f/poles
- PF correct
- Add capacitor
- Per-unit
- Actual/base
Electromagnetics
- Gauss law
- ∮D·dA = Qenc
- Faraday
- emf = −dΦ/dt
- Ampere
- ∮H·dl = Ienc
- Free-space η
- 377 Ω
- Wave speed
- c = 3×10⁸ m/s
- λ
- v/f
- Refl coeff Γ
- (ZL−Z0)/(ZL+Z0)
- VSWR
- (1+|Γ|)/(1−|Γ|)
Mealy vs Moore
Mealy
- Output on inputs
- Fewer states
- Reacts faster
Moore
- Output on state
- More states
- Glitch-free
Input-based vs state-based
Digital Logic
- De Morgan
- (AB)' = A'+B'
- XOR
- 1 if odd ones
- K-map
- Group powers of 2
- SOP
- Sum of products
- D flip-flop
- Q follows D
- JK toggle
- J=K=1 inverts
- n-bit counter
- 2^n states
- Mux 2^n:1
- n select lines
TCP vs UDP
TCP
- Connection
- Reliable, ordered
- ACK + retransmit
UDP
- Connectionless
- Best effort
- Low latency
Reliable vs fast
Computers + Networks
- Cache hit
- Fast memory found
- Locality
- Temporal + spatial
- Pipeline
- Overlap stages
- Big-O
- Growth bound
- OSI
- 7 layers
- TCP
- Reliable, ordered
- UDP
- Fast, no ACK
- IPv4
- 32-bit address
Control Systems
- Open loop
- No feedback
- Closed loop
- G/(1+GH)
- Stable poles
- Left-half plane
- Root locus
- Poles vs gain
- Gain margin
- Margin at −180°
- Phase margin
- Margin at 0 dB
- PID
- P + I + D terms
- Type number
- Integrators count
Common Traps
Thevenin vs Norton
Thevenin series R ≠ Norton parallel R
Power vs apparent
P uses cosθ ≠ S = VI only
Series vs parallel f0
Series min Z ≠ Parallel max Z
Laplace vs Fourier
Laplace has σ ≠ Fourier jω only
Mean vs RMS
Mean averages ≠ RMS heats resistor
Peak vs RMS
Vp is peak ≠ Vrms = Vp/√2
Last Minute
- 1.110 items, 5h 20m, $175
- 2.Only FE Handbook allowed
- 3.Vrms = Vp/√2 for sine
- 4.Xc = 1/(2πfC); Xl = 2πfL
- 5.Resonance: f = 1/(2π√LC)
- 6.Three-phase P = √3·VL·IL·cosθ
- 7.Op-amp: V+ = V−, Iin = 0
- 8.Sync speed = 120f/poles
- 9.Free-space η0 = 377 Ω
- 10.Stable poles = left-half plane
- 11.Ethics: public safety first
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