Cheat sheet
FE Electrical and Computer Cheat Sheet
Math, Prob, Ethics, Econ
- 21-33% of exam
- Calculus Laplace Linear Algebra Probability Ethics + Econ
Circuits + Materials
- 14-21% of exam
- KCL/KVL Thevenin/Norton AC Phasors RLC Resonance Materials
Electronics
- 6-10% of exam
- Diodes BJT/MOSFET Op-Amps Rectifiers Biasing
Signals, Systems, Comms
- 14-22% of exam
- Transfer Function Convolution Sampling Filters Modulation
Power + Electromagnetics
- 12-18% of exam
- Three-Phase Transformers Machines Maxwell Transmission Lines
Digital, Computers, Controls
- 21-32% of exam
- Boolean Flip-Flops Architecture Networks Root 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 MA
- 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 MA
- 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 MA
- 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 MA
- 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 CI
- V = IR | P = VI = I²R = V²/R
- V volts I amps R ohms P watts
Thevenin vs Norton CI
Thevenin
- Voltage source
- Series resistance
- Vth, Rth
Norton
- Current source
- Parallel resistance
- In = Vth/Rth
- Voltage vs current source
Circuit Method Picker CI
- 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 CI
- 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 CI
- ELI the ICE man
- ELI: L, V leads I ICE: C, I leads V
Series vs Parallel Resonance CI
Series
- Min impedance
- Max current
- Z = R only
Parallel
- Max impedance
- Min current
- Tank circuit
- Same f0, opposite Z
AC + Impedance CI
- 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 EL
- Inputs equal, no input current
- V+ = V− Iin = 0 Virtual short
BJT vs MOSFET EL
BJT
- Current driven
- Base current
- Ic = β·Ib
MOSFET
- Voltage driven
- Gate voltage
- High input Z
- Current vs voltage control
Electronics EL
- 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 SI
Laplace
- s = σ + jω
- Transients + ICs
- Stability
Fourier
- s = jω only
- Steady-state spectrum
- Frequency content
- Transient vs steady-state
Transform Picker SI
- 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 SI
- 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 SI
- 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 PO
- Y voltage up, Δ current up √3
- Y: VL = √3 Vp Δ: IL = √3 Ip
Power Systems PO
- 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 PO
- 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 DI
Mealy
- Output on inputs
- Fewer states
- Reacts faster
Moore
- Output on state
- More states
- Glitch-free
- Input-based vs state-based
Digital Logic DI
- 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 DI
TCP
- Connection
- Reliable, ordered
- ACK + retransmit
UDP
- Connectionless
- Best effort
- Low latency
- Reliable vs fast
Computers + Networks DI
- 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 DI
- 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
FE Electrical and Computer
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