TASC Electronics and Advanced Technologies Level 3 cheat sheet

Ohm's law: V = I × R; power P = V × I = I²R = V²/R.

Series: R_total = R1 + R2 + …; current is identical through all elements.

Parallel: 1/R_total = 1/R1 + 1/R2 + …; voltage is identical across all branches.

Capacitor impedance Z_C = 1/(jωC); impedance falls as frequency rises, and DC blocks.

Inductor impedance Z_L = jωL; impedance rises with frequency, and DC passes.

RC time constant τ = RC; voltage reaches ~63% of final value in one τ, ~99% in five τ.

Resonance: f₀ = 1/(2π√(LC)); at resonance X_L = X_C and impedance is purely resistive.

Kirchhoff: KCL sums currents at a node to zero; KVL sums voltages around a loop to zero.

RMS for a sinusoid: V_rms = V_peak/√2 ≈ 0.707 × V_peak.

Ideal op-amp rules: no input current, and V+ = V− when negative feedback is present.

Inverting gain = −R_f/R_in; non-inverting gain = 1 + R_f/R_g.

BJT regions: cutoff (V_BE < 0.7 V), active (I_C = βI_B), saturation (V_CE ≈ 0.2 V).

MOSFET saturation condition: V_DS > V_GS − V_th; I_D ∝ (V_GS − V_th)².

Boolean identities: De Morgan A·B = (A′+B′)′ and A+B = (A′·B′)′.

A full adder computes Sum = A ⊕ B ⊕ C_in and C_out = AB + C_in(A ⊕ B).

Nyquist criterion: sample above twice the highest signal frequency to avoid aliasing.

Quantization error of an ideal N-bit ADC is ±½ LSB, where LSB = V_ref/2^N.

Decoupling capacitors are placed close to IC power pins to shunt high-frequency current.

Harvard architecture separates program and data memory buses; von Neumann shares one bus.

A GPIO configured as input must not be driven as output, or bus contention may damage the pin.

Interrupt latency = time from request to first instruction of the ISR; keep ISRs short.

Volatile tells the compiler a variable may change outside program flow (registers, ISR flags).

UART frame: start bit, 5–9 data bits, optional parity, 1–2 stop bits; baud = bits per second.

SPI is full-duplex, master-driven, with separate MOSI, MISO, SCLK, and chip-select lines.

I²C uses two open-drain lines (SDA, SCL) with pull-ups and 7-bit addressing by default.

Watchdog timer resets the MCU if firmware fails to refresh it within the timeout period.

PWM duty cycle D sets average output: V_avg = D × V_supply.

A transducer converts one energy form to another; a sensor is the input-side device.

RTD resistance rises nearly linearly with temperature; thermistor response is strongly nonlinear.

Thermocouple output is a small Seebeck voltage requiring cold-junction compensation.

Strain gauge sensitivity is expressed by gauge factor GF = (ΔR/R)/(ΔL/L).

Wheatstone bridge nulls when R1/R2 = R3/R4; it converts small resistance changes to voltage.

A 4–20 mA current loop encodes zero at 4 mA; live-zero allows open-circuit detection.

LVDT measures linear displacement as a phase-sensitive AC output proportional to core position.

Stepper motor step angle = 360°/(steps per revolution); microstepping subdivides each full step.

Servo control uses closed-loop feedback of position, velocity, or torque to correct error.

Diode conducts when forward-biased above ~0.7 V (Si); it blocks reverse voltage up to its rating.

A thyristor (SCR) latches on with a gate pulse and turns off only when anode current drops below holding current.

Buck converter steps voltage down: V_out = D × V_in in continuous conduction mode.

Boost converter steps voltage up: V_out = V_in/(1 − D) in continuous conduction mode.

Buck-boost inverts: V_out = −V_in × D/(1 − D).

Duty cycle D = t_on/(t_on + t_off) = t_on × f_sw.

Full-bridge rectifier output ripple frequency is twice the AC line frequency.

Transformer turns ratio: V_s/V_p = N_s/N_p; power is ideally conserved (V_p I_p = V_s I_s).

Power factor = real power / apparent power = cos φ for sinusoidal loads.

Shannon capacity: C = B × log₂(1 + S/N), in bits per second.

Modulation maps information onto carrier amplitude (AM), frequency (FM), or phase (PM).

Bandwidth of a digital link is limited by the channel; Nyquist limit for M-ary signaling is 2B log₂M.

OSI layers (1–7): Physical, Data Link, Network, Transport, Session, Presentation, Application.

TCP is connection-oriented and reliable; UDP is connectionless and best-effort.

IPv4 addresses are 32 bits; IPv6 addresses are 128 bits.

Subnet mask /24 leaves 8 host bits, giving 254 usable host addresses.

Twisted-pair Ethernet categories: Cat5e supports 1 Gb/s, Cat6 supports 10 Gb/s up to limited distance.

Fiber optic uses total internal reflection; single-mode has a smaller core and longer reach than multimode.

Open-loop control has no feedback; closed-loop compares output to a setpoint and corrects error.

PID output: u(t) = K_p e + K_i ∫e dt + K_d de/dt.

Proportional gain reduces steady-state error but can cause overshoot and oscillation.

Integral action eliminates steady-state error but can cause windup; anti-windup limits it.

Derivative action anticipates error, reduces overshoot, and amplifies high-frequency noise.

First-order step response reaches 63.2% at one time constant τ; settling ≈ 4τ for 2% band.

Second-order system damping ratio ζ < 1 is underdamped; ζ = 1 is critically damped.

PLC scan cycle repeats: read inputs, execute logic, update outputs.

Ladder logic rungs: series contacts implement AND; parallel contacts implement OR.

A voltmeter is connected in parallel; an ammeter is connected in series with the load.

Ideal voltmeter has infinite input resistance; ideal ammeter has zero input resistance.

An oscilloscope vertical scale sets volts/div; horizontal scale sets time/div.

Oscilloscope probe 10× divides signal by 10 and raises input impedance and bandwidth.

A DMM reading OL (overload) usually means the measured value exceeds the selected range.

Continuity test verifies near-zero resistance; used for opens and shorts in wiring.

Root cause analysis: verify power rails first, then clock, then reset, then bus activity.

A logic analyzer captures multi-channel digital timing and decodes protocols like SPI and I²C.

Ground loops between instruments and DUT cause measurement noise and safety hazards.

ESD control: wrist straps, grounded mats, and ionizers protect sensitive CMOS devices.

Lockout/tagout isolates hazardous energy before servicing electrical equipment.

Class C fires involve energized electrical equipment; use non-conductive extinguishing agents.

Body current thresholds: ~1 mA perception, ~10 mA let-go, ~30 mA respiratory interference.

High-voltage capacitors retain charge after power-off; discharge and verify before touching.

Laser classes 3B and 4 require eye protection and controlled access areas.

RoHS restricts lead, mercury, cadmium, and other hazardous substances in electronics.

RF exposure is limited by specific absorption rate (SAR) and power density limits.

Battery safety: lithium cells require protection circuits; thermal runaway risk grows with overcharge.

Conductor resistance R = ρL/A; resistance grows with length and shrinks with cross-section.

Temperature coefficient: R(T) = R₀[1 + α(T − T₀)]; α is positive for most metals.

Capacitors in series: 1/C_total = 1/C1 + 1/C2 + …; parallel: C_total = C1 + C2 + …

Inductors in series add directly; parallel combine as 1/L_total = 1/L1 + 1/L2 + …

Energy stored: capacitor E = ½CV², inductor E = ½LI².

Thevenin equivalent: open-circuit voltage V_th in series with R_th = V_oc/I_sc.

Norton equivalent: short-circuit current I_N in parallel with the same R_th.

Superposition applies only to linear circuits; sum responses from each independent source.

Ideal op-amp: infinite open-loop gain, infinite input impedance, zero output impedance.

Comparator output saturates at supply rails; add hysteresis to avoid chatter near threshold.

Diode clipper limits signal peaks; clamper shifts DC level without changing peak-to-peak.

RC low-pass cutoff f_c = 1/(2πRC); above f_c the response rolls off at −20 dB/decade.

Active filter uses op-amp to buffer and amplify, allowing higher Q than passive RC.

Karnaugh maps minimize Boolean expressions by grouping 1s in powers of two.

Setup and hold times define the window a synchronous input must remain stable around a clock edge.

CMOS static power is low; dynamic power P = αCV²f dominates when switching.

A flip-flop stores one bit; a latch is level-sensitive and not edge-triggered.

Memory map regions: flash (program), SRAM (data), and peripherals mapped to addresses.

Stack grows downward on ARM Cortex-M; stack overflow corrupts adjacent SRAM.

DMA moves data between peripherals and memory without CPU intervention.

ADC resolution N bits: counts = 2^N; code = round(V_in/V_ref × 2^N).

UART baud rate error must stay under ~2–3% for reliable framing.

I²C addresses are 7 bits plus a read/write bit; 10-bit addressing is optional.

Real-time operating system (RTOS) schedules tasks by priority; use mutexes for shared resources.

Brown-out detector resets the MCU when supply voltage drops below a safe threshold.

Firmware update via bootloader preserves a recovery region if the main image is invalid.

Photodiode operates reverse-biased; photocurrent is proportional to incident light.

Phototransistor has higher gain than a photodiode but slower response.

Hall-effect sensor detects magnetic field; used for position, speed, and current sensing.

Ultrasonic ranging: distance = (speed of sound × time of flight)/2.

Accelerometer measures acceleration; a gyroscope measures angular rate; combine for IMU.

Load cell uses strain gauges in a bridge; output typically 1–3 mV/V of excitation.

Solenoid converts electrical current to linear motion; proportional valves vary force with current.

Piezoelectric actuator produces small displacement under high voltage; used in precision positioning.

Encoder resolution: counts per revolution = PPR × decoding factor (×1, ×2, or ×4).

Linear regulator dissipates P = (V_in − V_out) × I_load; efficiency = V_out/V_in.

Switching regulator efficiency typically 80–95%; losses come from conduction and switching.

PWM switching frequency trades ripple (higher f, lower ripple) against switching loss.

Freewheeling diode clamps inductive kickback when a switch turns off.

Inverter converts DC to AC; rectifier converts AC to DC.

Three-phase rectifier produces six ripple pulses per cycle; ripple frequency = 6 × line frequency.

Battery capacity in Ah × nominal voltage gives approximate watt-hours.

Maximum power transfer occurs when load resistance equals source resistance.

Isolation transformer breaks galvanic path for safety and noise reduction.

Signal-to-noise ratio in dB: SNR_dB = 10 log₁₀(P_signal/P_noise).

Free-space path loss grows with the square of distance and the square of frequency.

Manchester encoding embeds the clock in each bit transition; used in 10BASE-T.

CRC detects transmission errors but cannot correct them.

Ethernet CSMA/CD applies to half-duplex shared media; switched full-duplex does not collide.

Wi-Fi channels 1, 6, and 11 are non-overlapping in the 2.4 GHz band.

RS-485 uses differential signaling for long-distance, multi-drop serial buses.

Modbus RTU frame: address, function code, data, CRC.

Fiber attenuation is quoted in dB/km; splices and connectors add insertion loss.

Transfer function H(s) = output(s)/input(s) for a linear time-invariant system.

Closed-loop transfer function = G/(1 + GH) for forward gain G and feedback H.

Stability requires all closed-loop poles to lie in the left half of the s-plane.

Bode plot: gain margin and phase margin indicate relative stability.

Integrator adds −90° phase and −20 dB/decade slope to the open-loop response.

Feedforward control acts on measured disturbances; feedback acts on measured error.

Hysteresis (deadband) prevents actuator chatter in on/off control.

SCADA gathers field data via RTUs/PLCs and presents it to operators for supervisory control.

Safety instrumented systems (SIS) are independent of basic process control.

Accuracy is closeness to true value; precision is repeatability of the measurement.

Resolution is the smallest detectable change; sensitivity is output change per input change.

A DMM's digits: a 3½-digit meter shows up to 1999 counts.

True-RMS meters are required for non-sinusoidal AC waveforms.

Oscilloscope bandwidth should be at least 3–5× the highest signal frequency of interest.

Trigger modes (edge, pulse, video) stabilize repeating waveforms on screen.

Signal generator output impedance is typically 50 Ω; mismatched loads cause reflections.

Four-wire (Kelvin) measurement removes lead resistance for low-ohm readings.

Divide-and-conquer troubleshooting: isolate to a subsystem, then to a component.

Safety ground (earth) is separate from neutral in a TN-S distribution system.

RCD/GFCI trips at a residual current threshold, typically 30 mA for personnel protection.

Arc flash boundaries define approach distances; PPE category depends on incident energy.

SELV systems operate at voltages low enough to be safe under normal conditions (≤ 50 V AC).

IEC 61010 governs safety of electrical test and measurement equipment.

IP rating: first digit is solids protection, second is liquids protection (e.g., IP54).

Battery storage rooms require ventilation to prevent hydrogen accumulation from lead-acid cells.

Optocouplers provide galvanic isolation between high- and low-voltage circuits.

Fusing must be rated for the circuit's voltage and interrupting current, not just its nominal current.

Voltage divider: V_out = V_in × R2/(R1 + R2) when unloaded.

Current divider: I1 = I_total × R2/(R1 + R2) for two parallel resistors.

Capacitive reactance X_C = 1/(2πfC); inductive reactance X_L = 2πfL.

Impedance magnitude |Z| = √(R² + (X_L − X_C)²); phase angle φ = arctan((X_L − X_C)/R).

Real power P = V_rms I_rms cos φ; reactive power Q = V_rms I_rms sin φ.

Apparent power S = V_rms × I_rms, measured in volt-amperes.

A decibel expresses ratio: dB = 20 log₁₀(V2/V1) for voltage, 10 log₁₀(P2/P1) for power.

A 3 dB change is a factor of ~1.41 in voltage and ~2 in power.

Logic families: TTL input thresholds ~0.8 V low, ~2.0 V high; CMOS scales with supply.

Fan-out is the number of inputs a single output can drive within specified thresholds.

Noise margin = V_IH(min) − V_OH(min) for high state; V_OL(max) − V_IL(max) for low state.

Tri-state outputs allow bus sharing; only one driver may be enabled at a time.

Open-drain outputs require external pull-up resistors to define the high level.

Schmitt trigger inputs add hysteresis, rejecting noise on slow edges.

Successive-approximation ADC converts in N clock cycles for N bits.

Sample-and-hold circuit freezes the input during conversion to reduce error.

A differential pair rejects common-mode noise; twisted pair benefits from the same principle.

Clock sources: internal RC (fast start, less accurate), crystal (accurate), PLL (multiplies).

Prescaler divides the peripheral clock to set timers and ADC conversion rate.

GPIO alternate-function registers route pins to UART, SPI, I²C, or timer peripherals.

Interrupt priority nesting: higher priority preempts lower priority on Cortex-M NVIC.

Debouncing mechanical switches uses RC filtering or software delay of 5–20 ms.

Flash endurance is limited (typ. 10k–100k cycles); wear-leveling spreads writes.

Low-power modes: sleep, stop, standby - each trades wake latency for current savings.

JTAG/SWD provide in-circuit debug and programming access to the MCU.

Sensor transfer function maps physical input to electrical output (linear or nonlinear).

Calibration compares sensor output to a reference standard across the operating range.

Span is the output change over the full measurement range; offset is the zero-input output.

Linearity error is the maximum deviation from the best-fit straight line, as % of span.

Resolution is the smallest input change producing a detectable output change.

Response time is the time to reach a specified percentage (often 63% or 90%) of final value.

Hysteresis is the difference in output when approaching a value from opposite directions.

Common-mode rejection ratio (CMRR) is the ability to reject signals common to both inputs.

Optical encoders use a slotted disk and photo detector to count position increments.

IGBT combines MOSFET gate drive with BJT conduction; used in high-power inverters.

MOSFET is preferred for high-frequency switching; BJT for high-voltage, low-frequency.

Snubber networks suppress voltage spikes and ringing across switching devices.

Dead time prevents shoot-through in a half-bridge when both switches could conduct.

Gate driver provides isolated, level-shifted drive current to the power switch.

Soft-start limits inrush current by ramping output voltage or duty cycle.

Solar PV MPPT tracks the maximum power point as irradiance and temperature vary.

Battery state of charge can be estimated by coulomb counting or open-circuit voltage.

Isolated DC-DC converters use a transformer for galvanic isolation between input and output.

OSI layer 2 (Data Link) handles MAC addressing and framing; layer 3 handles IP routing.

ARP resolves an IP address to a MAC address on a local network.

DHCP assigns IP addresses, subnet masks, gateways, and DNS servers automatically.

TCP three-way handshake: SYN, SYN-ACK, ACK before data transfer.

TCP retransmits lost segments; UDP does not guarantee delivery or ordering.

Collision domain is bounded by switches; broadcast domain is bounded by routers.

VLANs segment a physical switch into multiple logical broadcast domains.

NAT translates private addresses to a public address for internet access.

Quality of service (QoS) prioritizes latency-sensitive traffic like voice and video.

Proportional band is the error range over which the controller output spans 0–100%.

Integral time (reset) is the time for integral action to repeat the proportional output.

Derivative time (rate) is the interval by which derivative action leads the error.

Ziegler–Nichols tuning uses ultimate gain and period to set PID gains.

Process variable (PV), setpoint (SP), and manipulated variable (MV) define a control loop.

Cascade control uses an inner fast loop and an outer slow loop for better disturbance rejection.

Ratio control maintains a fixed ratio between two process flows.

Dead time (transport delay) degrades stability and limits achievable gain.

PLC analog input scaling: engineering units = raw × (span/range) + offset.

Voltage measurement across a component with power applied; resistance measurement with power removed.

Diode test mode shows forward drop (~0.6 V for Si, ~0.3 V for Ge, ~0.2 V for Schottky).

Continuity beep indicates resistance below a few ohms (typically <50 Ω).

Capacitor ESR meter detects aging electrolytics that appear to have correct capacitance.

Thermal imaging reveals hot components and shorted traces before failure.

Oscilloscope probe compensation must be adjusted to the square-wave calibration signal.

Differential probe measures signals referenced to a non-ground node safely.

Signal tracing: inject a known signal at the input and follow it stage-by-stage to find the fault.

Intermittent faults often trace to cold solder joints, connectors, or thermal expansion.

Electrical shock severity depends on current path, magnitude, duration, and frequency.

Dry skin resistance can be >100 kΩ; wet skin can drop below 1 kΩ, raising shock risk.

Isolation transformers and isolated supplies reduce shock risk during bench work.

Lockout/tagout requires verifying zero energy state before servicing.

Personal protective equipment (PPE) for electrical work: insulated gloves, arc-rated clothing, face shield.

Ground fault circuit interrupters (GFCIs) are required in wet or outdoor locations.

Anti-static workstations use dissipative mats and grounded wrist straps.

Laser safety classes: 1 (safe), 2 (visible, blink reflex), 3R/3B (hazardous), 4 (fire/eye hazard).

Lithium-ion batteries require cell balancing and thermal monitoring to prevent thermal runaway.

Active elements (sources, amplifiers) can deliver power; passive elements cannot.

Ideal voltage source has zero internal resistance; ideal current source has infinite resistance.

Real sources have internal resistance that causes terminal voltage to sag under load.

Mesh analysis writes KVL around each independent loop; nodal analysis writes KCL at each node.

Linearity permits superposition; nonlinear elements (diodes, transistors) require other methods.

Maximum power transfer occurs when load resistance equals source resistance (efficiency 50%).

Time constant of an RL circuit is τ = L/R; of an RC circuit is τ = RC.

A transformer reflects impedance by the square of the turns ratio: Z_p = (N_p/N_s)² Z_s.

Instrumentation amplifier uses three op-amps for high input impedance and high CMRR.

Integrator op-amp circuit produces a ramp from a step input; differentiator produces a spike.

Precision rectifier uses an op-amp to overcome the diode's forward-drop dead zone.

Voltage regulator types: linear (low noise, low efficiency) and switching (high efficiency, more noise).

Bypass capacitor on a reference pin reduces noise and stabilizes the reference voltage.

Logic levels: LVCMOS 3.3 V interfaces directly with many 5 V TTL inputs but not vice versa.

Level shifters translate between logic voltage domains without damaging inputs.

PLLs synthesize stable high frequencies from a lower reference clock.

Clock jitter degrades timing margins in synchronous digital systems.

Memory-mapped I/O allows peripherals to be accessed like memory addresses.

Polling wastes CPU cycles; interrupts free the CPU between events.

A ring buffer decouples producer and consumer in serial communication.

Endianness: little-endian stores least-significant byte first; ARM Cortex-M defaults to little-endian.

Volatile and const qualifiers prevent unintended compiler optimizations on hardware registers.

Floating-point units enable hardware math but consume more power than integer math.

Firmware debugging uses breakpoints, watch variables, and trace output over SWO or UART.

Secure boot verifies firmware signatures before execution to prevent tampering.

Proximity sensors: inductive (metal), capacitive (any material), and photoelectric (line of sight).

Ultrasonic sensors struggle with soft, angled, or foam targets that absorb sound.

Infrared thermometers require emissivity compensation for accurate surface readings.

Flow sensors: turbine (pulse output), electromagnetic (conductive fluids), ultrasonic (non-invasive).

Pressure sensors: piezoresistive (common), capacitive (high accuracy), piezoelectric (dynamic only).

Piezoelectric sensors cannot measure static pressure; charge leaks away over time.

Servo motor control uses PWM pulse width (typically 1–2 ms) to set position.

Solenoid valve response time depends on coil inductance; flyback diode protects the driver.

Motor torque is proportional to current; speed is proportional to voltage (DC brushed).

Transformer core losses: hysteresis and eddy current; reduce eddy currents with laminated cores.

Copper losses in windings scale with I²R and dominate at high load.

Power factor correction (PFC) reduces reactive current drawn from the AC source.

Uninterruptible power supply (UPS): online (double conversion), line-interactive, and standby types.

Grid-tied inverters must synchronize phase and frequency and provide anti-islanding protection.

Battery chemistry comparison: lead-acid (low cost, heavy), lithium-ion (high energy density), NiMH (moderate).

Overcurrent protection: fuses (one-time) and circuit breakers (resettable).

Thermal management: heatsinks, forced air, and thermal pads keep junction temperatures within limits.

Insulation coordination selects creepage and clearance distances for operating voltage and pollution degree.

Antenna gain is directional; higher gain concentrates power into a narrower beam.

Impedance matching at the antenna minimizes reflected power (low VSWR).

VSWR = (1 + |Γ|)/(1 − |Γ|), where Γ is the reflection coefficient.

Return loss in dB: RL = −20 log₁₀|Γ|.

Frequency reuse in cellular networks increases capacity using sectorization and cell splitting.

Spread spectrum (DSSS, FHSS) improves interference resistance and security.

LoRa and NB-IoT target long-range, low-power IoT links with low data rates.

BLE advertises on three channels and connects on 37 data channels in the 2.4 GHz band.

Network segmentation improves security by limiting lateral movement between zones.

Root locus plots closed-loop pole locations as a gain parameter varies.

Nyquist criterion counts encirclements of −1 to determine closed-loop stability.

Phase margin is the additional phase lag that would make the closed-loop system unstable.

Gain margin is the factor by which gain can increase before instability.

Lead compensation adds phase margin and speeds response; lag compensation reduces steady-state error.

State-space model: ẋ = Ax + Bu, y = Cx + Du.

Observability means the internal state can be inferred from outputs; controllability means inputs can drive the state.

Discrete control uses a z-domain transfer function and a zero-order hold.

Motion control profiles: trapezoidal (accel, cruise, decel) and S-curve (smooth jerk).

Spectral analysis via FFT reveals harmonics, noise, and spurious signals.

Spectrum analyzer RBW (resolution bandwidth) controls sweep time and frequency resolution.

Time-domain reflectometry (TDR) locates cable faults by measuring reflection timing.

LCR meter measures inductance, capacitance, and resistance at a specified test frequency.

Insulation resistance tester applies high voltage to verify isolation between conductors.

Clamp meter measures current without breaking the circuit, using the magnetic field around the conductor.

Data logging captures measurements over time to reveal intermittent or drift faults.

Calibration traceability links measurements to national standards through a chain of comparisons.

Bench power supply current limit protects the DUT from overcurrent damage.

Machine safety categories (ISO 13849) define required performance level for control systems.

Emergency stop circuits use normally-closed contacts and must be hardwired, not software-only.

Light curtains and safety mats detect intrusion into hazardous zones.

Two-hand control requires both operators' hands to be occupied for safe operation.

Electrical enclosures require adequate ventilation to dissipate heat and prevent overheating.

Cable management: separate power and signal cables to reduce electromagnetic interference.

Surge protection devices (SPDs) divert transient overvoltages to ground.

Grounding system resistance for industrial installations is typically below 5 Ω.

Hazardous location equipment uses intrinsic safety or explosion-proof enclosures for flammable atmospheres.

A conductor has low resistance; an insulator has high resistance; a semiconductor lies between.

Doping: N-type adds donor impurities (extra electrons); P-type adds acceptor impurities (holes).

PN junction: forward bias narrows the depletion region; reverse bias widens it.

Diode equation: I = I_s(e^(V/(nV_T)) − 1), where V_T ≈ 26 mV at room temperature.

Zener diode operates in reverse breakdown to provide a stable reference voltage.

LED forward voltage depends on color: ~1.8 V (red), ~3.2 V (blue).

Photodiode converts light to current; LED converts current to light.

Bipolar transistor current gain β = I_C/I_B; α = I_C/I_E and β = α/(1 − α).

Differential amplifier gain = R_f/R_in when the input is applied differentially.

Common-mode rejection ratio (CMRR) = 20 log₁₀(A_diff/A_cm).

Slew rate limits the maximum frequency a signal can be amplified without distortion.

Gain-bandwidth product (GBW) is constant for an op-amp; higher gain means lower bandwidth.

Offset voltage and bias current cause DC errors; chopper-stabilized op-amps reduce them.

Power supply rejection ratio (PSRR) measures how well an amplifier rejects supply noise.

Oscillator requires Barkhausen criterion: loop gain ≥ 1 and loop phase = 0° (or 360°).

Crystal oscillators offer high Q and stable frequency; RC oscillators are simpler but less stable.

Analog-to-digital converter types: SAR (fast, moderate resolution), delta-sigma (high resolution, slower), flash (fastest, lower resolution).

Bootloader runs first and decides whether to load firmware or enter update mode.

Interrupt vector table maps interrupt sources to their handler addresses.

Peripheral clock gating saves power by disabling unused peripherals.

DMA channels free the CPU from byte-by-byte transfers between peripherals and memory.

Timer capture mode records the time of an external event; compare mode generates an output at a set time.

ADC oversampling improves effective resolution by averaging multiple samples.

Firmware versioning and checksum verification detect corrupted images.

Real-time constraints require deterministic response times, not just average throughput.

Embedded Linux vs bare-metal: Linux offers multitasking and drivers; bare-metal offers determinism.

Signal conditioning amplifies, filters, and linearizes sensor output before conversion.

Instrumentation amplifier is preferred for bridge sensors due to high input impedance and CMRR.

Excitation voltage affects bridge output; higher excitation increases sensitivity and self-heating.

Sensor fusion combines multiple sensors (e.g., IMU) for better state estimation.

Kalman filter estimates state from noisy measurements using a model and covariance.

Time-of-flight sensors measure distance by timing light or sound pulses.

Capacitive touch sensors detect changes in capacitance from a finger's proximity.

MEMS accelerometers use a proof mass and capacitive sensing to measure acceleration.

Actuator selection depends on force, speed, precision, and duty cycle requirements.

Switching loss P_sw ≈ ½ × V × I × (t_on + t_off) × f_sw.

Conduction loss in a MOSFET P_cond = I² × R_DS(on) × D.

Diode reverse recovery causes switching loss and EMI in high-frequency converters.

Synchronous rectification replaces a diode with a MOSFET to reduce conduction loss.

Resonant converters reduce switching loss by switching at zero voltage or zero current.

Three-phase inverter produces variable frequency and voltage for motor drives (V/f control).

Field-oriented control (FOC) decouples torque and flux in AC motor drives.

Battery management system (BMS) monitors cell voltage, current, and temperature for safety.

Energy storage sizing depends on peak demand, autonomy time, and depth of discharge.

Modulation index in AM affects sideband power; overmodulation causes distortion.

FM bandwidth is approximated by Carson's rule: BW ≈ 2(Δf + f_m).

Digital modulation: ASK, FSK, PSK, QAM; higher-order QAM increases bits/symbol but reduces noise margin.

Bit error rate (BER) depends on E_b/N₀ and the modulation scheme.

Forward error correction (FEC) adds redundancy to detect and correct errors at the receiver.

Duplexing: FDD uses separate uplink and downlink frequencies; TDD shares one frequency in time.

Multiple access: TDMA (time), FDMA (frequency), CDMA (code), OFDMA (orthogonal subcarriers).

Network topologies: star, bus, ring, mesh; mesh offers redundancy at higher cost.

Firewalls filter traffic by rules; VPNs encrypt traffic over untrusted networks.

Actuator saturation limits control authority; anti-windup prevents integrator buildup.

Feedforward plus feedback improves tracking when the plant model is known.

System identification estimates plant parameters from input-output data.

Sampling rate in digital control should be at least 10× the closed-loop bandwidth.

Deadbeat control drives the error to zero in a finite number of samples.

Model predictive control (MPC) optimizes future inputs subject to constraints.

Safety integrity level (SIL) rates the risk reduction of a safety function.

Human-machine interface (HMI) displays process state and accepts operator commands.

Industrial protocols: Modbus, Profibus, EtherNet/IP, and OPC UA for plant integration.

Signal integrity issues: reflections, crosstalk, ground bounce, and ringing.

Characteristic impedance of a trace depends on geometry and dielectric constant.

Termination resistors match trace impedance to prevent reflections at high speed.

Eye diagram reveals jitter, noise margin, and rise time in high-speed serial links.

Jitter is the deviation of a signal edge from its ideal timing position.

Crosstalk is coupling between adjacent traces; increase spacing or add ground guards.

Ground plane continuity reduces loop area and EMI.

ESD events can damage ICs without immediate failure; latent damage appears later.

Thermal cycling accelerates solder fatigue in connectors and BGA packages.

Electrical safety standards: IEC 60364 for installations, NFPA 70E for workplace safety.

Arc flash incident energy depends on fault current, clearing time, and working distance.

Approach boundaries: limited, restricted, and prohibited define required qualification levels.

Voltage-rated gloves must be tested periodically and inspected before each use.

Portable generator use requires proper grounding and carbon monoxide ventilation.

Battery disposal follows local regulations; lithium batteries require special handling.

Fire extinguisher classes: A (ordinary combustibles), B (flammable liquids), C (electrical), D (metals), K (cooking oils).

First aid for electrical shock: disconnect power, call emergency services, begin CPR if trained.

Documented lockout/tagout procedures and periodic audits maintain compliance.

Charge Q = C × V; current I = dQ/dt; capacitor voltage cannot change instantaneously.

Inductor current cannot change instantaneously; voltage can.

Faraday's law: induced EMF = −N × dΦ/dt.

Lenz's law: induced current opposes the change that produced it.

Magnetic field of a solenoid: B = μ₀μ_r n I, where n is turns per unit length.

Mutual inductance couples energy between coils; the basis of transformers.

Skin effect concentrates AC current near the conductor surface at high frequency.

Proximity effect further redistributes current in adjacent conductors at high frequency.

Logic minimization reduces gate count, cost, and propagation delay.

Propagation delay is the time from input transition to output transition.

Setup time is the minimum time data must be stable before the clock edge.

Hold time is the minimum time data must remain stable after the clock edge.

Metastability occurs when a flip-flop samples data too close to the clock edge.

Clock skew is the difference in clock arrival time between sequential elements.

Synchronous design uses a single clock; asynchronous design uses handshaking.

Finite state machines: Moore outputs depend only on state; Mealy outputs depend on state and input.

Test access: boundary scan (JTAG) verifies board-level interconnects.

Watchdog timers protect against firmware hangs; refresh only when the main loop is healthy.

Brown-out detection resets the MCU when the supply drops below a threshold.

Power-on reset ensures the MCU starts from a known state.

In-system programming (ISP) and in-application programming (IAP) allow field updates.

Non-volatile memory (EEPROM, flash) stores configuration across power cycles.

Real-time clock (RTC) keeps time with a low-power oscillator and backup battery.

Communication peripherals: UART, SPI, I²C, CAN, USB; each has different speed and topology.

CAN bus uses differential signaling and arbitration for multi-master networks.

Debugging embedded systems requires tools: oscilloscope, logic analyzer, and debugger.

Sensor accuracy includes offset, gain, linearity, hysteresis, and noise errors.

Calibration procedure: apply known inputs, record outputs, fit a curve, store correction coefficients.

Temperature compensation corrects sensor drift over the operating range.

Ratiometric sensors output a voltage proportional to supply voltage.

Digital sensors (I²C, SPI) simplify interfacing and reduce noise pickup.

Wireless sensor networks require low-power radios and duty-cycled operation.

Actuator feedback (encoder, resolver, Hall) closes the loop for precise motion control.

Hydraulic and pneumatic actuators offer high force but require fluid or air supply.

Piezoelectric actuators are used in inkjet printers and precision positioning stages.

Transformer efficiency peaks near full load; copper losses scale with I², core losses are roughly constant.

Power factor is corrected by adding capacitors (for inductive loads) or active PFC circuits.

Harmonics in power systems cause heating and require filtering.

Inverter output filters (LC) smooth PWM into a sinusoidal waveform.

Motor drive energy savings come from variable speed control instead of throttling.

Regenerative braking returns energy to the source or storage.

Grid codes specify voltage, frequency, and harmonic limits for grid-connected inverters.

Islanding detection protects utility workers during grid outages.

Battery cycle life depends on depth of discharge, temperature, and charge rate.

OSI layer 1 (Physical) defines voltage levels, connectors, and cable types.

Layer 2 switches forward frames by MAC address; layer 3 routers forward packets by IP.

TCP/IP model: Network Access, Internet, Transport, Application.

IP addressing: classful vs CIDR; /24 = 256 addresses, 254 usable.

Private address ranges: 10.0.0.0/8, 172.16.0.0/12, 192.168.0.0/16.

DNS resolves names to IP addresses; DHCP assigns addresses dynamically.

Wireless security: WPA2/WPA3 use AES encryption; WEP is deprecated and insecure.

Network monitoring uses SNMP, syslog, and packet capture.

Latency, jitter, and packet loss are key quality metrics for real-time traffic.

Feedback reduces sensitivity to plant variations and disturbances.

Loop gain determines steady-state error: higher gain reduces error but risks instability.

PID tuning methods: Ziegler–Nichols, Cohen–Coon, and manual tuning.

Integral windup occurs when the actuator saturates while the error persists.

Derivative kick occurs when the setpoint changes abruptly; filter the derivative term.

Feedforward compensates measurable disturbances before they affect the output.

Cascade control: inner loop rejects fast disturbances; outer loop tracks the setpoint.

Ratio control maintains a fixed ratio between two process variables.

Process control terminology: dead time, time constant, gain, and self-regulation.

Measurement uncertainty combines type A (statistical) and type B (systematic) contributions.

Calibration certificates state uncertainty and traceability to national standards.

Guard banding accounts for measurement uncertainty when comparing to limits.

Four-wire measurement removes lead resistance for low-ohm readings.

Kelvin connections are used in precision shunts and low-resistance standards.

Thermocouple cold-junction compensation corrects for ambient temperature at the meter terminals.

Oscilloscope probe loading affects high-impedance circuits; use a 10× probe.

Differential probes measure floating signals safely.

Data acquisition systems sample multiple channels; multiplexing introduces settling time.

Electrical safety training covers hazard recognition, PPE, and emergency response.

Arc flash risk assessment determines incident energy and required PPE.

Energized work permits are required when equipment cannot be de-energized.

Voltage detectors verify absence of voltage before work begins.

Temporary protective grounds protect workers from induced or back-feed voltage.

Battery rooms require ventilation, eyewash stations, and acid-resistant PPE.

Photovoltaic systems remain energized in sunlight; DC arc flash is a hazard.

Wind turbine safety includes lockout of rotor and electrical systems.

Electric vehicle high-voltage systems require insulated tools and trained personnel.

Semiconductor materials: silicon (most common), germanium, gallium arsenide (high speed).

Intrinsic semiconductor has equal electron and hole concentrations.

Depletion region width depends on doping and applied voltage.

Forward-biased diode: current rises exponentially above the knee voltage.

Reverse-biased diode: small leakage current until breakdown.

Bipolar transistor operates in active, saturation, and cutoff regions.

MOSFET operates in cutoff, triode (linear), and saturation regions.

Transconductance g_m = ΔI_D/ΔV_GS describes MOSFET gain.

Analog filters: low-pass, high-pass, band-pass, band-stop; defined by cutoff and roll-off.

Butterworth filter has maximally flat passband; Chebyshev has ripple but sharper roll-off.

Bessel filter has linear phase and best pulse response.

Filter order determines roll-off: n-th order gives −20n dB/decade.

Active filters use op-amps; passive filters use R, L, C only.

Switched-capacitor filters use clocked capacitors to emulate resistors.

Digital filters: FIR (linear phase, stable) and IIR (efficient, can be unstable).

Sampling theorem: f_s > 2 × f_max to avoid aliasing.

Anti-aliasing filter precedes the ADC to limit input bandwidth.

ARM Cortex-M cores: M0 (low power), M3/M4 (DSP), M7 (high performance).

Memory-mapped peripherals use base addresses and offset registers.

Bit-banding allows atomic bit manipulation in memory.

Interrupt latency depends on core, clock speed, and nesting.

DMA reduces CPU load for high-throughput transfers.

Low-power design: reduce clock frequency, disable unused peripherals, use sleep modes.

Firmware architecture: super-loop, RTOS, or event-driven state machines.

Debug interfaces: SWD (2-wire), JTAG (4/5-wire), and trace (SWO/ETM).

Secure boot and secure firmware update protect against tampering.

Sensor output types: analog voltage, current loop, digital (I²C, SPI), and pulse/frequency.

4–20 mA loop is immune to voltage drops and noise over long distances.

HART protocol overlays digital communication on a 4–20 mA loop.

Fieldbus protocols: Profibus PA, Foundation Fieldbus for process automation.

Smart sensors include signal conditioning, conversion, and communication in one package.

Sensor diagnostics detect faults like open circuit, short circuit, or out-of-range.

Redundant sensors improve reliability in safety-critical systems.

Actuator types: electric, pneumatic, hydraulic, and piezoelectric.

Motor selection: torque-speed curve, duty cycle, and thermal limits.

Power semiconductor types: diode, thyristor, MOSFET, IGBT, SiC, GaN.

SiC and GaN enable higher switching frequency and efficiency than silicon.

Gate drive requirements: voltage level, current, isolation, and protection.

Overcurrent protection: desaturation detection, current sensing, and fast shutdown.

Thermal design: junction temperature, thermal resistance, and heatsink sizing.

EMI reduction: snubbers, filters, shielding, and layout.

Power converter topologies: buck, boost, buck-boost, flyback, forward, half-bridge, full-bridge.

Isolated topologies use a transformer for safety and voltage conversion.

Battery charging profiles: CC/CV for lithium-ion, float for lead-acid.

Modulation types: analog (AM, FM, PM) and digital (ASK, FSK, PSK, QAM).

Bandwidth efficiency: bits per second per hertz.

Shannon limit defines the maximum error-free data rate for a given bandwidth and SNR.

Error detection: parity, checksum, CRC; error correction: Hamming, Reed-Solomon, LDPC.

Network protocols: Ethernet, Wi-Fi, Bluetooth, Zigbee, LoRa, cellular.

Ethernet standards: 10BASE-T, 100BASE-TX, 1000BASE-T, 10GBASE-T.

Wi-Fi standards: 802.11a/b/g/n/ac/ax; 802.11ax is Wi-Fi 6.

Bluetooth Classic vs BLE: Classic for streaming, BLE for low-power IoT.

Network security: encryption, authentication, firewalls, and intrusion detection.

Open-loop vs closed-loop control: feedback improves accuracy and disturbance rejection.

PID control is the most common industrial controller.

Controller tuning affects response speed, overshoot, and stability.

Process dynamics: first-order (single time constant), second-order (overshoot), and dead time.

Stability analysis: Routh-Hurwitz, root locus, Bode, and Nyquist.

Discrete control: sampling, z-transform, and digital PID implementation.

PLC programming languages: ladder, function block, structured text, instruction list, sequential function chart.

SCADA systems: RTUs, PLCs, HMIs, and historians.

Industrial networks: Modbus, Profibus, EtherNet/IP, OPC UA.

Test equipment types: DMM, oscilloscope, signal generator, spectrum analyzer, logic analyzer.

DMM specifications: accuracy, resolution, input impedance, and true-RMS.

Oscilloscope specifications: bandwidth, sample rate, memory depth, and channels.

Probe types: passive (10×), active, differential, and current.

Signal generator: frequency range, output level, modulation, and impedance.

Spectrum analyzer: frequency range, RBW, phase noise, and dynamic range.

Logic analyzer: channel count, sample rate, and protocol decoding.

Calibration and verification ensure measurement accuracy.

Troubleshooting strategy: observe, hypothesize, test, and confirm.

Electrical safety standards: IEC, NFPA, OSHA.

Personal protective equipment: gloves, arc-rated clothing, face shields, and safety glasses.

Lockout/tagout procedures isolate hazardous energy.

Arc flash and shock hazards require risk assessment.

Grounding and bonding protect personnel and equipment.

GFCI/RCD protection for wet locations.

Battery safety: ventilation, PPE, and spill kits for lead-acid; thermal monitoring for lithium-ion.

Laser safety: classes, eye protection, and controlled areas.

RF safety: exposure limits and signage.

Ohm's law and Kirchhoff's laws are the foundation of circuit analysis.

Series and parallel combinations simplify resistor networks.

Thevenin and Norton equivalents reduce complex circuits to simple sources.

Superposition applies to linear circuits with multiple sources.

Capacitors and inductors store energy and introduce frequency dependence.

Impedance combines resistance and reactance.

Resonance occurs when X_L = X_C.

Power factor describes the phase relationship between voltage and current.

Transformers change voltage and current levels while conserving power.

Op-amp configurations: inverting, non-inverting, differential, integrator, differentiator.

Op-amp specifications: gain-bandwidth, slew rate, input offset, and CMRR.

Diodes: rectifiers, clippers, clampers, and voltage references.

Transistor amplifiers: common emitter, common base, common collector.

MOSFET amplifiers: common source, common gate, common drain.

Logic gates: AND, OR, NOT, NAND, NOR, XOR, XNOR.

Boolean algebra and Karnaugh maps simplify logic.

Flip-flops and counters build sequential logic.

ADCs and DACs convert between analog and digital domains.

Microcontroller architecture: CPU, memory, peripherals, and buses.

GPIO configuration: input, output, alternate function, and analog.

Interrupts and exceptions handle asynchronous events.

Timers and counters generate delays, PWM, and capture events.

Communication peripherals: UART, SPI, I²C, CAN, USB.

ADC and DAC peripherals convert signals.

Power management: sleep, stop, standby, and clock gating.

Firmware development: C, assembly, debugging, and testing.

RTOS and scheduling for real-time applications.

Sensor characteristics: range, sensitivity, accuracy, resolution, and response time.

Sensor types: temperature, pressure, flow, position, proximity, and light.

Signal conditioning: amplification, filtering, and linearization.

Bridge circuits measure small resistance changes.

Actuator types: motors, solenoids, valves, and piezoelectric devices.

Motor control: PWM, H-bridge, and feedback.

Encoder types: incremental and absolute.

Sensor fusion combines multiple sensors for better accuracy.

Calibration ensures sensor accuracy over time.

Power semiconductor devices: diode, thyristor, MOSFET, IGBT.

Converter topologies: rectifier, inverter, chopper, and cycloconverter.

Switching losses and conduction losses determine efficiency.

Thermal management: heatsinks, fans, and thermal interface materials.

Isolation and safety in power converters.

Battery types and charging methods.

Renewable energy systems: solar, wind, and energy storage.

Grid integration and power quality.

Energy efficiency and power factor correction.

Communication system components: transmitter, channel, and receiver.

Modulation: analog and digital techniques.

Transmission media: copper, fiber, and wireless.

Network topologies and protocols.

OSI and TCP/IP models.

IP addressing and subnetting.

Network security: encryption, authentication, and firewalls.

Wireless standards: Wi-Fi, Bluetooth, Zigbee, LoRa.

Network troubleshooting tools: ping, traceroute, and packet capture.

Control system types: open-loop and closed-loop.

PID control and tuning.

Process dynamics and stability.

Sensors and actuators in control loops.

PLC and SCADA systems.

Industrial communication protocols.

Safety systems and standards.

Human-machine interfaces.

Control system design and implementation.

Measurement fundamentals: accuracy, precision, resolution, and uncertainty.

Test equipment: DMM, oscilloscope, signal generator, spectrum analyzer.

Measurement techniques: voltage, current, resistance, and frequency.

Signal integrity and noise.

Calibration and traceability.

Troubleshooting methodology.

Fault isolation techniques.

Documentation and reporting.

Safety in measurement.

Electrical safety principles.

Personal protective equipment.

Lockout/tagout procedures.

Arc flash and shock hazards.

Grounding and bonding.

Battery safety.

Laser and RF safety.

Emergency response.

Regulatory standards.

Basic electrical quantities: voltage, current, resistance, and power.

Ohm's law and power formulas.

Series and parallel circuits.

Kirchhoff's laws.

Thevenin and Norton equivalents.

Capacitors and inductors.

AC circuits and impedance.

Resonance and power factor.

Transformers.

Analog circuit components: resistors, capacitors, inductors, diodes, transistors.

Op-amp circuits and applications.

Filter design.

Amplifier design.

Digital logic gates and Boolean algebra.

Combinational and sequential logic.

ADC and DAC.

Signal processing.

Circuit simulation and testing.

Microcontroller architecture.

Memory types and organization.

GPIO and peripherals.

Interrupts and timers.

Communication interfaces.

Power management.

Firmware development.

Real-time operating systems.

Debugging and testing.

Sensor fundamentals.

Sensor types and applications.

Signal conditioning.

Actuator types and control.

Motor control.

Position and motion sensing.

Sensor calibration.

Sensor fusion.

Industrial sensor networks.

Power semiconductor devices.

Converter topologies.

Switching and conduction losses.

Thermal management.

Isolation and safety.

Battery technologies.

Renewable energy systems.

Grid integration.

Energy efficiency.

Communication fundamentals.

Modulation techniques.

Transmission media.

Network protocols and models.

IP addressing and routing.

Network security.

Wireless communication.

Network troubleshooting.

Emerging technologies.

Control system fundamentals.

PID control.

Process dynamics.

Stability analysis.

PLC and SCADA.

Industrial networks.

Safety systems.

HMI design.

Control system implementation.

Measurement fundamentals.

Test equipment.

Measurement techniques.

Signal integrity.

Calibration.

Troubleshooting methodology.

Fault isolation.

Documentation.

Safety.

Electrical safety.

PPE.

Lockout/tagout.

Arc flash.

Grounding.

Battery safety.

Laser and RF safety.

Emergency response.

Regulatory standards.