WBCHSE HS Vocational Electronics cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R. In series, R_total = R1 + R2 + …; in parallel, 1/R_total = 1/R1 + 1/R2 + …

Resistor colour code (4-band): band1 = first digit, band2 = second digit, band3 = multiplier (power of ten), band4 = tolerance (gold ±5%, silver ±10%, none ±20%).

Capacitor impedance X_C = 1/(2πfC) falls as frequency rises, so a capacitor blocks DC (f = 0) and passes AC; inductors behave oppositely, X_L = 2πfL.

Capacitors in parallel add (C = C1 + C2); in series they combine reciprocally (1/C = 1/C1 + 1/C2) - the reverse of resistors.

KCL: current into a node equals current out. KVL: the algebraic sum of voltages around any closed loop is zero.

Energy stored: capacitor W = ½CV²; inductor W = ½LI².

Diode forward drop ≈ 0.7 V for silicon, ≈ 0.3 V for germanium; LED drops range roughly 1.8–3.3 V depending on colour.

A potential divider gives V_out = V_in × R2/(R1 + R2) when no load current is drawn from the tap.

Silicon is tetravalent; doping with pentavalent atoms (P, As) gives n-type (majority carriers electrons), trivalent atoms (B, Al) give p-type (majority carriers holes).

Depletion region widens under reverse bias and narrows under forward bias; barrier potential ≈ 0.7 V (Si) and ≈ 0.3 V (Ge).

Half-wave rectifier: one diode, output ripple frequency = supply frequency f, efficiency ≈ 40.6%, PIV = V_m.

Full-wave centre-tap rectifier: two diodes, ripple frequency 2f, efficiency ≈ 81.2%, PIV = 2V_m.

Bridge rectifier: four diodes, ripple frequency 2f, efficiency ≈ 81.2%, PIV = V_m - the lowest PIV per diode.

Ripple factor r = (I_rms/I_dc); half-wave ≈ 1.21, full-wave/bridge ≈ 0.48. Lower is better.

Zener diode operates in reverse breakdown to regulate voltage; it is always reverse-biased with a series current-limiting resistor.

Rectifier output V_dc: half-wave = V_m/π ≈ 0.318V_m; full-wave = 2V_m/π ≈ 0.636V_m.

BJT relations: I_E = I_B + I_C; α = I_C/I_E; β = I_C/I_B; β = α/(1−α).

For a silicon BJT in active mode, V_BE ≈ 0.7 V; saturation occurs when V_CE ≈ 0.2 V, cutoff when I_B = 0.

Transistor as switch: cutoff (off, V_CE ≈ V_CC) and saturation (on, V_CE ≈ 0.2 V) are the two operating states; base resistor limits I_B.

CE amplifier has high voltage gain and 180° phase inversion; CB has high frequency response and no current gain (α < 1); CC (emitter follower) has voltage gain ≈ 1 and high input impedance.

Voltage gain A_v = −(R_C/r_e) for CE with bypassed emitter; r_e ≈ 26 mV/I_E(mA).

Class A conducts 360°, efficiency ≤ 25% (resistive load) or 50% (transformer-coupled); Class B conducts 180° and is ≈ 78.5% efficient; Class AB reduces crossover distortion.

Negative feedback reduces gain but improves bandwidth, linearity, input/output impedance and stability.

Darlington pair: current gain β_total ≈ β1 × β2, giving very high input impedance.

AND: Y = A·B (output 1 only when all inputs 1). OR: Y = A + B. NOT: Y = Ā.

NAND and NOR are universal gates - any logic function can be built from either alone.

XOR: Y = A⊕B = A'B + AB'; it gives 1 when inputs differ and is used for parity and half-adder sum.

De Morgan: (A·B)' = A' + B' and (A + B)' = A'·B'.

Half adder: Sum = A⊕B, Carry = A·B. Full adder: Sum = A⊕B⊕C_in, C_out = AB + C_in(A⊕B).

Binary to decimal: multiply each bit by 2^position from the right. Hex digits 0–F map to 4-bit groups.

Flip-flops: SR (set/reset), JK (toggles when J=K=1), D (data latch), T (toggle). A flip-flop stores 1 bit.

Boolean identity: A + A'B = A + B, and A + AB = A (absorption).

Ammeter is connected in series and should have very low resistance; voltmeter is in parallel and should have very high resistance.

Analog multimeter sensitivity is quoted in ohms per volt (Ω/V); higher Ω/V means less circuit loading.

A CRO time base (s/div) × horizontal divisions gives period; frequency = 1/period. Vertical (V/div) × divisions gives peak voltage.

Lissajous figures: a 1:1 circle or ellipse indicates equal frequencies; the ratio of horizontal to vertical tangencies gives the frequency ratio.

Continuity test uses the low-resistance range with the circuit unpowered; a beep or near-zero reading means a closed path.

Digital multimeter accuracy is quoted as ±(% of reading + number of counts); add the counts term for the true worst-case error.

An ohmmeter must never be used on a live circuit - the internal battery supplies the test current.

A signal generator supplies test waveforms (sine, square, triangle) at set amplitude and frequency for tracing a circuit stage by stage.

Linear supply chain: transformer → rectifier → filter capacitor → regulator (e.g. 78xx for positive, 79xx for negative fixed outputs).

Filter capacitor sizing: larger C and larger load resistance give smaller ripple; ripple V_r ≈ I_dc/(2fC) for full-wave.

78xx series: 7805 = +5 V, 7812 = +12 V; input must exceed output by about 2–3 V (dropout voltage).

Barkhausen criterion for oscillation: loop gain |Aβ| ≥ 1 and loop phase shift = 0° or 360°.

RC phase-shift oscillator uses three RC sections of 60° each (180° total) plus a CE amplifier's 180°; f = 1/(2πRC√6).

Colpitts uses a tapped capacitive divider, Hartley a tapped inductive divider, in the feedback tank circuit.

Crystal oscillator uses the piezoelectric resonance of quartz for very high frequency stability.

A 555 timer in astable mode oscillates: f ≈ 1.44/((R1 + 2R2)C); duty cycle = (R1 + R2)/(R1 + 2R2).

Modulation superimposes a baseband signal onto a carrier; need arises from antenna size, multiplexing and noise rejection.

AM: carrier amplitude varies; bandwidth = 2f_m; modulation index m = V_m/V_c; overmodulation when m > 1 causes distortion.

FM: carrier frequency varies; bandwidth ≈ 2(Δf + f_m) by Carson's rule; FM has better noise immunity than AM but needs more bandwidth.

Superheterodyne receiver: RF amplifier → mixer → local oscillator → IF amplifier (455 kHz AM, 10.7 MHz FM) → detector → AF amplifier.

Antenna length for a half-wave dipole ≈ 143/f(MHz) metres.

Sampling theorem: sample at least twice the highest signal frequency (Nyquist rate).

Remote control handsets commonly use infrared (≈38 kHz modulated carrier); TV tuners select channels by tuned resonant circuits.

Noise figure compares input to output signal-to-noise ratio; a lower figure means a quieter receiver front end.

A microcontroller integrates CPU, RAM, ROM/flash, I/O ports, timers and serial interfaces on one chip; a microprocessor needs external memory and peripherals.

8051 basics: 8-bit CPU, 4 KB ROM, 128 bytes RAM, four 8-bit ports (P0–P3), two 16-bit timers, 5 interrupt sources, 12 MHz crystal gives 1 µs machine cycle.

Harvard architecture (8051) has separate program and data memory spaces; von Neumann shares one space.

Port pins must be configured as input by writing 1 to the port latch before reading.

ADC resolution: step size = V_ref/2^n; a 10-bit ADC on 5 V gives ≈ 4.88 mV per step.

PWM duty cycle controls average output voltage: V_avg = D × V_supply, used for motor speed and LED dimming.

Embedded program flow: initialise ports/timers → main loop → interrupt service routines for time-critical events.

Watchdog timer resets the controller if firmware fails to service it within the set period.

Before soldering: clean the tip, tin it, heat the joint (not the solder), then apply solder and let it flow; a good joint is shiny and concave.

Use a solder sucker or desoldering braid to remove solder; never overheat a pad (keep iron contact to a few seconds).

Continuity and polarity checks precede power-up: verify supply polarity, IC orientation (notch/pin 1) and electrolytic capacitor polarity.

Breadboard rails: outer rails are the supply buses, inner columns of five holes are connected; the centre channel separates the two IC rows.

Resistor value from colour bands should be confirmed with a multimeter before insertion; tolerance explains small deviations.

Common faults: cold solder joint, reversed diode, open ground, shorted adjacent tracks, wrong resistor value, dry battery.

Use an isolation transformer and a series lamp/current-limited supply when first powering an untested mains circuit.

Signal tracing: inject a signal at the input and follow it stage by stage with a CRO to localise the faulty block.

A project report typically contains: title, aim/objective, block diagram, circuit diagram, component list with ratings, working principle, testing results, conclusion and references.

Component selection rule: resistor power rating ≥ 2× calculated dissipation; capacitor voltage rating ≥ 1.5× the maximum circuit voltage.

Block diagram first, then circuit diagram, then PCB/breadboard layout - each stage is verified before the next.

Record measured values in a table (expected vs observed) and state percentage error; this is the evidence section of the report.

Typical school projects: regulated power supply, LED flasher, water-level indicator, fire alarm, light-activated switch, digital counter.

Industrial exposure topics: PCB fabrication steps (layout, etching, drilling, masking), soldering standards, ESD precautions and quality inspection.

Safety documentation: fuse rating, earthing of metal enclosures, insulation testing and labelling of mains terminals.

Costing sheet lists component quantity, unit price and total; add a margin for wastage and spares.