Electronics

From Ohm’s law to op-amps and the 555 timer — a visual reference for the components, circuits, and power rules you reach for on every build.

Quick reference

The numbers and formulas you reach for on every build — each one expanded in its own section below.

• V = I × R — Ohm’s law — rearrange for I or R. Power: P = V × I = I² × R = V² ÷ R.
• digit · digit × multiplier ± tolerance — Resistor bands — black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9; gold ±5%, silver ±10%.
• Vout = Vin × R2 / (R1 + R2) — Voltage divider — scale a voltage down.
• fc = 1 / (2π × R × C) — RC filter — -3 dB cutoff for low- and high-pass.
• Gain = 1 + R2 / R1 — Op-amp non-inverting gain — inverting: Gain = -Rf / Rin; follower: Gain = 1.
• f = 1.44 / ((R1 + 2R2) × C) — 555 astable frequency — duty = (R1 + R2) / (R1 + 2R2), always >50%.
• R = (Vs - Vf) / I — LED series resistor — limit current to ~20 mA.
• 7805: 7–25 V in → 5 V out — Regulators — 7805/LDO linear (7805 dropout ≈ 2 V, LDO far lower); buck Vout = duty × Vin; boost Vout = Vin / (1 - duty).
• 100 nF + 10 µF — Decoupling — 100 nF ceramic at every IC power pin, 10 µF bulk per rail.

QR: Where to find it: fundamentals and passive parts → 01/02, gain and filters → 04, regulators and decoupling → 05, divider/555/LED → 06.

Fundamentals

Voltage pushes, current flows, resistance resists. Master these three quantities plus Ohm’s law, and every other rule on this page follows.

1. Voltage (V)

Electrical pressure that moves charge, in volts. Think of it as the height of a water tank — the higher, the harder the push.

2. Current (I)

The rate charge flows through a circuit, in amperes. Current only flows in a closed loop, and it is the same everywhere in a series path.

3. Resistance (R)

Opposition to current, in ohms. Wire is near 0 Ω; open air is near-infinite. Resistors set the current in a path.

4. Power (P)

Energy per second, in watts. In a resistor it becomes heat — the reason parts carry wattage ratings.

1 kΩ = 1000 Ω 1 mA = 0.001 A 1 µF = 10⁻⁶ F 1 nF = 10⁻⁹ F 1 pF = 10⁻¹² F

Ω: Ohm’s law: V = I × R — rearrange for whichever quantity is unknown: I = V ÷ R, R = V ÷ I. Power follows: P = V × I = I² × R = V² ÷ R.

Series & parallel

In series, current is shared and voltage divides. In parallel, voltage is shared and current divides.

series:   R_total = R1 + R2
parallel: R_total = (R1 × R2) / (R1 + R2)

series:   C_total = 1 / (1/C1 + 1/C2)
parallel: C_total = C1 + C2

Kirchhoff’s laws

KCL (current law): currents into a node sum to zero. KVL (voltage law): voltages around a loop sum to zero.

KCL:  Σ I_in = Σ I_out
KVL:  Σ V_loop = 0

Passive components

Parts that store or resist energy without amplifying: resistors, capacitors, inductors, and transformers.

Resistor

Limits current and drops voltage. Value in ohms, marked by color bands or printed digits.

Capacitor

Stores energy in an electric field; blocks DC and passes AC. Values are tiny — µF, nF, pF.

Inductor

Stores energy in a magnetic field; resists changes in current. Value in henries (H).

Transformer

Two inductors sharing a core; steps AC voltage up or down by the turns ratio V2/V1 = N2/N1.

4B: Reading a 4-band resistor: digit, digit, multiplier, tolerance — red red brown gold = 2, 2, ×10, ±5% → 220 Ω. Gold = ±5%, silver = ±10%, no band = ±20%.

Capacitor types

Pick by value, polarity, and frequency. Electrolytics are polarized — mind the stripe.

ceramic:     1 pF – 10 µF, non-polar, HF
electrolytic: 1 µF – 10000 µF, polarized, DC
film:         1 nF – 10 µF, precise, audio
tantalum:     0.1 µF – 470 µF, compact, polarized

Ratings & tolerance

Every part has a maximum voltage and power rating — stay well under it. Tolerance tells you the value spread.

±5% (E24) → 100 Ω = 95–105 Ω
±1% (E96) → tighter, for precision
0.25 W, 0.5 W  → resistor power ratings

Active components

Semiconductors that control, switch, and amplify current. Op-amps get their own section below.

Diode

Conducts one way only — anode to cathode. Drops about 0.7 V forward (silicon) or 0.3 V (Schottky) when on.

forward:  anode → cathode
reverse:  blocks (until it breaks)

LED

A diode that emits light. Always add a series resistor to limit current; forward voltage is ~1.8–3.3 V by color.

R = (Vs - Vf) / I
R = (5 - 2) / 0.02 = 150 Ω

Transistor (BJT)

A current-controlled switch and amplifier: a small base current switches a bigger collector–emitter current. NPN switches the low side.

Ic = β × Ib    (β = hFE, ~100–300)

Voltage regulator

Turns a varying input into a steady output. Linear types (7805, LDO) waste heat; switching types (buck, boost) are efficient.

7805: 7–25 V in → 5 V out

1N4148 1N4007 2N2222 BC547 LM358 LM7805 IRFZ44N

OP: Op-amps are the building block of amplification, filtering, and comparison — see section 04 for the circuits and formulas.

Op-amps

High-gain differential amplifiers tamed by feedback. Two golden rules plus a few circuits cover most real designs.

Inverting amplifier

Output is an inverted, scaled copy of the input. Gain is set by two resistors.

Gain = -Rf / Rin
Vout = -Vin × (Rf / Rin)

Non-inverting amplifier

Output follows the input in phase, amplified by 1 + R2/R1. Gain is always ≥ 1.

Gain = 1 + R2 / R1
Vout = Vin × (1 + R2 / R1)

V+ / V- (differential input) → A·(V+ - V-) (open-loop gain) → Vout (feedback sets it)

G: Golden rules (with negative feedback): 1) the inputs draw no current; 2) the op-amp drives Vout so that V+ = V- — on an inverting circuit that makes the input a virtual ground.

fc = 1 / (2π × R × C)

fc = 1 / (2π × R × C)

cascade LP + HP

twin-T, or a state-variable

Power supplies

Turning a wall wart or battery into a clean, stable rail — linear or switching, plus rectification and decoupling.

Linear vs switching

Linear regulators are simple and quiet but burn the difference as heat. Switching regulators are efficient but add ripple and EMI.

linear:    P_loss = (Vin - Vout) × I
switching: η ≈ 85–95%

buck:   Vout = duty × Vin
boost:  Vout = Vin / (1 - duty)

Rectification

Diodes turn AC into pulsing DC. A full-wave bridge uses both half-cycles, so it is smoother than a single diode.

half-wave:   Vdc ≈ 0.45 × Vac
full bridge: Vdc ≈ 0.9  × Vac

ripple shrinks as C × I grows

1. AC mains — 120/230 V AC from the wall outlet.
2. Transformer — Steps the voltage down to a safe, low AC level.
3. Rectifier — A diode bridge turns AC into pulsating DC.
4. Filter — A bulk capacitor smooths the ripple.
5. Regulator — A 7805 or LDO locks the output to a fixed DC rail.
6. DC rail — Clean, steady voltage for your circuit.

C: Decouple every IC: a 100 nF ceramic right at each power pin, plus a 10 µF bulk cap per rail. It soaks up the current spikes that cause glitches and resets.

Common circuits

Five breadboard staples with the formula for each — memorize these and you can build most beginner projects.

• Vout = Vin × R2 / (R1 + R2) — Voltage divider — scale a voltage down.
• fc = 1 / (2π × R × C) — RC low-pass filter — -3 dB cutoff.
• f = 1.44 / ((R1 + 2R2) × C) — 555 astable — oscillation frequency.
• duty = (R1 + R2) / (R1 + 2R2) — 555 astable — duty cycle (>50%).
• R = (Vs - Vf) / I — LED series resistor — current limiting.
• Rb = (Vin - Vbe) / Ib — Transistor switch — base resistor.

Vin (input) → R1 (top resistor) → Vout (tap point) → R2 (bottom resistor) → GND (0 V)

Vs = 5 V, Vf = 2 V, I = 20 mA
R = (5 - 2) / 0.02 = 150 Ω

R1 = 1 kΩ, R2 = 10 kΩ, C = 10 µF
f = 1.44 / ((1k + 2×10k) × 10µ) ≈ 6.9 Hz

Vin = 12 V, R1 = R2 = 10 kΩ
Vout = 12 × 10k / 20k = 6 V

R = 1 kΩ, C = 100 nF
fc = 1 / (2π × 1k × 100n) ≈ 1.6 kHz

Signals & measurement

Analog vs digital, PWM for fake analog, and the instruments that show you what is really on the wire.

Analog vs digital

Analog is a continuous voltage with infinite resolution but is noise-sensitive. Digital is two discrete levels, so it shrugs off noise.

analog:  0–5 V, continuous (sensor, audio)
digital: 0/1, thresholds (logic, I²C, SPI)

PWM

Pulse-width modulation fakes an analog level by switching a pin on and off fast. The average voltage tracks the duty cycle.

Vavg = duty × Vsupply
duty = t_on / (t_on + t_off)

• HIGH — Logic 1 — at or near Vcc. On 3.3 V CMOS that is roughly > 2 V.
• LOW — Logic 0 — at or near 0 V / ground.
• Floating — An unconnected input — undefined and oscillating. Always tie it high or low.
• PWM — Switching 0 to Vcc fast; the average is duty × Vcc.

!: Measure right: voltmeters go in parallel, ammeters in series. Connecting an ammeter across a supply shorts it and pops the fuse.

Pitfalls

The mistakes that smoke parts and confuse beginners — learn them once, save a breadboard.

Polarity

Electrolytic capacitors, LEDs, and diodes are polarized. Reverse an electrolytic and it vents; reverse a diode and it blocks until it breaks.

Ratings

Every part has a maximum voltage, current, and power. Stay under ~70% and read the datasheet — a resistor dissipating 0.25 W needs at least a 0.5 W part.

Heat

Regulators and transistors drop voltage and shed it as heat. Add a heatsink when P_loss makes the part too hot to hold.

Decoupling

ICs glitch without bypass caps. Random resets and noise are usually a missing 100 nF at the power pin.

Floating inputs

An unconnected CMOS input floats and oscillates randomly. Tie it high or low with a pull-up or pull-down resistor.

ESD

Static discharge destroys MOSFETs and CMOS. Ground yourself first, use a wrist strap, and store ICs in anti-static bags.

Shared ground

Every part of a circuit must share one common 0 V reference. Two boards or modules with no joined ground — or a forgotten GND jumper — is the classic “nothing works” cause.

Flyback / back-EMF

Switching off a relay coil, motor, or solenoid collapses its magnetic field into a voltage spike that can kill the driver transistor. Put a flyback diode across the coil, cathode to +V.

!: Before powering on: check polarity, confirm the supply voltage matches the board, and double-check capacitor orientation. Smoke is permanent.