V = I × R
I = V / R
R = V / I
| Color | Digit | Multiplier | Tolerance |
|---|---|---|---|
| Black | 0 | 1 | — |
| Brown | 1 | 10 | ±1% |
| Red | 2 | 100 | ±2% |
| Orange | 3 | 1k | — |
| Yellow | 4 | 10k | — |
| Green | 5 | 100k | ±0.5% |
| Blue | 6 | 1M | ±0.25% |
| Violet | 7 | 10M | ±0.1% |
| Grey | 8 | ||
| White | 9 | ||
| Gold | 0.1 | ±5% | |
| Silver | 0.01 | ±10% |
Mnemonic: "BBROY of Great Britain had a Very Good Wife" (Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, White)
Series Resistors: R_total = R1 + R2 + R3 + ...
Parallel Resistors: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
Series Capacitors: 1/C_total = 1/C1 + 1/C2 + 1/C3 + ...
Parallel Capacitors: C_total = C1 + C2 + C3 + ...
Series Inductors: L_total = L1 + L2 + L3 + ...
Parallel Inductors: 1/L_total = 1/L1 + 1/L2 + 1/L3 + ...
λ = c / f
where λ = wavelength (meters), c = speed of light (3×10⁸ m/s), f = frequency (Hz)
AM: Amplitude Modulation
FM: Frequency Modulation
PM: Phase Modulation
SSB: Single Sideband (LSB/USB)
VSWR: Voltage Standing Wave Ratio (ideal = 1:1)
Gain: Directivity + Efficiency (dB)
Bandwidth: Range of frequencies antenna can operate
Polarization: Linear (Vertical/Horizontal), Circular
Ohm's Law states: "A current flowing through a conductor is directly proportional to the voltage, provided the temperature remains constant."
V = I × R
Where V = Voltage (Volts), I = Current (Amperes), R = Resistance (Ohms).
Mnemonic: Cover the quantity you want to find; the other two give you the formula.
| Conductor | Insulator |
|---|---|
| Allows electricity to flow easily (e.g., metals: silver, copper, aluminum) | Blocks electricity (e.g., rubber, glass, plastic) |
| Electrons move freely | Electrons tightly bound |
| Used for wires, contacts | Used for insulation, safety |
Current (I): Flow of electric charge. Measured in Amperes (A).
EMF (Electromotive Force): Energy supplied by a source (e.g., battery). Measured in Volts (V).
Potential Difference (Voltage): Difference in electric potential between two points. Measured in Volts (V).
| Active Components | Passive Components |
|---|---|
| Require external power (e.g., transistors, diodes, ICs) | Do not require external power (e.g., resistors, capacitors, inductors) |
| Can amplify signals | Cannot amplify |
| Examples: Transistor, Diode, IC | Examples: Resistor, Capacitor, Inductor |
Function: Limits current, divides voltage, pulls up/down signals.
Color Code: See Quick Reference above. Remember "BBROY of Great Britain had a Very Good Wife".
Practical Tip: To calculate resistance from color bands, multiply the first two digits by the multiplier.
Resistor Diagram:
╔═════════════╗
║ Brown Black ║ Red (Gold)
╚═════════════╝
1 0 ×100 = 1000 Ω (1kΩ), 5% tolerance
Function: Stores electric charge, blocks DC, passes AC, filters ripples.
Types: Ceramic (no polarity), Electrolytic (polarity matters), Variable.
Marking: Ceramic caps use a 3-digit code (e.g., 683 = 68 × 10³ pF = 68 nF).
Series/Parallel: Parallel adds capacitance, series reduces it (opposite of resistors).
Capacitor Symbols:
Fixed: ──| |──
Variable: ──|(──
Electrolytic: ──|(+──
Function: Stores energy in a magnetic field, resists changes in current.
Core Types: Air core, iron core, ferrite core (increases inductance).
Color Code: Similar to resistors, but value in µH (microhenry).
Series/Parallel: Same as resistors: series adds, parallel reduces.
Inductor Symbols:
Fixed: ╔═══╗
║ ║
╚═══╝
Variable: ╔═══╤═╗
║ │ ║
╚═══╧═╝
Semiconductor: Material with conductivity between conductors and insulators (e.g., Silicon, Germanium).
Types: Intrinsic (pure), Extrinsic (doped – N-type: extra electrons, P-type: extra holes).
PN Junction: When P and N materials are joined, a depletion region forms, allowing current in one direction (diode).
Symbol: →|— (arrow points in direction of conventional current flow).
Function: Allows current in one direction (forward bias), blocks in reverse (reverse bias).
Types: Signal diode, Rectifier diode, Zener diode (voltage regulation), LED (Light Emitting Diode).
Diode Symbol: →|—
Forward bias: Anode (+), Cathode (–)
Reverse bias: Blocks current
Rectifiers:
Half-wave Rectifier:
AC ────[DIODE]───┬─── DC
│
[LOAD]
Bridge Rectifier:
+-----+
AC ────|>|──┬──|>|─── DC (+)
| | |
└──|>|──┬──|>|─── DC (–)
+-----+
Zener Diode: Conducts in reverse when voltage exceeds breakdown. Used for voltage regulation.
LED: Emits light when forward biased. Longer lead is anode (+).
Types: NPN, PNP (Bipolar Junction Transistor – BJT).
Terminals: Emitter (E), Base (B), Collector (C).
Function: Amplify signals, switch circuits, oscillators.
NPN Symbol: PNP Symbol:
C C
| |
B──┼──E B──┼──E
| |
[ ] [ ]
Arrow out Arrow in
Biasing: Proper DC voltages applied to operate transistor in active, cutoff, or saturation region.
Amplifier Configurations:
Darlington Pair: Two transistors cascaded for very high current gain (βtotal = β1 × β2).
Preamplifier: Amplifies weak signals (e.g., from microphone), removes noise.
Power Amplifier: Delivers high power to load (e.g., speaker). Needs clean input.
Transistor Amplifier: Amplifies voltage, current, or both. Key parameter: β (beta) – current gain.
Classes:
Function: Converts DC to AC (sine, square, sawtooth waves).
Requirements: Amplifier with positive feedback, loop gain ≥ 1, phase shift = 0° or 360°.
Types:
Hartley Oscillator:
┌─────L1─────┬─────L2─────┐
│ │ │
C │ │
│ │ │
└─────[AMP]──┴────[FB]────┘
Colpitts Oscillator:
┌─────C1─────┬─────C2─────┐
│ │ │
L │ │
│ │ │
└─────[AMP]──┴────[FB]────┘
Function: Pass or block specific frequencies.
Types:
Mnemonic: "BASS" = LOW pass, "TREBLE" = HIGH pass.
Active Filters: Use op-amps for precise control, no inductors needed.
Function: High-gain DC amplifier, used for amplification, filtering, math operations (add, subtract, integrate, differentiate).
Configurations:
Model: Information → Encoder → Channel → Decoder → Information
Radio Communication: Sound → Microphone → Transmitter → Antenna → Air → Antenna → Receiver → Speaker → Sound
Need for Modulation: Audio frequencies (AF) cannot be radiated directly; a high-frequency carrier is needed.
Definition: Superimposing AF on a carrier wave.
Types:
Modulation Types:
AM: ───/\───/\─── (carrier amplitude varies)
FM: ──/\/\/─── (carrier frequency varies)
PM: ──/|/|─── (carrier phase varies)
Double Sideband (DSB): Carrier + two sidebands (USB, LSB).
Single Sideband (SSB): Only one sideband transmitted (saves power, bandwidth).
Vestigial Sideband: One sideband + part of the other (used in TV).
AM Detector: Diode + capacitor + resistor (envelope detector).
FM Detector: Discriminator or ratio detector (converts frequency changes to audio).
Principle: Converts incoming RF to a fixed Intermediate Frequency (IF) for easier filtering/amplification.
Stages: RF amplifier → Mixer (with Local Oscillator) → IF amplifier → Detector → Audio amplifier → Speaker
Superhet Block Diagram:
Antenna → RF Amp → Mixer ← LO
↓
IF Amp → Detector → Audio Amp → Speaker
Advantages: Fixed IF allows precise filtering, high sensitivity, stable tuning.
Mixer: Produces sum and difference frequencies (IF = |RF – LO|).
Sensitivity: Ability to receive weak signals.
Selectivity: Ability to separate nearby signals.
Stability: Ability to stay on frequency.
Fidelity: Faithful reproduction of input.
Signal-to-Noise Ratio (SNR): Ratio of desired signal to noise.
ITU Codes: Three symbols (e.g., J3E = SSB suppressed carrier telephony).
First Symbol: Type of modulation.
Second Symbol: Nature of modulating signal.
Third Symbol: Type of information.
Definition: Electric and magnetic fields oscillating perpendicular to each other and to direction of propagation.
Speed: 3 × 10⁸ m/s (speed of light).
No medium needed. Can be polarized.
Propagation:
Ground: ────────────────
Sky: ────/ /────── (ionosphere reflection)
Space: ──────────────── (direct, line-of-sight)
Layers: D (50–90 km), E (90–140 km), F1 (140–210 km), F2 (>210 km).
F2 layer is most important for HF sky wave (present 24 hours, refracts highest frequencies).
Sporadic E: Thin, dense E layer that can reflect VHF signals unpredictably.
Skip distance: Shortest distance at which skywave returns to Earth.
Skip zone: Area between end of ground wave and start of skywave where no signal is received.
Repeater: Receives on one frequency, retransmits on another, extends range.
Duplexer: Allows single antenna for Tx/Rx at same time on different frequencies.
VHF: Better outdoor, line-of-sight, longer range.
UHF: Better indoor/urban, shorter wavelength, penetrates obstacles.
Definition: Device that converts RF electrical energy into electromagnetic waves (transmit) or vice versa (receive).
Types:
Frequency: Rate of oscillation (Hz).
Wavelength (λ): Distance between wave peaks (λ = c/f).
Impedance: Resistance to RF flow (typically 50 Ω for coax).
VSWR (Voltage Standing Wave Ratio): Measure of impedance match (ideal = 1:1).
Reflected Power: Power not radiated due to mismatch.
Bandwidth: Range of frequencies antenna works well.
Gain: Directivity + efficiency (dB).
Radiation Pattern: Diagram showing how antenna radiates in 3D space.
Polarization: Orientation of electric field (vertical, horizontal, circular).
Dipole: Two straight rods, omnidirectional, λ/2 length.
Yagi: Multiple elements, directional, high gain.
Collinear: Stacked dipoles, omnidirectional, higher gain.
Log-Periodic: Wide frequency range, moderate gain.
Dummy Load: Non-radiating resistor (50 Ω), used for testing.
Balanced: Twin lead, equal currents in opposite directions (e.g., dipole feed).
Unbalanced: Coaxial cable, center conductor + shield (e.g., coax).
Balun: Device to convert between balanced and unbalanced lines.
S-points: S1 to S9, each 6 dB change. S9+20 = 20 dB above S9.
Use: Indicates received signal strength on HF/VHF radios.