Electronics basics

The circuit calculations in the Technician pool use four quantities and two short formulas, Ohm’s law and the power formula (Technician pool, T5C08 to T5C11 and T5D01 to T5D12). This guide works through each with examples.

Four quantities

The Technician pool defines each quantity (Technician pool, T5A01 to T5A05, T5A10 and T5A11), and NIST lists their SI units (NIST Guide to the SI):

Metals are generally good conductors because they have many free electrons (Technician pool, T5A07). Glass, plastic, porcelain and dry wood are insulators that generally slow or stop current. Water with impurities in it, and wet skin, conduct far better than when dry, which matters for safety (OSHA 3075).

Ohm’s law

Voltage, current and resistance are linked by Ohm’s law (ARRL Radio Mathematics). The exams use E for voltage (Technician pool, T5D01 to T5D03):

• E = I × R (voltage equals current times resistance)
• I = E / R (current equals voltage divided by resistance)
• R = E / I (resistance equals voltage divided by current)

Worked examples:

1. A current of 0.25 A flows through a 48 Ω resistor. The voltage across it is E = 0.25 × 48 = 12 V.
2. A 4.6 Ω load is connected to a 13.8 V supply. The current is I = 13.8 / 4.6 = 3 A.
3. A circuit draws 2 A from a 12 V battery. Its resistance is R = 12 / 2 = 6 Ω.

A memory aid: cover the quantity you want in a triangle with E on top and I and R below. What remains shows the operation. The Ohm’s law calculator solves any of these.

Power

Power is voltage times current (ARRL Radio Mathematics; Technician pool, T5C08):

• P = I × E, which rearranges to I = P / E and E = P / I.

Worked examples:

1. A transceiver draws 20 A from a 13.8 V supply while transmitting. It uses P = 20 × 13.8 = 276 W from the supply.
2. A 60 W load runs on 12 V. It needs I = 60 / 12 = 5 A, so its wiring and fuse must handle at least that.
3. Substituting Ohm’s law into P = I × E gives P = I² × R and P = E² / R. A transmitter delivering 100 W into a 50 Ω antenna puts √(100 × 50) = 70.7 V across it and drives √(100 / 50) = 1.41 A through it.

Units and metric prefixes

Radio values span huge ranges, so they are written with metric prefixes (NIST):

Each step in this table is a factor of 1,000. To go to a smaller unit, multiply by 1,000; to go to a larger one, divide.

AC and DC

Direct current (DC) runs continually in one direction, as from a battery, while alternating current (AC) reverses direction (US Department of Energy). The number of complete cycles per second is its frequency, measured in hertz (Hz) (Technician pool, T5A04 and T5A06). Radio uses much higher frequencies than household power: the US amateur bands run from 135.7 kHz (135,700 cycles per second) to above 275 GHz (47 CFR 97.301).

Series and parallel circuits

In a series circuit, components are connected end to end, so the same current flows through all of them (Technician pool, T5D13). Series resistances add (OpenStax College Physics): 100 Ω + 220 Ω + 470 Ω = 790 Ω.

In a parallel circuit, components connect across the same two points, so the same voltage appears across all of them (Technician pool, T5D14). The total resistance is always less than the smallest of the individual resistances (OpenStax College Physics). For two resistors, use product over sum (ARRL Radio Mathematics):

• Two 100 Ω resistors: (100 × 100) / (100 + 100) = 50 Ω
• 100 Ω and 300 Ω: (100 × 300) / (100 + 300) = 75 Ω

Capacitors, inductors and reactance

A capacitor consists of conductive surfaces separated by an insulator. It stores energy in an electric field, and its value is measured in farads (F). An inductor is typically a coil of wire. It stores energy in a magnetic field, and its value is measured in henrys (H) (Technician pool, T5C01 to T5C04, T6A05 and T6A07). The examples below use microhenrys (µH) and picofarads (pF).

Both oppose the flow of AC. This opposition is called reactance (X), and it is measured in ohms (General pool, G5A02, G5A09 and G5A11). It depends on frequency (ARRL Radio Mathematics; General pool, G5A05 and G5A06):

• Inductive reactance XL = 2πfL rises with frequency. A 1 µH coil at 14 MHz: 2π × 14,000,000 × 0.000001 = about 88 Ω.
• Capacitive reactance XC = 1 / (2πfC) falls with frequency. A 100 pF capacitor at 14 MHz: 1 / (2π × 14,000,000 × 0.0000000001) = about 114 Ω.

Impedance is the opposition to AC current flow, measured in ohms (Technician pool, T5C05 and T5C12). It is the ratio of voltage to current (General pool, G5A08), and it has a resistive and a reactive component (Extra pool, E5C09).

Put an inductor and a capacitor together, in series or in parallel, and you have a resonant (tuned) circuit (Technician pool, T6D08 and T6D11). At resonance the inductive and capacitive reactances are equal and cancel; in a series LC circuit, the impedance there is very low (General pool, G5A01 and G5A12). Setting XL equal to XC gives the resonant frequency, f = 1 / (2π√(LC)). The 1 µH coil and 100 pF capacitor above resonate at about 15.9 MHz, where each has a reactance of about 100 Ω. The reactance calculator handles the arithmetic.

Common components

These descriptions follow the Technician pool (Technician pool, T6A, T6B and T6D), except where noted.

• Resistor: opposes the flow of current. A potentiometer is an adjustable resistor, often used as a volume control.
• Fuse: melts and opens the circuit when too much current flows through it (OSHA 3075).
• Switch: an SPDT (single pole, double throw) switch connects a single circuit to one of two other circuits. A relay is an electrically controlled switch.
• Diode: lets current flow in only one direction. Its electrodes are the anode and the cathode, and the cathode is often marked with a stripe. A rectifier changes AC into a varying DC signal. A light-emitting diode (LED) emits light when forward current flows through it.
• Transistor: can consist of three regions of semiconductor material, can provide power gain, and can be used as an electronic switch. A bipolar junction transistor has an emitter, base and collector; a field-effect transistor (FET) has a gate, drain and source.
• Transformer: changes AC power from one voltage to another, such as 120 V AC to a lower AC voltage. A voltage regulator controls the amount of voltage from a power supply.
• Integrated circuit (IC): several semiconductors and other components combined in one package.

Schematic diagrams

A schematic is an electrical diagram that uses standard component symbols. It accurately shows how the components are connected, not wire lengths or what the parts look like (Technician pool, T6C01 and T6C12). The Technician pool includes three schematic figures, T-1 to T-3 (NCVEC); practice naming each symbol on them in the study mode.

Decibels

A decibel (dB) expresses a ratio, usually of two powers, on a logarithmic scale (ARRL Radio Mathematics):

dB = 10 log (P2 / P1)

The common values, from the same source:

Because decibels are logarithmic, they add where ratios multiply, so +20 dB (10 dB plus 10 dB) is 10 × 10 = 100 times. Losses are negative: a feed line with 3 dB of loss delivers half your power to the antenna (ARRL Radio Mathematics). The decibel calculator converts any ratio.