Units of Measurement

Key units in telecommunications, including decibels (dBm, dBr) and information units (bit, byte).

The Foundation: SI Units and Prefixes

Telecommunications, like all fields of science and engineering, is built upon a standardized system of measurement: the International System of Units (SI). Understanding these basic units and their prefixes is essential for describing physical quantities.

The seven base SI units include the meter (m) for length, the kilogram (kg) for mass, the second (s) for time, and the ampere (A) for electric current. From these, we derive other crucial units used in telecommunications:

Unit	Application
Hertz Hz	for frequency
Watt W	for power
Volt V	for voltage
Ohm Ω	for resistance
Henry H	for inductance
Farad F	for capacitance

Prefix	Symbol	Value	Power of 10
Yotta	Y	1,000,000,000,000,000,000,000,000	10²⁴
Zetta	Z	1,000,000,000,000,000,000,000	10²¹
Exa	E	1,000,000,000,000,000,000	10¹⁸
Peta	P	1,000,000,000,000,000	10¹⁵
Tera	T	1,000,000,000,000	10¹²
Giga	G	1,000,000,000	10⁹
Mega	M	1,000,000	10⁶
Kilo	k	1,000	10³
Hecto	h	100	10²
Deca	da	10	10¹
Deci	d	0.1	10⁻¹
Centi	c	0.01	10⁻²
Milli	m	0.001	10⁻³
Micro	µ	0.000001	10⁻⁶
Nano	n	0.000000001	10⁻⁹
Pico	p	0.000000000001	10⁻¹²
Femto	f	0.000000000000001	10⁻¹⁵
Atto	a	0.000000000000000001	10⁻¹⁸
Zepto	z	0.000000000000000000001	10⁻²¹
Yocto	y	0.000000000000000000000001	10⁻²⁴

Prefixes like kilo- (k, $10^3$ ), Mega- (M, $10^6$ ), Giga- (G, $10^9$ ) are used for large values, while milli- (m, $10^{-3}$ ), micro- (µ, $10^{-6}$ ), and nano- (n, $10^{-9}$ ) are used for small values.

The Decibel (dB): The Language of Ratios

In telecommunications, we often deal with vast ranges of values. For example, a received signal's power might be a trillion times smaller than the transmitted power. Using a linear scale for such values is impractical. This is why engineers use a , and its fundamental unit is the Bel (B), or more commonly, the decibel (dB), which is one-tenth of a Bel.

Why Use Decibels?

Manages Large Numbers: It compresses a huge range of values into a smaller, more manageable scale.
Simplifies Calculations: Gains and losses in a signal chain (e.g., from amplifiers and cables) can be added and subtracted instead of multiplied and divided.

Calculating Decibels: Power vs. Voltage/Current

The way you calculate decibels depends on whether you are comparing power quantities or field quantities (like voltage or current).

Power Ratios

When comparing two power levels, $P_1$ and $P_2$ , the formula uses a factor of 10.

$\text{dB} = 10 \cdot \log_{10} \left( \frac{P_1}{P_2} \right)$

Voltage/Current Ratios

When comparing two voltages ( $U_1, U_2$ ) or currents ( $I_1, I_2$ ) across the same impedance, the formula uses a factor of 20.

$\text{dB} = 20 \cdot \log_{10} \left( \frac{U_1}{U_2} \right)$

Absolute vs. Relative Levels

The decibel itself is a relative unit; it always describes a ratio between two values. However, by fixing the reference value in the denominator, we can create absolute units that describe a specific level of power or voltage.

Relative Level (dBr): Expresses the power level at a certain point in a circuit relative to the power at a designated reference point (which has a level of 0 dBr). It's used to describe the gain or loss profile of a transmission system.
Absolute Power Level (dBm): This is one of the most common units. It represents a power level relative to a fixed reference of 1 milliwatt (mW).
$P_{\text{[dBm]}} = 10 \cdot \log_{10} \left( \frac{P_{\text{[mW]}}}{1 \text{ mW}} \right)$
A level of 0 dBm is exactly 1 mW.

A Glossary of Common dB Units

dBW: Absolute power level referenced to 1 Watt. $0 \text{ dBW} = 1 \text{ W} = 30 \text{ dBm}$ .
dBV: Absolute voltage level referenced to 1 Volt RMS.
dBµV: Absolute voltage level referenced to 1 microvolt (µV) RMS.
dBi: Antenna gain relative to a theoretical .
dBd: Antenna gain relative to a standard antenna. $0 \text{ dBd} = 2.15 \text{ dBi}$ .
dBc: Power level of a signal (e.g., a noise or harmonic) relative to the main signal.

Units of Information and Transmission Speed

It is crucial to distinguish between units that measure the quantity of information and those that measure the speed at which it is transmitted.

Units of Information Quantity

Bit (b): The most fundamental unit of information, derived from "binary digit". It represents one of two possible states (0 or 1).
Byte (B): A group of 8 bits, typically representing a single character (like a letter or symbol). $1 \text{ B} = 8 \text{ b}$ . Note the capitalization: B for Byte, b for bit.
Machine Word: The amount of data a computer's CPU can process in a single operation. Its length varies by architecture (e.g., 16, 32, or 64 bits).

Units of Transmission Speed

Baud (Bd): The unit of . It measures how many times the signal changes its state (symbol) per second.
Bits per second (bps): The unit of . It measures the actual number of information bits transmitted per second.

Baud vs. bps: A Crucial Distinction

Baud and bps are equal only when each signal state (symbol) represents exactly one bit. In modern modulation schemes, one symbol can represent multiple bits (e.g., in QPSK, one symbol represents 2 bits). In such cases, the bit rate is higher than the baud rate: $\text{Bit Rate} = \text{Baud Rate} \times \log_2(M)$ , where M is the number of possible symbols.