Units of Measurement | Teleinf Edu

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, the ampere (A) for electric current, the kelvin (K) for thermodynamic temperature, the mole (mol) for amount of substance, and the candela (cd) for luminous intensity. From these, we derive other 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

SI unit prefixes

Prefix	Symbol	Value	Power of 10
ronna	R	1,000,000,000,000,000,000,000,000,000	10²⁷
quetta	Q	1,000,000,000,000,000,000,000,000,000,000	10³⁰
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
Base unit	-	1	10⁰
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
ronto	r	0.000000000000000000000000001	10⁻²⁷
quecto	q	0.000000000000000000000000000001	10⁻³⁰

Prefixes like kilo- (k, $10^3$ ), mega- (M, $10^6$ ), and giga- (G, $10^9$ ) indicate large values. milli- (m, $10^{-3}$ ), micro- (µ, $10^{-6}$ ), and nano- (n, $10^{-9}$ ) indicate small values. SI prefixes refer to powers of ten. Binary powers use prefixes such as Ki, Mi, and Gi.

The decibel (dB): a ratio measure

Telecommunications often compares values across a wide range. For example, a received signal's power might be a trillion times smaller than the transmitted power. A linear scale is impractical in such cases, so engineers use a . The bel (B) is the base unit for a logarithmic ratio. More commonly, the decibel (dB) is used, which is one-tenth of a bel.

Uses of decibels

Range of values: It represents a wide range of values on a compact scale.
Chain calculations: Gains and losses in a signal chain, such as those from amplifiers and cables, can be added and subtracted instead of multiplied and divided.

Calculating decibels: power and voltage or current

The decibel formula depends on whether the comparison uses power quantities or field quantities such as 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 ( $I_1, I_2$ ) with equal impedances, use a factor of 20.

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

Absolute and relative levels

The decibel is a relative unit because it describes a ratio between two values. Fixing the reference value in the denominator defines an absolute unit that describes a specific power or voltage level.

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

Distinguish units that describe the quantity of information from units that describe the speed of transmission.

Units of information quantity

Bit (b):The basic unit of information. The name comes from "binary digit". A bit represents one of two possible states, 0 or 1.
Byte (B): A group of 8 bits, often used to represent a single character such as a letter or symbol. $1 \text{ B} = 8 \text{ b}$ . Capitalization matters: B denotes a byte and b denotes a 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 the number of symbols transmitted per second.
Bits per second (bps): The unit of . It measures the number of bits transmitted per second. Useful bit rate excludes overhead and error-correction bits.

Baud and bps: the distinction

The numerical values expressed in baud and bps are equal only when each symbol represents exactly one bit. In multilevel modulation, one symbol can represent multiple bits, for example, one QPSK symbol represents 2 bits. With uniform symbol mapping, the bit rate is $\text{Bit Rate} = \text{Baud Rate} \times \log_2(M)$ , where M is the number of possible symbols. The formula describes the rate before protocol overhead and error-correction bits are removed.