# 1.4: SI Units

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The main SI units used in microwave engineering are given in Table $$\PageIndex{1}$$.

• Symbols for units are written in upright roman font and are lowercase unless the symbol is derived from the name of a person. An exception is the use of $$\text{L}$$ for liter to avoid possible confusion with $$\text{l}$$.
SI unit Name Usage In terms of fundamental units
$$\text{A}$$ ampere current (abbreviated as amp) Fundamental unit
$$\text{cd}$$ candela luminous intensity Fundamental unit
$$\text{C}$$ coulomb charge $$\text{A}\cdot\text{s}$$
$$\text{F}$$ farad capacitance $$\text{kg}^{-1}\cdot\text{m}^{-2}\cdot\text{A}^{-2}\cdot\text{s}^{4}$$
$$\text{g}$$ gram weight $$=\text{kg}/1000$$
$$\text{H}$$ henry inductance $$\text{kg}\cdot\text{m}^{2}\cdot\text{A}^{-2}\cdot\text{s}^{-2}$$
$$\text{J}$$ joule unit of energy $$\text{kg}\cdot\text{m}^{2}\cdot\text{s}^{-2}$$
$$\text{K}$$ kelvin thermodynamic temperature Fundamental unit
$$\text{kg}$$ kilogram SI fundamental unit Fundamental unit
$$\text{m}$$ meter length Fundamental unit
$$\text{mol}$$ mole amount of substance Fundamental unit
$$\text{N}$$ newton unit of force $$\text{kg}\cdot\text{m}\cdot\text{s}^{-2}$$
$$\Omega$$ ohm resistance $$\text{kg}\cdot\text{m}^{2}\cdot\text{A}^{-2}\cdot\text{s}^{-3}$$
$$\text{Pa}$$ pascal pressure $$\text{kg}\cdot\text{m}^{-1}\text{s}^{-2}$$
$$\text{s}$$ second time Fundamental unit
$$\text{S}$$ siemen admittance $$\text{kg}^{-1}\cdot\text{m}^{-2}\cdot\text{A}^{2}\cdot\text{s}^{3}$$
$$\text{V}$$ volt voltage $$\text{kg}\cdot\text{m}^{2}\cdot\text{A}^{-1}\cdot\text{s}^{-3}$$
$$\text{W}$$ watt power $$\text{J}\cdot\text{s}^{-1}$$

Table $$\PageIndex{1}$$: Main SI units used in RF and microwave engineering.

• A space separates a value from the symbol for the unit (e.g., $$5.6\text{ kg}$$). There is an exception for degrees, with the symbol $$^{\circ}$$, e.g. $$45^{\circ}$$.

When SI units are multiplied a center dot is used. For example, newton meters is written $$\text{N}\cdot\text{m}$$. When a unit is derived from the ratio of symbols then either a solidus ($$/$$) or a negative exponent is used; the symbol for velocity (meters per second) is either $$\text{m/s}$$ or $$\text{m}\cdot\text{s}^{-1}$$. The use of multiple solidi for a combination symbol is confusing and must be avoided. So the symbol for acceleration is $$\text{m}\cdot\text{s}^{-2}$$ or $$\text{m/s}^{2}$$ and not $$\text{m/s/s}$$.

Consider calculation of the thermal resistance of a rod of cross-sectional area $$A$$ and length $$\ell$$:

$\label{eq:1}R_{\text{TH}}=\frac{\ell}{kA}$

If $$A = 0.3\text{ cm}^{2}$$ and $$\ell = 2\text{ mm}$$, the thermal resistance is

\label{eq:2}\begin{align} R_{\text{TH}}&=\frac{(2\text{ mm})}{(237\text{kW}\cdot\text{m}^{-1}\cdot\text{K}^{-1})\cdot (0.3\text{ cm}^{2})} \\ &=\frac{(2\cdot 10^{-3}\text{ m})}{237\cdot (10^{3}\cdot\text{W}\cdot\text{m}^{-1}\cdot\text{K}^{-1})\cdot 0.3\cdot (10^{-2}\cdot\text{m})^{2}}\nonumber \\ &=\frac{2\cdot 10^{-3}}{237\cdot 10^{3}\cdot 0.3\cdot 10^{-4}}\cdot\frac{\text{m}}{\text{W}\cdot\text{m}^{-1}\cdot\text{K}^{-1}\cdot\text{m}^{2}}\nonumber \\ &=2.813\times 10^{-4}\text{ K}\cdot\text{W}^{-1} = 281.3\:\mu\text{K/W} \end{align} \nonumber

This would be an error-prone calculation if the thermal conductivity was taken as $$237\text{ kW/m/K}$$.

SI prefixes are given in Table $$\PageIndex{2}$$ and indicate the multiple of a unit (e.g., $$1\text{ pA}$$ is $$10^{−12}\text{ amps}$$). (Source: 2015 ISO/IEC 8000 [3].) In 2009 new definitions of the prefixes for bits and bytes were adopted [3] removing the confusion over the earlier use of quantities such as kilobit to represent either $$1,000\text{ bits}$$ or $$1,024\text{ bits}$$. Now kilobit ($$\text{kbit}$$) always means $$1,000\text{ bits}$$ and a new term kibibit ($$\text{Kibit}$$) means $$1,024\text{ bit}$$. Also the now obsolete usage of $$\text{kbps}$$ is replaced by $$\text{kbit/s}$$ (kilobit per second). The prefix $$\text{k}$$ stands for kilo (i.e. $$1,000$$) and $$\text{Ki}$$ is the symbol for the binary prefix $$\text{kibi}$$- (i.e. $$1,024$$). The symbol for byte ($$= 8\text{ bits}$$) is “$$\text{B}$$”.

SI Prefixes SI Prefixes Prefixes for bits and bytes
Symbol Factor Name Symbol Factor Name Name
$$10^{-24}$$ $$\text{y}$$ yocto $$10^{1}$$ $$\text{da}$$ deca kilobit $$\text{kbit}$$ $$1000\text{ bit}$$
$$10^{-21}$$ $$\text{z}$$ zepto $$10^{2}$$ $$\text{h}$$ hecto megabit $$\text{Mbit}$$ $$1000\text{ kbit}$$
$$10^{-18}$$ $$\text{a}$$ atto $$10^{3}$$ $$\text{k}$$ kilo gigabit $$\text{Gbit}$$ $$1000\text{ Mbit}$$
$$10^{-15}$$ $$\text{f}$$ femto $$10^{6}$$ $$\text{M}$$ mega terabit $$\text{Tbit}$$ $$1000\text{ Gbit}$$
$$10^{-12}$$ $$\text{p}$$ pico $$10^{9}$$ $$\text{G}$$ giga kibibit $$\text{Kibit}$$ $$1024\text{ bit}$$
$$10^{-9}$$ $$\text{n}$$ nano $$10^{12}$$ $$\text{T}$$ tera mebibit $$\text{Mibit}$$ $$1024\text{ Kibit}$$
$$10^{-6}$$ $$\mu$$ micro $$10^{15}$$ $$\text{P}$$ peta gibibit $$\text{Gibit}$$ $$1024\text{ Mibit}$$
$$10^{-3}$$ $$\text{m}$$ milli $$10^{18}$$ $$\text{E}$$ exa tebibit $$\text{Tibit}$$ $$1024\text{ Gibit}$$
$$10^{-2}$$ $$\text{c}$$ centi $$10^{21}$$ $$\text{Z}$$ zetta kilobyte $$\text{kB}$$ $$1000\text{ B}$$
$$10^{-1}$$ $$\text{d}$$ deci $$10^{24}$$ $$\text{Y}$$ yotta kibibyte $$\text{KiB}$$ $$1024\text{ B}$$

Table $$\PageIndex{2}$$: SI prefixes.

This page titled 1.4: SI Units is shared under a CC BY-NC license and was authored, remixed, and/or curated by Michael Steer.