1.4: SI Units

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.