Skip to main content
Engineering LibreTexts

1.4: SI Units

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    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.

    • Was this article helpful?