Performance size

In different contexts, especially of electrical engineering and acoustics (eg. As audio level , voltage gain , shielding effectiveness ) are physical quantities not stated directly, but only as a ratio to a second variable or fixed size of the same type. Preferably, the two sizes the ratio of which is specified, in each case by performance quantities or performance root quantities .

If the ratios extend over several powers of ten , it makes sense to specify them as a logarithmic quantity .

Performance size

A performance quantity is a quantity that is proportional to a performance . ${\displaystyle P}$

Examples: electrical power , electromagnetic and acoustic power and associated power densities

In this context, energy quantities, i.e. quantities that are related to an energy , are also referred to as power quantities .

Examples: electrical energy , electromagnetic and acoustic energy and associated energy densities ( sound power , sound intensity , sound energy density )

Achievement root size

A performance root quantity is a quantity whose square is proportional to a performance quantity. Power root quantities were previously referred to as field quantities . ${\displaystyle F}$

Examples: electrical voltage , electrical current strength , electrical and magnetic field strength , electrical and magnetic flux density , sound pressure , sound velocity

Power root quantities are usually effective values ; for a sine- shaped alternating quantity their can amplitude , complex amplitude or its complex RMS may be used. ${\displaystyle {\hat {F}}}$ ${\displaystyle {\underline {\hat {F}}}}$ ${\displaystyle {\underline {F}}}$

Logarithmic ratios

Determinations
${\displaystyle {\begin{aligned}{\text{Mit }}F^{2}&\sim P\Leftrightarrow {\frac {F_{1}^{2}}{F_{2}^{2}}}={\frac {P_{1}}{P_{2}}}\\Q_{(F)}&=\ln {\frac {F_{1}}{F_{2}}}\,\mathrm {Np} =2\lg {\frac {F_{1}}{F_{2}}}\,\mathrm {B} =20\lg {\frac {F_{1}}{F_{2}}}\,\mathrm {dB} \\Q_{(P)}&={\frac {1}{2}}\ln {\frac {P_{1}}{P_{2}}}\,\mathrm {Np} =\lg {\frac {P_{1}}{P_{2}}}\,\mathrm {B} =10\lg {\frac {P_{1}}{P_{2}}}\,\mathrm {dB} \end{aligned}}}$
Logarithmic ratio with field sizes ${\displaystyle Q_{(F)}}$ Logarithmic ratio with performance quantities ${\displaystyle Q_{(P)}}$

→ Main articles : Logarithmic quantity , Bel (unit)  and Neper (auxiliary unit of measurement)

Example for the gain of a two-port with the real voltages at the output and at the input: ${\displaystyle Q_{U}}$
${\displaystyle U_{2}}$ ${\displaystyle U_{1}}$

${\displaystyle Q_{U}=\left(\ln {\frac {U_{2}}{U_{1}}}\right)\,\mathrm {Np} =\left(\lg {\frac {U_{2}^{2}}{U_{1}^{2}}}\right)\,\mathrm {B} =20\,\left(\lg {\frac {U_{2}}{U_{1}}}\right)\,\mathrm {dB} }$

or with the complex sizes : ${\displaystyle {\underline {U}}_{2}=|U_{2}|\cdot \mathrm {e^{j\varphi _{2}}} {\text{ und }}{\underline {U}}_{1}=|U_{1}|\cdot \mathrm {e^{j\varphi _{1}}} }$

${\displaystyle {\underline {Q}}_{U}=\left(\ln {\frac {|U_{2}|}{|U_{1}|}}\right)\,\mathrm {Np} +\mathrm {j} (\varphi _{2}-\varphi _{1})\,\mathrm {rad} }$

literature

• Horst Clausert, Gunther Wiesemann, Volker Hinrichsen , Jürgen Stenzel: Basic areas of electrical engineering. Volume 2: Alternating currents, three-phase currents, cables, applications of Fourier, Laplace and Z transformation. 11th, corrected edition. Oldenbourg, Munich et al. 2011, ISBN 978-3-486-59719-6 .

Individual evidence

1. ↑ ^{a b c} DIN 5493: 2013-10: Logarithmic quantities and units
2. ↑ ^{a b c} DIN EN 60027-3: 2007-11: Symbols for electrical engineering - Part 3: Logarithmic and related quantities and their units