Detuning (electrical engineering)

In electrical engineering, detuning is the term used to describe the relative representation of a frequency ratio , whereby one of the frequencies is specified and viewed as fixed. The specified frequency is usually a resonance frequency or the center frequency of a filter. The detuning thus describes in a standardized form how a current frequency deviates from the expected resonance or center frequency.

Based on the frequency ratio ${\displaystyle \eta }$

${\displaystyle \eta (f)=\eta (\omega )={\frac {\omega }{\omega _{r}}}={\frac {f}{f_{r}}}}$

with the given (desired, expected) frequency , ${\displaystyle f_{r}}$

the current frequency and ${\displaystyle f}$

the corresponding circular frequencies and ${\displaystyle \omega _{r}}$ ${\displaystyle \omega }$

the detuning is defined as ${\displaystyle v}$

${\displaystyle v(f)=v(\omega )=\eta (f)-{\frac {1}{\eta (f)}}={\frac {\omega }{\omega _{r}}}-{\frac {\omega _{r}}{\omega }}={\underline {\underline {{\frac {f}{f_{r}}}-{\frac {f_{r}}{f}}}}}}$.

The detuning is a quantity of the dimension number and indicates the relative deviation from the reference frequency. For it is negative, for zero and for positive. ${\displaystyle f<f_{r}}$ ${\displaystyle f=f_{r}}$ ${\displaystyle f>f_{r}}$

Plotting a frequency-dependent transmission behavior over the detuning or over the frequency ratio results in diagrams that show the characteristic behavior of a circuit regardless of the specific frequency. This normalization allows the properties of circuits that have different reference frequencies to be viewed uniformly.

For example, if you determine the frequency ratios and (with the lower and upper limit frequency or ), the following relation to the loss factor or quality factor of a resonant circuit or filter results: ${\displaystyle \eta _{go}=\eta (f_{go})}$ ${\displaystyle \eta _{gu}=\eta (f_{gu})}$ ${\displaystyle f_{gu}}$ ${\displaystyle f_{go}}$ ${\displaystyle d}$ ${\displaystyle Q}$

${\displaystyle \Delta \eta =\eta _{go}-\eta _{gu}=d={\frac {1}{Q}}}$

For the bandwidth B we get:

${\displaystyle B=\Delta \eta \cdot f_{r}}$

literature

• Jürgen Detlefsen, Uwe Siart: Basics of high frequency technology. 2nd edition, Oldenbourg Verlag, Munich Vienna, 2006, ISBN 3-486-57866-9

See also

• Figure of merit