Cutoff frequency

In the communications technology that is limit frequency , crossover or cut-off frequency ( English : c utoff frequency = "maximum frequency") that value of the frequency , beyond which the signal amplitude (voltage) or the modulation amplitude at the output of a component below a certain value decreases. ${\displaystyle f_{\mathrm {g} }=f_{\mathrm {c} }}$

Electrical engineering

amplifier

The cut-off frequency of an amplifier is, in common convention, the frequency at which the voltage or current gain has dropped to twice the value of the maximum gain (around 70.7%). The power delivered to a purely ohmic load resistor (consumer) is exactly half the value of the maximum power. ${\displaystyle {\tfrac {1}{\sqrt {2}}}=2^{-{\frac {1}{2}}}}$

The voltage gain expressed in dB at this cut-off frequency is −3 dB (exactly:) less than the maximum gain. The area of ​​application of amplifier circuits is limited to a certain frequency range due to physical effects in the active components and their external circuitry (e.g. coupling capacitors ); this is called the transmission range . The cut-off frequencies limit this range. ${\displaystyle 20\log _{10}\left({\tfrac {1}{\sqrt {2}}}\right)\approx -3{,}0103\,\mathrm {dB} }$

1st order high and low passes

In the case of simple RC or RL high and low passes , the voltage transfer factor has the maximum value 1. At the cutoff frequency, the transferred amplitude drops to twice the value. At the cutoff frequency, there is a phase shift of 45 ° between the input and output signal . ${\displaystyle {\tfrac {1}{\sqrt {2}}}}$

In the case of a 1st order low-pass, there is the following relationship between the cut-off frequency and the rise and fall times : ${\displaystyle f_{\mathrm {c} }}$ ${\displaystyle {\tfrac {t_{\mathrm {r} }}{t_{\mathrm {f} }}}}$

${\displaystyle {\frac {t_{\mathrm {r} }}{t_{\mathrm {f} }}}{\Biggl (}{\frac {10\,\%}{90\,\%}}{\Biggr )}={\frac {0{,}35}{f_{\mathrm {c} }}}\,.}$

The relationship to the time constant is: ${\displaystyle \tau }$

${\displaystyle \tau ={\frac {1}{2\pi \cdot f_{c}}}\,.}$

physics

In physics, the limit angular frequency is often chosen instead of the limit frequency . In some technical applications, e.g. B. for emphasis , it is common to specify the time constant instead of the cutoff frequency . In the case of a bandpass , the center frequency is the geometric mean between the upper and lower limit frequency . ${\displaystyle f_{\mathrm {c} }}$ ${\displaystyle \omega _{\mathrm {c} }=2\pi f_{\mathrm {c} }}$ ${\displaystyle \tau =RC={\frac {1}{\omega _{\mathrm {c} }}}={\frac {1}{2\pi f_{\mathrm {c} }}}}$

Quantum physics

In quantum physics , the cutoff frequency refers to the photo effect . Light quanta with a frequency below this cut-off frequency no longer have enough energy to remove electrons from the atomic shell . The necessary minimum energy is equal to the work function of the material. ${\displaystyle E=h\cdot f}$

Cutoff frequency in the waveguide

Signals only propagate in the waveguide above a certain frequency ( ). This depends on the dimensions of the waveguide, especially the longer side (for a waveguide with a rectangular cross-section). The geometric structure and dimensions of a waveguide are therefore standardized and divided into frequency ranges (bands). Propagation conditions exist when the wavelength becomes smaller than the so-called cut-off wavelength . The propagation can take place in different vibration modes. ${\displaystyle f>f_{\mathrm {c} }}$ ${\displaystyle a}$ ${\displaystyle \lambda _{g}}$

The cutoff wavelength for the first propagate mode (fundamental mode) rectangular waveguide is given by the equation:

${\displaystyle \lambda _{\mathrm {g} }=2a}$ (Free space wavelength).

For the cutoff frequency it follows: ${\displaystyle f_{\mathrm {c} }}$

${\displaystyle f_{\mathrm {c} }={\frac {c}{2a}}}$.

Example: Rectangular waveguide with the longer side length of the waveguide (cutoff wavelength ). ${\displaystyle a=3\,\mathrm {cm} }$ ${\displaystyle \lambda _{g}=6\,\mathrm {cm} }$

${\displaystyle f_{\mathrm {c} }={\frac {c}{0{,}06\,\mathrm {m} }}=5\,\mathrm {GHz} }$

with ( speed of light in vacuum) ${\displaystyle c=299\,792\,458\,\mathrm {\frac {m}{s}} }$

See also

• Bandwidth
• Spreading band technology
• High pass

literature

• Jürgen Detlefsen, Uwe Siart: Basics of high frequency technology. 2nd edition, Oldenbourg Verlag, Munich / Vienna 2006, ISBN 3-486-57866-9 .
• Curt Rint : Handbook for high frequency and electrical technicians Volume 2. 13th edition, Hüthig and Pflaum Verlag, Heidelberg 1981, ISBN 3-7785-0699-4 .

Web links

• Conversion of limit frequency and time constant
• Calculation of the center frequency as a geometric mean compared to the arithmetic mean
• Explanations of cutoff frequency, crossover frequency or corner frequency and time constant (PDF; 228 kB)
• Spatial cutoff frequency (English)