# 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.

## 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.

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.

### 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 .

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 :

The relationship to the time constant is:

## 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 .

## 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.

## 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.

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

- (Free space wavelength).

For the cutoff frequency it follows:

- .

Example: Rectangular waveguide with the longer side length of the waveguide (cutoff wavelength ).

- with ( speed of light in vacuum)

## See also

## 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 .