# 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)${\ displaystyle c = 299 \, 792 \, 458 \, \ mathrm {\ frac {m} {s}}}$