# High pass

As a **high-pass** (also **low barrier** , English low-cut filter , *high-pass filter* ) is known filters , the frequencies above its cut-off frequency can be approximately unattenuated pass and attenuate lower frequencies.

Such filters are common in electronics , but corresponding filter functions can also be found in other areas, such as mechanics , acoustics , hydraulics or electrical engineering, although they are usually not called that there.

## Applications

Are high-pass filter in the low frequency technology application specific as *depth lock* , *bass filter* , *low-cut filter* , *bass-cut filter* , *low-cut filter* , respectively. These terms are common in sound engineering; They indicate that such a filter, for example in an equalizer, attenuates the "depths" of the signal or corresponding hum interferences which mainly contain low frequencies; see also equalization (sound engineering) . Furthermore, high-pass filters are connected upstream of the tweeters.

High- pass filters are also used for coupling in and out high-frequency signals , e.g. B. used in antenna switches , ADSL or RF signal transmission over power lines.

With the help of filter transformations , a low pass or a bandstop filter can be formed from the high pass .

## 1st order high pass

The function of an electrical filter circuit is given below as an example of a high pass . The image shows the basic structure of a capacitor *C* and a resistor *R* . At a low frequency, the reactance ( ) of the capacitor largely blocks the current.

According to the voltage divider formula , only the portion of the input voltage appears at the output :

- (For derivation see low-pass formula derivation )

*Phase response* :

where and denote the amounts of the input and output voltage.

The cut-off frequency (ger .: *cutoff frequency* ) of such a high-pass filter is . The cutoff frequency is the frequency at which is, i.e. i.e., is weakened by 3 decibels compared to this . The attenuation increases below the cutoff frequency by 20 decibels per decade . With a logarithmic representation on both axes, this results in a straight line. Since it becomes smaller with increasing frequency, the division ratio tends towards 1 with increasing frequency, and becomes for high frequencies .

- With

The attenuation is then 0 dB.

The frequency response of the circuit is also often represented by a locus curve in the complex plane . It turns * A* the tension in complex notation is:

- .

The length of the time-independent pointer * A* represents the amplitude ratio as it changes with frequency; the angle to the positive real axis stands for

*φ*.

## 2nd order high pass

A second order high-pass filter is obtained by *R* by an inductance *L* is replaced, since this in turn is a - although in opposite direction and to the capacitor - has frequency dependence, and a resistor *R* in series with the capacitor *C* on. Here, *R* is selected so large that no or only a small resonance step-up occurs the frequency response.

The frequency response of such a high pass is

- with .

The magnitude of the transfer function is

This reduces the output voltage below *f *_{G to a} greater extent (by 40 dB / decade), since now not only | *X *_{C} | larger, but at the same time *X *_{L} becomes smaller.

With static frequency response change, emphasis and deemphasis , the time constant is usually specified instead of the cutoff frequency .

Nowadays, high-pass filters of the second and higher order are usually implemented using operational amplifier circuits. These filters are known as active high-pass filters (or active filters) and are also known as Sallen-Key filters after their inventors .

## Higher order high pass

By connecting several high passes in series, their order is increased. Two second-order high-pass filters connected in series accordingly form a fourth-order high-pass filter. The damping changes below the cutoff frequency with:

- ,

which corresponds to a slope of 24 dB / octave. 6 dB per octave is equal to 20 dB per decade: a change by one octave (change by a factor of 2) corresponds to the -fold change by one decade:

- .

## See also

## Web links

- RL high pass
- Filter (RC element) with 6 dB per octave under the microscope (PDF; 548 kB)
- Video:
*low and high pass*. Institute for Scientific Film (IWF) 2004, made available by the Technical Information Library (TIB), doi : 10.3203 / IWF / C-14821 .

## Individual evidence

- ↑ Frequency response and equalization (EQ filter) - sound engineering calculator at sengpielaudio.com