Low-pass filter

A low-pass filter passes low frequencies fairly well, but attenuates 'high' frequencies. Therefore it is better called a high-cut filter or treble cut filter. Also the term hiss filter sometimes used. See also: high-pass filter and bandpass filter.

Low-pass filters are used to block unwanted high-frequency signals, whilst passing the lower frequencies. The low frequencies to be filtered out are relative to the unwanted higher frequencies and therefore do not have a definitive range. The frequencies that are cut vary from filter to filter. A low-pass filter is the opposite of a high-pass filter.

Examples of low-pass filters

A physical barrier acts as a low-pass filter for waves. When music is playing in another room, the low notes are easily heard, while the high notes are largely filtered out. Similarly, very loud music played in one car is heard as a low throbbing by occupants of other cars, because the closed vehicles (and air gap) function as a very low-pass filter.

Low-pass filters are also used in subwoofers and other types of loudspeaker, to block high pitches that they can't efficiently broadcast.

Radio transmitters use low-pass filters to block harmonic emissions which might cause interference with other communications.

DSL splitters use low-pass and high-pass filters to separate DSL and POTS signals sharing the same pair of wires.

Types of low-pass filters

There are a great many different filter circuits, with different responses to changing frequency. The frequency response of a filter is generally represented using a Bode plot.

• A first-order filter, for example, will reduce the signal strength by half (-6 dB) every time the frequency doubles (goes up one octave). The magnitude Bode plot for a first-order filter looks like a horizontal line below the cutoff frequency, and a straight line approaching zero above the cutoff frequency. There is also a "knee curve" at the boundary between the two, which smoothly transitions between the two regions. (See RC circuit.)

• A second-order filter (with a Butterworth response) will reduce the signal strength to one fourth its original level every time the frequency doubles (-12 dB per octave). The Bode plot for this type of filter resembles that of a first-order filter, except that it falls off more quickly. Third and higher order filters are defined similarly. (See RLC circuit.)

The meanings of 'low' and 'high'--i.e. the cutoff frequency--depend on the characteristics of the filter. (The term "low-pass filter" merely refers to the shape of the filter's response. A high-pass filter could be built that cuts off at a lower frequency than any low-pass filter. It is their responses that set them apart.) A physical barrier acts as a filter at audio frequencies (between about 20 and 20000 Hz). Electronic circuits can be devised for any desired frequency range, right up through microwave frequencies (above 1000 MHz) and higher.

One simple electrical circuit that will serve as a low-pass filter consists of a resistor in series with a load, and a capacitor in parallel with the load. The capacitor exhibits reactance, and blocks low-frequency signals, causing them to go through the load instead. At higher frequencies the reactance drops, and the capacitor effectively functions as a short circuit. The break frequency, also called the turnover frequency (in radians per second), is determined by the choice of resistance and capacitance, f_c = 1/RC.

Another type of electrical circuit is an active low-pass filter.

In this example, the cutoff frequency (in Hertz) is defined as:

<math> f_0 = {1 \over 2 \pi C R_2} <math>

The gain in the passband is −R2/R1, and the stopband drops off at −6 dB per octave, as it is a first-order filter.

Many times, a simple gain or attenuation amplifier is turned into a lowpass filter by adding the capacitor C. This decreases the frequency response at high frequencies and helps to avoid oscillation in the amplifier. For example, an audio amplifier can be made into a lowpass filter with cutoff frequency 100 kHz to reduce gain at frequencies which would otherwise oscillate. Since the audio band only goes up to 20 kHz, the frequencies of interest fall entirely in the passband, and the amplifier behaves the same way as far as audio is concerned.

A low-pass filter can also be realized as a digital filter.