What is a Low Pass Filter?

A low-pass filter is an electronic filtering device that allows signals below the cut-off frequency to pass, but cannot pass signals above the cut-off frequency.

Chinese name: Low-pass filter
Foreign name: Low-pass filter
nickname: HF Shear Filter, Treble Elimination Filter

Common species: Butterworth filter, Chebyshev filter
Features: Allows signals below cut-off frequency
Common topologies: Sallen Key

Low-pass filter basic information

Low-pass filter introduction

Low-pass filter For different filters, the strength of the signal at each frequency is different. When used in audio applications, it is sometimes referred to as a high frequency cut filter, or a treble cancellation filter.

The concept of low-pass filters comes in many different forms, including electronic circuits (such as hiss filters used in audio equipment), digital algorithms for smoothing data, acoustic barriers, image blurring, etc. Both tools By eliminating short-term fluctuations and retaining long-term development trends, a smooth form of signal is provided.

The role of the low-pass filter in signal processing is equivalent to that of moving averages in other fields such as the financial field;

There are many types of low-pass filters, the most common of which are Butterworth filters and Chebyshev filters.

Low-pass filter Butterworth filter

Butterworth filter is a design classification of filters. It uses Butterworth transfer function, and it has many types of filters such as high-pass, low-pass, band-pass and band-stop.

The Butterworth filter has stable amplitude-frequency characteristics in and outside the passband, but has a long transition band, which can easily cause distortion in the transition band.

Chebyshev filter

Low-pass filter The Chebyshev filter is a design classification of filters. It uses the Chebyshev transfer function. There are also various filter types such as high-pass, low-pass, band-pass, high-impedance, and band-stop.

Compared with the Butterworth filter, the Chebyshev filter has a narrow transition band, but its internal amplitude-frequency characteristics are very unstable.

Low-pass filter type

The most common topology for high-pass and low-pass filters is Sallen Key.

Suttons low-pass filter (2 photos)

Low-pass filter

It requires only one op amp (Figures 1a and 1b). A multipass (channel) filter is often used as a bandpass filter (Figure 1c), and it requires only one op amp. Figures 2 and 3 show the topology of the biquad filter section. Each structure can implement a complete universal filter transfer function. The circuit shown in Figure 2 uses three op amps, and the purpose of using a central op amp is only to make the overall feedback path negative. The same filter with switched capacitors requires only two op amps (Figure 3). References 1 and 2 describe these filter structures.

And the purpose of using the central op amp is only to make the total feedback path negative.

Low-pass filter

A low-pass filter allows signals from DC to a certain cut-off frequency (fCUTOFF) to pass. By setting the high-pass and band-pass coefficients of the second-order transfer function of the general filter to zero, a second-order low-pass filter transfer formula is obtained:

For frequencies above f0, the signal drops at a rate squared at that frequency. At frequency f0, the damping value attenuates the output signal. You can cascade multiple such filter sections to get a higher order (steeper transition) filter. Assume that the design requires a fourth-order Bessel low-pass filter with a cutoff frequency of 10 kHz. According to reference 1, the turn-down frequency of each part is 16.13 and 18.19 kHz, the damping values are 1.775 and 0.821, and the high-pass, band-pass and low-pass coefficients of these two filter partitions are 0, 0, and 1, respectively. You can use these two filter sections with the above parameters to achieve the required filter. The cutoff frequency is the frequency at which the output signal is attenuated by 3 dB.

Active low-pass filter

A filter is an electronic device that can pass useful frequency signals while suppressing unwanted frequency signals. It is often used in signal processing, data transmission, and interference suppression. Active low-pass filtering Capacitor composition. Its function is to allow signals from zero to a certain cutoff frequency to pass without attenuation, while suppressing signals at other frequencies. Active low-pass filter circuit can be used to filter high-frequency interference signals ^[1] .

Low-pass filter basic concepts

The function of the wave circuit is to allow signals in a certain frequency range to pass, while blocking or weakening signals in other frequency ranges. Active filter circuit is composed of resistor, capacitor and integrated operational amplifier, also known as active filter. Active filters can amplify signals while filtering, which is not possible with passive filtering. Filter circuits can be divided into low-pass, high-pass, and band-pass band-stop circuits according to the frequency range of the filter circuit that passes or blocks the signal. This article discusses the design and simulation of an active low-pass filter circuit. Active low-pass filter circuits can suppress or attenuate high-frequency signals through low-frequency signals ^[1] .

The second-order voltage-controlled voltage source low-pass filter circuit is composed of two RC links and an amplifier circuit of the same comparative example. Through analysis, it can be known that when the signal frequency is greater than the cutoff frequency, the attenuation rate of the signal is only 20dB / decade. Also near the cutoff frequency, the useful signal is attenuated. The attenuation of the second-order voltage-controlled active low-pass filter circuit can reach 40dB / octave. And near the cutoff frequency, the useful signal can be improved to some extent. If Q = 0.707, the amplitude-frequency characteristic of the filter is the most flat; if Q> 0.707, the amplitude-frequency characteristic will show a peak. Therefore, we will use Butterworth's normalization method to design circuit diagram parameters ^[1] .

Low-pass filter op amp

Operational amplifier is currently the most widely used device. Although different op amps have different structures, their characteristics are the same for external circuits. Operational amplifiers generally consist of 4 parts: bias circuit, input stage, intermediate stage, and output stage. Among them, the input stage generally uses a differential amplifier circuit (suppressing power), and the intermediate stage generally uses a common-radiation load circuit of active loads ( Increase the magnification), the output stage generally adopts complementary symmetrical output stage circuit (improving the ability of the circuit to drive the load) ^[1] .

Operational amplifier performance indicators include five, open loop differential mode voltage amplification, maximum output voltage, differential mode input resistance, output resistance, and common mode rejection ratio CMRR. (Open-loop differential mode amplification factor refers to the amplification factor of the differential mode voltage of the integrated op amp without an external feedback loop. The maximum output voltage refers to the maximum undistorted output voltage of the integrated op amp at a certain voltage. Peak-to-peak. The size of the differential mode input resistance reflects the current demanded by the integrated op amp input terminal to the differential mode input signal source. It is required to be as large as possible. The size of the output resistance reflects the integrated op amp's small signal output The common mode rejection ratio shows the ability of the integrated op amp to suppress common mode input signals. The definition is the same as that of the differential amplifier circuit. The larger the CMRR, the better. ^[1] )

There are actually requirements. First, the input impedance of the op amp must be large enough to prevent the input impedance from having an excessive impact on the actual resistance in the circuit. Secondly, the open-loop gain AV0 of the op amp must be large enough. However, because these conditions are very easy to meet, they are not considered when designing an active second-order low-pass filter. However, in the simulation, different op amps still have an impact on the specifications of the filter ^[1] .

Low-pass filter other related

Low -pass filter example

A solid barrier is a low-pass filter for sound waves. When playing music in another room, it is easy to hear the bass of the music, but most of the treble is filtered out. A similar situation is that very loud music in one car sounds low in the other car, because the closed car (and air space) at this time acts as a low-pass filter, weakening Got all the treble.

Electronic low-pass filters are used to drive subwoofers and other types of loudspeakers, and to block high-pitched beats that they cannot effectively propagate.

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

The DSL splitter uses low-pass and high-pass filters to separate the shared DSL and POTS signals using twisted pair.

Low-pass filters also play an important role in the processing of electronic music sounds synthesized by analog synthesizers such as Roland.

Ideal and practical filters An ideal low-pass filter can completely remove all frequency signals above the cutoff frequency and signals below the cutoff frequency can pass through unaffected. The actual transition area no longer exists. An ideal low-pass filter can be obtained mathematically (theoretically) by multiplying a signal with a rectangular function in the frequency domain. As a method with the same effect, it can also be obtained by convolution in the time domain with the sinc function.

However, such a filter is not achievable for actual signals. This is because the sinc function is an function that extends to infinity, so such a filter requires prediction in order to perform convolution. Future and need all the data from the past. This is achievable for pre-recorded digital signals (zero-padded on the back of the signal and making the resulting filtered error less than the quantization error) or infinitely cyclic signals.

Real filters in real-time applications approximate the ideal filter by delaying the signal for a short period of time so they can "see" a small part of the future, as demonstrated by phase shifts. The higher the accuracy, the longer the delay required.

The sampling theorem (Nyquist-Shannon sampling theorem) describes how to use a perfect low-pass filter and Nyquist-Shannon interpolation formula to reconstruct continuous signals from digital signal samples. Practical D / A converters use approximation filters.

Electronic low-pass filter

There are many different types of filter circuits with different frequency responses. The frequency response of the filter is usually represented by a Bode plot.

For example, a first-order filter reduces the signal strength by half (approximately -6dB) as the frequency doubles (increases octave). The first-order filter amplitude Bode plot is a horizontal line below the cutoff frequency and a diagonal line above the cutoff frequency. There is also a "knee curve" at the boundary between the two that smoothly transitions between two straight areas.

Second-order filters can have a higher effect on reducing high-frequency signals. The Bode plot of this type of filter is similar to a first-order filter, except that its roll-off rate is faster. For example, doubling the frequency of a second-order Butterworth filter (a critical attenuation RLC circuit without spikes) attenuates the signal strength to the original quarter (-12dB per octave). The initial roll-off speed of other second-order filters may depend on their Q factor, but the final speed is -12dB per octave.

Third-order and higher-order filters are similar. In summary, the roll-off rate of the last n-th order filter is 6ndB per octave.

For any Butterworth filter, if you extend the horizontal line to the right and the diagonal line to the upper left (the asymptote of the function, they will intersect at the "cutoff frequency". The frequency response of the first-order filter at the cutoff frequency is below the horizontal line- 3dB. Different types of filters-Butterworth filters, Chebyshev filters, etc.-have different shapes of "knee curves". Many second-order filters are designed to have "peaks" or resonances to get the cutoff frequency The frequency response above is above the horizontal line.

The meanings of 'low' and 'high'-such as the cutoff frequency-depend on the characteristics of the filter. (The term "low-pass filter" simply refers to the shape of the filter response. A high-pass filter can be designed to have a cut-off frequency lower than the cut-off frequency of any low-pass filter. Different frequency responses are the basis for distinguishing them.) Electronics The filter can be designed to any desired frequency range-up to microwave frequencies (over 1000 MHz) and higher. ^[2]

In many cases, a simple gain or suppression amplifier (see Operational Amplifier) is converted to a low-pass filter by adding capacitor C. This reduces the frequency response at high frequencies and avoids oscillations inside the amplifier. For example, an audio amplifier can be made as a low-pass filter with a cutoff frequency of 100kHz to attenuate gain at frequencies that may cause oscillation. Since the human ear can hear audio up to about 20kHz, the frequency of interest falls completely within the passband, so that the performance of the amplifier is exactly the same as the audio of interest.