The low-pass filter allows signals below the cut-off frequency to pass, but abovecut-off frequencyThe signal of cannot pass through the electronicFilter device。
Chinese name
low pass filter
Foreign name
Low-pass filter
Alias
High frequency shear filter、Treble cancellation filter
For differentwave filterFor each frequency, the strength of the signal is different.When used in audio applications, it is sometimes referred to as a high-frequency shear filter, or treble cancellation filter.
The concept of low-pass filter has many different forms, including electronic circuits (such asAudio equipmentHis filter used in), digital algorithm for smoothing datasound barrier(acoustic barriers), image blur processing, and so on. These two tools both eliminateShort term volatility. Long term retentionDevelopment trendProvides a smooth form of the signal.
Low pass filter atsignal processing Its role is equal to that of other fields, such as the financial fieldMoving average(moving average);
ChebyshevFilter is a design classification of filter, which uses Chebyshev transfer function, and also has high pass, low pass, bandpassHigh resistance, band stop and other filter types.
Compared with Butterworth filter,Chebyshev filterThe transition band of is very narrow, but the internal amplitude frequency characteristics are very unstable.
The most common topology of high pass and low pass filters is Sallen Key.
high pass
It only needs one operational amplifier (Figures 1a and 1b).Multi pass (channel) filter is commonly used asBandpass filter(Figure 1c), and it only needs one operational amplifier.Figures 2 and 3 showBiquadratic filterPartial topology.Each structure can realize a complete universal filter transfer function.The circuit shown in Figure 2 uses three operational amplifiers, and the purpose of using the central operational amplifier is only to make the total feedback path negative feedback.The same filter with switched capacitor only needs two operational amplifiers (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
Low pass filter is allowed to move from DC to a certaincut-off frequency(fCUTOFF).Set both the high pass and band-pass coefficients of the second-order transfer function of the universal filter to zero to obtain a second-order low-pass filter transfer formula:
For frequencies higher than f0, the signal decreases at the rate of the square of the frequency.At frequency f0, the damping value makesoutput signalAttenuation.You can cascade multiple such filter parts to get a higher order (steeper droop) filter.It is assumed that the design requires a fourth order Bessel low-pass filter with a cut-off frequency of 10kHz.According to Reference 1, the droop frequencies of each part are 16.13 and 18.19 kHz, the damping values are 1.775 and 0.821 respectively, 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 implement the required filter.The cut-off frequency is the frequency point where the output signal attenuates by 3 dB.
The function of wave circuit is to allow a certain sectionfrequency range The signal in other frequency ranges is blocked or weakened by the signal passing through.Activefilter circuit fromresistance, capacitance andIntegrated operational amplifierComposition, also known asActive filter。Active filter can amplify signals while filtering, which is impossible for passive filter.The filter circuit can be divided into low-pass, high pass, band-pass and band stop circuits according to the different frequency range of the signal that the filter circuit passes or stops.This paper discusses the design and simulation of active low-pass filter circuit.Active low-pass filter circuit can suppress or attenuate low-frequency signalsHigh frequency signal[1]。
Second order voltage controlVoltage sourceLow-pass filteringThe circuit consists of two RC links andin-phaseproportionAmplification circuitComposition.The analysis shows that: whensignal frequency When the cut-off frequency is greater thanAttenuation rateOnly 20dB/10 octave.And near the cut-off frequency,useful signal It is also attenuated.The attenuation of second-order voltage controlled active low-pass filter circuit can reach 40dB/frequency doubling.Moreover, the useful signal can be improved near the cut-off frequency.If Q=0.707, the filter'sAmplitude frequency characteristicThe flattest;If Q>0.707, the amplitude frequency characteristic will have a peak value.Therefore, we will use Butterworth normalization method laterCircuit diagramparameter[1]。
Operational amplifier
Operational amplifierIt is the most widely used device at present. Although different operational amplifiers have different structures, their characteristics are the same for external circuits.The operational amplifier is generally composed of four parts,Bias circuit, input stage, intermediate stage, output stage, of which the input stage generally adoptsdifferential amplifier (suppression power supply), the intermediate stage generally adoptsActive loadCommon emitter load circuit (increasedMagnification）The output stage generally adopts complementary symmetrical output stage circuit (to improve the ability of the circuit to drive the load)[1]。
Operational amplifierperformance index Including 5,open loopDifferential mode voltage magnification, maxoutput voltage ，Differential modeInput resistance，Output resistance，common modeSuppression ratio CMRR.(Open loop differential mode amplification means that the integrated operational amplifier is not externally appliedFeedback loopIn the case ofDifferential mode voltageThe magnification of.The maximum output voltage refers to the peak peak value of the maximum undistorted output voltage of the integrated operational amplifier under a certain voltage.The value of the differential input resistance reflects that the input end of the integrated operational amplifier transfers to the differential inputsignal sourceAsk for the size of the current.The bigger it is, the better.The size of the output resistance reflects theLoad capacity。Common mode rejection ratioShowed the integrated operational amplifier versus common modeInput signalIts definition is the same as that of differential amplifier circuit.The bigger the CMRR, the better.[1]）
Actually, there are requirements.First operationalInput impedanceIt shall 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 operational amplifier should be large enough.However, because these conditions are very easy to meet, they are not considered in the design of active second-order low-pass filter.However, in the simulation, different operational amplifiers have an impact on the filter indicators[1]。
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Example of low-pass filter
A solid barrier is a low-pass filter for sound waves.When music is played in another room, it is easy to hear the bass of the music, but the high part is mostly filtered out.Similarly, the very loud music in a car sounds like a bass beat to people in another car, because the closed car (and the air gap) acts as a low-pass filter, weakening all the treble.
Electronic low-pass filter is used to drive heavyWoofer(subwoofer) and other types ofLoudspeakerAnd block the treble beats that they cannot effectively spread.
Low pass filters are also synthesized by analog synthesizers such as Rolandelectronic musicSound processing plays an important role.
Ideal and actual filter An ideal low-pass filter can completely eliminatecut-off frequencyAll frequency signals of and below the cut-off frequency can pass through without influence.The actual conversion area no longer exists.An ideal low-pass filter can be mathematicallyfrequency domainIntermediate signal multiplied byRectangular functionIt is obtained that, as a method with the same effectsinc function doconvolutionGet.
However, such awave filterFor actual real signals, it is impossible to achieve. This is because the sinc function is a function that extends to infinitywave filteringIn order to perform convolution, it needs to predict the future and have all the data in the past.For prerecordeddigital signal(Make up zero at the back of the signal, and make the resulting filtered error less thanquantization error）OrInfinite loopPeriodic signalThis is achievable.
Actual filters in real-time applications are approximately implemented by delaying signals for a short period of time so that they can "see" a small part of the futureIdeal filterThis has been proved by phase shifting.The higher the approximation accuracy, the longer the delay required.
There are so many differencesfrequency responseDifferent types of filter circuits.The frequency response of the filter is usuallyBode diagramexpress.
For example, the first-order filter willsignal intensity Half off (about - 6dB).First order filter amplitudePorter diagramBelow the cut-off frequency is alevelAnd a slash above the cut-off frequency.There is also a "knit curve" at the boundary of the two lines to smoothly convert between the two straight areas.
Second order filter for reductionHigh frequency signalCan play a higher effect.The baud diagram of this type of filter is similar to that of a first-order filter, except that its roll off rate is faster.For example, a second-order Butterworth filter (which is a critical attenuation RLC circuit without spikes) doubles the frequency of the signalIntensity attenuationTo the first 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 conclusion, the roll off rate of the last n-order filter is 6ndB per octave.
For anyButterworth filter, if the horizontal line is extended to the right and the diagonal line is extended to the left (Asymptote, they will intersect at the "cut-off frequency".The frequency response of the first-order filter at the cut-off frequency is - 3dB below the horizontal line.Different types of filters - Butterworth filter, Chebyshev filter, etc. - have different shapes of "knee curves".Many second-order filters are designed to have "peaks" orresonanceSo that the frequency response at the cut-off frequency is above the horizontal line.
The meaning of 'low' and 'high' - such as cut-off frequency - depends on the characteristics of the filter.(The term "low-pass filter" only refers to the shape of the filter response. A high pass filter can be designed to have a lower cut-off frequency than any low-pass filter. Different frequency responses are the basis for distinguishing them.)Electronic filterCan be designed into any desiredfrequency range ——It can reach microwave frequency (over 1000 MHz) or higher.[2]
In many cases, a simplegainOr suppression amplifier (seeOperational amplifier）It is converted into a low-pass filter by adding capacitor C.This weakens the frequency response at high frequencies and avoids the internal oscillation of the amplifier.For example, aAudio amplifierA low-pass filter with a cut-off frequency of 100kHz can be made to reduce the gain at the frequency that may cause oscillation.Since the maximum audio frequency that can be heard by the human ear is about 20kHz, the frequency of interest falls completelyPassbandIn this way, the performance of the amplifier is exactly the same as the audio concerned.
