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Feb 18 2019

Principle and Function of the Filter

Warm hints: This article contains about 4000 words and reading time is about 18 min.

Introduction

Filters, as the name suggests, are devices that filter waves. "Wave" is a very broad physical concept. In the field of electronic technology, "wave" is narrowly limited to the process of describing the fluctuations of various physical quantities over time. This process is converted into a time function of voltage or current through the action of various types of sensors, which is called a time waveform of various physical quantities, or a signal. Since the argument time ‘ is continuous, it is called a continuous time signal and is customarily called an analog signal. With the development and rapid development of digital electronic computers (referred to as computer) technology, in order to facilitate the computer to process the signals, a complete theory and method for transforming continuous time signals into discrete time signals under the guidance of the sampling theorem is generated. That is to say, the original signal can be expressed only by the sample values of the original analog signal at a series of discrete time coordinate points without losing any information. Since the concepts of waves, waveforms and signals express the changes of various physical quantities in the objective world, Nature is the carrier of all kinds of information that modern society depends on. Information needs to be transmitted, relying on the transmission of waveform signals. The signal may be distorted at every stage of its generation, conversion, and transmission due to the presence of environment and interference. Even in a considerable number of cases, the distortion is so severe that the signal and the information it carries are Deeply buried in the noise.

Article Core

Filter

Purpose

Introduce what the principle and function of the filter are.

Application

Semiconductor industry.

Keywords

Filter

Catalog

Introduction


ⅠPrinciple of the Filter


 

Ⅱ The Role of the Filter

2.1 Butterworth Filter

2.2 Chebyshev Filter

2.3 Elliptical Filter

2.4 Bessel Filter

Ⅲ Comparison of the Four Filters


Ⅳ Advantages and Disadvantages of Active and Passive Filters

4.1 Active filtering reflects rapid action and high price.

4.2 Passive filtering has low cost and low harmonic filtering rate.

Ⅴ Filter Common Applications



ⅠPrinciple of the Filter

The filter is one of the indispensable key components in the RF system. It is mainly used for frequency selection, allowing the required frequency signal to pass and reflecting the unwanted interference frequency signal. An example of a classic filter application is the receiver or transmitter front end, as shown in Figure 1:

Figure 1 Superheterodyne receiver front end

Figure 1 Superheterodyne receiver front end

As can be seen from Figure 1, the filter is widely used in the RF, IF, and baseband portions of the receiver. Although the development of this digital technology uses a digital filter to replace the analog band filter of the baseband portion or even the intermediate frequency portion, the filter of the radio frequency portion is still irreplaceable. Therefore, the filter is one of the essential components in the RF system. There are many ways to classify filters. E.g:

The characteristics selected by frequency can be divided into: low pass, high pass, band pass, band stop filter, etc.;

According to the implementation, it can be divided into: LC filter, surface acoustic wave/body acoustic wave filter, spiral filter, dielectric filter, cavity filter, high temperature superconducting filter, planar structure filter. According to different frequency response functions can be divided into: Chebyshev, general Chebyshev, Butterworth, Gauss, Bessel function, elliptic function and so on.

BOKELA DYNO Filter for Dynamic Cross Flow Filtration - Function Principle

For different filter classifications, the different characteristics of the filter are mainly described from different filter characteristic requirements. The many different characteristics of the filter described by this multi-classification method of the filter embodies the need for the filter in practical engineering applications, which means that the design needs to be comprehensive for the user's needs. Consider user needs. When selecting a filter, the first thing to determine is whether a low pass, high pass, band pass or band stop filter should be used. The following is a description of the frequency response characteristics of high-pass, low-pass, band-pass, and band-stop, and their effects, which are classified by frequency.

filter

filter

filter

Butterworth Chebyshev high-pass filter

The most common filters are low pass and band pass. Low-pass is widely used in image suppression in the mixer section and harmonic suppression in the frequency source section. Bandpass is widely used in signal selection at the front end of the receiver, spurious suppression after transmitter power amplifier, and spurious suppression of frequency source. Filters are widely used in microwave radio frequency systems. As a functional component, there must be corresponding electrical performance indicators to describe the performance requirements of the system for the component. Corresponding to different applications, there are different requirements for certain electrical performance characteristics of the filter. The technical indicators describing the filter electrical performance are:

Order (number of stages), absolute bandwidth, relative bandwidth, cutoff frequency, standing wave, out-of-band rejection, ripple, absolute group delay, group delay fluctuation, power capacity, phase consistency, amplitude uniformity, operating temperature range .

The following explains the electrical performance indicators of the filter one by one:

Order (number of stages): For high-pass and low-pass filters, the order is the sum of the number of capacitors and inductors in the filter. For a bandpass filter, the order is the total number of parallel resonators; for a bandstop filter, the order is the total number of series resonators and parallel resonators.

Absolute Bandwidth/Relative Bandwidth: This indicator is typically used in bandpass filters to characterize the frequency range of the filter that can be passed through the filter. The relative bandwidth is the percentage of absolute bandwidth to center frequency.

Fifth-order high-pass filter

Fifth-order high-pass filter

Cutoff frequency: The cutoff frequency is typically used for high pass and low pass filters. For the low-pass filter cut-off characterizes the highest possible frequency range of the filter; for high-pass filters, the cutoff frequency characterizes the lowest possible frequency range of the filter.

Standing wave: S11 measured by the vector network indicates the matching degree of the filter port impedance with the required impedance of the system. Indicates how much of the input signal has failed to enter the filter and is reflected back to the input.

Nine-order low-pass filter simulation curve

Nine-order low-pass filter simulation curve

Loss: Loss represents the energy lost after the signal passes through the filter, which is the energy consumed by the filter.

Passband Flatness: The absolute value of the difference between the maximum loss and the minimum loss in the passband of the filter. Characterizes the difference in energy consumption of filters for different frequency signals.

Out-of-band Rejection: The “attenuation amount” outside the filter passband frequency range. Characterizes the ability of the filter to select unwanted frequency signals.

Ripple: The difference between the peaks and valleys of the S21 curve in the passband of the filter.

Phase Linearity: The phase difference between the phase of the filter passband frequency range and a transmission line equal to the center frequency delay. Characterizes the dispersion characteristics of the filter.

Absolute Group Delay: The time it takes for a signal to pass from the input port to the output port within the passband of the filter.

Group Delay Fluctuation: The difference between the maximum and minimum values of the absolute group delay in the passband of the filter. Characterizes the dispersion characteristics of the filter.

Power Capacity: The maximum power that can be input to the passband signal of the filter.

Phase Consistency: The difference in phase of the transmitted signal between different filters of the same indicator in the same indicator. Characterize the difference (consistency) between batch filters.

Amplitude consistency: The difference in transmission signal loss between different filters of the same indicator in the same indicator. Characterize the difference (consistency) between batch filters.

Phase linearity: The phase difference between the phase of the filter passband frequency range and a transmission line equal to the center frequency delay. Characterizes the dispersion characteristics of the filter.

Absolute Group Delay: The time it takes for a signal to pass from the input port to the output port within the passband of the filter.

Group Delay Fluctuation: The difference between the maximum and minimum values of the absolute group delay in the passband of the filter. Characterizes the dispersion characteristics of the filter.

Power Capacity: The maximum power that can be input to the passband signal of the filter.

Phase Consistency: The difference in phase of the transmitted signal between different filters of the same indicator in the same indicator. Characterize the difference (consistency) between batch filters.

Amplitude Consistency: The difference in transmission signal loss between different filters of the same indicator in the same indicator. Characterize the difference (consistency) between batch filters.

LC filter

LC filter

Surface Acoustic Wave / Bulk Acoustic Wave Filter

The sound table uses the method of converting electric energy into surface acoustic waves and using the acoustic resonance effect to achieve filtering. The surface acoustic wave filter is characterized by a very small volume, a high Q value relative to LC, and is suitable for mass production using a semiconductor process. A filter with an output of around 800MHz is only about one 0805 capacitor. The disadvantage is that the power capacity is small, it is not suitable for small-volume customized products, the development cycle is long, and the research and development cost is high.

Sound meter filters are commonly used in end consumer electronics.

Spiral filter

Spiral filter

Spiral Filter

A spiral filter is a filter with a semi-lumped parameter that implements a resonator using self-resonance of a spiral inductor placed in a cavity, which is coupled by a spatial magnetic field of an adjacent resonator. The advantage is that the volume is smaller than the cavity, and the Q value and power capacity are higher than LC. The disadvantage is that it is difficult to achieve broadband, and the high-frequency part of the inductor is not easy to achieve. The spiral filter is usually used in the case of a 20% relative bandwidth below 500 MHz, 100 W average power, and there are certain requirements for insertion loss.

Dielectric Filter

Dielectric Filter

Ripple: The difference between the peaks and valleys of the S21 curve in the passband of the filter. Dielectric Filter The dielectric filter is a half lumped filter implemented with a dielectric filled quarter-wave short-circuit or a half-open path. The advantage is that the Q value is higher than LC, and a filter with a higher frequency than the LC filter can be realized. The disadvantage is that the parasitic is closer and the resonator needs to be customized.

Comb Cavity Filter

The biggest feature of the interdigital filter is that it can achieve broadband. If a redundant resonant rod is used, the relative bandwidth can be as wide as 60%, considering that the machine is linear. At the same time, in the K-band, the wide-band comb filter is basically unable to process and the debugging screw cannot be placed, so the interdigitated structure is usually used under this condition. The interdigitated structure is closer to the parasitic passband than the comb, and its parasitic passband is usually around 1.8F0. Under the same volume, the interdigital filter has a larger power capacity than the comb filter. Filters are an essential component of wireless communication systems. There are many kinds of filters, and various filters have different performance characteristics. Therefore, when selecting filters, it is usually necessary to comprehensively consider the customer's actual use environment and customer performance requirements in order to make correct, effective, and reliable choices. When the customer's concept of the filter index is vague, it is usually necessary to ask the customer for the volume, loss, frequency of the out-of-band suppression, and the degree of suppression, power capacity, and so on. According to these simple indicators, the filter type can be basically judged.


Ⅱ The Role of the Filter

Today's filters have been widely infiltrated into everyday life. So what are the four most commonly used filters? Which four categories is it mainly divided into? For the time being, the most classic digital filters are Butterworth filters, Chebyshev filters, elliptical filters, and Bessel filters.

2.1 Butterworth Filter

The Butterworth filter is characterized in that the frequency response curve in the passband is as flat as possible, without undulations, and gradually decreases to zero in the blocking band. On the Bode plot of the logarithmic diagonal frequency of the amplitude, starting from a certain corner frequency, the amplitude gradually decreases with the increase of the angular frequency, and tends to negative infinity. The frequency characteristic of the Butterworth filter is a monotonic function of frequency both in the passband and in the stopband. Therefore, when the boundary of the passband meets the requirements of the index, there will be a margin in the passband. Therefore, a more efficient design method should be to distribute the accuracy evenly throughout the passband or stopband, or both. This makes it possible to meet the requirements with a lower order system. This can be achieved by selecting an approximation function with equal ripple characteristics.

2.2 Chebyshev Filter

The Chebyshev filter is a filter with ripple response such as frequency response amplitude on the passband or stopband, and the amplitude characteristic is equal ripple in the passband. In the stopband, it is monotonously called the Chebyshev I-type filter; the amplitude characteristic is monotonic in the passband, and the equal-ripple inside the stopband is called the Chebyshev II filter. The type of Chebyshev filter used depends on the application.

2.3 Elliptical Filter

An elliptic filter (EllipTIc filter), also known as a Cauer filter, is a filter that is corrugated in passbands and stopbands. It goes further than the Chebyshev method at the expense of both the passband and stopband undulations in exchange for the steeper nature of the transition zone. Compared to other types of filters, elliptical filters have minimal passband and stopband fluctuations under the same order.

2.4 Bessel Filter

The Bessel filter is a linear filter with maximum flat group delay (linear phase response). Bessel filters are commonly used in audio flyover systems. The analog Bezier filter is depicted as a constant group delay that spans almost the entire passband, thus maintaining the filtered signal waveform over the passband.

The Bessel filter has the flattest amplitude and phase response. The phase response of the bandpass (usually the user's area of interest) is nearly linear. Bessel filters can be used to reduce the nonlinear phase distortion inherent in all IIR filters. The Bessel linear phase filter is used in audio equipment because it has the same delay to all frequencies below its cutoff frequency. In audio equipment, it must be in the band without damage. Under the premise of the phase relationship of the signal, the out-of-band noise is eliminated. In addition, the Bessel filter has a fast step response and no overshoot or ringing, which makes it a smoothing filter at the output of the audio DAC or an anti-aliasing filter at the input of the audio ADC. Excellent choice. Bessel filters can also be used to analyze the output of Class D amplifiers and to eliminate switching noise in other applications to improve the accuracy of distortion measurements and oscilloscope waveform measurements.

filter


 Comparison of the Four Filters

The Butterworth filter is characterized in that the frequency response curve in the passband is as flat as possible, without undulations, and gradually decreases to zero in the blocking band.

The Chebyshev filter has a faster attenuation in the transition band than the Butterworth filter, but the amplitude-frequency characteristics of the frequency response are not as flat as the latter. The error between the Chebyshev filter and the ideal filter's frequency response curve is minimal, but there is amplitude fluctuations in the passband.

The Bessel filter has the flattest amplitude and phase response. The phase response of the bandpass (usually the user's area of interest) is nearly linear.

Same Order

The amplitude-frequency curve of the elliptic filter drops steepest, followed by the Chebyshev filter, again the Butterworth filter, and the most gradual drop is the Bessel filter.

The Butterworth filter has the flattest passband and slower stopband.

The ripple of the Chebyshev filter passband and the stopband drop faster.

Bessel filter passband and other ripples, the stopband drops slowly. That is to say, the frequency-selective characteristic of the amplitude-frequency characteristic is the worst. However, Bessel filters have the best linear phase characteristics.

The elliptical filter has a ripple in the pass band (stop band flat or equal ripple), and the stop band drops the fastest.

Butterworth Filter

Butterworth Filter

Bessel Filter

Bessel Filter

Elliptical Filter

Elliptical Filter

Chebyshev Filter

Chebyshev Filter


Ⅳ Advantages and Disadvantages of Active and Passive Filters

4.1 Active filtering reflects rapid action and high price.

Active filtering is itself a source of harmonics. It relies on power electronics to generate a set of harmonic vectors with equal amplitude and opposite phase of the system while detecting system harmonics, which can cancel out the system harmonics and make it a sinusoidal waveform. In addition to filtering harmonics, active filtering can also dynamically compensate reactive power. The advantage is that it reflects the action quickly, and the harmonics can be filtered out to reach more than 95%, and the compensation is reactive and meticulous.

Compared with the passive filter, the active filter has good control effect, and can mainly filter out multiple and higher harmonics at the same time without causing resonance.

The disadvantages of active filters are high price and small capacity. Due to the current immature capacity of large-capacity silicon valve technology in the world, the current common active filter capacity does not exceed 600 kW. Its operational reliability is not as passive.

Generally, low-frequency signal filtering can still use ordinary op amps, but once the frequency of the signal increases, especially when the signal reaches MHz, this time the ordinary op amp is still difficult to meet the requirements, you need to choose high-speed op amp, but the high-speed op amp The price is really expensive. Once a high-cost, high-speed op amp is added to the active filter, the cost is greatly increased.


4.2 Passive filtering has low cost and low harmonic filtering rate.

Generally, passive filtering refers to the parallel low-resistance (tuning filtering) state of a certain harmonic through the matching of the inductor and the capacitor, and forms a low-resistance path for a certain harmonic current. This harmonic current will not flow into the system. The advantages of passive filtering are low cost, stable operation, relatively mature technology and large capacity. The disadvantage is that the harmonic filtering rate is generally only 80%, and the reactive power compensation for the fundamental wave is also certain. At present, in the place where the capacity is large and the compensation is required to be fine, the active plus passive hybrid type is generally used, that is, the passive large-capacity filter compensation is performed, and the active fine adjustment is performed.

The passband variation of the passive filter is also affected by the input resistance and the output resistance, that is, the internal resistance of the input signal source has an effect on the filter network, and the subsequent load change also affects the filter network, so the design is Consider this when you are.

Impedance effect

Passive filters are severely affected by system impedance, and there is a danger of harmonic amplification and resonance; active filtering is not affected.

Frequency effect

Passive filter resonance point offset, the effect is reduced; active filter is not affected.

Load impact

The passive filter may be damaged due to overload; the active filter is not damaged, and when the harmonic amount is greater than the compensation capability, only the compensation effect is insufficient. The passive filter compensation effect varies with load; the active filter is unaffected by load changes.


Ⅴ Filter Common Applications

Filtering is a fundamental and important technique in signal processing. Filtering technology can extract the desired signal from various signals and filter out unwanted interference signals. A filter is an important component in the frequency domain analysis of a signal. Filters are commonly used in the following industries: communications, semiconductor, petrochemical, chemical fiber, steel/intermediate heating, automotive, DC motor harmonics, hospital systems, theaters/sports, etc.


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2 comments

    • article on 2019-4-8 6:00:31

    Thanks, it's quite informative

    • conquests on 2019-5-14 3:48:45

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