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Basic knowledge of filters
21 Jun 2023

The Line filter is a filter circuit composed of capacitance, inductance and resistance. A filter can effectively filter out a specific frequency point in the power line or frequencies outside of that frequency point, obtaining a specific frequency power signal or eliminating a specific frequency power signal.


A filter, as the name suggests, is a device that filters waves. Wave "is a very broad physical concept, and in the field of electronic technology," wave "is narrowly limited to describing the process of varying the values of various physical quantities over time. This process is converted into a time function of voltage or current through the action of various sensors, known as the time waveform of various physical quantities, or as a signal. Because the independent variable 'time' is a continuous value, it is called a continuous time signal, also commonly referred to as an analog signal. With the emergence and rapid development of digital electronic computer (commonly referred to as computer) technology, in order to facilitate computer processing of signals, a complete theory and method of transforming continuous time signals into discrete time signals under the guidance of sampling theorem has emerged. That is to say, the original analog signal can be expressed using only the sample values of the original analog signal on a series of discrete time coordinate points without losing any information. Since the concepts of wave, waveform, and signal express changes in various physical quantities in the objective world, they are naturally carriers of various information that modern society relies on for survival.


Information needs to be transmitted through the transmission of waveform signals. The signal may undergo distortion at every stage of its generation, conversion, and transmission due to the presence of environment and interference. In many cases, this distortion is even severe, resulting in the signal and the information it carries being deeply buried in the noise.
Filter is one of the essential key components in RF systems, mainly used for frequency selection - allowing the desired frequency signal to pass through and reflect unwanted interference frequency signals.
A classic example of filter application is the receiver or transmitter front-end, as shown in the figure:

From the figure, it can be seen that filters are widely used in the RF, IF, and baseband parts of receivers. Although digital filters have been used to replace analog filters in the baseband or even intermediate frequency parts of the development of digital technology, filters in the RF part are still irreplaceable. Therefore, filters are one of the essential key components in RF systems.


There are many methods for classifying filters.
For example:
The characteristics selected by frequency can be divided into: low-pass, high pass, band-pass, Band-stop filter, etc;According to different frequency response functions, it can be divided into: Chebyshev, generalized Chebyshev, Butterworth, Gauss, Bessel function, elliptic function, etc.
It can be divided into LC filter, SAW/BAW filter, spiral filter, dielectric filter, cavity filter, High-temperature superconductivity filter and plane structure filter according to the implementation mode.


For different filter classifications, the main approach is to describe the different characteristics of filters based on their specific requirements.

The numerous classification methods of filters describe the diverse features of filters, which collectively reflect the need for comprehensive consideration of filter requirements in practical engineering applications. That is to say, when designing for user needs, it is necessary to comprehensively consider user needs.
When selecting a filter, the first thing to determine is whether to use low-pass, high-pass, bandpass, or bandstop filters.


Below, we will first introduce the frequency response characteristics and their effects of high pass, low pass, bandpass, and bandstop, which are classified according to the characteristics selected by frequency.



The most commonly used filters are low-pass and bandpass. 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, suppression of post amplifier noise in the transmitter, and suppression of frequency source noise.
Filters are widely used in microwave and radio frequency systems, and as a functional component, there must be corresponding electrical performance indicators to describe the performance requirements of the system for this component.
Corresponding to different application scenarios, there are different requirements for certain electrical performance characteristics of filters. The technical indicators describing the electrical performance of filters include: order (series), absolute bandwidth/relative bandwidth, cutoff frequency, standing wave, out of band suppression, ripple, loss, passband flatness, phase linearity, absolute group delay, group delay fluctuation, power capacity, phase consistency, amplitude consistency, and operating temperature range.


The following will explain the electrical performance indicators of the filter one by one.

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


Absolute bandwidth/relative bandwidth: This indicator is usually used for bandpass filters, characterizing the signal frequency range that can pass through the filter and reflecting the frequency selection of the filter. Relative bandwidth is the percentage of absolute bandwidth to center frequency.




Cutoff frequency: Cutoff frequency is usually used for high pass and low pass filters. For low-pass filters, the cutoff characterizes the highest frequency range that the filter can pass through; For high pass filters, the cutoff frequency represents the lowest frequency range that the filter can pass through.


Standing wave: The S11 measured by the vector network represents the degree of matching between the filter port impedance and the required impedance of the system. Indicates how many input signals fail to enter the filter and are reflected back to the input end.



Loss: Loss represents the energy lost by a signal after passing through a 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 within the passband range of the filter. Characterize the difference in energy consumption of filters for signals of different frequencies.


Out of band suppression: The "attenuation" beyond the passband frequency range of the filter. Characterize the filter's ability to select unwanted frequency signals.Ripple: The difference between the peaks and valleys of the S21 curve fluctuation within the passband of the filter.


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


Absolute group delay: The time taken for a signal to be transmitted from the input port to the output port within the passband range of the filter.


Group delay fluctuation: The difference between the maximum and minimum absolute group delay within the passband range of the filter. Characterize the dispersion characteristics of filters.


Power capacity: The maximum power of the passband signal that can be input into the filter. Phase consistency: The difference in phase of transmission signals between different filters in the same batch and the same indicator. Characterize the differences (consistency) between batch filters.


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


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


Absolute group delay: The time taken for a signal to be transmitted from the input port to the output port within the passband range of the filter.


Group delay fluctuation: The difference between the maximum and minimum absolute group delay within the passband range of the filter. Characterize the dispersion characteristics of filters.


Power capacity: The maximum power of the passband signal that can be input into the filter.


Phase consistency: The difference in phase of transmission signals between different filters in the same batch and the same indicator. Characterize the differences (consistency) between batch filters.


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

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