Filters Explained: Principles, Parameters and Application Guide

Ⅰ. What is Filters?

The filter is a frequency selection device that allows certain frequency components in the signal to pass while drastically attenuating others. Filters work by using components like resistors, capacitors, and inductors to manipulate the frequency response of a signal, ensuring only desired frequencies are transmitted.

Interference noise can be filtered out or spectrum analysis performed using the filter's frequency selection function. A filter, in other terms, is any device or system that allows specified frequency components in a signal to pass while drastically attenuating or suppressing other frequency components. A filter is a wave-filtering device. The term "wave" refers to a broad physical idea. The term "wave" is used in the field of electronic technology to represent the process of fluctuations in the value of various physical properties throughout time. Through the action of numerous sensors, this process is turned into a time function of voltage or current, which is referred to as the time waveform of various physical quantities, or signals. It's called a continuous-time signal since the independent variable time is a continuous value, and it's also known as an analog signal (Analog Signal).

Waveforms before and after filtering

In signal processing, filtering is a crucial concept. The filter circuit's job in a DC stabilized power supply is to reduce the AC component in pulsating DC voltage as much as possible while retaining the DC component and lowering the output voltage ripple coefficient, resulting in a relatively smooth waveform.

Ⅱ. The Main Parameters of the Filters

Center Frequency: The frequency f0 of the filter passband is normally f0=(f1+f2)/2, where f1 and f2 are the bandpass or bandstop filter left and right side frequency points with a 1dB or 3dB relative decrease. Narrowband filters frequently determine the passband bandwidth using the center frequency with the lowest insertion loss.

Cutoff Frequency: Refers to the frequency point on the right of the low-pass filter's passband and the frequency point on the left of the high-pass filter's passband. It's commonly characterized as a 1dB or 3dB relative loss point. Low-pass insertion loss is based on DC insertion loss, while high-pass insertion loss is based on insertion loss at a sufficiently high passband frequency without a parasitic stopband.

Passband bandwidth: refers to the spectrum width that needs to be passed, BW=(f2-f1). f1 and f2 are based on the insertion loss at the center frequency f0.

Insertion Loss: The loss at the center or cut-off frequency describes the attenuation of the original signal in the circuit owing to the insertion of the filter. It is important to emphasize the full-band interpolation loss if it is required.

Ripple: refers to the peak value of the insertion loss fluctuating with frequency on the basis of the average loss curve within the 1dB or 3dB bandwidth (cutoff frequency).

Passband Ripple: In the passband, the insertion loss varies with frequency. Within a 1dB bandwidth, the in-band fluctuation is 1dB.

In-band standing wave ratio (VSWR): An crucial metric for determining whether the signal in the filter's passband is well-matched and transmitted. When VSWR=1:1, the ideal match, VSWR is larger than 1. When mismatched, VSWR is greater than 1. The bandwidth that satisfies a VSWR of less than 1.5:1 for an actual filter is often less than BW3dB, and its proportion to BW3dB is dependent on the filter order and insertion loss

Return Loss: The ratio of port signal input power to reflected power in decibels (dB), which is also equivalent to 20Log10, where is the voltage reflection coefficient. The return loss is infinite when the input power is fully absorbed by the port.

Stopband rejection: a crucial metric for evaluating the effectiveness of filter selection The higher the index, the greater the out-of-band interference signal suppression. There are usually two formulations: one is to propose an index that characterizes the closeness of the filter's amplitude-frequency response to the ideal rectangle —— Rectangular coefficient (KxdB is greater than 1), KxdB=BWxdB/BW3dB, and the calculation method is the attenuation at fs; the other is to propose an index that characterizes the closeness of the filter's amplitude-frequency response to the ideal rectangle (X can be 40dB, 30dB, 20dB, etc.). The greater the filter order, the higher the rectangularity—that is, the closer K gets to the ideal value 1, the harder it is to produce.

Delay (Td): The amount of time it takes for a signal to pass through a filter. The answer is Td=df/dv, which is the derivative of the diagonal frequency of the transmission phase function.

In-band phase linearity: The degree of phase distortion introduced by the filter to the transmission signal in the passband is shown by this indication. The phase linearity of the filter developed using the linear phase response function is good.

Ⅲ. The Classification of Filters

Filters are classified as active filters, passive filters, ceramic filters, crystal filters, mechanical filters, phase-locked loop filters, switched-capacitor filters, and so on, based on their component categorization.

The filter can be classified into two categories based on how it processes signals: analog filter and digital filter.

The filter can be classified as a low pass filter, a high pass filter, a bandpass filter, a band-stop filter, and so on, depending on the passband classification.

There are also certain unique filters, such as linear phase shift filters, time delay filters, forked network filters in audio, TV The mid-amp acoustic surface wave filter in the machine, and others, that fulfill specified frequency response and phase shift characteristics.

Active filters are classified as low pass filters (LPF), high pass filters (HPF), bandpass filters (BPF), bandstop filters (BEF), and so on, based on the passband categorization.

• Low-Pass Filter: Allows frequencies below a cutoff frequency to pass, blocking higher frequencies. For example, in audio systems, a low-pass filter can isolate bass frequencies (e.g., below 200 Hz) for a subwoofer.

• High-Pass Filter: Permits frequencies above a cutoff frequency, blocking lower ones. In a tweeter speaker, a high-pass filter ensures only treble frequencies (e.g., above 2 kHz) are processed.

• Band-Pass Filter: Allows a specific range of frequencies to pass, blocking those outside this range. For instance, in radio receivers, a band-pass filter might allow frequencies between 88-108 MHz for FM radio signals.

• Band-Stop Filter: Blocks a specific range of frequencies while allowing others to pass. This is useful in eliminating 50 Hz power line noise in audio recordings."

Active filters can be classified into three types based on their passband filtering characteristics: maximum flat type (Butterworth type), equal ripple type (Chebyshev type), and linear phase shift type (Bessel type).

The active filter can be classified as an infinite gain single feedback loop filter, infinite gain multiple feedback loop filters, voltage-controlled power supply filter, negative resistance converter filter, rotary Type filter, and so on, depending on the operational amplifier circuit's composition.

The frequency response properties of the filter are clearly described by the filter index.

1) A bandwidth of 3dB When the minimal insertion loss point of the passband (the highest point of the passband transmission characteristic) is pushed down by 3dB, the passband width is measured.

2) Loss of insertion The loss is caused by the filter's interference in the system. The highest loss in the filter's passband includes the resistive loss of all of the filter's components (such as inductance, capacitance, conductor, and medium flaws) as well as the filter's return loss (the voltage standing wave ratio at both ends is not 1). At both ends of the application, the insertion loss restricts the operational frequency and impedance.

3) Ripple within the band The insertion loss fluctuation range. The lower the in-band ripple, the better; otherwise, the power fluctuations of the various frequency signals flowing through the filter will be increased.

4) Suppression in the out-of-band range. It specifies the frequency at which the filter will block the signal by describing the rectangularity of the filter features. Out-of-band roll-off, which defines the number of decibels per frequency drop beyond the filter's passband, can also be used to characterize it. The lower the second and third high-order resonance peaks of the resonant circuit, the better. The larger the parasitic passband loss of the filter, the better.

5) Be able to withstand force The filter used at the end of a high-power transmitter should be constructed for high power and have a large component volume; otherwise, it will break down and spark, resulting in a sudden decline in transmission power.

Ⅳ. The Working Principle and Functions of Filters

Working Principle

The filter is composed of a low-pass filter circuit composed of an inductor and a capacitor, which allows the current of the useful signal to pass, and has a greater attenuation of the interference signal with a higher frequency. Since there are two types of interference signals, differential mode and common mode, the filter must attenuate both types of interference.

(1) Utilize the characteristics of high frequency and low-frequency isolation of capacitors to introduce the high-frequency interference current of the live wire and the neutral wire into the ground wire (common mode), or introduce the high-frequency interference current of the live wire into the neutral wire (differential mode);

(2) Use the impedance characteristics of the inductor to reflect the high-frequency interference current back to the interference source;

(3) The use of interference suppression ferrite can absorb the interference signal in a certain frequency band and convert it into heat. For the frequency band of a certain interference signal, select the appropriate interference suppression ferrite magnetic ring and magnetic beads directly on the cable that needs to be filtered. That's it.

Functions

(1) Separate useful signals from noise to improve signal anti-interference and signal-to-noise ratio;

(2) Filter out uninteresting frequency components to improve analysis accuracy;

(3)Separate a single frequency component from the complex frequency component.

Ⅴ. Precautions for Filters Use

While the filter isn't suitable for high-frequency filtering, it can meet the electromagnetic compatibility standards of most civilian items if used correctly. When using, keep the following points in mind:

If you're going to utilize an onboard filter, make sure to leave a "clean ground" at the cable port during wiring, then attach the filter and connector there. We can see from the previous explanation that the signal ground line interference is highly problematic. If the cable's filter capacitor is connected directly to this ground wire, major common-mode radiation issues will result. A clean space must be prepared in order to provide a greater filtering effect. At one time, it can only be connected to the signal ground. A "bridge" is the name for this circulation point. To reduce the signal loop area, all signal wires run across the bridge.

Side by side setting: All wires in the same group of cables have their unfiltered parts together, and their filtered parts are also together. Otherwise, the filtered portion of one wire will contaminate the filtered portion of the other wire, rendering the cable's total filtering ineffective.

Close to the cable: The filter's distance from the panel should be as short as feasible. To isolate near-field interference, cover it with a metal plate if necessary.

Connect with the chassis: The dry ground where the filter will be installed should be securely overlapped with the metal chassis. Set a bigger metal plate under the circuit board as the filter ground if the chassis is not metal. The clean ground's overlap with the metal chassis must have a very low RF impedance. Electromagnetic sealing gaskets can be utilized to overlap if necessary to enhance the overlap area and lower the RF impedance.

Short ground wire: Special attention should be paid to the local wiring of the filter and the design of the connection structure between the circuit board and the chassis, taking into consideration the inductance impact of the pin (metal plate).

Reference

• Electronics Tutorials. (n.d.). Passive Filters. Retrieved from https://www.electronics-tutorials.ws/filter/filter_1.html

• ScienceDirect Topics. (n.d.). Electronic Filter: An Overview. Retrieved from https://www.sciencedirect.com/topics/engineering/electronic-filter

• All About Circuits. (n.d.). An Introduction to Filters. Retrieved from https://www.allaboutcircuits.com/technical-articles/an-introduction-to-filters/

• Wikipedia contributors. (2024). Electronic Filter: Definition and Types. In Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Electronic_filter