Filters introduction

Introduction to filters – Analog and digital filters

Analog and digital filters – (in electronics) a part of electrical circuit that is designed to pass or block signals of a specific frequency range or containing specific harmonics of the signal. Filters consist of RLC components (resistor, capacitor, coil) that can be combined in different configurations to achieve desired results.

In electronics, filters are divided into:

  • active fliters – RLC with power supplying components to the circuit, eg. operational amplifiers,
  • passive flters – contain only RLC components,
  • analog and digital fliters – used in such electronic circuits,
  • high-pass, low-pass, band-pass, band-stop filters, depending on the desired result.

Analog and digital filters

Active filters

Active filters, as the name suggests, contain the combination of active electronic components (such as power amplifiers and external power supplies) and passive ones (R – resistor, L – inductor, C – capacitor).

We distinguish between many types of active filters, as an example we will mention the most popular ones:

  • Bessel filters,
  • Butterworth filters,
  • Chebyshev filters.

Examples of simple active filters:

High pass filter

High-pass filter – passes signals of frequencies higher than a certain cutoff frequency and attenuates lower ones

low pass filters

Low-pass filter – passes signals of frequencies lower than a certain cutoff frequency and attenuates higher ones

band pass filters

Band-pass filter – passes only a limited range of frequencies and attenuates frequencies outside of that range

band stop filter

Band-stop filter (2nd order) – attenuates signals in desired frequency range and passes only frequencies above and below that frequency range. The one presented in the picture is called notch filter

Passive filters

Passive filters are built from passive (RLC) electronic components and do not contain (as in the case of active filters) amplifying and power supplying components in the circuit. The number of inductors and capacitors (not resistors or amplifiers) in circuit determines the order of the filter. It affects the shape of the filter’s frequency response.

Inductors are used for conducting low-frequency signals and blocking high-frequency ones. However, capacitors are used for conducting high-frequency signals and blocking low-frequency ones. Resistors are used for determining the circuit’s time constants, so it influences the frequencies to which it responds.

Examples of simple passive filters

high pass rc filter

High-pass RC filter

low pass rc filter

Low-pass filter as an RC circuit

band pass rc filters

Band-pass RC filter

band stop rlc filters

Band-stop RLC filter

Digital filters

The operation and design of analog and digital filter’s circuits is essentially identical. Small differences can only occur during construction processes. Even the operation of fully digital filters used in Digital Signal Processing (DSP) is based on the same rights and relations as used in traditional filters. The difference lies only in the type of signal being processed – in case of DSP, the processing is performed on numerical strings of sampled (discrete) signal by an ADC (Analog-to-Digital Converter) that represents the given continuous-time signal. Filters used in DSP have a wide variety of uses and are inexpensive, although there may be problems with noise accompanied to the signal conversions, but it can be negated with usage of other filters.

The separation of digital filters (FIR and IIR filters) is as follows:

  • FIR digital filter (Finite Impulse Response) – the main feature of this filter is that the current sample and the previous input signal are used to obtain the current output sample. For this reason, they are sometimes called as non-recursive filters.
  • IIR digital filter (Infinite Impulse Response) – the main factor distinguishing IIR filters from FIR filters is the need of feedback loop. Each output sample depends on the previous samples of the input AND output signal. It is called a recursive filter.

Ideal filter characteristics

ideal high pass filters

High-pass filter

ideal low pass filters

Low-pass filter

ideal band pass filters

Band-pass filter

ideal band stop filters

Band-stop filter

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