low pass filters

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. Filters consist of RLC elements (resistor, capacitor, coil) that can be present in different configurations to achieve the desired results.

The separation of filters in electronics is as follows:

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

Analog and digital filters

Active filters

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

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

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

Examples of simple active filters:

High pass filter

High-pass filter – passes high-frequency signal components and blocks lower ones

low pass filters

Low-pass filter – passes low-frequency signal components and blocks higher ones

band pass filters

Band-pass filter – passes only a limited range of frequencies

band stop filter

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

Passive filters

Passive filters are based on 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 do the reverse. 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 filters circuits is essentially identical. Small differences can only occur in constructional processes. Even the operation of fully digital filters used in Digital Signal Processing (DSP) is based on the same rights and relationships 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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