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Passive filters – basic information

Date of publication: 13-09-2024 Update date: 10-04-2026 🕒 6 min read

Filters are very important and widely used circuits in electronic engineering. They pass through or block selected frequency components of electric signals. Although the name may be misleading, they do not contain any active components requiring an external power supply. They comprise solely resistors, inductors and capacitors, which is why they are called “passive”.

Passive filter types

Depending on the range of frequencies passed, four basic types of passive filters can be distinguished:

Low-pass filters
As the name suggests, they allow lower frequencies to pass and block higher ones. They act as a barrier to high signal frequencies.

High-pass filters
Their principle of operation is similar to low-pass filters. They allow higher frequencies to pass and block lower ones.

Band-pass filters
Instead of allowing the extreme frequency ranges to pass, this filter type allows only a narrow band of centre frequencies to pass. The upper and lower frequencies are blocked.

Trap circuits
Unlike band-pass filters, they block a narrow range of centre frequencies, while the extreme frequencies are allowed to pass.

Passive filter design

The simplest passive filters can be built from resistors and capacitors (RC filters) or resistors and coils (RL filters). More advanced ones combine these elements. They are not equipped with any power supply modules or transistors,, as they operate exclusively as passive RC or LC circuits.

Even though the filter design is simple, their application possibilities are limitless. Among others, they are used in antenna lines, resonance systems and actuation systems, as impedance adjusting systems or for signal constituent separation. Their versatility results from design simplicity and operation reliability.

What are passive filters? Why are they called “passive”?

They are called “passive filters,” because they are built exclusively from passive elements which do not generate electricity, but only pass or block it. Passive filters do not need any additional power supply modules, as they consist only of resistors, inductors and capacitors. They do not generate electricity, but only process signals based on their circuit properties. Resistors ensure resistance and attenuation, while coils and condensers create resonance circuits, but none of these components generate signals or energy.

Low-pass filters – design and principle of operation

A low-pass filter (sometimes referred to as a low-cut filter) is one of the most basic types of passive filters. It is designed to allow low signal frequencies to pass and to block higher frequencies.

It is often useful for various applications, for example:

  1. Removing high-frequency interfering components (noise) from low-frequency signals, e.g. in audio, telecommunications circuits, etc.
  2. Separating low-frequency and high-frequency signals, e.g. separation of audio and video signals in antenna lines.
  3. Resonant circuit design, e.g. in tuned circuits.
  4. Impedance matching between circuits with different frequency properties.
  5. Shaping the frequency response of equipment input/output lines.

Low-pass filters can be made from various configurations of RC (resistors and capacitors) or LC (resistors and coils) circuits. They operate by using the properties of these elements to achieve the desired low-frequency pass and high-frequency attenuation characteristics.

High-pass filters – design and principle of operation

A high-pass filter is another basic passive filter type. It can be treated as the opposite of a low-pass filter. It allows higher electric signal frequencies to pass, while blocking and attenuating frequencies below a certain limit.

High-pass filter applications include:

  1. Removal of low frequencies from high-frequency signals, e.g. in antenna lines and RF circuits.
  2. Separation of low-frequency and high-frequency signals into separate lines, e.g. audio and video signal separation.
  3. Design of selective resonance circuits for higher frequencies.
  4. Shaping the electronic circuit frequency response by blocking unwanted low frequencies.
  5. Impedance matching between circuits differing in frequency characteristics.

Similarly to low-pass filters, high-pass filters can be built using RC or LC circuits in various resistor, capacitor and inductor combination configurations.

Formulas for RC filters

The RC band filters use resistor and capacitor configurations to filter electric signals. See below for basic formulas describing operation of low-pass and high-pass RC filters.

RC low-pass filter: Approximated transmittance formula: T(jω) = 1 / (1 + jωRC)

A more detailed formula, taking into account the parallel resistance of a resistor and the ESR of a capacitor: T(jω) = 1 / (1 + jωC(Rp || ESR) + ω2C2(R||Rp||ESR)^2)

Limit frequency fg, for which transmittance decreases by 3 dB: fg = 1 / (2πRC)

RC high-pass filter:
Approximated transmittance formula: T(jω) = jωRC / (1 + jωRC)

A more detailed formula, taking into account parallel resistance and ESR: T(jω) = jωRC / (1 + jωC(R||Rp) + ω2C2(R||Rp||ESR)^2)

Limit frequency fg: fg = 1 / (2πRC)

where:
ω = angular frequency
R – resistance [Ω]
C – capacitor capacitance [F]
Rp – resistor parallel resistance [Ω]
ESR – equivalent resistance of losses in capacitor [Ω]

These formulas facilitate calculating RC filter frequency response in the frequency function and determine their limit lockout frequencies. They constitute the basis for designing this type of filters with the desired frequency properties.

Formulas for LC filters

The LC filters use resistor, coil and capacitor configurations to filter electric signals. See below for basic formulas describing operation of low-pass and high-pass LC filters.

LC low-pass filter:
Transmittance formula: T(jω) = 1 / (1 + jωL/R + (ω2LC - 1/(ω2LC)))
Limit frequency fg: fg = 1 / (2π√(LC))

LC high-pass filter:
Transmittance formula: T(jω) = jωL / (R + jωL + 1/(jωC))
Limit frequency fg: fg = 1 / (2π√(LC))
where:
ω = angular frequency
L – coil inductance [H]
C – capacitor capacitance [F]
R – resistance [Ω]

These formulas make it possible to determine the frequency-domain response of LC filters and their lockout frequencies. They are crucial components for designing filters with the desired transmission and attenuation characteristics of specific frequency ranges.

In practice, RC and LC filters are often cascaded together to achieve more distinct characteristics, and additional input and output impedance matching circuits are used for optimum filter performance.

Diagrams for example RC and LC filters – various possible configurations

Low-pass RC system:

  1. Basic configuration:
    ---||--- ---| |--- Output | | === === R C ---||--- | | ---| |--- Input
  2. With a serial resistor:
    ---||--- ---| |--- Output | | R1 | === === R2 C ---||--- | | ---| |--- Input

High-pass RC filter diagram:

  1. Basic configuration:
    === ---| | |--- Output | | | R C R ---||--- --- | | ---| |--- Input
  2. With a serial resistor:
    === ---| | |--- Output | | | R1 C R2 ---||--- --- | | ---| |--- Input

Low-pass LC system:
=== ---| |--- Output | | ---||--- L C ---||--- | | ---| |--- Input ===

High-pass LC filters:
=== ---| | |--- Output | | | ---||--- --- L C R ---||--- | | ---| |--- Input

These basic diagrams can be extended with additional RC/LC sections to obtain more distinct filter characteristics. Various connection variants can also be implemented, e.g. cascade connections with impedance matching circuits, etc.

The above examples illustrate typical RC and LC passive filter configurations for low-pass and high-pass filtration. Selection of a given diagram depends on the required filter properties and applications.

Bode diagram for passive filters

The Bode diagram is a very useful tool for analysing and presenting the frequency characteristics of various circuits, including passive RC and LC filters. It displays the dependence of the transmittance (gain) modulus and frequency phase shift on a logarithmic scale. Thanks to that, the system behaviour over a wide frequency range can be clearly illustrated.

In the context of passive filters, the Bode diagram makes it possible to:

  1. Visualise the response characteristics of low-pass and high-pass RC and LC filters as a function of frequency. The lockout frequencies fg, at which the transmittance decreases by a certain value (e.g. -3dB), can be read out.
  2. Determine the filter selectivity by the slope of the characteristic near fg, i.e. the greater selectivity, the more distinct filtering.
  3. Analyse the influence of the R, L, C element values on the shape of the characteristics and filter parameters.
  4. Select optimum component values to achieve the desired filter characteristics.
  5. compare the actual characteristics with the theoretical ones derived from formulas;
  6. evaluate the filter cascading effects to obtain more distinct characteristics.

Therefore, the Bode diagrams provide key information that is necessary to design and analyse passive filters. They make it easy to see the impact of parameter change on frequency filtering characteristics. Their logarithmic scale facilitates covering a huge range of frequencies on a single diagram. They are commonly used by engineers and scientists to visualise and optimise the RC and LC filter properties.

Determining the Bode characteristic of a system, such as an RC or LC filter, involves determining and plotting the dependence of the transmittance (gain) modulus and frequency phase shift on a logarithmic scale.

RC and LC filters – practical applications

RC and LC filters are commonly used in numerous fields of electric and electronic engineering. See below for some practical applications of these passive filters:

  1. Audio circuits:
    • Low-pass filters to filter off interferences and high-frequency noise from audio signals.
    • High-pass filters to separate bass and treble channels in Hi-Fi systems.
    • Tone quality correction by filtering selected frequency ranges.
  2. Telecommunication systems:
    • Low-pass filters to limit the signal bandwidth in subscriber’s lines.
    • High-pass filters in antenna lines to separate audio and video signals.
    • Frequency characteristic shaping in transmission lines.
  3. RF and microwave circuits:
    • Low-pass filters to attenuate unwanted high frequency constituents.
    • High-pass filters to separate RF signals from low frequencies.
    • Impedance tuning and matching circuits in transmission and reception circuits.
  4. Power supply circuits:
    • Low-pass filters to filter off ripples and interferences from chopper power supply modules.
    • High-pass filters to block the constant constituent in power supply circuits of various devices.
  5. Digital circuits:
    • Low-pass filters to limit the digital signal bandwidth and attenuate high-frequency interferences.
    • High-pass filters to attenuate residual signals in high-speed digital waveforms.
  6. Control and measurement systems:
    • RC and LC filters to isolate or lock out specific frequency ranges from measured signals.
    • Shaping measuring line characteristics for sensors and converters..
  7. Automation and control systems:
    • RC and LC filters to filter and stabilise signals in control systems and feedback loops.

These examples show the extensive and varied applications of passive RC and LC filters in various fields of technology. Their simplicity, reliability and ability to filter signals precisely make them an indispensable component of numerous electronic circuits.

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