Active filter

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An example of high-pass active filter of the Sallen-Key topology. The operational amplifier is used as a buffer amplifier. Sallen-Key Highpass Example.svg
An example of high-pass active filter of the Sallen–Key topology. The operational amplifier is used as a buffer amplifier.

An active filter is a type of analog circuit implementing an electronic filter using active components, typically an amplifier. Amplifiers included in a filter design can be used to improve the cost, performance and predictability of a filter. [1]

Electronic filter electronic circuit that removes unwanted components from the signal, or enhances wanted ones, or both

Electronic filters are circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both. Electronic filters can be:

Amplifier electronic device that can increase the power of a signal

An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It is a two-port electronic circuit that uses electric power from a power supply to increase the amplitude of a signal applied to its input terminals, producing a proportionally greater amplitude signal at its output. The amount of amplification provided by an amplifier is measured by its gain: the ratio of output voltage, current, or power to input. An amplifier is a circuit that has a power gain greater than one.


An amplifier prevents the load impedance of the following stage from affecting the characteristics of the filter. An active filter can have complex poles and zeros without using a bulky or expensive inductor. The shape of the response, the Q (quality factor), and the tuned frequency can often be set with inexpensive variable resistors. [2] In some active filter circuits, one parameter can be adjusted without affecting the others. [1]


Using active elements has some limitations. Basic filter design equations neglect the finite bandwidth of amplifiers. Available active devices have limited bandwidth, so they are often impractical at high frequencies. Amplifiers consume power and inject noise into a system. Certain circuit topologies may be impractical if no DC path is provided for bias current to the amplifier elements. Power handling capability is limited by the amplifier stages. [3]

Bandwidth (signal processing) difference between the upper and lower frequencies in a continuous set of frequencies

Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth. Passband bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum. Baseband bandwidth applies to a low-pass filter or baseband signal; the bandwidth is equal to its upper cutoff frequency.

Active filter circuit configurations (electronic filter topology) include:

Electronic filter topology

Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those components are connected.

The Sallen–Key topology is an electronic filter topology used to implement second-order active filters that is particularly valued for its simplicity. It is a degenerate form of a voltage-controlled voltage-source (VCVS) filter topology.

A state variable filter is a type of active filter. It consists of one or more integrators, connected in some feedback configuration. Any LTI system can be described as a state-space model, with n state variables for an nth-order system. A state variable filter realizes the state-space model directly. The instantaneous output voltage of one of the integrators corresponds to one of the state-space model's state variables.

Max Karl Werner Wien was a German physicist and the director of the Institute of Physics at the University of Jena. He was born in Königsberg, Prussia. He was a cousin of Nobel laureate Wilhelm Wien.

Active filters can implement the same transfer functions as passive filters. Common transfer functions are:

Combinations are possible, such as notch and high-pass (in a rumble filter where most of the offending rumble comes from a particular frequency). Another example is an elliptic filter.

Design of active filters

To design filters, the specifications that need to be established include:



See also

Related Research Articles

Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. This results from systems composed solely of components classified as having a linear response. Most filters implemented in analog electronics, in digital signal processing, or in mechanical systems are classified as causal, time invariant, and linear signal processing filters.

Operational amplifier thid is functional :D DC-coupled high-gain electronic voltage amplifier with a differential input and usually a single-ended outp

An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op-amp produces an output potential that is typically hundreds of thousands of times larger than the potential difference between its input terminals. Operational amplifiers had their origins in analog computers, where they were used to perform mathematical operations in many linear, non-linear, and frequency-dependent circuits.


A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level. Depending on application, the required attenuation within the stopband may typically be a value between 20 and 120 dB higher than the nominal passband attenuation, which often is 0 dB.

Audio crossover

Audio crossovers are a type of electronic filter circuitry used in a range of audio applications, to split up an audio signal into two or more frequency ranges, so that the signals can be sent to drivers that are designed for different frequency ranges. Crossovers are often described as "two-way" or "three-way", which indicate, respectively, that the crossover splits a given signal into two frequency ranges or three frequency ranges. Crossovers are used in loudspeaker cabinets, power amplifiers in consumer electronics and pro audio and musical instrument amplifier products. For the latter two markets, crossovers are used in bass amplifiers, keyboard amplifiers, bass and keyboard speaker enclosures and sound reinforcement system equipment.

<i>Q</i> factor

In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is, and characterizes a resonator's bandwidth relative to its centre frequency. Higher Q indicates a lower rate of energy loss relative to the stored energy of the resonator; the oscillations die out more slowly. A pendulum suspended from a high-quality bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low one. Resonators with high quality factors have low damping, so that they ring or vibrate longer.

Band-pass filter filter that passes signals within a certain frequency range, and attenuates signals outside that range

A band-pass filter, also bandpass filter or BPF, is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.

Audio filter

An audio filter is a frequency dependent amplifier circuit, working in the audio frequency range, 0 Hz to beyond 20 kHz. Audio filters can amplify (boost), pass or attenuate (cut) some frequency ranges. Many types of filters exist for different audio applications including hi-fi stereo systems, musical synthesizers, sound effects, sound reinforcement systems, instrument amplifiers and virtual reality systems.

Voltage-controlled filter

A voltage-controlled filter (VCF) is a processor, a filter whose operating characteristics can be applied to control inputs. It can be considered to be a frequency-dependent amplifier. Although popularly known for their use in analogue music synthesizers, in general, they have other applications in military and industrial electronics.

A total harmonic distortion analyzer calculates the total harmonic content of a sinewave with some distortion, expressed as total harmonic distortion (THD). A typical application is to determine the THD of an amplifier by using a very-low-distortion sinewave input and examining the output. The figure measured will include noise, and any contribution from imperfect filtering out of the fundamental frequency. Harmonic-by-harmonic measurement, without wideband noise, can be measured by a more complex wave analyser.

Zobel network type of filter section based on the image-impedance design principle

Zobel networks are a type of filter section based on the image-impedance design principle. They are named after Otto Zobel of Bell Labs, who published a much-referenced paper on image filters in 1923. The distinguishing feature of Zobel networks is that the input impedance is fixed in the design independently of the transfer function. This characteristic is achieved at the expense of a much higher component count compared to other types of filter sections. The impedance would normally be specified to be constant and purely resistive. For this reason, Zobel networks are also known as constant resistance networks. However, any impedance achievable with discrete components is possible.

Network synthesis is a method of designing signal processing filters. It has produced several important classes of filter including the Butterworth filter, the Chebyshev filter and the Elliptic filter. It was originally intended to be applied to the design of passive linear analogue filters but its results can also be applied to implementations in active filters and digital filters. The essence of the method is to obtain the component values of the filter from a given rational function representing the desired transfer function.

Analogue filters are a basic building block of signal processing much used in electronics. Amongst their many applications are the separation of an audio signal before application to bass, mid-range and tweeter loudspeakers; the combining and later separation of multiple telephone conversations onto a single channel; the selection of a chosen radio station in a radio receiver and rejection of others.

In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, image processing, and computer graphics.

Distributed element filter

A distributed element filter is an electronic filter in which capacitance, inductance and resistance are not localised in discrete capacitors, inductors and resistors as they are in conventional filters. Its purpose is to allow a range of signal frequencies to pass, but to block others. Conventional filters are constructed from inductors and capacitors, and the circuits so built are described by the lumped element model, which considers each element to be "lumped together" at one place. That model is conceptually simple, but it becomes increasingly unreliable as the frequency of the signal increases, or equivalently as the wavelength decreases. The distributed element model applies at all frequencies, and is used in transmission line theory; many distributed element components are made of short lengths of transmission line. In the distributed view of circuits, the elements are distributed along the length of conductors and are inextricably mixed together. The filter design is usually concerned only with inductance and capacitance, but because of this mixing of elements they cannot be treated as separate "lumped" capacitors and inductors. There is no precise frequency above which distributed element filters must be used but they are especially associated with the microwave band.

RLC circuit

An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent components of this circuit, where the sequence of the components may vary from RLC.

A double-tuned amplifier is a tuned amplifier with transformer coupling between the amplifier stages in which the inductances of both the primary and secondary windings are tuned separately with a capacitor across each. The scheme results in a wider bandwidth and steeper skirts than a single tuned circuit would achieve.


  1. 1 2 Don Lancaster, Active-Filter Cookbook, Howard W. Sams and Co., 1975 ISBN   0-672-21168-8 pages 8-10
  2. "Op-amp Band Pass Filter". Basic Electronics Tutorials. 2013-08-14. Retrieved 2018-12-26.
  3. Muhammad H. Rashid, Microelectronic Circuits: Analysis and Design, Cengage Learning, 2010 ISBN   0-495-66772-2, page 804
  4. "Band Stop Filters are called Reject Filters". Basic Electronics Tutorials. 2015-10-20. Retrieved 2018-12-26.
  5. "Basic Introduction to Filters - Active, Passive, and Switched-Cap (Rev. A) Analog & Mixed-Signal SNOA224A -". Retrieved 2018-04-26.