Active filter
Encyclopedia
An active filter is a type of analog electronic filter
Electronic filter
Electronic filters are electronic circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both...

 that uses an amplifier
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

 stage. Amplifiers included in a filter design can be used to improve the performance, stability and predictability of a filter. An amplifier prevents the impedance of source or load stages from affecting the characteristics of the filter. An active filter can simulate circuits that would in a passive filter require an inductor. Inductors can be large, expensive or hard to adjust. The shape of the response, the Q (quality factor), and the tuned frequency can often be set easily by varying resistors. In some active filter circuits, one parameter can be adjusted without affecting the others.

Inclusion of active elements in a filter design also imposes some limitations. Basic filter design equations neglect the finite bandwidth
Bandwidth
Bandwidth is the difference between the upper and lower frequencies in a contiguous set of frequencies. It is typically measured in hertz, and may sometimes refer to passband bandwidth, sometimes to baseband bandwidth, depending on context...

 of amplifiers. Available active devices are limited in speed; complex active filter designs are impractical or at best expensive at radio frequency. Amplifiers consume power and inject noise into a system. Certain circuit topologies may not be practical if no DC path is provided for bias current to the amplifier elements. Power handling capability is limited by the amplifier stages.

Active filter circuit configurations (electronic filter topology
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....

) include:
  • Sallen and Key, and VCVS
    Sallen Key filter
    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 filter topology...

     filters (low dependency on accuracy of the components)
  • State variable
    State variable filter
    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...

     and biquadratic filters
  • Dual Amplifier Bandpass (DABP)
  • Wien
    Max Wien
    Max Wien was a German physicist and the director of the Institute of Physics at the University of Jena. He was born in Königsberg, Prussia.Wien studied under Helmholtz and Kundt. He invented the "Löschfunkensender" during the years 1906 to 1909 and the Wien bridge in 1891...

     notch
  • Multiple Feedback Filter
  • Fliege  (lowest component count for 2 opamp but with good controllability over frequency and type)
  • Akerberg Mossberg (one of the topologies that offer complete and independent control over gain, frequency, and type)


All the varieties of passive filters can also be found in active filters. Some of them are:
  • High-pass filter
    High-pass filter
    A high-pass filter is a device that passes high frequencies and attenuates frequencies lower than its cutoff frequency. A high-pass filter is usually modeled as a linear time-invariant system...

    s – attenuation of frequencies below their cut-off points.
  • Low-pass filter
    Low-pass filter
    A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...

    s – attenuation of frequencies above their cut-off points.
  • Band-pass filter
    Band-pass filter
    A band-pass filter is a device that passes frequencies within a certain range and rejects frequencies outside that range.Optical band-pass filters are of common usage....

    s – attenuation of frequencies both above and below those they allow to pass.
  • Notch filters
    Band-stop filter
    In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter...

     – attenuation of certain frequencies while allowing all others to pass.
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 elliptic filter
Elliptic filter
An elliptic filter is a signal processing filter with equalized ripple behavior in both the passband and the stopband...

s.

Design of active filters

To design filters, the specifications that need to be established include:
  • The range of desired frequencies (the passband) together with the shape of the frequency response. This indicates the variety of filter (see above) and the center or corner frequencies.
  • Input and output impedance
    Electrical impedance
    Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

     requirements. These limit the circuit topologies available; for example, most, but not all active filter topologies provide a buffered (low impedance) output. However, remember that the internal output impedance of operational amplifiers, if used, may rise markedly at high frequencies and reduce the attenuation from that expected. Be aware that some high-pass filter topologies present the input with almost a short circuit to high frequencies.
  • The degree to which unwanted signals should be rejected.
    • In the case of narrow-band bandpass filters, the Q determines the -3dB bandwidth but also the degree of rejection of frequencies far removed from the center frequency; if these two requirements are in conflict then a staggered-tuning bandpass filter may be needed.
    • For notch filters, the degree to which unwanted signals at the notch frequency must be rejected determines the accuracy of the components, but not the Q, which is governed by desired steepness of the notch, i.e. the bandwidth around the notch before attenuation becomes small.
    • For high-pass and low-pass (as well as band-pass filters far from the center frequency), the required rejection may determine the slope of attenuation needed, and thus the "order" of the filter. A second-order all-pole filter gives an ultimate slope of about 12 dB per octave (40dB/decade), but the slope close to the corner frequency is much less, sometimes necessitating a notch be added to the filter.
  • The allowable "ripple" (variation from a flat response, in decibels) within the passband of high-pass and low-pass filters, along with the shape of the frequency response curve near the corner frequency, determine the damping factor (reciprocal of Q). This also affects the phase response, and the time response to a square-wave
    Square wave
    A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels...

     input. Several important response shapes (damping factors) have well-known names:
    • Chebyshev filter
      Chebyshev filter
      Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple or stopband ripple than Butterworth filters...

       – slight peaking/ripple in the passband before the corner; Q>0.7071 for 2nd-order filters
    • Butterworth filter
      Butterworth filter
      The Butterworth filter is a type of signal processing filter designed to have as flat a frequency response as possible in the passband so that it is also termed a maximally flat magnitude filter...

       – flattest amplitude response; Q=0.7071 for 2nd-order filters
    • Linkwitz–Riley filter – desirable properties for audio crossover applications; Q = 0.5 (critically damped)
    • Paynter or transitional Thompson-Butterworth or "compromise" filter – faster fall-off than Bessel; Q=0.639 for 2nd-order filters
    • Bessel filter
      Bessel filter
      In electronics and signal processing, a Bessel filter is a type of linear filter with a maximally flat group delay . Bessel filters are often used in audio crossover systems...

       – best time-delay, best overshoot response; Q=0.577 for 2nd-order filters
    • Elliptic filter
      Elliptic filter
      An elliptic filter is a signal processing filter with equalized ripple behavior in both the passband and the stopband...

      or Cauer filter – add a notch (or "zero") just outside the passband, to give a much greater slope in this region than the combination of order and damping factor without the notch.

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