100px-Sallen-Key Highpass Example

An example of high-pass active filter of the Sallen Key topology. The operational amplifier, U1, is used as a buffer amplifier.


An active filter is a type of analog electronic filter, distinguished by the use of one or more active components i.e. voltage amplifiers or buffer amplifiers. Typically this will be a vacuum tube, or solid-state (transistor or operational amplifier).

Active filters have three main advantages over passive filters:

  • Inductors can be avoided. Passive filters without inductors cannot obtain a high Q (low damping), but with them are often large and expensive (at low frequencies), may have significant internal resistance, and may pick up surrounding electromagnetic signals.
  • The shape of the response, the Q (Quality factor), and the tuned frequency can often be set easily by varying resistors, in some filters one parameter can be adjusted without affecting the others. Variable inductances for low frequency filters are not practical.
  • The amplifier powering the filter can be used to buffer the filter from the electronic components it drives or is fed from, variations in which could otherwise significantly affect the shape of the frequency response.

Active filter circuit configurations (electronic filter topology) include:

  • Sallen and Key, and VCVS filters (low dependency on accuracy of the components)
  • State variable, and biquadratic filters
  • Twin T filter (fully passive)
  • DABP Dual Amplifier Bandpass
  • Wien notch
  • Multiple Feedback Filter
  • Fliege (lowest component count for 2 opamp but with good control ability 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 filters – attenuation of frequencies below their cut-off points.
  • Low-pass filters – attenuation of frequencies above their cut-off points.
  • Band-pass filters – attenuation of frequencies both above and below those they allow to pass.
  • Notch filters – attenuation of certain frequencies while allowing all others to pass.

Combinations are possible, such as notch and high-pass (for example, in a rumble filter where most of the offending rumble comes from a particular frequency), e.g.Elliptic filters.

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 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), this indicates the slope of attenuation, and thus the "order" of the filter. A second-order filter gives an ultimate slope of about 12dB 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 input. Several important response shapes (damping factors) have well-known names:
    • Chebyshev filter – slight peaking/ripple in the passband before the corner; Q>0.7071 for 2nd-order filters
    • Butterworth filter – flattest amplitude response; Q=0.7071 for 2nd-order filters
    • Paynter or transitional Thompson-Butterworth or "compromise" filter – faster fall-off than Bessel; Q=0.639 for 2nd-order filters
    • Bessel filter – best time-delay, best overshoot response; Q=0.577 for 2nd-order filters
    • Elliptic filter or Cauer filters – 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.