page_title: Zobel network
section_title: Low pass
hierarchical_section_title: Zobel network / Types of section / Low pass
context_page_description: 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.
  Zobel networks were formerly widely used in telecommunications to flatten and widen the frequency response of copper land lines, producing a higher performance line from one originally intended for ordinary telephone use. Analogue technology has given way to digital technology and they are now little used.
  When used to cancel out the reactive portion of loudspeaker impedance, the design is sometimes called a Boucherot cell.
context_section_description: For a low-pass filter section, Z is an inductor and Z ' is a capacitor;
  and
  where
  The transfer function of the section is given by
  The 3 dB point occurs when ωL = R₀ so the 3 dB cut-off frequency is given by
  where ω is in the stop band well above ωc,
  it can be seen from this that A(ω) is falling away in the stop band at the classic 6 dB/8ve (or 20 dB/decade).
caption: Z and Z ' for a Zobel low-pass filter section