page_title: Zobel network
section_title: Cauer equaliser
hierarchical_section_title: Zobel network / Video equalisers / Cauer equaliser
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: To equalise long video lines, a network with Cauer topology is used as the Z impedance of a Zobel constant resistance network.  Just as the input impedance of a Bode network is used as the Z impedance of a Zobel network to form a Zobel Bode equaliser, so the input impedance of a Cauer network is used to make a Zobel Cauer equaliser.  The equaliser is required to correct an attenuation increasing with frequency and for this a Cauer ladder network consisting of series resistors and shunt capacitors is required.  Optionally, there may be an inductor included in series with the first capacitor which increases the equalisation at the high end due to the steeper slope produced as resonance is approached.  This may be required on longer lines.  The shunt resistor R₁ provides the basic loss of the Zobel network in the usual way.
  The dual of a RC Cauer network is a LR Cauer network which is required for the Z' impedance as shown in the example.  Adjustment is a bit problematic with this equaliser.  In order to maintain the constant resistance, the pairs of components C₁/L₁', C₂/L₂' etc., must remain dual impedances as the component is adjusted, so both parts of the pair must be adjusted together.  With the Zobel Bode equaliser, this is a simple matter of ganging two pots together - a component configuration available off-the-shelf.  Ganging together a variable capacitor and inductor is not, however, a very practical solution.  These equalisers tend to be "hand built", one solution being to select the capacitors on test and fit fixed values according to the measurements and then adjust the inductors until the required match is achieved.  The furthest element of the ladder from the driving point is equalising the lowest frequency of interest.  This is adjusted first as it will also have an effect on higher frequencies and from there progressively higher frequencies are adjusted working along the ladder towards the driving point.
caption: Cauer topology network to be used as the Z impedance of a Zobel network equaliser