page_title: Lattice network
section_title: Darlington Synthesis
hierarchical_section_title: Lattice network / Lattice Synthesis / Darlington Synthesis
caption_attribution_description: The figure shows the basic circuit used by the Darlington synthesis method.
context_page_description: A symmetrical lattice is a two-port electrical wave filter in which diagonally-crossed shunt elements are present – a configuration which sets it apart from ladder networks. The component arrangement of the lattice is shown in the diagram below. The filter properties of this circuit were first developed using image impedance concepts, but later the more general techniques of network analysis were applied to it.
  There is a duplication of components in the lattice network as the "series impedances" and "shunt impedances" both occur twice, an arrangement that offers increased flexibility to the circuit designer with a variety of responses achievable. It is possible for the lattice network to have the characteristics of: a delay network, an amplitude or phase correcting network, a dispersive network or as a linear phase filter, according to the choice of components for the lattice elements.
context_section_description: The Darlington Method forms the basis for synthesis of lossless two terminal-pair networks with resistive termination for prescribed transfer characteristics.
  The figure shows the basic network configuration.   The associated transfer impedance is
  The first step is to express the input impedance ZI of a terminated network in terms of its z-parameters.  This is 
  in which z₁₁, z₂₂ and z₁₂ are z-parameters of the network, as defined earlier.
  For a normalized network, put R = 1, and rearrange the expression thus:
  In practice, ZI consists of a ratio of two polynomials in p:
  where m₁ and n₁ are the even and odd parts of the numerator polynomial, respectively and m₂ and n₂ are the even and odd parts of the denominator polynomial, respectively.
  Rearranging   
  By comparing the two expressions for ZI, the following relationships are suggested
caption: Network for Darlington's Method
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