page_title: Lattice network
section_title: Example 6
hierarchical_section_title: Lattice network / Lattice Synthesis / Synthesis of Constant-Resistance Lattice Networks / Example 6
caption_attribution_description: The figure shows the circuit diagram for a basic first-order bridged-T circuit.
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 all-pass response of the second order is
  This has two zeroes located at  and two poles at  where a = 2.x and b = x² + y².  For such a response, the phase varies with frequency, but the magnitude of T6 is unity at all frequencies.
  For this characteristic, Zₐ is found from
  So Zₐ is a parallel combination of a capacitance 1/a and an inductance with value a/b.
  Similarly Zb is an inductor 1/a in series with a capacitor of value a/b and the network is shown at the right hand side below.
  The lattice networks can be converted to unbalanced circuits by using the properties of lattices with common elements in both Zₐ and Zb, shown earlier, and Bartlett’s Bisection theorem.
  In the case of the second order network, when a2 > b (i.e. L1 > L2 or C2 > C1 or y > √3x), it is necessary to use the circuit containing mutually coupled coils for the second order all-pass network.
  A cascade of second order networks with, maybe, a single first order network, can be used to give a high order response.  For example, the article Lattice delay network gives pole-zero locations for many all-pass transfer functions which approximate to a linear phase characteristic.  That article also includes some examples.
caption: First order all-pass
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