Lattice network

Key takeaways

Lattice network belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Lattice network to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Lattice network from memory before moving on to harder problems.

Reference excerpt

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" (instances of Za) and "shunt impedances" (instances of Zb) 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.

Configuration The basic configuration of the symmetrical lattice is shown in the left-hand diagram. A commonly used short-hand version is shown on the right, with dotted lines indicating the presence the second pair of matching impedances.

It is possible with this circuit to have the characteristic impedance specified independently of its transmission properties, a feature not available to ladder filter structures. In addition, it is possible to design the circuit to be a constant-resistance network for a range of circuit characteristics. The lattice structure can be converted to an unbalanced form (see below), for insertion in circuits with a ground plane. Such conversions also reduce the component count and relax component tolerances. It is possible to redraw the lattice in the Wheatstone bridge configuration (as shown in the article Zobel network). However, this is not a convenient format in which to investigate the properties of lattice filters, especially their behavior in cascade.

Basic properties

Results from image theory Filter theory was initially developed from earlier studies of transmission lines. In this theory, a filter section is specified in terms of its propagation constant and image impedance (or characteristic impedance). Specifically for the lattice, the propagation function, γ, and characteristic impedance, Zo, are defined by,

γ = ln ⁡ ( Z a Z b + 1 Z a Z b − 1 ) = 2 artanh ⁡ Z a Z b {\displaystyle \gamma =\ln \left(\ {\frac {\ {\sqrt {{\frac {\ Z_{\mathsf {a}}\ }{Z_{\mathsf {b}}}}+1\ }}\ }{\ {\sqrt {\ {\frac {\ Z_{\mathsf {a}}\ }{Z_{\mathsf {b}}}}-1\ }}\ }}\ \right)=2\ \operatorname {artanh} {\sqrt {{\frac {\ Z_{\mathsf {a}}\ }{Z_{\mathsf {b}}}}\ }}\qquad \;} and Z o = Z a ⋅ Z b {\displaystyle \;\qquad Z_{\mathsf {o}}={\sqrt {\ Z_{\mathsf {a}}\cdot Z_{\mathsf {b}}\ }}}

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Lattice network

Start with the simplest possible case. Write down what Lattice network claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Lattice network before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Lattice network ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Lattice network

In research: Lattice network appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Lattice network in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Lattice network is common in secondary-school and first-year university syllabi. It links to neighbouring topics Electronic filter topology, Image impedance filters, Linear filters, so understanding it makes those chapters shorter.
In everyday life: Look for Lattice network outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Lattice network in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Lattice network means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Lattice network out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Lattice network in simple terms?

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.

Why does Lattice network matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Lattice network?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Lattice network.