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Solving Planarity Problems in PCB Design: Ensuring No Wire Crossings

As an electronic engineer designing printed circuit boards (PCBs), you may encounter the challenge of wire crossings in your circuit layout. This case study explores the concept of planarity in graph theory, where we aim to determine if it is possible to redraw a graph without any edges crossing. Understanding planarity is crucial in various applications, including utility companies laying pipes. Over the upcoming lessons, we will delve into methods to effectively address these types of design challenges.

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Solving Planarity Problems in PCB Design: Ensuring No Wire Crossings

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  1. Operational Research (O.R.) case studies

  2. What’s the problem? www.LearnAboutOR.com

  3. You are an electronic engineer… www.LearnAboutOR.com

  4. You are designing a Printed Circuit Board (PCB) PCBs are used in electronics to connect electrical components using conductive pathways Since the wires are not insulated, they must not cross www.LearnAboutOR.com

  5. You have designed the circuit that you want, but some of the wires cross www.LearnAboutOR.com

  6. Is it possible to redraw your circuit in such a way thatno wires cross? www.LearnAboutOR.com

  7. Let’s summarise the problem We have a graph with some edges which cross We want to know if it is possible to re-draw it in such a way that none of the edges cross www.LearnAboutOR.com

  8. This is an example of aPlanarity Problem www.LearnAboutOR.com

  9. Planarity Problems A graph is planar if it can be drawn • in a plane • so that no two edges meet (except at a vertex to which they are both incident) www.LearnAboutOR.com

  10. Another example where this is used Utilities (gas, water, electricity) companies trying to lay pipes that do not cross each other… www.LearnAboutOR.com

  11. What next? Over the next few lessons, we will look at ways of approaching problems of this type… www.LearnAboutOR.com

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