Flexi-Circuit is a high density interconnects for microelectronic packaging. These flexi-circuits were considered revolutionary, because most technology we are commonly exposed to are considered to be "stiff" and are usually mounted on metal backings. Flexi-cricuits are used in a wide variety of applications such as data storage, printers and medical devices.
The picture below shows a flexible circuit that has been constructed through 3M’s additive technology.
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What is really surprising is how flexi-circuits are extensively used in medical industry. It is used in medical imaging devices, such as ultrasound transducers and digital X-ray sensors, allowing the devices to deliver readings with much greater sensitivity. This is definitely helpful in resolving minute anomalies that might not be detected with older technology in such devices.
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Moreover, the flex-circuits are extremely small and light. Hence, they are applicable in many appliances as it also brings about a reduction of space usage. The video below relates to the idea of how flexible technology could be applied to even more everyday appliances, such as watches or mobile phones.

DIY - Modelling a Flexi-Circuit

Here, we teach you how to possibly make a model of a single-sided flexible printed circuits yourself!

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Step 1: Get Copper-Coated Film

  • Get some thin sheets of polyimide which have copper on one or both sides.
    *Polyimide is a yellow polymer with a high melting temperature
    *A common type of copper-coated polyimide is DuPont "Pyralux" material
  • Cut the Pyralux sheets to 8.5x11 or 8.5x14 inches with scissors or a knife.
  • Avoid smudging the copper with fingerprints or oil, which can block the etch solution.
  • To protect the printer, try to keep the edges relatively flat and free of burrs.
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Step 2: Use Solid-Ink Printer

  • Locate a solid-ink printer, which prints melted wax. Wax makes a good protective layer for copper etching.
  • Unlike laser printers, solid ink printers do not rely on locally charging the paper surface, which could be troublesome when the paper is replaced by a copper sheet.
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Step 3: Print on Film

  • Draw up a design.
  • Use manual feed tray to print it on your sheet in black.
  • Printed areas will be protected with wax and wind up as copper traces on your layout.
    *Use "high resolution" or "photo" mode when printing
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Step 4: Etch It

  • Put the printed sheet in ferric chloride (copper etchant) for at least 5 minutes.
    *Keep the etchant from getting on your eyes and skin
  • Etch time depend on temperature, copper thickness and other factors - up to 25 minutes.
  • Keep watching for copper areas to dissolve and the polyimide film to show up
  • Remaining wax can be scrubbed off with ScotchBrite and warm water - this can take some effort
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Step 5: Populate The Board

  • Flexible PCB is now ready to cut apart into small circuits and solder on.
  • Can tape onto metal or fiberglass circuit board to hold it steady while working on it
  • Because it is a 1-sided PCB, without holes, it is most useful as a tiny cable or as a board for surface mount parts.

Resources obtained from: http://www.instructables.com/id/DIY-Flexible-Printed-Circuits/