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36 The PCB Design Magazine • March 2017 The classic coplanar waveguide (CPW) is formed by a microstrip conductor strip sepa- rated from a pair of ground planes pours, all on the same layer, affixed to a dielectric medium. In the ideal case, the thickness of the dielectric is infinite. But in practice, it is thick enough so that electromagnetic fields die out before they get out of the substrate. A variant of the copla- nar waveguide is formed when a ground refer- ence plane is provided on the opposite side of the dielectric. This is referred to a conductor- backed or grounded CPW. CPWs have been used for many years in RF and microwave design as they reduce radiation loss, at extremely high frequencies, compared to traditional microstrip. And now, as edge rates continue to rise, they are coming back into vogue. In this month's col- umn, I will look at how conformal field theory can be used to model the electromagnetic ef- fects of microstrip coplanar waveguides. Simplistically, space has three dimensions. Picturing a box, we observe the three dimen- sions of width, height and depth (x,y,z). But, there is an obvious fourth dimension–time. The box will only exist for a certain period of time. These three spatial dimensions plus the tempo- ral dimension are referred to as space-time. But in the intricate world of quantum physics, there can be as many as 26 dimensions used to model the complexities of quantum fields. In 1921, Theodor Kaluza, a mathematician, proposed that our intuition has misled us and suggested that space-time actually has five di- mensions. Kaluza adapted Einstein's General by Barry Olney IN-CIRCUIT DESIGN PTY LTD / AUSTRALIA Microstrip Coplanar Waveguides BEYOND DESIGN Figure 1: A Higgs boson quantum fireworks display (source: CERN).