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42 The PCB Design Magazine • March 2017 behavior of the nickel component in ENIG increases insertion loss. This resonance is at- tributed to the ferromagnetic properties of the nickel layer. It is therefore wise to avoid us- ing full body ENIG coating of microstrip and CPW traces at high frequencies. In fact, it may just be an odd 3 rd or 5 th harmonic, which falls on this particular lossy region, that causes ra- diation with much lower fundamental frequen- cies. Therefore, solder mask over bare copper (SMOBC) processing should be considered for all high-speed designs. In conclusion, conformal transformation is a technique that allows one to take difficult problems, map them into a coordinate system, where they are convenient to solve, and then find a relatively simple solution. Having the property to modify only the geometry of a po- lygonal structure, preserving its physical mag- nitudes, conformal mapping is an exceptional tool to solve electromagnetic problems with known boundary conditions. Points to Remember: • 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. • Space-time has three spatial dimensions plus the temporal dimension. • Kaluza adapted Einstein's General Theory of Relativity, which was formulated to the familiar four dimensions, and rewrote it to apply to five. • By adding the extra dimension, Kaluza had unified gravitation and electromagnetism. • This fifth dimension is not apparent to us at the macro scale, as it is a minuscule curling spatial dimension bound by the other larger di- mensions. It represents the varying electric and magnetic fields that radiate at right angles to the central line. • String theory seeks unification of quantum theory and general relativity by replacing par- ticles with the minute motion of strings. • Conformal mapping techniques is another approach that can be effectively used to evaluate semi-infinite conformal microstrip symmetry. • All electrical systems function based on the action of electric fields produced by charges, and magnetic fields produced by currents. • The conformal mapping or transformation of two intersecting curves from the z-plane to the w-plane, preserves the angles between every pair of curves. • The capacitance of a system of conductors remains unchanged on the transformation of the arrangement of conductors. • A conventional CPW, on a dielectric sub- strate, consists of a center strip conductor with semi-infinite ground planes on either side. • CPWs reduce radiation loss at very high microwave frequencies. • CPW impedance is determined by the ra- tio of trace width to clearance, so size reduction is possible without limit, the only penalty being higher losses. • Grounded CPW structures should have a fence of stitching vias that are placed at less than a quarter wave length apart to form a bar- rier to electromagnetic wave propagation. • The use of CPWs is also extremely useful when dealing with isolated differential pairs without a ground reference plane. MICROSTRIP COPLANAR WAVEGUIDES Figure 5: Dual coplanar strip, isolated.