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Coplanar waveguides play an important role in the field of solid state quantum computing, e.g. for the coupling of microwave photons to a superconducting qubit.In particular the research field of circuit quantum electrodynamics was initiated with coplanar waveguide resonators as crucial elements that allow for high field strength and thus strong coupling to a superconducting qubit by confining ...
The coplanar group members have a fairly rigid structure, with their two phenyl rings in the same plane. It renders their structure similar to polychlorinated dibenzo- p -dioxins (PCDDs) and polychlorinated dibenzofurans , and allows them to act like PCDDs, as an agonist of the aryl hydrocarbon receptor (AhR) in organisms.
Congener descriptors give a shorthand notation for geometry and substituent positions. The twelve congeners that display all four of the descriptors are referred to as being "dioxin-like", referring both to their toxicity and structural features which make them similar to 2,3,7,8-tetrachlorodibenzo-p-dioxin (2378-TCDD). [1]
Via fences are used to shield microstrip and stripline transmission lines, guard edges of printed circuit boards, shield functional circuit units from each other, and to form the walls of waveguides integrated into a planar format. Via fences are cheap and easy to implement, but use up board space and are not as effective as solid metal walls.
There are 209 PCB compounds. Analogously to PCDDs at least two lateral chlorines in each ring in positions 3,4, and/or 5 are needed for dioxin-like activity. Because the AH receptor requires a planar (flat) structure, only PCB congeners that can rotate freely along the C—C axis between the rings can attach the receptor.
Exposure to the coplanar stereoisomer 3,3',4,4',5,5'-hexabromobiphenyl (but not the non-coplanar stereoisomer) in genetically susceptible mice is known to cause immunotoxicity and disorders related to the central nervous system, and even at doses as low as 2.5 mg/kg, excess neonatal fatalities are observed (LD 50 is from 5–10 mg/kg). [1]
For example, butane has three conformers relating to its two methyl (CH 3) groups: two gauche conformers, which have the methyls ±60° apart and are enantiomeric, and an anti conformer, where the four carbon centres are coplanar and the substituents are 180° apart (refer to free energy diagram of butane).
The example begins by computing the value of log(k), then k, and goes on to use k, ε r, substrate geometry, and conductor geometry to compute the capacitances and subsequently the even and odd mode impedance and effective dielectric constant (Z oe, Z oo, ε re and ε ro).