Add citations to woven coil related work
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@ -102,16 +102,16 @@ air core inductors that were commonly used in old radio sets.
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\subsection{A Short Historical Diversion on Basket-Woven Air Coils}
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Since the early days of radio engineering, the parasitic capacitance of inductors has been a point of concern. Going
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back to the early days of wireless telegraphy after the turn of the twentieth century, coils with high inductance were
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needed for the construction of both transmitters and receivers, but the ferrites that would later permit their compact
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construction were still being developed. The ferromagnetic core material of choice back then was laminated iron, which
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was only useful at low frequencies due to eddy current losses. As a result, the inductors in radio circuits of the era
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were constructed as air-core coils. While air core inductors are immune to core saturation, the poor magnetic
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permeability of air leads necessitates many large turns of wire for practical inductance values, which for reasons of
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practicality or leakage inductance often could not be wound in a single layer. Winding an inductor with many turns on
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multiple layers improves compactness and leakage inductance, but in turn gives rise to increased distributed
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capacitance.
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Since the early days of radio engineering, the parasitic capacitance of inductors has been a point of
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concern\cite{nesperHandbuchDrahtlosenTelegraphie1921,flemingPrinciplesElectricWave1910}. Going back to the early days of
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wireless telegraphy after the turn of the twentieth century, coils with high inductance were needed for the construction
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of both transmitters and receivers, but the ferrites that would later permit their compact construction were still being
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developed. The ferromagnetic core material of choice back then was laminated iron, which was only useful at low
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frequencies due to eddy current losses. As a result, the inductors in radio circuits of the era were constructed as
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air-core coils. While air core inductors are immune to core saturation, the poor magnetic permeability of air leads
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necessitates many large turns of wire for practical inductance values, which for reasons of practicality or leakage
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inductance often could not be wound in a single layer. Winding an inductor with many turns on multiple layers improves
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compactness and leakage inductance, but in turn gives rise to increased distributed capacitance.
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Back then, a number of ways were devised to decrease distributed capacitance in multilayer inductors. These methods can
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be divided into two general categories: Optimizing the connecting order of turns to minimize the voltage differential
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@ -132,11 +132,20 @@ technique was only feasible for winding by hand, and could not be executed relia
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\end{figure}
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This lack of a way to wind high frequency inductors with a machine led to the creation of a number of related winding
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schemes that including honeycomb and basket woven coil. Examples of both from contemporary literature are shown in
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Figure\ \ref{fig_illust_honeycomb_basket}. In a honeycomb coil, subsequent winding layers are wound at a criss-cross
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pattern similar to how in sewing, a spool of thread is wound. The characteristic feature of honeycomb coils is that the
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winding machine is adjusted to produce large air gaps between adjacent windings on the same layer. When multiple layers
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like this are stacked, a rhomboid pattern results that is vaguely reminiscent of a honeycomb's structure.
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schemes that including honeycomb and basket woven coil
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\cite{eppenAnforderungenEinzelteileRundfunkempfanger1927,
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filbigLehrbuchHochfrequenztechnik1942,
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kleinSpulenUndSchwingungskreise1941,
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meinkeTaschenbuchHochfrequenztechnik1956,
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nottebrockSpulen1950,
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struttVerstarkerUndEmpfanger1951,
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wiggeRundfunktechnischesHandbuch1930,
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zicknerSpulen1927}.
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Examples of both from contemporary literature are shown in Figure\ \ref{fig_illust_honeycomb_basket}. In a honeycomb
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coil, subsequent winding layers are wound at a criss-cross pattern similar to how in sewing, a spool of thread is wound.
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The characteristic feature of honeycomb coils is that the winding machine is adjusted to produce large air gaps between
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adjacent windings on the same layer. When multiple layers like this are stacked, a rhomboid pattern results that is
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vaguely reminiscent of a honeycomb's structure.
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In basket-woven coils, a mandrel consisting of an odd number of sticks pointing either radially or axially is used, and
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the wire is fed woven between adjacent sticks in an alternating direction. While visually similar to honeycomb coils,
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@ -148,7 +157,9 @@ cross.
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Both construction techniques apply similar principles to those leading to the improved high-frequency behavior of
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twisted inductors. Interestingly, both honeycomb and basket-woven coils are also governed by the same coprimality
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condition between the number of turns and the number of inversions within each turn that we describe for our twisted
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inductors below, although in contemporary literature, this condition is never explicitly stated.
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inductors below, although in contemporary literature, this condition is never explicitly stated
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\cite{eppenAnforderungenEinzelteileRundfunkempfanger1927, kleinSpulenUndSchwingungskreise1941,
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wiggeRundfunktechnischesHandbuch1930}.
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\subsection{Twisted Inductors in RFIC Design}
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