diff --git a/paper/paper.tex b/paper/paper.tex index db1a6e7..19d80f5 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -102,16 +102,16 @@ air core inductors that were commonly used in old radio sets. \subsection{A Short Historical Diversion on Basket-Woven Air Coils} -Since the early days of radio engineering, the parasitic capacitance of inductors has been a point of concern. Going -back to the early days of wireless telegraphy after the turn of the twentieth century, coils with high inductance were -needed for the construction of both transmitters and receivers, but the ferrites that would later permit their compact -construction were still being developed. The ferromagnetic core material of choice back then was laminated iron, which -was only useful at low frequencies due to eddy current losses. As a result, the inductors in radio circuits of the era -were constructed as air-core coils. While air core inductors are immune to core saturation, the poor magnetic -permeability of air leads necessitates many large turns of wire for practical inductance values, which for reasons of -practicality or leakage inductance often could not be wound in a single layer. Winding an inductor with many turns on -multiple layers improves compactness and leakage inductance, but in turn gives rise to increased distributed -capacitance. +Since the early days of radio engineering, the parasitic capacitance of inductors has been a point of +concern\cite{nesperHandbuchDrahtlosenTelegraphie1921,flemingPrinciplesElectricWave1910}. Going back to the early days of +wireless telegraphy after the turn of the twentieth century, coils with high inductance were needed for the construction +of both transmitters and receivers, but the ferrites that would later permit their compact construction were still being +developed. The ferromagnetic core material of choice back then was laminated iron, which was only useful at low +frequencies due to eddy current losses. As a result, the inductors in radio circuits of the era were constructed as +air-core coils. While air core inductors are immune to core saturation, the poor magnetic permeability of air leads +necessitates many large turns of wire for practical inductance values, which for reasons of practicality or leakage +inductance often could not be wound in a single layer. Winding an inductor with many turns on multiple layers improves +compactness and leakage inductance, but in turn gives rise to increased distributed capacitance. Back then, a number of ways were devised to decrease distributed capacitance in multilayer inductors. These methods can be divided into two general categories: Optimizing the connecting order of turns to minimize the voltage differential @@ -132,11 +132,20 @@ technique was only feasible for winding by hand, and could not be executed relia \end{figure} This lack of a way to wind high frequency inductors with a machine led to the creation of a number of related winding -schemes that including honeycomb and basket woven coil. Examples of both from contemporary literature are shown in -Figure\ \ref{fig_illust_honeycomb_basket}. In a honeycomb coil, subsequent winding layers are wound at a criss-cross -pattern similar to how in sewing, a spool of thread is wound. The characteristic feature of honeycomb coils is that the -winding machine is adjusted to produce large air gaps between adjacent windings on the same layer. When multiple layers -like this are stacked, a rhomboid pattern results that is vaguely reminiscent of a honeycomb's structure. +schemes that including honeycomb and basket woven coil +\cite{eppenAnforderungenEinzelteileRundfunkempfanger1927, +filbigLehrbuchHochfrequenztechnik1942, +kleinSpulenUndSchwingungskreise1941, +meinkeTaschenbuchHochfrequenztechnik1956, +nottebrockSpulen1950, +struttVerstarkerUndEmpfanger1951, +wiggeRundfunktechnischesHandbuch1930, +zicknerSpulen1927}. +Examples of both from contemporary literature are shown in Figure\ \ref{fig_illust_honeycomb_basket}. In a honeycomb +coil, subsequent winding layers are wound at a criss-cross pattern similar to how in sewing, a spool of thread is wound. +The characteristic feature of honeycomb coils is that the winding machine is adjusted to produce large air gaps between +adjacent windings on the same layer. When multiple layers like this are stacked, a rhomboid pattern results that is +vaguely reminiscent of a honeycomb's structure. In basket-woven coils, a mandrel consisting of an odd number of sticks pointing either radially or axially is used, and the wire is fed woven between adjacent sticks in an alternating direction. While visually similar to honeycomb coils, @@ -148,7 +157,9 @@ cross. Both construction techniques apply similar principles to those leading to the improved high-frequency behavior of twisted inductors. Interestingly, both honeycomb and basket-woven coils are also governed by the same coprimality condition between the number of turns and the number of inversions within each turn that we describe for our twisted -inductors below, although in contemporary literature, this condition is never explicitly stated. +inductors below, although in contemporary literature, this condition is never explicitly stated +\cite{eppenAnforderungenEinzelteileRundfunkempfanger1927, kleinSpulenUndSchwingungskreise1941, +wiggeRundfunktechnischesHandbuch1930}. \subsection{Twisted Inductors in RFIC Design}