An Empirical Expression to Predict the Resonant Frequencies of Archimedean Spirals

Hooker, Jerris W.; Ramaswamy, V.; Arora, Rishabh; Edison, Arthur S.; Withers, R.S.; Nast, Robert E.; Brey, Wallace S.

doi:10.1109/tmtt.2015.2434814

Cited by 15 publications

(10 citation statements)

References 18 publications

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“…A similar approach to that used in [9] for freestanding spirals, was applied here to model the effect of thin substrates on planar Archimedean spirals. The resonances of a collection of spirals on substrates of varying thicknesses and dielectric constants were simulated.…”

Section: Observationsmentioning

confidence: 99%

“…In an earlier study, the effect of geometric parameters on the resonance frequencies of spiral resonators was investigated by simulating a large collection of freestanding Archimedean spirals and analyzing the results [9]. In [9] and in this paper, several parameters are used in the description of these spirals and are defined in Table I.…”

Section: Introductionmentioning

confidence: 99%

“…In [9] and in this paper, several parameters are used in the description of these spirals and are defined in Table I. The independent parameters defining an Archimedean spiral are annotated in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…1. In [9] it was shown that the resonance mode frequencies of the spirals are a linear function of the mode number. Further it was shown that the y-intercept of that function does not in general fall on the origin.…”

Section: Introductionmentioning

confidence: 99%

“…The observed values for D in freestanding Archimedean spirals range from −0.6 to −0.2. In [9] an empirical expression (1) was given to express D in terms of the spiral's parameters.

D = - true((0.29 + 0.043 F) true(\frac{r_{i}}{r_{o}} true) + 0.22 true) true((F - 0.5) true(2.65 true(\frac{P}{r_{o}} true) + 0.03 true) + 1 true)

Further, D was used within the empirical formula (2), developed to calculate the fundamental and higher order resonance frequencies of freestanding spirals.…”

Section: Introductionmentioning

confidence: 99%

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Effects of Dielectric Substrates and Ground Planes on Resonance Frequency of Archimedean Spirals

Hooker

Ramaswamy

Arora

et al. 2016

IEEE Trans. Appl. Supercond.

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Superconducting self-resonant spiral structures are of current interest for applications both in metamaterials and as probe coils for nuclear magnetic resonance (NMR) spectroscopy for high-sensitivity chemical analysis. Accurate spiral models are available in the literature for behavior of a spiral below and up to self-resonance. However, knowledge of the higher modes is also important. We present the relationships between the spiral parameters and the multiple mode frequencies of single sided spirals on dielectric substrates as modeled by method of moments simulation. In the absence of a ground plane, we find that the mode frequency has a linear though not necessarily harmonic dependence on the mode number. The effect of a thick substrate can be approximated by an effective dielectric constant. But when the thickness is less than 20% of the spiral trace width (router – rinner) this approximation is no longer accurate. We have developed a simple empirical formula to predict the higher modes.

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Section: Observationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The observed values for D in freestanding Archimedean spirals range from −0.6 to −0.2. In [9] an empirical expression (1) was given to express D in terms of the spiral's parameters.

D = - true((0.29 + 0.043 F) true(\frac{r_{i}}{r_{o}} true) + 0.22 true) true((F - 0.5) true(2.65 true(\frac{P}{r_{o}} true) + 0.03 true) + 1 true)

Further, D was used within the empirical formula (2), developed to calculate the fundamental and higher order resonance frequencies of freestanding spirals.…”