Antenna Theory for Psionic Devices

Antenna Theory for Psionic Devices

Audience

Difficulty	Intermediate

Notation on this page

Device at a glance

Antenna theory for psionic devices adapts classical antenna engineering — Chu-Harrington bounds, Wheeler radiation resistance, near-field coupling — to the specific demands of HelmKit-class wearable systems. These devices operate at the boundary of electrically small (D ≪ λ) and resonant, in the reactive near-field, with biological matter (the brain) only centimetres away.

This page collects the engineering-relevant equations and bounds.

Electrically-small regime

An antenna is electrically small when its largest dimension D is much less than the wavelength λ. For 5 cm coils at 2.45 GHz (λ = 12.24 cm), the ratio D/λ ≈ 0.4 — at the boundary of electrically small.

In this regime, antennas exhibit:

• Reactive near-field dominance (see Reactive_Near_Field).
• Low radiation resistance — most input power is reactive, not radiated.
• High Q (narrow bandwidth) — fundamental Chu-Harrington bound.
• Strong sensitivity to detuning by nearby matter (the wearer).

Chu-Harrington bound

The fundamental limit on the radiation Q of an electrically small antenna (Chu 1948; Harrington 1960):

 Qmin = 1/(ka)3 + 1/(ka)

— with k = 2π/λ the wavenumber and a the radius of the smallest sphere enclosing the antenna. This is the minimum Q achievable; real antennas have Q ≥ Q_min.

The bandwidth is bandwidth ~ f / Q.

Worked example: 5 cm coil at 2.45 GHz

• a = 2.5 cm, k = 2π/0.1224 = 51.3 /m → ka = 51.3 × 0.025 = 1.28.
• Q_min = 1/1.28³ + 1/1.28 = 0.477 + 0.781 ≈ 1.26.
• Bandwidth Δf = f/Q ≈ 2.45 GHz / 1.26 ≈ 1.94 GHz — broad.

For ka = 1.28, the antenna is just barely electrically small. Bandwidth is workable.

Worked example: 1 cm coil at 2.45 GHz

• a = 0.5 cm → ka = 0.26.
• Q_min = 1/0.26³ + 1/0.26 ≈ 60.0 + 3.85 ≈ 63.8.
• Bandwidth ≈ 38 MHz — moderate.

Worked example: 5 cm coil at 300 MHz

• λ = 1 m, ka = 2π · 0.025 / 1 ≈ 0.157.
• Q_min ≈ 1/0.157³ + 1/0.157 ≈ 258 + 6.4 ≈ 264.
• Bandwidth ≈ 1.1 MHz — narrow.

At 300 MHz, a 5 cm coil is deeply sub-wavelength — high Q, large stored-energy ratio, narrow bandwidth. This is the preferred regime for high near-field efficiency.

Wheeler radiation resistance

For an electrically small loop antenna of circumference $ C $:

$ R_{\text{rad}}=20\pi ^{2}\,(C/\lambda )^{4}\quad [\Omega ] $

The $ (C/\lambda )^{4} $ scaling is characteristic of magnetic dipole radiation. $ R_{\text{rad}} $ sets the antenna's radiative efficiency relative to its ohmic loss resistance $ R_{\text{loss}} $:

$ \eta ={\frac {R_{\text{rad}}}{R_{\text{rad}}+R_{\text{loss}}}} $

For a 5 cm coil at 2.45 GHz ($ C\approx 15 $ cm, $ \lambda =12.24 $ cm):

$ R_{\text{rad}}=20\pi ^{2}\cdot 1.22^{4}\approx 437\ \Omega $

— a substantial radiation resistance. For the same coil at 300 MHz ($ C/\lambda =0.15 $):

$ R_{\text{rad}}=20\pi ^{2}\cdot 0.15^{4}\approx 0.1\ \Omega $

— small, and likely dominated by R_loss. At lower frequencies, the coil becomes a near-perfect near-field source (almost all stored energy, almost no radiation).

Impedance matching

For an electrically small antenna to absorb input power, its driving-point impedance must be matched to the source impedance (typically 50 Ω). Practical techniques:

• Series tuning capacitor — cancels the inductive reactance.
• L-network (series-L + shunt-C or shunt-L + series-C).
• Transformer coupling — for impedance step-up.
• Distributed matching (stubs, microstrip) — for narrow-band high-precision matching.

Matched, an electrically small antenna can absorb essentially all the input power. Unmatched, most is reflected back to the source.

Detuning by the wearer

A critical effect for wearable psionic devices: the wearer's body changes the antenna's impedance. The brain is a high-permittivity, conductive medium and acts as a strong dielectric load. Practical consequences:

• Resonance frequency shifts downward by 5-20% when the device is placed on a head vs. in free space.
• Q-factor drops due to ohmic loading by tissue.
• Matching network must compensate for body presence.

Solutions: adaptive matching networks, in-situ calibration, body-proximity sensing.

Helical-antenna design

For higher-radiation applications (longer-range devices, not HelmKit), helical antennas provide circular polarisation and broad beam. See Double-Helix_Antenna for the helical mode with circular polarisation (Kraus 1947).

Caduceus and bifilar geometries

For HelmKit's near-field-only requirement, caduceus coils and bifilar coils are preferred because they:

• Suppress far-field radiation by having opposite-current crossings or opposing windings (net dipole moment ≈ 0).
• Maintain strong near-field due to the local field of each winding being large.
• Provide non-trivial field structure (e.g. axial scalar/longitudinal components at crossings).

These geometries are non-standard in conventional antenna engineering but are described historically in Tesla and Bedini work (and modern reactive-resonator literature).

Sanity checks

• ka → 0 (deeply electrically small) → Q_min → ∞; antenna becomes pure near-field source. ✓
• ka → 1 (resonant size) → Q_min ~ 2; antenna is a good radiator. ✓
• ψ → 0 (in framework) → standard antenna theory; no ψ-coupling enhancement. ✓ (Sanity_Check_Limits §6.)

See Also

• Near_Field_Electromagnetics
• Reactive_Near_Field
• Caduceus_Coil
• Bifilar_Coil
• Double-Helix_Antenna
• Psionic_Device_Overview

References

• Chu, L. J. (1948). "Physical limitations of omni-directional antennas." Journal of Applied Physics 19: 1163.
• Harrington, R. F. (1960). "Effect of antenna size on gain, bandwidth, and efficiency." Journal of Research of the National Bureau of Standards 64D: 1–12.
• Wheeler, H. A. (1947). "Fundamental limitations of small antennas." Proceedings of the IRE 35: 1479–1484.
• Balanis, C. A. (2016). Antenna Theory: Analysis and Design. 4th ed., Wiley.
• Kraus, J. D. (1988). Antennas. 2nd ed., McGraw-Hill.