The theoretical limit for small antenna performance that was derived decades ago by Wheeler and Chu governs design tradeoffs for size, bandwidth, and efficiency. Theoretical guidelines have also been derived for other details of small antenna design such as permittivity, aspect ratio, and even the nature of the internal structure of the antenna. In this paper, we extract and analyze experimental performance data from a large body of published designs to establish several facts that have not previously been demonstrated: (1) The theoretical performance limit for size, bandwidth, and efficiency are validated by all available experimental evidence. (2) Although derived for electrically small antennas, the same theoretical limit is also generally a good design rule for antennas that are not electrically small. (3) The theoretical predictions for the performance due to design factors such as permittivity, aspect ratio, and the internal structure of the antenna are also supported by the experimental evidence. The designs that have the highest performance are those that involve the lowest permittivity, have an aspect ratio close to unity, and for which the fields fill the minimum size enclosing sphere with the greatest uniformity. This work thus validates the established theoretical design guidelines.

Experimental Validation of Performance Limits and Design Guidelines for Small Antennas

The high Q-factor (low bandwidth) and low efficiency make the design of small antennas challenging. Here, convex optimization is used to determine current distributions that provide upper bounds on the antenna performance. Optimization formulations for maximal gain Q-factor quotient, minimal Q-factor for superdirectivity, and minimum Q for given far-fields are presented. The effects of antennas embedded in structures are also discussed. The results are illustrated for planar geometries.

Optimal Antenna Currents for Q, Superdirectivity, and Radiation Patterns Using Convex Optimization

Electrically small electric and magnetic dipole antennas are introduced that are based on electric and magnetic near-field resonant parasitic (NFRP) elements that are electrically coupled to the driven element. By properly combining these two NFRP antenna types, electrically small Huygens sources are realized. The proposed Huygens sources have one feed point, are well matched to 50 Ω, and have high radiation efficiencies. Their predicted directivity patterns approach the known Huygens source theoretical limit.

Metamaterial-Inspired, Electrically Small Huygens Sources

General expressions are obtained for the lower bounds on the quality factor (Q) of electrically small electric- and magnetic-dipole antennas confined to an arbitrarily shaped volume V and excited by general sources or by global electric-current sources alone. The lower-bound expressions depend only on the direction of the dipole moment with respect to V , the electrical size of V , and the static electric and magnetic polarizabilities per unit volume of hypothetical perfectly electrically conducting and perfectly magnetically conducting volumes V . The lower bounds are obtained directly from the electromagnetic field expressions for Q with the help of current equivalence principles and the uncoupling of Maxwell's equations for electrically small volumes into quasi-electrostatic and quasi-magnetostatic fields.

Lower Bounds on the Q of Electrically Small Dipole Antennas

Three novel electrically small antenna configurations radiating a TE10 spherical mode corresponding to a magnetic dipole are presented and investigated: multiarm spherical helix (MSH) antenna, spherical split ring resonator (S-SRR) antenna, and spherical split ring (SSR) antenna. All three antennas are self-resonant, with the input resistance tuned to 50 ohms by an excitation curved dipole/monopole. A prototype of the SSR antenna has been fabricated and measured, yielding results that are consistent with the numerical simulations. Radiation quality factors (Q) of these electrically small antennas (in all cases ka <; 0.26) approach the limit of 3.0 times the Chu lower bound for a given antenna size, which is in line with a theoretical prediction made by Wheeler in 1958.

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Low-Q Electrically Small Spherical Magnetic Dipole Antennas

We examine the behavior of a matched electrically small antenna that exhibits two impedance resonances within its defined voltage standing wave ratio (VSWR) bandwidth. The exact quality factor (Q), computed indirectly from the antenna's input reactance and far field, is compared to twice the inverse of the matched half-power VSWR bandwidth (Q BW) and to an approximate quality factor (Qz) determined from the frequency derivative of the antenna's input impedance. The well-established approximate equalities Q ap Q BW ap Q z for antennas exhibiting an isolated single impedance resonance within their operating band are shown to become highly inaccurate for an electrically small antenna exhibiting two closely spaced impedance resonances.

Limitations in Relating Quality Factor to Bandwidth in a Double Resonance Small Antenna

Electrically small antennas can be made to exhibit omnidirectional, dipole-like radiation patterns when operating in the transverse magnetic (electric dipole) mode, the transverse electric (magnetic dipole) mode or some combination of transverse magnetic (TM) and transverse electric (TE) mode radiation. When designing electrically small antennas whose performance properties closely approach theoretical limits, engineers generally focus on the design of electric dipoles or TM mode radiators. These radiators can be designed to exhibit low voltage standing wave ratio (VSWR), high radiation efficiency, and a low quality factor. TM mode radiators also have the advantage of a straightforward transition from the dipole to the monopole configuration for use over metallic ground planes or surfaces. Following our previous work in the design of small electric dipoles, we present the design of a new, electrically small magnetic dipole or TE mode radiator. This new design is shown to exhibit low VSWR, high radiation efficiency, and a low quality factor. We show that the quality factor of the magnetic dipole radiator approaches the lower bound (the Chu-limit) to within a ratio consistent with recent limits presented by Thal.

A Low Q Electrically Small Magnetic (TE Mode) Dipole

With proper adjustment of the amplitude and phase of the element excitations, the directivity of an N-element end-fire array of isotropic radiators can approach N2 as the spacing between the elements approaches zero. To achieve this end-fire superdirectivity for a 2-element array, the excitation phase difference between the elements must closely approach 180deg. When closely spaced elements are driven nearly 180deg out-of-phase, the element radiation resistances approach zero, resulting in a high input Voltage Standing Wave Ratio (VSWR) and reduced radiation efficiency. At the same time, there is also a significant decrease in the operating bandwidth. In this letter we present the design of a 2-element, superdirective multiple arm folded monopole array that achieves a near 50 Omega input radiation resistance at each element, resulting in a matched input VSWR, higher radiation efficiency and therefore, a substantial increase in realized or overall efficiency.

An Impedance-Matched 2-Element Superdirective Array

In discussions of antenna noise figure, the effect of antenna impedance mismatch is often neglected or not correctly accounted for. Antenna impedance mismatch can degrade signal-to-noise ratio, even with a lossless antenna, particularly when the received signal and/or the received external noise powers approach the receiver's noise floor. This letter presents a formula for the realized noise figure of the general receiving antenna expressed as a function of the antenna's radiation efficiency and impedance mismatch loss. This realized noise figure is defined for the situations where the antenna is connected to a receiving system at a noise temperature of T0 as well as a general noise temperature Tr. This formula for realized antenna noise figure allows the antenna engineer to understand how the antenna design, particularly the tradeoffs between impedance matching and radiation efficiency, affect the signal-to-noise ratio performance in the general receiving system.

Realized Noise Figure of the General Receiving Antenna

An electrically small supergain endfire transmitting and receiving array antenna comprising at least one first resonant element with a first input terminal. The first resonant element driven by a power supply voltage supplied at the first input terminal. The electrically small supergain endfire transmitting and receiving array antenna further includes at least one second resonant parasitic element with a second input terminal. The second input terminal shorted and the second resonant element spaced less than about 0.25λ from the first resonant element at any corresponding point. The antenna has a gain of at least 6 db and ka<1.0.

S.R. Best

Papers

Limitations in Relating Quality Factor to Bandwidth in a Double Resonance Small Antenna

A Low Q Electrically Small Magnetic (TE Mode) Dipole

An Impedance-Matched 2-Element Superdirective Array

Realized Noise Figure of the General Receiving Antenna

Electrically small supergain endfire array antenna