To address the need for fundamental universally valid definitions of exact bandwidth and quality factor (Q) of tuned antennas, as well as the need for efficient accurate approximate formulas for computing this bandwidth and Q, exact and approximate expressions are found for the bandwidth and Q of a general single-feed (one-port) lossy or lossless linear antenna tuned to resonance or antiresonance. The approximate expression derived for the exact bandwidth of a tuned antenna differs from previous approximate expressions in that it is inversely proportional to the magnitude |Z'/sub 0/(/spl omega//sub 0/)| of the frequency derivative of the input impedance and, for not too large a bandwidth, it is nearly equal to the exact bandwidth of the tuned antenna at every frequency /spl omega//sub 0/, that is, throughout antiresonant as well as resonant frequency bands. It is also shown that an appropriately defined exact Q of a tuned lossy or lossless antenna is approximately proportional to |Z'/sub 0/(/spl omega//sub 0/)| and thus this Q is approximately inversely proportional to the bandwidth (for not too large a bandwidth) of a simply tuned antenna at all frequencies. The exact Q of a tuned antenna is defined in terms of average internal energies that emerge naturally from Maxwell's equations applied to the tuned antenna. These internal energies, which are similar but not identical to previously defined quality-factor energies, and the associated Q are proven to increase without bound as the size of an antenna is decreased. Numerical solutions to thin straight-wire and wire-loop lossy and lossless antennas, as well as to a Yagi antenna and a straight-wire antenna embedded in a lossy dispersive dielectric, confirm the accuracy of the approximate expressions and the inverse relationship between the defined bandwidth and the defined Q over frequency ranges that cover several resonant and antiresonant frequency bands.

Impedance, bandwidth, and Q of antennas

Electrically-small antennas present high-Q impedances characterized by large reactances and small radiation resistances. For such antennas, the effectiveness of passive matching is severely limited by gain-bandwidth theory, which predicts narrow bandwidths and/or poor gain. With receivers, the inability to resolve this impedance mismatch results in poor signal-to-noise (S/N) ratio, as compared to using a full-size antenna. With transmitters, the consequence is poor power efficiency. However, in many applications full-size antennas are impractical, and a means is required to effectively match their electrically-small counterparts. This paper presents the technique of non-Foster impedance matching, which employs active networks of negative inductors and capacitors to bypass the restrictions of gain-bandwidth theory. We first review the origins and development of non-Foster impedance matching, and then present experimental results for the non-Foster impedance matching of electrically-small dipoles and monopoles. For receivers, our best measurements on the antenna range demonstrate up to 20 dB improvement in S/N over 20-120 MHz; for transmitters, we show a power efficiency improvement which exceeds a factor of two over an 5% bandwidth about 20 MHz with an average signal power of 1 W to the radiation resistance.

Non-Foster Impedance Matching of Electrically-Small Antennas

The purpose of this paper is twofold: (1) to derive an approximate expression for the bandwidth of a tuned antenna in terms of its input impedance that holds at every frequency, i.e., throughout its entire antiresonant and resonant frequency ranges; (2) to relate this expression for bandwidth to the antenna quality factor Q. The approximate expression for the bandwidth and its relationship to Q are both more generally applicable and more accurate than previous formulas. The validity and accuracy of the expressions are confirmed by the numerical solutions to straight-wire and wire-loop, lossy and lossless tuned antennas over a wide enough range of frequencies covering several resonant and antiresonant frequency bands. We show that the matched VSWR bandwidth is a more fundamental measure of bandwidth than conductance bandwidth because it exists in general for all frequencies at which an antenna is tuned. We also find that the Foster reactance theorem does not hold at all frequencies (whether or not the antenna is lossless). Although the general formula we derive for the bandwidth of an antenna involves the frequency derivative of resistance as well as the frequency derivative of reactance, quite remarkably, the half-power matched VSWR bandwidth of a general tuned lossy or lossless antenna is proven to approximately equal to 2/Q for all frequencies if Q/spl gsim/4.

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

A method is presented to calculate the quality factor (Q) of small antennas, which is based on the understanding that for a small antenna the total energy in Poynting theorem can be easily separated into the stored energy and radiated energy by using the low frequency expansions. The Poynting theorem in frequency domain provides an equation on the stored electric and magnetic energy while the Poynting theorem in time domain can be used as another independent equation for the stored electric and magnetic energy. By solving these equations the stored electric and magnetic energy can be obtained, thus, making the Q calculation possible.

A method for the evaluation of small antenna Q

The calculation of antenna Q has been an interesting and a controversial topic for years. We first give a rigorous study of antenna Q by introducing a complete description of the complex power balance relation for an antenna system. Using the complex Poynting theorem, we have shown that the antenna is essentially equivalent to a one port lossy network. The Foster reactance theorem is usually stated for a lossless network. The main purpose of this paper is to determine whether the Foster reactance theorem holds for antennas. By making use of a complex frequency domain version of the Poynting theorem, we have shown that the Foster reactance theorem is valid for an antenna. Finally, the Foster reactance theorem for the antenna has been applied to demonstrate the widely held assumption Q/spl ap/1/B, provided Q/spl Gt/1, where B stands for the fractional bandwidth of an arbitrary antenna.

P. Jarmuszewski

Papers

The Foster reactance theorem for antennas and radiation Q