Fundamentals of Antenna Bandwidth and Quality Factor

After a brief history of the development of quality factor, useful expressions are derived for the robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q_Z</i> (ω) quality factor that accurately determines the VSWR input-impedance fractional bandwidth of antennas for isolated resonances and a small enough bandwidth power drop. For closely spaced multiple resonances/antiresonances, a definitive formula is given for the increase in fractional bandwidth enabled by Bode-Fano tuning. Methods are given for determining the conventional and complexenergy quality factors of antennas from RLC circuit models. New field-based quality factors <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i>(ω) are derived for antennas with known fields produced by an input current. These <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i>(ω) are remarkably robust because they equal <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q_Z</i> (ω) when the input impedance is available. Like <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q_Z</i> (ω), the field-based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i>(ω) is independent of the choice of origin of the antenna fields and is impervious to extra lengths of transmission lines and surplus reactances. These robust field-based quality factors are used to derive new lower bounds on the quality factors (upper bounds on the bandwidths) of spherical-mode antennas that improve upon the previous Chu/CR (Collin-Rothschild) lower bounds for spherical modes. A criterion for antenna supergain is found by combining the Harrington maximum gain formula with the recently derived formula for the reactive power boundaries of antennas. Maximum gain versus minimum quality factor for spherical antennas are determined using the improved lower bounds on quality factor for different values of electrical size ka. Lastly, reduced antenna quality factors allowed by dispersive tuning overcome the traditional Chu/CR lower bounds for lower radiation efficiencies and small enough bandwidth power drops.