Minimum phase / all-pass decomposition of LPDA transfer functions

Characterization of Wideband Antennas for Point-to-Point Communications

“…The all-pass component does not exist in minimum phase antennas (such as horn and Vivaldi antennas) in their principal axes. The Hilbert transform provides the relationship between the real and imaginary part of a function , which is analytic in the right-hand side (RHS) of the s-plane [19]: (9) where and are the attenuation and phase of the function, respectively. The attenuation can be calculated by taking logarithms of (9), and the Hilbert transform is used to derive the phase [19]:…”

“…Recalling that the antenna S21 phase consists of three components-minimum, linear, and all-pass phases [9]-the phase of S21 with the two orientations is then analyzed from the frequency response to study the antenna's behavior.…”

“…Antennas can be categorized into minimum and nonminimum phase [9]- [11]. The phase of S21 is related to the path of energy transmission across its equivalent circuit [12].…”

“…Research shows that not all antennas provide a minimum phase. Well-known minimum-phase examples include the horn and Vivaldi designs [9]- [11], both of which are minimum phase only at their principal axes [12], [13]. To the best of the authors' knowledge, no comprehensive studies have yet been conducted to determine the transmission phase response in the performance of non-minimum phase antennas.…”

Antenna Modeling Technique for Digital Communication Systems

“…The radiation resistance is identified in the second port and the radiated power is the power dissipated in that resistance. Antennas are also categorized into minimum and non-minimum phase [3]- [5]. Minimum-phase antennas have only a single path for the energy transferred through the antenna's equivalent circuit [6].…”