How do I design a cavity backed spiral antenna for wideband direction finding?

Designing a cavity backed spiral antenna for wideband direction finding creates a unidirectional, circularly polarized antenna with multi-octave bandwidth, ideal for ESM/ELINT direction finding (DF) receivers. The antenna consists of a planar spiral element (Archimedean or equiangular) mounted above a metallic cavity that acts as a reflector, directing all radiation forward (eliminating the back lobe of a free-standing spiral). The design parameters are: spiral type (Archimedean: constant growth rate, easier to design and fabricate; equiangular (log-spiral): frequency-independent pattern and impedance, wider bandwidth. Both types provide circular polarization), outer diameter (determines the low-frequency cutoff: f_low = c/(pi × D_outer); for D=150 mm: f_low approximately 640 MHz), inner radius (determines the high-frequency cutoff: f_high = c/(pi × D_inner); for D_inner=5 mm: f_high approximately 19 GHz), number of turns (more turns = smoother pattern and better low-frequency performance, but: the current must decay before reaching the outer edge to avoid reflections and pattern distortion; use resistive loading at the outer arms if needed), cavity depth (the cavity depth affects the bandwidth and pattern: a quarter-wave cavity (depth = lambda/4 at the center frequency) provides maximum gain but limits the bandwidth; a shallow cavity with absorber loading (depth = lambda/8 or less) provides wider bandwidth but lower gain; absorber-loaded cavities achieve 10:1+ bandwidth), and feed (a wideband balun at the center of the spiral transforms the balanced spiral feed point to the unbalanced 50-ohm coaxial connector; the balun is critical for maintaining impedance match and pattern symmetry over the bandwidth).