Teaching Beyond Directivity and Gain: Unraveling Metallic Loss Dynamics and Spectral Derivatives of Electrically-small All-metal Antennas for RF to THz

Classical antenna design and teaching prioritize metrics like gain and directivity, often relegating detailed analysis of conductor loss to a secondary role. This oversight creates a knowledge gap regarding the hidden variables of metallic dissipation, especially their behavior across multi-decade bandwidths. This work bridges that gap by constructing a complete simulation matrix benchmarking the Vertical Monopole (VM) against the Circular Disk Monopole (CDM) from 1 kHz to 200 GHz. The investigation rigorously characterizes not only absolute metallic loss but also its frequency derivatives, which describe how loss evolves across the spectrum. The comprehensive simulation matrix, benchmarked across 23 resonant frequencies from 1 kHz to 200 GHz, provides a detailed, first-principles characterization of metallic loss dynamics in two canonical all-metal monopoles. The results, encapsulated in the novel metrics of Gain Degradation due to Metallic Dissipation (GDMD) and its spectral and geometric derivatives, reveal profound implications for antenna design, education, scaling laws, and practical implementation in next-generation systems.