Causal Models of Frequency Dependent R-cards Suitable for Time Domain Simulations

Resistive materials are often employed in antenna or absorber design for radio frequency (RF) applications. Causal material models are needed when modeling wideband RF systems using time-domain numerical models (e.g. FDTD). To this end, the frequency-dependence, from 10's of MHz to 10's of GHz, of spatially patterned and un-patterned resistive-cards (R-cards) were measured using free space and specialty materials measurements fixtures. Specifically, the complex sheet-impedance of two R-card specimens were measured at VHF frequencies using either an 8.5-inch slotted rectangular-coax (R-coax) or a recently developed resistive material mapping probe (RMMP). At GHz frequencies measurements were conducted using a standard 2' focused beam lens system. The multi-band complex-impedance data were fit using a set of causal sheet material models. Typically, the fit errors are in the 1-3% range for causal models of measured data over two-plus decades of bandwidth.