Wideband frequency-domain characterization of FR-4 and time-domain causality

FR-4 is one of the most widely used dielectric substrates in the fabrication of printed circuits for fast digital devices. This material exhibits substantial losses and the loss tangent is practically constant over a wide band of frequencies. This paper presents measured data for the complex permittivity of this material from power frequencies up to the microwave region. In addition it gives simple closed-form expressions that approximate the measured data and provide a causal response in the time domain.