Wideband measurement of the dielectric constant of an FR4 substrate using a parallel-coupled microstrip resonator

We have made a wideband measurement of the real part of the dielectric constant of flame retardant #4 epoxy (FR4), a common high-frequency printed-circuit-board insulator. We designed a novel test circuit, an electrically long parallel-coupled microstrip resonator, which was etched on a 0.014-in FR4 substrate, manufactured by NELCO, Melville, NY. We used a computer model of the resonator to extract the dielectric constant at the frequencies of zeroes in its measured transmission response. By adjusting the model´s dielectric constant, we tuned the frequency of each zero to match the measured frequency, yielding the dielectric constant at that frequency. To validate our method and results, we present a simple, but original proof that the frequencies of zeroes in the resonator´s transmission response are insensitive to input and output mismatches. Additionally, we compare the measured and predicted response of a two-stub filter designed with our measured data. The fabricated filter´s measured return loss and insertion loss from 3 to 12 GHz are within 1% of the predictions of Agilent Technology´s Momentum.