Transmission-line directional couplers for impedance transforming

Normalized scattering parameters of a two-port circuit terminated in arbitrary impedances are derived and design equations of directional couplers for impedance transforming are derived. To verify the design equations, a microstrip directional coupler is designed at a center frequency of 2 GHz, fabricated on a substrate (epsilon(r) = 3.5, H = 30 mil, tan delta = 0.04) and measured. The measured performance shows good agreement with the simulated one.