Substrate Integrated Waveguide Filter With Flat Passband Based on Complex Couplings

A lossy filter with flat passband and asymmetric response is proposed by using complex couplings. The complex coupling coefficients with positive and negative imaginary parts are realized with transmission lines loaded with series and shunt resistors, respectively. Design formulas are derived for the critical parameters. A filter prototype is developed at 4.97 GHz and substrate integrated waveguide resonators with unloaded Q-factor of 450 are used. One transmission zero is located in its upper stopband. The 0.2-dB bandwidth of 279 MHz is achieved and the equivalent Q -factor is about 1900. Good agreement is obtained among the synthesized, simulated, and measured results.