Synthesis of dual-band filters with an arbitrary load and asymmetric responses

An analytical approach for the synthesis of an asymmetric dual-band bandpass filter with a frequency-invariant arbitrary load is proposed. Based on numerical approximation technique and exchange-Remez algorithm, one can design a symmetric or asymmetric frequency response beside two passband. Different equiripple characteristic and orders can be achieved in each passband. Under the definition of power wave, the objective filter response with an arbitrary load can be converted to the measurable response and its referenced impedance is unity at the terminal. Finally, a synthesis example is presented and validated by the circuit theory.