Frequency-dependent admittance (J-) inverter is incorporated in synthesis of microstrip trisection filters to achieve a quasi-elliptic function response. In the admittance matrix of the lowpass prototype, certain coupling is modeled by a constant J-inverter multiplied by the complex frequency variable s. Direct synthesis of three lowpass prototypes is presented. Based on the standard lowpass to bandpass transformation, coupled microstrip resonators with both electric and magnetic coupling are devised to implement the J-inverter with desired frequency-dependent characteristics. Tapped-line input/output is used and several transmission zeros can be created in the upper and lower rejection bands. In experiments, a third-order filter with four zeros, a fourth-order circuit with three zeros, and a fourth-order filter with five zeros are designed and fabricated. Measured results are compared with the simulation responses to validate the theory.
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