Passband Flatness Optimization of Low-Q Filters via Direct Lossy Coupling Matrix Synthesis

This paper presents a passband flatness optimization framework for low quality factor (Q) filters using lossy coupling matrix (CM) synthesis. A lossy CM synthesis method is first proposed in the complex-frequency domain, accurately producing an initial CM that captures passband degradation caused by finite resonant Q, providing an effective starting point for passband flatness optimization. A simple gradient-based algorithm is then applied to enhance passband flatness and obtain a lossy CM with a flattened response. The approach is validated through synthesis and experimental results on two sixth-order microstrip open-loop resonator filters with different Q. The proposed technique offers significant advantages for designing highly flat filters with low-Q resonator.