Synthesis of 4th order lossy filters with uniform Q distribution

This paper outlines the synthesis procedure for obtaining the folded coupling matrix of lossy filters of 4th order with uniform Q distribution. The method is applied to Butterworth, Chebyshev and Chebyshev with a single pair of symmetrical transmission zeros responses. Closed-form expressions to relate a prescribed insertion loss and filter bandwidth with the required resonator quality factor for an infinite Q flatness filter responses have been obtained. Experimental results on a Chebyschev microstrip filter coincide with the theoretical predictions.