Filters with single transmission zeros at real or imaginary frequencies
Abstract
A unified theory is presented for the synthesis of exactly equiripple lowpass prototypes having one simple pole of attenuation at a real frequency or a single pair of realaxis transmission zeros (giving linearphase performance). These types of filters may be regarded as representing the least possible degree of complication over the conventional Chebyshev filter, and are usually realized with one extra cross coupling in the structure. It is demonstrated that this gives much improved skirt selectivity in the case of a finite frequency pole, making it a viable intermediate case between the Chebyshev and ellipticfunction filters. In the case of realfrequency zeros, very flat group delay over 50 percent of the passband is achieved with minimal cost in insertion loss and skirt rejection. Approximate and exact synthesis techniques are described, including results for the previously neglected odddegree case. Experimental results demonstrate agreement with theory.
 Publication:

IEEE Transactions on Microwave Theory Techniques
 Pub Date:
 April 1976
 DOI:
 10.1109/TMTT.1976.1128811
 Bibcode:
 1976ITMTT..24..172L
 Keywords:

 Frequency Response;
 Insertion Loss;
 Low Pass Filters;
 Microwave Filters;
 Network Synthesis;
 Chebyshev Approximation;
 Cost Effectiveness;
 Elliptic Functions;
 Equivalent Circuits;
 Microwave Attenuation;
 Prototypes;
 Electronics and Electrical Engineering