A revision of cascade synthesis theory covering cross-coupled filters

Abstract

The classical zero-shifting technique is generalized to cover extraction of complex transmission zeros (TZs) in the form of fourth-order LC sections whereby the -and -axis TZs appear as special cases. Using this approach, bandpass filters can be synthesized in direct coupled resonator forms by pole placement instead of designing them through low-pass prototypes. By using circuit transformations, the resulting direct coupled resonator filter circuits can then be transformed into a variety of cross-coupled forms like a fully cross-coupled form or cascaded -tuplet form. It is shown that one or more finite -axis, -axis, or complex TZs can be extracted as direct coupled resonator circuit blocks, which can be converted into cross-coupled triplets, quadruplets, or other -tuplets of resonators. In particular, it is shown that a cascaded quadruplet section can be used to realize a complex TZ quadruplet = , as well as two pairs of -axis TZs, = , and = .

Biobjective Hybrid Evolutionary Algorithm Applied to Resonator Filters of Arbitrary Topology

“…We used an initialization with 30 circuits having size at most of ten nodes, crossover probability of 100%, topology mutation of 20%, and parameters mutation of 5%. The performance circuit was observed at 100 frequencies Experiment 1: The first experiment is a bandpass filter in the 1800-MHz frequency range, described in [14]. The specifications are: passband edges (1703.4, 1787.3) MHz, upper stopband selectivity > 65 dB for f > 1805 MHz.…”

“…The specifications are: passband edges (1703.4, 1787.3) MHz, upper stopband selectivity > 65 dB for f > 1805 MHz. The topology obtained in [14] containing two triplet sections. Fig.…”

“…This approach provides the balance between performance and size of the solutions, and, consequently, makes it possible to naturally reduce the tendency of the process for producing larger circuits as the population evolves. Additionally, it allows the extraction of coupled resonator building-blocks, derived from the evolution process, which can be used in the next stage to produce the competitive circuits with some degrees of structural redundancy (resonator building-blocks naturally generated by the classification/ selection mechanism as triplet, quadruplet, box section etc, in conventional approach [14]. In this hybrid method, a local search process assists the Evolutionary Algorithm for fitness improvement of candidate circuits, refining their parameters in order to avoid good topologies with non-optimized parameters values to be prematurely discarded.…”

Synthesis of resonators filters with arbitrary mixed topology using hybrid method

“…Over the past few decades, plenty of efforts have been made for the direct synthesis of narrowband microwave filters [1,2,3,4,5,6]. Basically, two topological configurations, namely cross-coupled [1,2,3] and extracted-pole [4,5,6], are introduced to generate the finite transmission zeros (TZs).…”

“…Basically, two topological configurations, namely cross-coupled [1,2,3] and extracted-pole [4,5,6], are introduced to generate the finite transmission zeros (TZs). The cross-coupled topology is widely applied for its ability of realizing all kings of TZs (i.e.…”