General Synthesis Method for Dispersively Coupled Resonator Filters With Cascaded Topologies
Bibliographic record
Abstract
This article presents a new synthesis technique for circuits that may include dispersively coupled resonators and admitting an overall cascaded topology. A decomposition technique of the Darlington type is first introduced to split the original response S of the filter, taken as its scattering matrix, into m subresponses S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> ,⋯, S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> corresponding to each subblock of the cascaded circuital structure. Each individual subresponse Sk is then synthesized separately. In this article, the state space equations governing the model of dispersively coupled resonators are detailed. An extension to the case of dispersive coupling of the shortest path rule, which determines the maximum number of finite TZs realizable by a given topology, is then introduced. Congruent transformations that extend the concept of rotations or similarity transformations while preserving the filter response are exploited to reduce the individual synthesis problems to the determination of a basis of vectors verifying certain orthogonality relations. A direct synthesis technique for dispersive building blocks, such as duplets, triplets, and quadruplets, is then given in the form of an orthogonalization procedure used for the computation of the desired basis. This approach is then combined with the aforementioned decomposition technique to produce a versatile algorithm able to synthesize hybrid circuits made of cascaded subblocks of different orders and types that implement each a subset of the overall TZs by means of coupling topologies containing a mixture of dispersive and nondispersive couplings. The first synthesis example is detailed where two dispersive duplets are combined with a classical quadruplet to realize a symmetric 6-4 response. A hardware implementation of the synthesized circuit is presented in combline technology. The second example proposes a slightly more involved coupling topology able to realize 10-8 asymmetric responses by means of four cascaded basic dispersive blocks.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".