On the Fractional‐Order Input Impedance of Equal‐ <i>R</i> Equal‐ <i>C</i> Infinite Two‐Dimensional Ladder/Tree Networks
Bibliographic record
Abstract
ABSTRACT Many complex systems found in nature, such as lung tissues, transmission lines, and porous energy storage materials, can be modeled by fractal electrical circuit networks. In this work, we compare the input impedance of four different two‐dimensional (2‐D) infinite network topologies with different locations being considered in each network for the resistors and capacitors, leading to a number of distinct universal expressions. In particular, we consider the cases of a (i) ladder–tree, (ii) tree–ladder, (iii) ladder–ladder, and (iv) tree–tree network topologies where 1‐D ladder and/or 1‐D tree networks are used to construct the 2‐D planar structures. We only focus on symmetrical self‐similar equal‐ , equal‐ networks for simplicity, and derive the networks input impedances in normalized form. Although some topologies yield unique impedance functions not obtainable from other topologies, we find that some impedance functions are more universal in the sense that they can be obtained from multiple topologies with simple scaling of the employed and/or component values. For these specific functions, we derive closed‐form expressions for the time‐domain voltage and current resulting from a step‐current excitation or a step‐voltage excitation, respectively. Circuit simulations and experimental results are provided to validate some of our findings.
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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 | 0.002 | 0.001 |
| 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 | 0.001 | 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".