State variable harmonic balance analysis of nonlinear circuits based on waves
Bibliographic record
Abstract
Circuit simulation involving nonlinear elements can be a challenging task. From these challenges rises a demand for finding better and more efficient ways of solving such problems. This work provides a novel approach for performing harmonic balance (HB) analysis using the fREEDA circuit simulator. The proposed method is an extension of the method of multiple reflections for multiple ports. In addition the method is formulated in terms of power waves and state variables at the nonlinear devices. The HB problem is then solved using a procedure which resembles the signal propagation within the actual circuit. This method could be efficiently parallelized since it does not require a large matrix decompositions at each iteration. Several approaches to improve convergence properties are investigated. The first involves adding capacitors in parallel with the nonlinear device ports, this allows the fixed-point iterations to always be convergent. These capacitors are only active in a separate time dimension and do not affect the steady-state solution. The harmonic balance solution is found when the transient response in this time dimension is extinguished. Another strategy to improve convergence is the combination of fixed-point iterations with the gradient descent method. The effect of a vector extrapolation method to accelerate convergence is also investigated. Simulation results for various strongly nonlinear circuits is presented. This thesis covers the background of harmonic balance analysis, literature review, derivation of the proposed method, improvements, preliminary results, as well as future work.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".