A useful pseudo‐logarithmic circuit
Bibliographic record
Abstract
Purpose This paper proposes a useful pseudo‐logarithmic circuit as a basic building block in the construction of a logarithmic amplifier made from piecewise approximations. Design/methodology/approach The circuit employs two operational and a handful of resistors, and mimics the logarithmic function over a predefined range. Control of the pseudo‐logarithmic function is achieved by a ratio of resistances defined as x, one of which may be digitally switched, or implemented by tunable transconductors. When controlled by digitally switched resistors, the circuit is particularly attractive because of the commercial availability of such resistors, and with the aid of simple control logic, individual blocks can be algebraically summed to extend the dynamic range of the basic pseudo‐logarithmic block which is 28 dB Findings Experimental results using off the shelf operational amplifiers (opamps) and a handful of resistors show that the circuit yields a maximum log error of 0.6915 dB for x in (0.22, 4.65). Originality/value Proposes a novel circuit capable of realizing the pseudo‐logarithmic function (x−1)/(1+x). The circuit is simple and easily implemented using readily available opamps.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".