01
Bode Plots & Frequency Response
Plotting amplifier gain and filter cutoff frequencies across 3 to 5 frequency decades (10 Hz to 1 MHz).
Papiers Techniques & Ingénierie
paper.semi-log
paper.semi-log.desc
A4 Portrait · 210 × 297 mm
100%
Échelle physique 100% exacte. Vérifiez avec le bloc de 50 mm.
CSS: 96 DPISection 02 — Principes Mathématiques
Fondements Géométriques et Formules Coordonnées
Logarithmic Spacing Formula
Semi-logarithmic paper features one logarithmic axis and one linear axis. Within each decade interval [1, 10], line spacing contracts proportionally to log10(k), allowing exponential functions y = a · e^(bx) to plot as straight linear lines.
Formule :
d(k) = D · log10(k), k ∈ {1, 2, 3, ..., 10}; Decade width = DOrigine Historique et Évolution Scientifique
Semi-logarithmic paper was developed in the late 19th century to linearize power and exponential data before digital computers, becoming a staple in acoustics, epidemiology, and electronics (Bode plots).
Sur GraphPages.com, tous les calculs vectoriels sont exécutés directement dans votre navigateur sans compression serveur, assurant une précision de 0,05 mm sur les marges et dimensions physiques.
Section 03 — Applications Pratiques
Cas d'Usage Réels à Travers les Industries
02
Radioactive Decay & Half-Life Curves
Tracking isotope decay rates where exponential decay N(t) = N0 · e^(-λt) appears as a straight line with slope -λ.
03
Epidemiological Growth Rates
Analyzing early virus reproduction rates and bacterial culture population doubling times.
04
Financial Interest & Inflation Tracking
Plotting compound interest growth and long-term equity valuations over multiple decades.
Section 04 — Tutoriel de Dessin
Guide Étape par Étape pour Tracer sur paper.semi-log
ÉTAPE 01
Label the Logarithmic Decades
Assign power-of-ten multipliers to each decade marker along the log axis (e.g. 10⁰ = 1, 10¹ = 10, 10² = 100, 10³ = 1000).
ÉTAPE 02
Scale the Linear Axis
Assign uniform arithmetic steps along the linear axis (e.g. time in hours, or voltage in volts).
ÉTAPE 03
Plot Log-Linear Data Pairs
For a point (x, y), find x along the logarithmic decades using the intermediate tick marks (2, 3, 4... 9), then align with y on the linear scale.
ÉTAPE 04
Evaluate Exponential Slope
Because exponential curves plot as straight lines, you can calculate the rate constant directly from the linear slope.
Section 05 — Étalonnage d'Impression
Configuration de l'Imprimante et Contrôle d'Échelle
Garantir l'Exactitude Physique à l'Échelle 1:1
Ensure decade spacing is exact. A true decade must measure uniformly across all cycle repeats.
- Dans les options d'impression, choisissez impérativement Échelle : 100 % ou Taille réelle.
- Désactivez 'Ajuster à la zone d'impression' pour éviter toute déformation du pilote.
- Mesurez la barre d'étalonnage de 50 mm dans la marge avec une règle physique.
Section 06 — Questions Fréquentes
Foire Aux Questions (FAQ)
Why do lines bunch together within each decade?
The distance from 1 to 2 represents log10(2) ≈ 0.301 of the cycle, while the distance from 8 to 9 represents log10(9/8) ≈ 0.051. This nonlinear compression reflects logarithmic scale mathematics.
How many decades are included on this sheet?
Our standard template provides 4 full logarithmic decades along the horizontal axis with a 20-division linear vertical axis.
Can semi-log paper plot negative numbers?
No. The logarithm of zero or a negative number is undefined (log10(x) → -∞ as x → 0+). Data on the log axis must be strictly positive.
What is the difference between semi-log and log-log paper?
Semi-log paper has one logarithmic axis and one linear axis. Log-log paper features logarithmic scaling on both axes.
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