01
Bode Plots & Frequency Response
Plotting amplifier gain and filter cutoff frequencies across 3 to 5 frequency decades (10 Hz to 1 MHz).
Technische & Ingenieurspapiere
paper.semi-log
paper.semi-log.desc
A4 Portrait · 210 × 297 mm
100%
100% maßstabsgetreu. Messen Sie den 50-mm-Kalibrierungsblock.
CSS: 96 DPIAbschnitt 02 — Mathematische Prinzipien
Geometrische Grundlagen & Koordinatenformeln
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.
Formel:
d(k) = D · log10(k), k ∈ {1, 2, 3, ..., 10}; Decade width = DHistorischer Ursprung & Wissenschaftliche Entwicklung
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).
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Abschnitt 03 — Praktische Anwendungen
Reale Einsatzbereiche in Industrie & Forschung
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.
Abschnitt 04 — Zeichen- und Plottanleitung
Schritt-für-Schritt-Anleitung für paper.semi-log
SCHRITT 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).
SCHRITT 02
Scale the Linear Axis
Assign uniform arithmetic steps along the linear axis (e.g. time in hours, or voltage in volts).
SCHRITT 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.
SCHRITT 04
Evaluate Exponential Slope
Because exponential curves plot as straight lines, you can calculate the rate constant directly from the linear slope.
Abschnitt 05 — Druckerkalibrierung
Drucker-Setup & Maßstabsverifikation
Physikalische Maßstabstreue sicherstellen
Ensure decade spacing is exact. A true decade must measure uniformly across all cycle repeats.
- Wählen Sie im Druckdialog 'Skalierung: 100 %' oder 'Tatsächliche Größe'.
- Deaktivieren Sie 'Auf Druckbereich anpassen', um Verzerrungen zu vermeiden.
- Messen Sie den gedruckten 50-mm-Kalibrierbalken am Rand mit einem Lineal nach.
Abschnitt 06 — Häufig gestellte Fragen
Häufig gestellte Fragen (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.
Im Virtuellen Studio öffnen — paper.semi-log
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