01
Bode Plots & Frequency Response
Plotting amplifier gain and filter cutoff frequencies across 3 to 5 frequency decades (10 Hz to 1 MHz).
Fogli Tecnici e per Ingegneria
paper.semi-log
paper.semi-log.desc
A4 Portrait · 210 × 297 mm
100%
Scala fisica 1:1 reale. Misura il blocco di calibrazione da 50 mm sui fogli stampati.
CSS: 96 DPISezione 02 — Principi Matematici
Fondamenti Geometrici e Formule Coordinate
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.
Formula:
d(k) = D · log10(k), k ∈ {1, 2, 3, ..., 10}; Decade width = DOrigine Storica ed Evoluzione Scientifica
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).
Su GraphPages.com tutti i calcoli vettoriali sono eseguiti direttamente nel browser client senza compressioni, garantendo tolleranze dimensionali entro 0,05 mm.
Sezione 03 — Applicazioni Pratiche
Applicazioni Pratiche nei Settori Professionali
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.
Sezione 04 — Guida al Tracciamento
Guida Passo dopo Passo per Disegnare su paper.semi-log
PASSO 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).
PASSO 02
Scale the Linear Axis
Assign uniform arithmetic steps along the linear axis (e.g. time in hours, or voltage in volts).
PASSO 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.
PASSO 04
Evaluate Exponential Slope
Because exponential curves plot as straight lines, you can calculate the rate constant directly from the linear slope.
Sezione 05 — Calibrazione di Stampa
Guida alla Configurazione e Verifica di Scala
Garantire l'Accuratezza in Scala 1:1 Reale
Ensure decade spacing is exact. A true decade must measure uniformly across all cycle repeats.
- Nel menu di stampa scegli sempre Scala: 100% o Dimensioni effettive.
- Disattiva 'Adatta all'area di stampa' per evitare rimpicciolimenti indesiderati.
- Verifica con un righello la barra di calibrazione da 50 mm stampata sul margine.
Sezione 06 — Domande Frequenti
Domande Frequenti (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.
Apri nello Studio Virtuale — paper.semi-log
Traccia diagrammi, annota coordinate o crea forme geometriche su questa griglia direttamente nel tuo browser.