01
Bode Plots & Frequency Response
Plotting amplifier gain and filter cutoff frequencies across 3 to 5 frequency decades (10 Hz to 1 MHz).
Papeles Técnicos y de Ingeniería
paper.semi-log
paper.semi-log.desc
A4 Portrait · 210 × 297 mm
100%
Escala física 1:1 real. Mida el bloque de calibración de 50 mm.
CSS: 96 DPISección 02 — Principios Matemáticos
Fundamento Geométrico y Fórmulas de Coordenadas
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.
Fórmula:
d(k) = D · log10(k), k ∈ {1, 2, 3, ..., 10}; Decade width = DOrigen Histórico y Evolución Científica
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).
En GraphPages.com, todas las operaciones de renderizado vectorial se ejecutan directamente en su navegador sin compresión de servidor, garantizando que los márgenes, divisiones y dimensiones físicas se preserven con una precisión de 0,05 mm.
Sección 03 — Aplicaciones Prácticas
Aplicaciones Reales en Diversas Industrias
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.
Sección 04 — Guía de Dibujo y Trazado
Guía Paso a Paso para Trazar en paper.semi-log
PASO 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).
PASO 02
Scale the Linear Axis
Assign uniform arithmetic steps along the linear axis (e.g. time in hours, or voltage in volts).
PASO 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.
PASO 04
Evaluate Exponential Slope
Because exponential curves plot as straight lines, you can calculate the rate constant directly from the linear slope.
Sección 05 — Calibración de Impresión
Configuración de la Impresora y Verificación de Escala
Garantizar la Precisión de la Escala Física Real
Ensure decade spacing is exact. A true decade must measure uniformly across all cycle repeats.
- En el cuadro de diálogo de impresión, elija Escala: 100% o Tamaño Real.
- Desactive 'Ajustar al área imprimible' o 'Reducir páginas sobredimensionadas'.
- Mida la barra de calibración de 50 mm impresa en el margen inferior con una regla física.
Sección 06 — Preguntas Frecuentes
Preguntas Frecuentes
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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