01
Bode Plots & Frequency Response
Plotting amplifier gain and filter cutoff frequencies across 3 to 5 frequency decades (10 Hz to 1 MHz).
Papéis Técnicos e de Engenharia
paper.semi-log
paper.semi-log.desc
A4 Portrait · 210 × 297 mm
100%
Escala física 1:1 exata. Meça o bloco de calibração de 50 mm.
CSS: 96 DPISeção 02 — Princípios Matemáticos
Fundamento Geométrico e 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 = DOrigem Histórica e Evolução 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).
No GraphPages.com, todas as operações vetoriais rodam diretamente no navegador sem compressão de servidor, garantindo precisão milimétrica de até 0,05 mm nas margens e divisões.
Seção 03 — Aplicações Práticas
Casos de Uso Reais na Indústria e Academia
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.
Seção 04 — Tutorial de Desenho
Guia Passo a Passo para Desenhar em 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.
Seção 05 — Calibração da Impressora
Configuração de Impressão e Verificação de Escala
Garantindo Precisão Física na Escala 1:1
Ensure decade spacing is exact. A true decade must measure uniformly across all cycle repeats.
- No diálogo de impressão, selecione Escala: 100% ou Tamanho Real.
- Desative 'Ajustar à página' para evitar distorções do driver.
- Meça a barra de calibração de 50 mm impressa na margem com uma régua física.
Seção 06 — Perguntas Frequentes
Perguntas Frequentes
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.
Abrir no Estúdio Virtual — paper.semi-log
Esboce diagramas, anote coordenadas ou desenhe formas geométricas sobre esta grade no seu navegador.