01
Bode Plots & Frequency Response
Plotting amplifier gain and filter cutoff frequencies across 3 to 5 frequency decades (10 Hz to 1 MHz).
工程与技术制图纸
paper.semi-log
paper.semi-log.desc
A4 Portrait · 210 × 297 mm
100%
严格1:1物理打印比例。请用直尺测量纸面上的 50mm 校准框。
CSS: 96 DPI第二部分 — 数学原理与几何标准
几何基础与坐标解析公式
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.
数学公式：
d(k) = D · log10(k), k ∈ {1, 2, 3, ..., 10}; Decade width = D历史渊源与科学演变
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).
在 GraphPages.com 中，所有矢量渲染均在您的浏览器客户端直接执行，无需服务器二次压缩，确保纸张边距、分度刻度与物理尺寸精度达到 0.05 毫米以内。
第三部分 — 行业与学术应用
跨行业的真实专业应用
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.
第四部分 — 绘图实操教程
paper.semi-log 分步绘图与打点指南
步骤 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).
步骤 02
Scale the Linear Axis
Assign uniform arithmetic steps along the linear axis (e.g. time in hours, or voltage in volts).
步骤 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.
步骤 04
Evaluate Exponential Slope
Because exponential curves plot as straight lines, you can calculate the rate constant directly from the linear slope.
第五部分 — 打印机物理校准
打印机设置与实际物理比例校验
确保物理尺寸 1:1 绝对精准
Ensure decade spacing is exact. A true decade must measure uniformly across all cycle repeats.
- 在打印设置中选择“缩放：100%”或“实际大小”。
- 切勿勾选“适应可打印区域”或“缩小超大页面”，以避免打印驱动缩放失真。
- 用实体直尺实测页面下边缘印制的 50 毫米校准条予以核对。
第六部分 — 常见问题解答
常见问题解答 (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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