01
Bode Plots & Frequency Response
Plotting amplifier gain and filter cutoff frequencies across 3 to 5 frequency decades (10 Hz to 1 MHz).
Kertas Teknikal & Kejuruteraan
paper.semi-log
paper.semi-log.desc
A4 Portrait · 210 × 297 mm
100%
Skala fizikal 1:1 sebenar. Ukur kotak penentukuran 50 mm pada cetakan.
CSS: 96 DPIBahagian 02 — Prinsip Matematik
Asas Geometri dan Formula Koordinat
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 = DAsal-usul Sejarah & Evolusi Saintifik
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).
Di GraphPages.com, semua operasi vektor diproses terus dalam pelayar anda tanpa mampatan pelayan, menjamin ketepatan ukuran fizikal dan margin sehingga 0.05 mm.
Bahagian 03 — Kegunaan Praktikal
Aplikasi Sebenar Merentasi Industri
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.
Bahagian 04 — Tutorial Melakar
Panduan Langkah demi Langkah Melakar pada paper.semi-log
LANGKAH 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).
LANGKAH 02
Scale the Linear Axis
Assign uniform arithmetic steps along the linear axis (e.g. time in hours, or voltage in volts).
LANGKAH 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.
LANGKAH 04
Evaluate Exponential Slope
Because exponential curves plot as straight lines, you can calculate the rate constant directly from the linear slope.
Bahagian 05 — Penentukuran Pencetak
Panduan Persediaan Pencetak & Pengesahan Skala
Menjamin Ketepatan Skala Fizikal 1:1 Sebenar
Ensure decade spacing is exact. A true decade must measure uniformly across all cycle repeats.
- Dalam dialog cetakan, pilih Skala: 100% atau Saiz Sebenar.
- Nyahaktifkan 'Fit to Printable Area' bagi mengelakkan herotan cetakan.
- Ukur palang penentukuran 50 mm pada margin bawah dengan pembaris fizikal.
Bahagian 06 — Soalan Lazim
Soalan Lazim (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.
Buka dalam Studio Maya — paper.semi-log
Lakarkan rajah, tandakan koordinat atau lukis bentuk geometri di atas grid ini secara terus dalam pelayar anda.