Bode Plot Generator from Transfer Function

What can you enter?

• Numerator coefficients in descending powers of s, such as 1, 2 for s + 2.
• Denominator coefficients in descending powers of s, such as 1, 1.4, 1 for s^2 + 1.4s + 1.
• Overall gain K, frequency range, frequency units, and sample count.
• Presets for common systems including low-pass, high-pass, integrator, lead compensator, and notch filter.

How the calculator works

The tool evaluates H(jω) = K · N(jω) / D(jω) at logarithmically spaced frequencies. Magnitude is calculated as 20 log10 |H(jω)| and phase is calculated from the complex angle, then unwrapped so the phase curve is easier to read. Crossover frequencies and margins are estimated from curve crossings.

When should you use it?

• Use it for quick control-system checks before moving to MATLAB, Python, or lab measurement tools.
• Use it to understand how poles, zeros, damping, and gain change magnitude and phase.
• Use it for teaching examples, homework verification, filter prototyping, and report visuals.
• Use the SVG, PNG, or CSV export when you need the plot in slides, notes, worksheets, or documentation.

Accuracy notes

This calculator is designed for continuous-time rational transfer functions. Margin values are interpolated from sampled frequency points, so they are useful for quick analysis and teaching. For high-stakes engineering decisions, verify final values in your course-approved or project-approved control-system software.