Can I enter a transfer function directly?

This version accepts numerator and denominator coefficients in descending powers of s. For example, 10 / (s^2 + 2s + 10) is entered as numerator 10 and denominator 1, 2, 10.

Does the generator show both magnitude and phase?

Yes. It draws magnitude in dB and phase in degrees on a logarithmic frequency axis.

Can I calculate gain margin and phase margin?

Yes. The tool estimates gain crossover, phase crossover, phase margin, and gain margin when the response crosses the relevant thresholds.

Can I plot in hertz instead of radians per second?

Yes. You can switch the frequency input and axis labels between rad/s and Hz. Internally the transfer function is still evaluated using angular frequency.

Can I download the Bode plot?

Yes. You can export the current plot as SVG, PNG, or CSV data for slides, reports, and further analysis.

Does this support time delays or discrete-time systems?

No. This page focuses on continuous-time rational transfer functions. For delays, use a Pade approximation before plotting. For discrete-time models, verify in dedicated control-system software.

Control Systems Calculator

Bode Plot Generator from Transfer Function

Generate Bode magnitude and phase plots from numerator and denominator coefficients. Calculate crossover frequencies, gain margin, phase margin, and export SVG, PNG, or CSV.

Magnitude and phase plotsGain and phase marginsRad/s or Hz frequency axisSVG, PNG, and CSV export

Transfer function

Coefficients are descending powers of s.

Numerator coefficientsDenominator coefficientsGain K

Min frequencyMax frequency

Frequency unitPoints

Presets

Frequency response

H(s) = 1 · [1] / [1, 1]

Gain crossover

- rad/s

Phase crossover

- rad/s

Phase margin

- deg

Gain margin

- dB

Bode Plot Examples

Explore common transfer-function responses for filters and control systems

View:

First-Order Low-Pass Filter

Magnitude rolls off after the corner frequency and phase approaches -90 degrees.

low-passfiltercorner-frequency

Second-Order Control System

A typical second-order response for control-system homework and stability checks.

second-ordercontrolphase

First-Order High-Pass Filter

A high-pass response with rising low-frequency magnitude and phase moving toward zero.

high-passfilterfrequency-response

Lead Compensator

A control-design example that changes phase and gain across a target band.

leadcompensatormargin

Notch Filter

A frequency-selective example for signal processing and vibration analysis.

notchsignal-processingfilter

Integrator Response

An integrator response with -20 dB per decade slope and -90 degree phase.

integratorcontrolslope

What is a Bode plot generator?

A Bode plot generator evaluates a transfer function across a logarithmic frequency range and draws two frequency-response plots: magnitude in decibels and phase in degrees. Engineers and students use these plots to inspect filters, amplifiers, control loops, compensators, and signal-processing systems.

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.

Frequently Asked Questions

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What is a Bode plot generator?

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

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