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Bode Plot

Analysis

The Bode Plot block performs a frequency response analysis of a linear system. It generates two simultaneous plots:

Magnitude (dB) vs Frequency (rad/s): Shows the gain of the system across a range of frequencies.
Phase (degrees) vs Frequency (rad/s): Shows the phase shift of the output relative to the input.

This block is essential for analyzing system stability, bandwidth, and resonance characteristics in the frequency domain. It performs an automated frequency sweep by injecting a sinusoidal signal at varying frequencies into the system and measuring the steady-state response.

Inputs & Outputs

Direction	ID	Label	Type	Status
→ In	`in1`	Input	number	Required
← Out	`out`	Result	number	Output

Parameters

Parameters	Label	Type	Default
`inputSource`	Input Source ID	text	`sine1`
`startFreq`	Start Frequency (rad/s)	number	`0.1`
`endFreq`	End Frequency (rad/s)	number	`100`
`pointsPerDecade`	Points Per Decade	number	`10`

Usage Examples

1-pole Low-Pass Filter

System: $G(s) = \frac{1}{s + 1}$ . The Bode plot shows a -3dB cutoff at 1 rad/s and a magnitude slope of -20dB/decade at higher frequencies.

Second-Order Resonant System

System: $G(s) = \frac{\omega_n^2}{s^2 + 2\zeta\omega_ns + \omega_n^2}$ . The Bode plot shows a peak (resonance) near $\omega_n$ if the damping ratio $\zeta < 0.707$ .

Remarks & Best Practices

Steady State: The sweep algorithm waits for the system to reach steady state at each frequency before measuring magnitude and phase.
Linearity: This analysis assumes the system is linear. Results for non-linear systems may be non-deterministic or vary with input amplitude.
Interactive Tuning: You can adjust the sweep range in real-time to focus on specific regions of interest, such as crossover frequencies.

Related Components

NyquistPlot: Alternative frequency-domain visualization.
TransferFunction: Define the system being analyzed.
SignalGenerator: Provide the reference sine wave for the sweep.