Analyze the frequency response of control systems and filters using this online Bode Plot Generator. Input your transfer function's numerator and denominator coefficients to calculate gain and phase at a specific frequency. Essential for understanding system stability and performance in electrical engineering.
Formula:
A Bode plot visually represents the frequency response of a linear time-invariant system. It consists of two sub-plots: the Bode magnitude plot (gain in decibels) and the Bode phase plot (phase shift in degrees).
To calculate these values, we evaluate the system's transfer function H(s) at s = jω, where j is the imaginary unit and ω is the angular frequency (rad/s).
- Magnitude (Gain in dB): 20 ⋅ log10(|H(jω)|)
- Phase (Phase Shift in Degrees): arg(H(jω)) ⋅ (180/π)
Where:
- H(s): The system's transfer function, typically represented as a ratio of two polynomials in 's'.
- s: The Laplace variable (jω for frequency response analysis).
- j: The imaginary unit (√-1).
- ω: The angular frequency in radians per second (rad/s). If input as Hz, it's converted to ω = 2πf.
- |H(jω)|: The magnitude of the complex number H(jω).
- arg(H(jω)): The phase angle (argument) of the complex number H(jω) in radians.
This calculator computes these critical values for a given transfer function and a specific frequency.