Bode Plot Parameters

A Bode plot is a graph of a transfer function, and it represents the magnitude (expressed in decibels, dB) and phase (expressed in degrees) of the transfer function plotted on a logarithmic frequency scale. A Bode plot can be used to estimate the stability and dynamic performance in a closed-loop system. There are three major parameters to be considered:

Crossover Frequency

The system crossover frequency is the point where the gain of the system becomes 0 dB. A higher crossover frequency means better dynamic performance and better transient response. However, due to possible noise issues, the crossover frequency cannot be set infinitely high.

Phase Margin

In a closed-loop system that uses negative feedback, the system phase margin is defined by the difference between the phase at the crossover frequency and 0 degrees. This parameter is directly related to the stability of the closed-loop system.

Gain Margin

The system gain margin is defined as the amount of gain that has to be added to the system gain to reach 0 dB, calculated at the point where the phase reaches 0 degrees. This parameter is also directly related to stability, and it indicates how far the system is from becoming unstable.

For the system to be considered stable in real-life situations where noise and high-order effects may occur, the following two conditions have to be concurrently satisfied:

  • phase margin ≥ 45 degrees
  • gain margin ≥ 6 dB

The higher these values, the more stable the system is. However, over-increasing these two parameters decreases the crossover frequency, making the system slower and with poor dynamic response to external perturbations. By modifying external components (the inductor, capacitor or feedback loop), you can tune the frequency response of the system.

The MCP16311/2 Buck Converter Design Analyzer provides information about the expected stability and dynamic performance of the converter through the Bode plot of the closed-loop system.

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