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 decrease the crossover frequency, making the system slower and with a 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.