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Gain margin is the maximum gain increase or decrease (measured in dB) that doesn’t compromise stability. We can usually read the gain margin directly from the Bode plot (as shown in the diagram above).
Bode plots are used to assess the stability of negative-feedback amplifiers by finding the gain and phase margins of an amplifier. The notion of gain and phase margin is based upon the gain expression for a negative feedback amplifier given by = +,
Gain margins are expressed in dB on the plot. Solid vertical lines mark the gain margin and phase margin. The dashed vertical lines indicate the locations of Wcp, the frequency where the phase margin is measured, and Wcg, the frequency where the gain margin is measured.
The gain margin is typically expressed in decibels (dB) and is calculated by finding the gain (magnitude) of the loop-gain transfer function at the Phase crossover frequency (PCF). The gain margin is the amount by which this gain can be increased before instability occurs.
Based on these plots, a graphical alternative can be found to calculating the Gain margin from the gain and phase equation. Note that since it is customary to use decibel units on frequency response plots, Gain margin will now be also expressed in decibel units, rather than in Volt/Volt units.
Definition: Gain Margin. The gain margin (GM) denotes the factor by which the loop gain,\(\ \left|KGH\left(j\omega \right)\right|\), can be increased without compromising the closed-loop stability.
We have defined and illustrated gain and phase margins for stable and unstable feedback control using the physical system of Figures 16.3.1, 16.3.2, and \(\PageIndex{2}\).
The gain margin value can help identify how sensitive a control system is to changes in system parameters or external disturbances. Control engineers often target specific gain margin values during the design process to achieve desired stability and performance characteristics.
Stability margins measure how close a closed-loop system is to instability, that is, how large or small a change in the system is required to make it become unstable. The two commonly used measures of stability are the gain margin and the phase margin.
Gain Margin [latex]G_{m}[/latex] becomes the additional system specification ensuring good relative Stability. We will hear more about it in a context of frequency response design, and we will define its measure using Bode plots.