Question
Download Solution PDFIf the gain margin of a system in decibels is negative, the system is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Gain Margin is reciprocal of gain which is calculated at phase cross over frequency (ωpc).
i.e. Gain margin \(= \frac{1}{{{{\left| {Gain} \right|}_{ω = {ω _{pc}}}}}}\)
∵ \(Gain = {\left| {G\left( ω \right). M\left( ω \right)} \right|_{ω = {ω _{pc}}}}\)
Gain margin = \( - 20\log _{10}{\left| {G\left( ω \right). H\left( ω \right)} \right|_{ω = {ω _{pc}}}}\)
Analysis:
|
|
\({\left. {Gain} \right|_{ω = {ω _{pc}}}}\) |
GM |
System |
|
1) |
> 1 |
-ve |
Unstable |
|
2) |
= 1 |
0 |
Marginally stable |
|
3) |
< 1 |
+ve |
stable |
Important Points
Phase cross over frequency of system-defined when the phase of the system is -180 degrees. Gain cross over frequency of system-defined when the gain of the system is unity.
REMEMBER:
- For the system to be unstable GM and PM both will be negative.
- For the system to be stable GM and PM both will be positive
- For the system to be marginally stable PM and GM both will be Zero.
- PM and GM are use to understand the concept of relative stability.
- PM is calculated at Gain crossover frequency and GM calculated at Phase crossover frequency.
Last updated on Jun 23, 2025
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