What is Gain? Gain is a proportional value that shows the relationship between the magnitude of the input to the magnitude of the output signal at steady state. Many systems contain a method by which the gain can be altered, providing more or less "power" to the system. However, increasing gain or decreasing gain beyond a particular safety zone can cause the system to become unstable. Consider the given second-order system: We can include an arbitrary gain term, K in this system that will represent an amplification, or a power increase: In a state-space system, the gain term k can be inserted as follows: The gain term can also be inserted into other places in the system, and in those cases the equations will be slightly different. Example: Gain Here are some good examples of arbitrary gain values being used in physical systems: Volume Knob On your stereo there is a volume knob that controls the gain of your amplifier circuit. Higher levels of v
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