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In the bode plot, when we encounter a pole then the gain magnitude decreases but in the value of transfer function increases (gain) .How is it explained?
It`s not true that the BODE magnitude plot (always) decreases at the pole frequency. Depending on the pole location in the s-plane (pole quality) the magnitude may exhibit a peak - sometimes rather large - in this frequency region.
More than that, the answer to your question touches the difference between the complex frequency s=sigma+jw and the real frequency w. Try to become familiar with the meaning of s and you will understand.
but by definition the system has infinite gain at pole frequency rite ? so the gain should always increase ? :sad:
What definition? That is true only if the pole is purely imaginary.
I think, for an imaginary pole pair we have dynamic instability (oscillations).
@Fizzbug: The magnitude goes to infinity for s=s(p)=sigma(p)+jw(p) (s(p)=complex pole frequency).
However, in reality you never can excite the circuit with s(p). It is a mathematical operation only.
I repeat: Try to become familiar with the concept of complex frequencies.