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cianfa72

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- About the definition of resonance angular frequency for RLC or more complex networks

Hi, I'm confused about the meaning of resonance angular frequency for an RLC series circuit.

Call ##\omega_0=\sqrt { 1/LC }## and ##Q= {\omega_0 L} /R##.

Then consider the admittance as transfer function $$Y(s) = \frac {1} {L} \frac {s} {s^2 + s \omega_0/Q + \omega_0^2}$$

This transfer function has one zero in ##s=0## and two complex coniugate poles when ##Q > 1/2##.

Note that the c.c. poles define a "natural or ringing" angular frequency, i.e. $$\omega_r = \omega_0 \sqrt {1 - \frac {1} {4Q^2}}$$

So the question is: what is meant by resonance frequency of a network?

Thanks.

Call ##\omega_0=\sqrt { 1/LC }## and ##Q= {\omega_0 L} /R##.

Then consider the admittance as transfer function $$Y(s) = \frac {1} {L} \frac {s} {s^2 + s \omega_0/Q + \omega_0^2}$$

This transfer function has one zero in ##s=0## and two complex coniugate poles when ##Q > 1/2##.

Note that the c.c. poles define a "natural or ringing" angular frequency, i.e. $$\omega_r = \omega_0 \sqrt {1 - \frac {1} {4Q^2}}$$

So the question is: what is meant by resonance frequency of a network?

Thanks.

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