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Addition of Quality factor

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GGAPBE96

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I can't understand the following relationship of parallel LC circuit.
Does anyone explain this?

1/Q = 1/QL + 1/Qc

where

Q : net Q value of the circuit.
QL : Q value of inductor itself.
Qc : Q value of capacitor itself.

This formula is always correct??
How's the series LC circuit?
 

LvW

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Take the definiton of Q applied to passive elements L and C: Q=1/tan(phi) ,
and phi is the loss angle in the pointer/vector (expression ?) diagram as a result of some losses within L resp. C.

If you visualize in this diagram the 3 different angles and the corresponding ratios which give the tan function, you will see that tan(phi)=tan(phiL)+tan(phiC).
 

    GGAPBE96

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