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Solved Problems-12

Problems-12
Show that the high-Q coil resonant circuit can be approximated as shown in figure.
 
Description: 1805.png
High-Q Coil Resonant Circuit

Description: 1815.png
Approximated Equivalent Circuit
 
Solution
For the approximated circuit, the resonant frequency is given as,
 
Description: 3973.png
 
For the high-Q resonant circuit, the resonant frequency is given as,
 
Description: 3979.png (i)
 
Therefore, Q-factor of the inductance is,
 
Q = Description: 3985.png
 
⇒ Description: 3992.png
⇒ Description: 3998.png
 
Putting this value in (i), we get,
 
Description: 4005.png
 
For very high values of Q, the term Description: 4011.png becomes negligible and we get the resonant frequency as, Description: 4017.png which is the same as that for the approximated equivalent circuit.
 




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