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Here is proof for conversion of a series to a parallel combination in Razavi book.
Could you explain why frequency should be in a narrow range here?
(it is highlighted by yellow color below)
Calculation of equation 6.29 is valid for one frequency only. Taking Q in account bandwidth can be found where transformation at one frequency is useful.
I think that from 6.29 to 6.33 should be valid for any frequency.
6.34 to 6.36 are valid for any frequency that quality factor at that frequency is much larger than 1.
Could you explain why 6.36 is only for a specific frequency?
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