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Load resistance transformation for matchin

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atris

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Hi, I was studying RF Microelectronics 2ed by Razavi.
In the paragraph 2.5.3 pp 65-69, he analyzes ways of
transformation the load resistance RL to higher or lower values.
This method is based on the serial to parallel (StoP) and PtoS
transformations in paragraph 2.5.1 and 2.5.2 pp63-64 of the same book.
These relations are: Rp=RsQs^2, cp=cs and Rs=RpQp^2, cs=cp.
These relations are used in example 2.28 p67 that I can undersand.
The main problem and question is (what I can not understand):
The analyses that he does from pp. 65-66.
More specifically: In eq. 2178 p65 for instance, he writes:
Re(Zin)=RL/(1+Qp^2) which I can not understand. I would write (I would find as correct):
Re(Zin)=RLQp^2 based on pp 63-64.
The same with the analyses that he does in p66 (he writes Rs=(Rl(c1w)^2)^-1 in the 4th line after the example 2.27.
Any answers for this?????
Thank you for your help.....
 

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