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Qestion about Oscillator

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wulingking

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I've read a paper named"High-Performance Crystal Oscillator Circuits:Theory and Application",by Eric A Vittoz, Marc G.R.Degrauwe and Serge Bitz. What I am confused is following:
Zc=(Z1Z3+Z2Z3+gmZ1Z2Z3)/(Z1+Z2+Z3+gmZ1Z3)
Zc is a bilinear function of gm. Therefore, the locus of Zc(gm) in the complex plane is a circle.
Why?
 

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