I wanted to know how to derive the expression for the Noise Figure (NF) equation of Low Noise Amplifier (LNA).

I have taken diagrams of equivalent circuits of a low noise amplifier and also derivations of Noise Figures of Low Noise Amplifier (LNA) from other research papers. They have directly given equations of noise figures, but I am not able to understand the in between steps of the noise figure of derived equations of low noise amplifier. Can you help me to understand derived equations shown in the below links?

    The first two links give information about capacitive shunt feedback low noise amplifier noise equivalent diagram and its noise figure derived equation.

     Next third and fourth links give information about power constrained simultaneous noise and impedance matching noise equivalent diagram and derived equation of noise figure of PCSNIM LNA.

1) https://drive.google.com/file/d/0BwF-am-wbq-XZnljQ3pTbHNTTlU/view?usp=sharing

2) https://drive.google.com/file/d/0BwF-am-wbq-XWjNzODZPQ2JrNzQ/view?usp=sharing

3) https://drive.google.com/file/d/0BwF-am-wbq-XOW1oQ3ExRm5EaUk/view?usp=sharing

4) https://drive.google.com/file/d/0BwF-am-wbq-XRUxSZWVrM2RHdEk/view?usp=sharing

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