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Need help in deriving equation 7, 8 and 9 in Input Impedance Matching With Fully Differential Amplifiers by James Karki

Hi

The article in question is: www.ti.com/.../slyt310.pdf

I am going through the derivation of how to calculate the input impedance and the gain of differential amp with single input ( not differential input) for my design. I cannot verify formula 7, 8 and 9. I read all the articles provided by Ti that are written by James Karki already. I understand the formulas from SLAO54E and "Analysis of fully differential amplifiers" by James Karki, but I just cannot jump the gap from all these to formula 7, 8 and 9.

It would be nice if I can write directly to Jame Karki if it is all possible.

Thanks

Alan

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