need help to understand common mode to differential conversion

[glias]

Hello
I have read a book to better understand the differential mode and common mode and I don't understand how they could deduce this equation 2.142... I have tried with Kirchhoff law but I can't find it
Could you please help me ?

 

[chuckey]

If you take something like an OP-amp with differential inputs and then put a common mode voltage across them then the common mode voltage sends a currents into each differential input. If the impedances as seen down each leg of the differential inputs are not exactly the same the currents flowing down each line will be different. If the currents flowing are different then the voltage drops across each line will be different so the inputs will see a different voltage due to the different currents and will amplify this difference and it will appear at the output.
I could not read your circuits/formuli.
Frank

 

[glias]

Hello Frank thanks a lot for your explanation, I agree with you but I don't know how they found the equation 2.142, to zoom on the picture that I have included in my first post, you just have to click on it (it works for me).