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Simplifying transfer function

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promach

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How to obtain the expression on the right hand side of the second equal sign in the first line ?

Same question for the second line.

Zd_short_miller_capacitance_calculation.png
 

To simplify the expression write re||RL=Rp.
Then we have (left side):
Rp/(Rg+Rp)
Now - divide numerator and denominator by the expressin RgRp.
As a result, we have in the denominator the inverse of Rg||Rp which, therefore, goes to the numerator - thats all.
 

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    promach

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What about right hand side of the second equal sign in the SECOND line ?
 

promach said:
What about right hand side of the second equal sign in the SECOND line ?
Click to expand...
I must admit - it looks more complicated and I have not enough motivation and time....sorry.
 

BJT.jpg

--- Updated ---

beta is approximately equal to (beta+1) because when beta is much gr5eater than 1, Ib is much smaller than Ic and so Ic is approximately equal to Ie.
 
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