How did they come up with that expression for \(R_{icm}\)?

Here's what I came up with,

\(R_{icm} = \frac{v_{id}}{i_{b}}\)

\(i_{e} = \frac{v_{id}}{\frac{R_{E} + r_{e}}{2} + R_{EE}}\)

\(i_{e} = (\beta + 1)i_{b}\)

\(\Rightarrow R_{icm} = (\beta + 1)( \frac{R_{E} + r_{e}}{2} + R_{EE})\)

Am I doing this incorrectly?

 

Still looking for clarification on this one.

 

The expression from the book has Rc and ro involved, and you don't.

Your work involves re, which the book doesn't.

 

The expression from the book has Rc and ro involved, and you don't.

Your work involves re, which the book doesn't.

Is mine correct if we were to neglect ro?

Also where does ro sit? Across Rc or across the collector to emitter?

 

ro is across the collector-emitter.

The expression in the book appears to be correct with one exception; where they have β they should have β+1. That being the case, I don't think your expression is correct.

You also have RE and REE; what is RE?