Z(out) for small signal analysis with BJT for unbypassed emitter and r0 in place

Question

from

this BJT small signal I try to solve Z(out) but I find
RC || (ro + RE)
because Z(out) is calculated with ib = 0 => beta ib = 0
from this link too V(in) was calculated
But the expression for Zo given in the book by Boylestad and Nashelsky is
Zo = RC || [ro + β (ro + re) / (1 + β re / RE)]
Can You explain how to retrieve this ?

user7058377 · Answer

If you put the equations correctly:
point C :   io vo ve ib
point E :      vo ve ib
ib def  :         ve ib

3 unknowns : (vo OR io) AND ve AND ib
to get vo = function(io) OR io = function(vo)

user7058377 · Answer

Solution : Vi = 0 not => ib = 0

Z(out) for small signal analysis with BJT for unbypassed emitter and r0 in place

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