Zₒ for small signal analysis with BJT for unbypassed emitter and rₒ in place

Question

I try to solve Z_out for this BJT small-signal model but I find

R_C || (r_o + R_E)

because Z_out is calculated with I_b = 0 => βI_b = 0.

From this link too V_in was calculated.

But the expression for Z_o given in the book by Boylestad and Nashelsky is:

Z_o = R_C || (r_o + β (r_o + r_e) / (1 + β r_e / R_E)])

Can you explain how to derive this?

Just a question for you. What happens to \$Z_o\$ when \$R_\text{E}=0\:\Omega\$ from your last equation? Is it sensible? — jonk, Jun 14 '20 at 21:05
If RE=0 Ω (short circuit) from the last equation Zo = RC || [ ro + β (ro + re) / (1 + infinity)] = Zo = RC || [ ro ] = RC . It is sensible but considering ib = 0 — user7058377, Jun 14 '20 at 21:35
But what do You want to show me by thinking about "RE= 0 Ω" jonk ? — user7058377, Jun 14 '20 at 23:39

user7058377 · Answer 1 · 2020-07-24T08:43:06.030

1

Solution : Vi = 0 not => ib = 0

edited Jul 24 '20 at 08:43

answered Jun 14 '20 at 23:29

user7058377

compare it with my solution https://electronics.stackexchange.com/questions/265046/calculation-of-output-impedance-of-ce-emitter-bias-configuration-unbypassed-wi/276764#276764 and here https://electronics.stackexchange.com/questions/342859/bjt-common-base-output-resistance-derivation/342989#342989 – G36 Jun 15 '20 at 13:10

score 0 · Answer 2 · answered Apr 27 '21 at 09:19

0

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)

answered Apr 27 '21 at 09:19

user7058377

2 Answers2