Are the AC resistances in the hybrid pi model and the T model of BJT the same?

Question

I have been wondering if the AC resistances in the two models of BJT circuit mean the same thing, that is $$r_{c} = r_{c'}$$ $$r_{b} = r_{b'}$$ $$r_{ex} = r_{e'}$$

If they are different, please explain how.

T model at Page 6

Hybrid Pi Model at Page 526

Answer 1

The answer is No. They are not the same. Maybe except \$r_b\$.

\$r_b =r_b' = r_{bb}\$ - is a base spreading resistance (semiconductor resistance, bonding wires resistance).

And the same is true for \$r_{ex}\$ and \$r_c\$. They are just emitter and collector ohmic resistance (bonding wires resistance etc. ) Not included in the T-model.

So, the dynamics resistance are:

$$r_{\pi} =\frac{V_T}{I_B} = (\beta +1)r_e'= (\beta +1) \frac{V_T}{I_E} \approx (\beta +1) \frac{26\text{ mV}}{I_E}$$

$$r_e' = r_e = \frac{V_T}{I_E} \approx \frac{26\text{ mV}}{I_E}$$

$$r_o = r_c' \approx \frac{V_A}{I_C}$$

\$V_T\$ - thermal voltage equal to about \$25\text{ mV}...26\text{ mV}\$ at room temperature.

\$V_A\$ - Early voltage (Early effect).