Frequency response of BJT frequencies with CE bypassed

Solution:

1. The error done is that it is necessary to include all the branches of the current sources (ic was forgotten).
2. Another error is that since

to get

a bad representation of the current branches which does not respect the transistor (with its currents ie, ic, ib) gives an unusable diagram

[fig. 1] is the good choice.

[fig. 2] it makes no sense.

So the solution is [fig. 1] and you get

thus the calculation of z1 gives

and finally you can give this representation

and for the calculation of Z you do not have to worry about the current flowing in Re nor in Z1.


Likewise, you must remember of considering the BJT with its current on its ports (ie, ib, ic) so make the extensions of the wires with their currents.

• Case of a good calculation from RE : put the pen between RE and ie : you'll see it's RE || Z1. In this case, you can calculate Z1 with the branch ib, ic :

• Case of a bad calculation of Z1 :

Likewise, the BJT with its current on its ports (ie, ib, ic) so make the extensions of the wires with their currents. In theses pictures you'll see a demonstration with $ r_e $ and $ pi $ model.

Demonstration with $ r_e $ (or T) model :

Demonstration with $ pi $ model ($ pi $ model obtained with the T model) :