# Frequency response of BJT frequencies with CE bypassed

In a lot of reference I see divergence like Zce = RE || (beta re + Rb || Rs) / (beta + 1) etc. $$Z_{ce} = R_E || \left(\frac{\beta.r_e + R_b || R_s}{\beta + 1}\right)$$

but from a trivial example I get

Zce = RE || (beta re + Rb || Rs) / (beta) $$Z_{ce} = R_E || \left(\frac{\beta .r_e + R_b || R_s}{\beta}\right)$$

Note : with that, i get the same result than here with the result of Electronic Devices and Circuit Theory, by Boylestad and Nashelsky.

Note : I know with beta >= 100 it is the same but i like to have a rigourous demonstration.

Do you think it is a good reasoning here ?

• Why bypass Collector Emitter? What's that all about then? What has your question got to do with the links at the top? Do we need to read these first? If so, then ermm no. Commented Jul 24, 2020 at 16:12
• That the correct equation is $Z = R_E|| (r_e + \frac{R_B||R_S}{\beta +1})$
– G36
Commented Jul 24, 2020 at 16:28
• Because in $\beta r_e$ is just an approximation the correct version is $r_\pi = (\beta +1)r_e$
– G36
Commented Jul 24, 2020 at 16:30
• $r_e = \frac{dV_{BE}}{dI_E} = \frac{V_T}{I_E}$ electronics.stackexchange.com/questions/429716/…
– G36
Commented Jul 24, 2020 at 16:32
• Did you notice the mistake in your analysis?
– G36
Commented Jul 24, 2020 at 18:22

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) :

• Is this an answer to your question? If not it belongs as an edit to the original question and this post should be deleted. Please use capital letters at the start of sentences and punctuation marks (.) at the end.. Commented Jul 26, 2020 at 14:41
• I'm glad that you manage to figure it out.
– G36
Commented Jul 27, 2020 at 13:33