# Low Frequency Response of BJT amplifier(effect of bypass capacitor)

Doubt related to impedance seen by the bypass capacitor:

or

What is the impedance seen by the bypass capacitor $C_E$ To calculate the impedance as seen by $C_E$, we attach a Thevenin volatge source as shown.

Applying Kirchoff's current law:

$$\frac{V_T}{\beta r_e+R_S||R1||R_2}-\beta I_B+\frac{V_T}{R_E}=I_T$$ $$\frac{V_T}{\beta r_e+R_S||R1||R_2}+\beta \frac{V_T}{\beta r_e+R_S||R1||R_2} +\frac{V_T}{R_E}=I_T$$ $$V_T[\frac{(1+\beta)}{\beta r_e+R_S||R_1||R_2}+\frac{1}{R_E}]=I_T$$ $$V_T[\frac{1}{\beta r_e+R_S||R1||R_2}+\frac{1}{r_e+\frac{R_S||R_1||R_2}{\beta}}+\frac{1}{R_E}]=I_T$$

From here I get the resistance as $$\frac{1}{R_e}=\frac{1}{\beta r_e+R_S||R1||R_2}+\frac{1}{r_e+\frac{R_S||R_1||R_2}{\beta}}+\frac{1}{R_E}$$

However in book, the resistance has been given as:

$$R_e=R_E||(\frac{R_s||R1||R2}{\beta}+r_e)$$

It seems the first term in $\frac{1}{R_e}$ vanishes! Where might have I gone wrong?

(I have referred to the following text book: Electronic Devices and Circuit Theory, by Boylestad and Nashelsky.)

• Do you know the voltage gain of a common-emitter stage with degeneration? If you know, then it would be much easier to figure out the gain with the capacitor added in parallel with Re Feb 27, 2017 at 8:22
• I'm not even sure what your question is! Also, you might get a better response if you learnt how to formally accept answers to questions you've raised. If you don't understand an answer then comment but, basically, the only fee that you are charged for receiving good information is pressing a button on the best answer. Feb 27, 2017 at 8:36
• I think he wants to calculate the gain w/ the cap added Feb 27, 2017 at 8:38
• @Andyaka I want to calculate the impedance seen by the bypass capacitor Feb 27, 2017 at 8:38
• My wild guess would be assuming beeta*re value is too high and so the first part is negligible. Feb 27, 2017 at 8:41

Here put It=0 because according to KCL algebraic sum of currents in the node is zero. $1+b = b$ (it doent make any change)