Electrical – Low Frequency Response of BJT amplifier(effect of bypass capacitor)


Doubt related to impedance seen by the bypass capacitor:


What is the impedance seen by the bypass capacitor \$C_E\$

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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:


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.)

Best Answer

Soumee, I cannot identify any error in your calculation.

However, if you replace in the third line of your calculation the term (1+β) by β, your result will be identical to the expression as given in the book. As you know the current gain β is relatively large (mostly > 100), not a constant but dependent on Ic and - more important - equipped with large tolerances.

Therefore, we often simplify (1+β) to β (without expecting not acceptable errors) - and this seems to be the only reason for the discrepancy you have observed.