Electronic – Calculating output impedance of Vbe multiplier

analogbjtcircuit analysis

I am trying to calculate the output impedance of the following Vbe multiplier,

schematic

simulate this circuit – Schematic created using CircuitLab

I have calculated the Vout = 4.2V and now I am trying to calculate the output impedance, so in order to do this I tried to do it by AC analysis. So got the below figure,

schematic

simulate this circuit

So now I am not sure how to process further, I know re//R1 and re = 1 / (40 * Ic) but after this how do I proceed further?

Best Answer

Since we have seen some different approaches to arrive at the (correct) solution, here comes my version:

1.) From feeback theory we know that r,out=r,open/(1-LG) (with r,open: output resistance without feedback; LG=Loop gain).

2,) For calculation of r,open and LG we open the feedback loop at a point which does not require a load mirror (no loading errors due to opening): Such a node is at the base because r,be may be assumed to be infinite (ib=0 because of beta infinite).

3.) From simple inspection: r,open=R1+R2 and LG=-gm*(R1+R2)*R2/(R1+R2)=-gm*R2.

4.) Inserting into the expression under 1) gives r,out=(R1+R2)/(1+gm*R2).

5.) Setting gm=Ic/Vt=0.235 A/V we have r,out=25.4 ohms.

Related Topic