Sunday, 22 April 2018

bjt - Why the input resistance of a common emitter amplifier is like this?


I am trying to find the input resistance of this BJ common-emitter amplifier:


enter image description here


I replace the transistor with the hybrid-pi model


enter image description here



It appears clear to me that the input impedance will be


$ R_{in} = R_1 // R_2 // (R_E + r_\pi) $


but some authors say


$ R_{in} = R_1 // R_2 // h_{FE}(R_E + r_\pi) $


What is the correct value?



Answer



Draw this small-signal equivalent circuit:


$R_{IN} = \frac{V_X}{I_B}$


schematic


simulate this circuit – Schematic created using CircuitLab



And we can see that $R_{IN} = \frac{V_X}{I_B}$


VX=IBrπ+IERE=IBrπ+(IB+IC)RE=IBrπ+(IB+hFEIC)RE

=IBrπ+IB(hFE+1)RE


Therefore


$R_{IN} = \frac{V_X}{I_B} =r_\pi + (h_{FE}+1)R_E$


Or simply think about emitter current


$I_E = I_B + I_C = I_B + \beta I_C = I_B(\beta+1) $


Try read this http://www.ittc.ku.edu/~jstiles/412/handouts/5.6%20Small%20Signal%20Operation%20and%20Models/section%205_6%20%20Small%20Signal%20Operation%20and%20Models%20lecture.pdf


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