I am trying to find the input resistance of this BJ common-emitter amplifier:
I replace the transistor with the hybrid-pi model
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:
$R_{IN} = \frac{V_X}{I_B}$
simulate this circuit – Schematic created using CircuitLab
And we can see that $R_{IN} = \frac{V_X}{I_B}$
VX=IB⋅rπ+IERE=IB⋅rπ+(IB+IC)RE=IB⋅rπ+(IB+hFEIC)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) $
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