Impedance is defined as Z = V/I. In linear circuits (with resistors, capacitors, inductors, batteries, etc.) this ratio is the reciprocal of the slope of the I versus V graph. In circuits with nonlinear elements such as a transistor, the input impedance of the resistor is defined as the reciprocal of the slope of the I versus V graph. This is simply the derivative of Vin with respect to Iin-
Vin = VB = VBE +VE = VBE + IERE [IR = IC + IB = βIB + IB = (β + 1)IB]
Vin =VBE + IERE = IB(β + 1)RE [IB = Iin]
Vin = VBE + Iin (β + 1) RE
Taking the derivative of Vin with respect to Iin, remembering that VBE is a constant, we get the result:
Zin = dVin/dIin = d/dIin(VBE + Iin (β + 1)RE) = (β + 1)RE
Zin = (β + 1)RE ≈ βRE |
Because IE = IB (β + 1). The IR drop across RE is greater then it would be for IB alone. The amplification of the base current causes RE to appear larger to a source looking into the input by (β + 1).
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