Definition of Bipolar Junction Transistor (BJT)

The Bipolar Junction Transistor (BJT) is an active device. In simple terms, it is a current controlled valve. The base current (IB) controls the collector current (Ic).

Tuesday, March 17, 2009

Input Impedance of a Transistor

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-

Zin = dVin / dIin





We can easily find Zin from what we know already of the behavior of the transistor. We know that the sum of VBE and the IR drop across RE must equal Vin.

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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