Electronics Engineering (ELEX) Board Practice Exam

What is the DC input resistance looking into the base of a transistor with a β_DC of 125?

1. 125 kΩ

2. 125 Ω

3. 1.25 kΩ

4. 12.5 kΩ

The correct answer is: 125 kΩ

The DC input resistance looking into the base of a bipolar junction transistor (BJT) can be calculated using the relationship involving the current gain (β) of the transistor. The input resistance can be defined as the resistance seen at the base, which is influenced by the transistor's beta value. The formula for determining the input resistance (R_in) at the base is approximately given by: \[ R_{in} \approx \beta \times r_e \] where r_e is the small-signal emitter resistance. For practical calculations, if the emitter is unbypassed, then the dynamic emitter resistance r_e can be evaluated as: \[ r_e \approx \frac{26 \, mV}{I_E} \] where \( I_E \) is the emitter current. In applications where I_E is known, you could calculate r_e and subsequently R_in. However, when specific values of I_E are not provided, it is acceptable to take r_e as a general value. In this specific instance, if we assume a typical operating condition where the input resistance could be approximated or modeled directly from the β value, a common approach is to consider a value of input resistance around 1 kΩ per unit of beta. Therefore