Question E6A06:
What is the beta of a bipolar junction transistor?  

Choices:  
A: The frequency at which the current gain is reduced to 0.707  
B: The change in collector current with respect to the change in base current  
C: The breakdown voltage of the base-to-collector junction  
D: The switching speed    

Correct Answer is  B: The change in collector current with respect to the change in base current  

Correct answer: B — The change in collector current with respect to the change in base current

1) Why the correct answer is correct
- In a BJT, beta (β) is the current gain from base to collector, defined as the ratio of collector current to base current. For small-signal changes:
  $$\beta = \frac{\Delta I_C}{\Delta I_B}$$
- For DC (large-signal) operation, it’s often approximated as:
  $$\beta \approx \frac{I_C}{I_B}$$
- This parameter is also known as h_FE (DC) or h_fe (AC small-signal).

2) Why the other choices are incorrect
- A: “The frequency at which the current gain is reduced to 0.707”  
  That describes a -3 dB bandwidth point, not beta. A related transistor figure is the transition frequency $f_T$, where current gain drops to 1 (0 dB), not 0.707.
- C: “The breakdown voltage of the base-to-collector junction”  
  That’s a breakdown rating (e.g., $BV_{CBO}$ or $BV_{CBO}$/$BV_{CEO}$), not a gain parameter.
- D: “The switching speed”  
  Switching speed involves rise/fall/storage times and $f_T$, not beta. While beta can influence switching behavior, it is not itself a speed.

3) Useful formulas and rules of thumb
- Basic relationships:
  $$I_C \approx \beta I_B,\quad I_E = I_C + I_B = (\beta + 1) I_B$$
- Relation to alpha (common-base gain):
  $$\alpha = \frac{I_C}{I_E},\quad \beta = \frac{\alpha}{1 - \alpha},\quad \alpha = \frac{\beta}{\beta + 1}$$
- Small-signal model links:
  $$g_m = \frac{I_C}{V_T},\quad r_\pi = \frac{\beta}{g_m}$$
  where $V_T \approx 25.9\ \text{mV}$ at room temperature.
- Rule of thumb: β varies widely (roughly 20–200+), depends on device, collector current, temperature, and decreases at higher frequencies.