Cut-off frequencies in Bipolar Junction Transistors (BJTs) mark the transition between the signal's pass band and stop band, influencing their performance in amplifying or attenuating frequencies. These frequencies are crucial for designing BJTs to meet specific operational requirements in electronic circuits.

Alpha Cut-Off Frequency: Pertinent to the common-base configuration, the alpha cut-off frequency defines the upper-frequency limit at which the current gain, alpha, remains stable. As frequencies increase beyond this critical point, alpha decreases, reducing the transistor's effectiveness in amplifying signals.

Beta Cut-Off Frequency: More relevant in common-emitter configurations, the beta cut-off frequency is significantly lower than its alpha counterpart. It describes the frequency at which the common-emitter current gain, beta, starts to fall off, adversely impacting the amplifier's performance.

Transition Frequency: This frequency, slightly lower than the beta cut-off frequency, signifies the gain-bandwidth product of the BJT. It is the frequency at which the amplifier's gain equals unity, indicating the highest frequency at which the transistor can function effectively as an amplifier.

Carrier Transit Times: The transition frequency also reflects the total time carriers take to travel from the emitter to the collector, incorporating the emitter delay time, base transit time, and collector transit time. The base transit time is especially critical; minimizing it through a narrower base width enhances the BJT's high-frequency response.

These cut-off frequencies are essential for understanding and optimizing BJTs' frequency behavior, particularly in high-frequency applications, ensuring they operate within their effective range.