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BJT Operating Regions

Defines the three operational states (Cutoff, Active, Saturation) of a Bipolar Junction Transistor (BJT), governed by biasing voltages and current flow. The key transition is between the active region and saturation.
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The statement of the theorem

Let VBEV_{BE} and VCBV_{CB} be the base-emitter and collector-base voltages, respectively. The BJT operating regions are defined by the following conditions:\n\n1. **Cutoff Region:** VBE<VonV_{BE} < V_{on} and VCB<0V_{CB} < 0 (or IC→0I_C \to 0).\n2. **Active Region:** VBE≮VonV_{BE} \nless V_{on} and VCB≮0V_{CB} \nless 0. In this regime, the collector current ICI_C is modeled by the relationship:\nIC≈βαrIE≈βη1+VCEVAIE\quad I_C \approx \frac{\beta}{\alpha_r} I_E \approx \frac{\beta \eta}{1 + \frac{V_{CE}}{V_A}} I_E (where β\beta is the current gain, αr\alpha_r is the reverse transfer ratio, and η\eta is the emitter efficiency).\n3. **Saturation Region:** VCB≤VCE(sat)V_{CB} \le V_{CE(sat)}. In this regime, the collector current ICI_C is limited by the external circuit and is approximated by:\nIC≈VCC−VCERL≤IC(sat)\quad I_C \approx \frac{V_{CC} - V_{CE}}{R_L} \le I_{C(sat)}