BJT Transistor Equations
When operating in the forward active region (used for amplification), the collector current is proportional to the base current, controlled by the gain (β or hFE).
Where:
- Ib = Base current
- Ic = Collector current
- Ie = Emitter current
- β (hFE) = Forward DC current gain
Frequently Asked Questions
For a BJT operating in the active region, multiply the base current (Ib) by the transistor's DC gain (Beta or hFE).
A Bipolar Junction Transistor (BJT) is a three-terminal semiconductor device (Base, Collector, Emitter) in which a small base current controls a larger collector current. In NPN transistors: current flows from Collector to Emitter when base current flows into the Base (VBE ≈ 0.7V for silicon). The collector current IC = β × IB, where β (hFE) is the current gain, typically 50–500.
DC current gain β (also called hFE) = IC / IB. Typical values: small-signal transistors (2N2222, BC547) — β = 100–500; power transistors — β = 20–100; high-frequency transistors — β = 50–200. β varies with temperature, collector current, and VCE, and has wide spread between devices (e.g., 2N2222A datasheet specifies β = 75–300). Never design a circuit that relies on a specific β value.
Active region: VBE ≈ 0.7V, VCE > ~0.2V; IC = β × IB; transistor amplifies. Used in analog circuits. Saturation: transistor fully ON, VCE(sat) ≈ 0.1–0.3V; IC is circuit-limited, not β-limited; excess base drive; used as ON switch. Cutoff: VBE < 0.5V; IC ≈ 0; transistor fully OFF; used as OFF switch. Switching circuits (digital logic, motor drivers) operate between saturation and cutoff.
To switch a load (e.g., relay, motor, LED array): (1) Choose a transistor with IC(max) > load current and hFE > 10× overdrive factor. (2) Calculate base resistor: RB = (Vsupply − VBE) / IB, where IB = IC(load) / (hFE / 10). (3) Add a freewheeling diode across inductive loads (relays, motors). (4) Add a 1kΩ resistor between driving logic pin and base for logic protection.
The Early Effect (base-width modulation) is the increase in collector current as VCE increases, even in the active region. A higher VCE widens the collector-base depletion region, narrowing the effective base and increasing IC. This shows as slightly sloped (non-horizontal) IC vs VCE output curves. The Early Voltage VA (15–150V typical) quantifies it: IC = β×IB×(1 + VCE/VA). The Early Effect limits output impedance of BJT amplifiers.