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Transistor Biasing Calculator

Learn the operating modes of one of the most important electronic components with our transistor biasing calculator.

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Base current24.0426 µA(12 − 0.7) ÷ 470,000
Collector current3.6064 mAβ × I_B, in the active region
Collector-emitter voltage4.066 Vin the active region
Voltage gain-306.7×−I_C R_C ÷ V_T — note it depends on the COLLECTOR CURRENT, not on beta, which is why bipolar gain is predictable despite beta varying wildly between parts
Transconductance g_m139.4314 mSI_C ÷ V_T — far higher than a MOSFET at the same current
Quiescent power14.6634 mW
Why fixed-bias is fragilebeta varies 3:1 between partsthis circuit sets the BASE current, so the collector current follows beta and drifts with temperature — an emitter resistor with a divider bias is used instead for anything real

The formula

I = I_s(e^(V/nV_T) − 1); I_D = ½k(V_GS − V_th)²

Exponential, square law, and why it matters

A diode's current rises exponentially with voltage — about a decade for every 60 mV at room temperature. That steepness is why a diode behaves like a fixed 0.7 V drop over a wide current range, and why driving one from a voltage source is destructive: 60 mV of error is a factor of ten in current.

A MOSFET in saturation follows a square law in the overdrive voltage, which is far gentler. That makes MOSFETs easier to bias and much better at paralleling, helped by their threshold falling with temperature so a hot device turns on harder and shares current — whereas a hot bipolar takes more current and runs hotter still.

The bipolar result worth knowing is that voltage gain depends on the collector current and the load resistor, not on beta. Since beta varies threefold between nominally identical parts and drifts with temperature, that independence is what makes bipolar amplifiers designable at all. The fixed-base-resistor bias shown here sets base current rather than collector current, so it inherits all of beta's variability — which is why real circuits use an emitter resistor and a divider.

The thermal voltage kT/q scales with absolute temperature, so every one of these relations shifts as a device warms. Hard-coding 25 mV is a room-temperature approximation, not a constant.