Large-signal models

Ebers-Moll model

Ebers-Moll Model for an NPN transistor

• I_B, I_C, I_E: collector, base, and emitter currents
• I_CD, I_ED: collector and emitter diode currents
• α_F, α_R: forward and reverse common base current gains

Ebers Moll Model for a PNP transistor

The DC emitter and collector currents in active mode are well modeled by an approximation to the Ebers Moll model:

The base internal current is mainly by diffusion and

here

• V_T is thermal voltage kT / q (approximately 26 mV at 300 K ≈ room temperature).
• I_E is emitter current
• I_C is collector current
• α_T is common base forward short circuit current gain (0.98 to 0.998)
• I_ES is reverse saturation current of the base-emitter diode (on the order of 10-15 to 10-12 amperes)
• VBE is base-emitter voltage
• Dn is diffusion constant for electrons in the p-type base
• W is base width

The unapproximated Ebers-Moll equations used to describe the three currents in any operating region are given below. These equations are based on the transport model for a bipolar junction transistor.

where

• i_C is the collector current
• i_B is the base current
• i_E is the emitter current
• β_F is the forward common emitter current gain (20 to 500)
• β_R is the reverse common emitter current gain (0 to 20)
• I_S is the reverse saturation current (on the order of 10-15 to 10-12 amperes)
• V_T is the thermal voltage(approximately 26 mV at 300 K ≈ room temperature).
• V_BE is the base-emitter voltage
• V_BC is the base-collector voltage

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