EBERS Moll Model Presented by K.Pandiaraj Assistant Professor ECE Department Kalasalingam University
BJT Device Models The primary function of a model is to predict the behaviour of a device in particular operating region. Small-signal models Hybrid (h) Parameter Model Hybrid-pi model Large-signal models Ebers Moll model: Voltage & current control model Gummel Poon model : charge-control model
Ebers Moll Model The classic mathematical model for the bipolar junction transistor is the Ebers-Moll model formulated by J. J. Ebers and J. L. Moll from Bell Laboratories in the early 1954. Ebers-Moll model also known as Coupled Diode Model The Ebers-Moll model provides an alternative view or representation of the voltage-current equation model. Model includes configurationally series resistances, depletion Model includes configurationally series resistances, depletion capacitances and the charge carrier effects.
Ebers Moll model Designing Ebers Moll model for pnp transistor involves two ideal diodes placed back to back with saturation current I eo & I co and two current dependent controlled sources shunting the ideal diodes. Transistor currents and Voltages direction Ebers-moll model for a PNP transistor
Ebers Moll Model Equation By applying KCL to emitter node we get I E + α I I C = I or I E = I α I I C or I E = - α I I C + I I E = - α I I C + I 0 (e V E / V T 1) I E = -α I I C I E0 (e V E / V T 1)... (1) This model is valid for both forward & reverse static voltages applied across the transistor junction. In the above model, by making the base width much large than the diffusion length of minority carriers in the base, all minority carriers will recombine in the base and none will survive to reach the collector.
Ebers Moll Model Equation Let us see the equations of I c and I E from Ebers moll model. Applying KCL to the collector node, we get α N I E + I C = I I C = I α N I E I C = - α N I E + I ; Where, I is diode current. C N E I C = - α N I E + I 0 (e V c / V T 1) Note: I 0 = - I C0 ; Where, I 0 is the magnitude of reverse saturation current. I C = - α N I E I CO (e V C / V T ).. (2)
Ebers Moll model Parameters General expression for collector current I C of a transistor for any voltage across collector junction V c and emitter current I E is I C = -α N I N I CO (e V C / V T 1) Subscript N to α indicates that we are using transistor in a normal manner. When we interchange the role of emitter and collector we operate transistor in a inverted function. In such case current and junction voltage relationship for transistor is given by I E = - α I I C I EO (e v E / V T 1) Subscript I to α indicates that we are using transistor in a inverted manner, α I is the inverted common base current Gain. I EO: The emitter junction reverse saturation current. V E : The voltage drop from p side to N side at the emitter junction.
Forward Characteristics of the npn Transistor The total current crossing the emitter-base junction in the forward direction is described as (equation-1) Equation (1) Where IES represents the reverse saturation current of the base-emitter diode. Collector current can be rewritten in terms of IES as (equation-2) Equation (2) Forward common-base current gain αf represents the fraction of the emitter current that crosses the base and appears in the collector terminal.
Reverse Characteristics of the npn Transistor For the reverse direction, the current crossing the collector-base junction is described as (equation-3) Equation (3) The new parameter ICS represents the reverse saturation current of the base-emitter diode. The emitter current can be rewritten in terms of ICS as (equation-4) Equation (4) The reverse common-base current gain αr represents the fraction of the collector current that crosses the base from the emitter terminal.
Ebers-Moll Model for the npn Transistor Complete Ebers-Moll equations are obtained by combining Equations 1-4. Equation (5) This model contains four parameters, IES, ICS, αf, and αr. From the definitions of IES and ICS, we can obtain the important auxiliary relation Equation (6) which shows that there are only three independent parameters in the Ebers-Moll model, just as in the transport formulation. The base current, given by ib = ie ic, is Equation (7)
Equivalent Circuit Representations for the Ebers-Moll Models npn transistors
Equivalent Circuit Representations for the Ebers-Moll Models pnp transistors
Ebers Moll Operating Characteristic
BJT Ebers-Moll Model SPICE model: DC model SPICE uses the Ebers-Moll transistor model You know the following BJT equations:
Ebers-Moll model Versions