Ebers–Moll model for an NPN transistor. mode are well modeled by an approximation to the Ebers–Moll model. Ebers and Moll created a model between the current and voltages in the transistor terminals. This model is knowned as the Ebers Moll model. The Ebers-Moll model is an ideal model for a bipolar transistor, which can be used, in the forward active mode of.

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From this equation, we conclude that the current gain can be larger than one if the emitter doping is much larger than the base doping. E refers to the transistor operating in a common emitter CE configuration. The collector current in a BJT when operated in normal mode is given as. This variation in base width often is called the Early effect after its discoverer James M. Although these regions are well defined for sufficiently large applied voltage, they overlap somewhat for small less than a few hundred millivolts biases.

Arrow according to schematic. The device thus loses all gain when in this state.

It is this gain that allows BJTs to be used as the building blocks of electronic amplifiers. However, current in many metal conductors is due to the flow of electrons which, because they carry a negative charge, move in the direction opposite to conventional current.

Chapter 5: Bipolar Junction Transistors

The hybrid-pi model is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. Physics and Technology of Heterojunction Devices. These views are related by the current—voltage relation of the base—emitter junction, which is the usual exponential current—voltage curve of a p—n junction diode.

However, to accurately and reliably design production BJT circuits, the voltage-control for example, Ebers—Moll model is required. Because the base current is approximately proportional to the collector and emitter currents, they vary in the same way. In this mode, the transistor has an emitter efficiency and base transport factor as described by equations 5.


These have been addressed in various more advanced models: That is, a PNP transistor is “on” when its base is pulled low relative to the emitter.

The emitter current due to electrons and holes are obtained using the “short” diode expressions derived in section 4. The discussion of the ideal transistor starts with a discussion of the forward active mode of operation, followed by a general description of the four different bias modes, the corresponding Ebers-Moll model and a calculation of the collector-emitter voltage when the device is biased in saturation.

As shown, the term, xin the model represents a different BJT lead depending on the topology used. The minority carrier lifetime in the base is 10 ns. Holt, Reinhart, and Winston. In an NPN transistor, when positive bias is applied to the base—emitter junction, the equilibrium is disturbed between the thermally generated carriers and the repelling electric field of the n-doped emitter depletion region.

Instead, they drift through the base-collector depletion region and end up as majority carriers in the collector region. This ratio usually has a value close to unity; between 0.

The collector—base junction is reverse-biased, and so little electron injection occurs from the collector to the base, but electrons that diffuse through the base towards the collector are swept into the collector by the electric field in the depletion region of the collector—base junction.

Poon, “An integral charge control model of bipolar transistors”, Bell Syst. For a diode with voltage V applied between its terminals, the current flowing through the junction in terms of applied voltage between its terminals is given by.

The forward- and reverse-bias transport factors are obtained by measuring the current gain in the forward active and reverse active mode of operation. The base internal current is mainly by diffusion see Fick’s law and.

The ideal transistor hransistor is based on the ideal p-n diode model and provides a first-order calculation of the dc parameters of a bipolar junction transistor. Because base—emitter voltage varies as the logarithm of the base—emitter and collector—emitter currents, a BJT can also be used to compute logarithms and anti-logarithms. Microelectronic Circuits, second ed. The common-base current gain is approximately the gain of current from emitter to collector in the forward-active region.


The emitter efficiency defined by equation 5. By convention, the direction of current on diagrams is shown as the direction that a positive charge would move. Tansistor is convenient to rewrite the emitter current due to electrons, I E,nas a function of the total excess minority charge in the base, D Q n,B.

A typical current gain for a silicon bipolar transistor is 50 – Early transistors were made from germanium but most modern BJTs are made from silicon. The Base to emitter voltage and base to collector voltage in terms of currents can be derived as follows.

Ebers Moll Model of a Bipolar Transistor – Electronics Area

A diode can also perform these nonlinear functions but the transistor provides more circuit flexibility. The collector diode is reverse-biased so I CD is virtually zero.

In terms of junction biasing: Connecting two diodes with wires will not make a transistor, since minority carriers will not be able to get from one P—N junction to the other through the wire.

Saturation is rransistor avoided in high-speed bipolar logic circuits. This barrier arrangement helps reduce minority carrier injection from the base when the emitter-base junction is under forward bias, and thus reduces base current and increases emitter injection efficiency.

This can be trwnsistor as follows: Transistor Manual 6th ed. The base transport factor, as defined in equation 5. The base is physically transietor between the emitter and the collector and is made from lightly doped, high-resistivity material.

Various methods of manufacturing bipolar transistors were developed. The proportion of electrons able to cross the base and reach the collector is a measure of the BJT efficiency.