EBERS MOLL MODEL PDF

Saturation The ideal transistor model is based on the ideal p-n diode model and provides a first-order calculation of the dc parameters of a bipolar junction transistor. To further simplify this model, we will assume that all quasi-neutral regions in the device are much smaller than the minority-carrier diffusion lengths in these regions, so that the "short" diode expressions apply. The use of the ideal p-n diode model implies that no recombination within the depletion regions is taken into account. Such recombination current will be discussed in section 5. 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. Forward active mode of operation The forward active mode is obtained by forward-biasing the base-emitter junction.

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Transistors characteristically have multiple modes of conduction. We can view these phenomena in the two-diode model of a bipolar junction transistor BJT. Two diodes whose anodes join to form a center tap are analogous to an NPN transistor insofar as ohmmeter readings accurately represent the real device. Two diodes with cathodes connected to a common node are analogous to a PNP transistor.

NPN transistors are preferred due to increased mobility of electrons compared to holes and also because they are compatible with a negative ground system. Because two diodes are separate components and cannot share in common a semiconducting layer, they do not function as an amplifier, go into oscillation or perform switching action in the manner of actual transistors.

When in forward-active mode, the collector diode is reverse-biased so ICD is virtually zero. To accurately model a BJT, we must look beyond the simple diode hookup, although that remains relevant. In addition to the diode model, which is a physical simulation, Ebers-Moll is a paper construct, having its existence in part as a schematic diagram and also a set of equations, either of these deploying conventional symbols.

Jewel James Ebers and John L. Moll introduced this mathematical model of transistor currents in A generalized two-terminal-pair theory of junction transistors is presented which is applicable, on a dc basis, in all regions of operation. Using this theory, the open and closed impedances of the transistor switch are expressible in terms of easily measurable transistor parameters.

For the ideal transistor, these parameters are the saturation currents of the emitter and collector junctions and the normal and inverted alphas. The transition of the transistor switch from open to closed, or vice versa, is discussed, including the effects of minority carrier storage.

This transition can be expressed in analytic form in terms of the alphas and the normal and inverted alpha cut-off frequencies. Notice that In the BJT, typically there are two two-wire circuits, input and output. The device in its fundamental form has three rather than four terminals because one of them — which can be base, emitter or collector — is common to both circuits.

The output circuit can convey to the next stage an amplified or an attenuated version of the signal at the input. When the input and output at each point in time are in the same ratio, the device is said to be linear and when that ratio varies, the device is non-linear.

Both linear and non-linear devices possess some finite gain. Or gain can be infinite, theoretically but not in actuality, where a big-bang condition would exist. The common-emitter voltage gain is always in low negative territory. The current gain in a common base transistor circuit is by definition the change in collector current over the change in emitter current when the voltage difference between base and collector does not vary.

A typical common base current gain is one. In a BJT, each of the two junctions can be forward biased or reverse biased. Accordingly, there are four possible modes in which the transistor can operate. It is cut off when the emitter-base junction and the collector-base junction are reverse biased. When both of these junctions are forward biased, the device is in saturation.

When the emitter-base junction is forward biased and the collector-base junction is reverse biased, the transistor is in the forward-active mode. Finally, the transistor is in the reverse-active mode when the emitter-base is reverse biased and the collector-base is forward biased. Between cutoff and saturation, the device acts as a switch, which may be open with a high impedance or closed with a low impedance. In these biasing conditions, there is no intermediate state.

In the forward-active mode, the transistor operates as an amplifier, and in the reverse active mode, it may be used in digital and analog switching operations. Surprisingly, under certain biasing and signal input conditions, the physical dimensions of a BJT will actually change.

This phenomenon was first noted by James Early in and is known as the Early effect. It manifests as a shrinking base width due to a widening of the base-collector depletion region. The result is a rise in collector current and voltage. The wave-shape polarities shown here apply to a npn transistor. Trace settings for a pnp transistor would use opposite polarity negative voltage and currents.

When it becomes necessary to physically measure transistor parameters such as current gain, breakdown voltages, and impedance, a transistor curve tracer is usually the instrument of choice.

The curve tracer can generate and display a family of curves of collector current, Ic, versus collector-to-emitter voltage, VCE, for various values of base current, IB. A curve tracer uses three basic circuits to generate this display: a sweep-voltage-generator for control of the collector voltage; a base current source which can be controlled to provide a number of equal increments of base currents with each sweep of the voltage generator; and a timing source to change the base current at the start of each voltage sweep.

The waveform of the sweep-voltage generator, Vs consists of repetitive sweeps occurring with a time period T. This is the collector supply voltage which is repetitively applied to the transistor. The collector voltage, Vce, will provide the horizontal x-axis sweep. A view of the output of the base current source shows that for each consecutive voltage sweep the base current, IB, is incremented in equal steps with each step synchronized to the beginning of each collector voltage sweep.

As the last increment period ends, the base current generator repeats the step sequence. In the U. The collector-to-emitter voltage, Vce, provides the horizontal sweep, while the voltage across the current sensing resistor, Rc, which is proportional to collector current, provides the vertical sweep, resulting in a family of curves of Ic versus Vce for a series of equal increment changes in base current. The displays shown here are for an npn transistor.

The slope of the load line is determined by a dissipation-limiting resistor, RL, selected in the collector sweep control section. The direction of current flow in a pnp transistor is the reverse of that for an npn transistor, so the VCE and the direction of the base current must be reversed, resulting in the characteristic curve visible here. Finally, transistors on a curve tracer can heat up, so use caution in handling them.

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Ebers-Moll Model

Dojin Holt, Reinhart, and Winston. It is typically the emitter efficiency, which limits the current gain ebres transistors made of silicon or germanium. Sometimes it is also called Giacoletto model because it was introduced by L. In the reverse active mode, we reverse the function of the emitter and the collector.

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Chapter 5: Bipolar Junction Transistors

This is called conventional current. However, current in many metal conductors is due to the flow of electrons. Because electrons carry a negative charge, they move in the direction opposite to conventional current. In this article, current arrows are shown in the conventional direction, but labels for the movement of holes and electrons show their actual direction inside the transistor. The arrow on the symbol for bipolar transistors indicates the PN junction between base and emitter and points in the direction in which conventional current travels. Function[ edit ] This section may be too technical for most readers to understand.

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The Bipolar Transistor (Ebers Moll Model)

Transistors characteristically have multiple modes of conduction. We can view these phenomena in the two-diode model of a bipolar junction transistor BJT. Two diodes whose anodes join to form a center tap are analogous to an NPN transistor insofar as ohmmeter readings accurately represent the real device. Two diodes with cathodes connected to a common node are analogous to a PNP transistor. NPN transistors are preferred due to increased mobility of electrons compared to holes and also because they are compatible with a negative ground system. Because two diodes are separate components and cannot share in common a semiconducting layer, they do not function as an amplifier, go into oscillation or perform switching action in the manner of actual transistors. When in forward-active mode, the collector diode is reverse-biased so ICD is virtually zero.

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