Ebers-Moll model
currents emitter and collector of the DC in active mode are well modeled by an approach to model Ebers-Moll:
low internal current is mainly by diffusion (see Fick's law) and
Where
VT is thermal voltage kT / q (approximately 26 mV at room temperature of ≈ 300 K).
IE is the emitter current
IC is the collector current
αT is the short circuit current gain of the common front (0.98 to 0.998)
IES is the reverse current saturation of the base-emitter diode (on the order of 10-15 to 10-12 amps)
VSEA is the base-emitter voltage
Dn is the diffusion constant for electrons in the p-type base
is the base width W
The collector current is slightly unless the emitter current from the value of αT is very close to 1.0. In the BJT a small amount of base-emitter current causes a larger amount of collector-emitter current. The ratio of the current allowable collector-emitter to the base-emitter current is called current gain, β or hFE. A β value of 100 is typical for bipolar transistors smaller. In a typical configuration, a very small current signal passes through the base-emitter junction to control the emitter-collector current. the β is related to α by the following relations:
Efficiency issuer: that is, the ratio of the current injected into the base to the emitter current, the two differ due to injection of the base at the emitter and recombination. See carrier generation and recombination.
Unapproximated the Ebers-Moll equations used to describe the three streams in any region of operation is given below. These equations are based on transport model for a bipolar junction transistor. See, for example, Sedra and Smith. [21]
where
iC is the collector current
iB is the base current
iE is the emitter current
βF is the common emitter current gain of the front (20 to 500)
βR is the common emitter current gain reverse (0 to 20)
IS is the saturation reverse current (on the order of 10-15 to 10-12 amps)
VT is thermal voltage ( approximately 26 mV at room temperature of ≈ 300 K).
VSEA is the base-emitter voltage Vac
is the base-collector voltage
Modulation of Base-width
As the collector-base voltage applied (VBC ) varies, the region of collector-base depletion varies in size. An increase in the collector-base voltage, for example, causes a greater reverse bias across the collector-base junction, increasing the width of the depletion region of the collector-base, and reducing the width of the base. This variation in base width is often called "Early Effect" after after its discoverer James M. Early.
The narrowing of the base width has two consequences:
There is little chance for recombination within the base region "smaller."
The gradient of the load is increased through the base, and therefore, the flow of minority carriers injected across the junction increases the issuer.
Both factors increase the collector or "make out" the current of the transistor in response to an increase in the collector-base voltage.
active region forward in the early effect adjust the collector current (IC) and the common-emitter current gain of the front (βF) as given by the following equations: [citation needed]
Where
VCBES the collector-base voltage
VA is the early voltage (15 V to 150 V)
βF0 is the current rise common-emitter forward when VCB = 0 V
Current-voltage characteristics
The following assumptions are involved in deriving the current-voltage characteristics of ideal BJT
low level injection
uniform Doping each region with the hasty junctions
dimensional current flow
negligible recombination-generation in space charge regions
negligible electric fields outside the space charge regions.
is important characterize the diffusion currents induced by the minority carrier injection.
With respect to the pn junction diode, a key relationship is the diffusion equation.
A solution of this equation is down, and two boundary conditions used to solve and to find C1 and C2.
The following equations apply to the region of the emitter and collector, respectively, and the origins 0, 0 'and 0''be applied to the base, the collector, and the issuer.
A boundary condition of the issuer is below:
values \u200b\u200bof the constants A1 and B1 is zero due to the following conditions of the regions of the emitter and collector as and.
Since then A1 = B1 = 0, the values \u200b\u200bof ΔnE (0'') and Δnc (0 ') is A2 and B2, respectively.
IEN and nCI Expressions can be evaluated.
Since recombination occurs insignificant, the second derivative of ΔpB (x) is zero. There is therefore a linear relationship between excess hole density x.
The following are ΔpB boundary conditions.
Replace the above linear relationship.
.
With this result, derive the value of IEP.
Use IEP expressions, IEN, ΔpB (0), and ΔpB (W) to develop an expression of the emitter current.
Similarly, an expression of the collector current is derived.
An expression of the current floor is with previous results.
Punchthrough
When the base-collector voltage reaches a certain (device specific value), the limit of the depletion region base-collector resolve the boundary region of base-emitter depletion. When in this state the transistor does not have any base effectively. The device loses all of the increase when in this state.
charge-control model of Gummel-Poon
Gummel-Poon model [23] is a charge-controlled model detailed BJT dynamics, which has been adopted and elaborated by others to explain dynamics of the transistor in greater detail than do terminal-based models typically [2]. This model also includes the dependence of the transistor β-values \u200b\u200bover current levels in DC transistor, which are currently assumed independent in the Ebers-Moll model. See, for example, Sedra and Smith.
CRF
Lenny Z. Perez M
0 comments:
Post a Comment