Early effect - Wikipedia, the free encyclopedia http://en.wikipedia.
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Early effect
From Wikipedia, the free encyclopedia
The Early effect is the variation in the width of the base in a bipolar
junction transistor (BJT) due to a variation in the applied base-to-
collector voltage, named after its discoverer James M. Early. A
greater reverse bias across the collector–base junction, for example,
increases the collector–base depletion width, decreasing the width
of the charge neutral portion of the base.
In Figure 1 the neutral (i.e. active) base is green, and the depleted
base regions are hashed light green. The neutral emitter and
collector regions are dark blue and the depleted regions hashed light
blue. Under increased collector–base reverse bias, the lower panel
of Figure 1 shows a widening of the depletion region in the base and
the associated narrowing of the neutral base region.
The collector depletion region also increases under reverse bias,
more than does that of the base, because the collector is less heavily
doped. The principle governing these two widths is charge
neutrality. The narrowing of the collector does not have a significant
effect as the collector is much longer than the base. The Figure 1. Top: NPN base width for low
emitter–base junction is unchanged because the emitter–base collector–base reverse bias; Bottom:
voltage is the same. narrower NPN base width for large
collector–base reverse bias. Hashed areas
Base-narrowing has two consequences that affect the current: are depleted regions.
There is a lesser chance for recombination within the
"smaller" base region.
The charge gradient is increased across the base, and
consequently, the current of minority carriers injected
across the emitter junction increases.
Both these factors increase the collector or "output" current
of the transistor with an increase in the collector voltage.
This increased current is shown in Figure 2. Tangents to the Figure 2. The Early voltage (VA) as seen in the
characteristics at large voltages extrapolate backward to output-characteristic plot of a BJT.
intercept the voltage axis at a voltage called the Early
voltage, often denoted by the symbol VA.
Contents
1 Large-signal model
2 Small-signal model
3 References and notes
4 See also
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Early effect - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Early_effect
Large-signal model
In the forward active region the Early effect modifies the collector current (IC) and the forward common-
emitter current gain (βF), as typically described by the following equations:[1][2]
Where
VCE is the collector–emitter voltage
VT is the thermal voltage kT / q; see thermal voltage: role in semiconductor physics
VA is the Early voltage (typically 15 V to 150 V; smaller for smaller devices)
βF0 is forward common-emitter current gain at zero bias.
Some models base the collector current correction factor on the collector–base voltage VCB (as described in
base-width modulation) instead of the collector–emitter voltage VCE.[3] Using VCB may be more physically
plausible, in agreement with the physical origin of the effect, which is a widening of the collector–base depletion
layer that depends on VCB. Computer models such as those used in SPICE use the collector–base voltage
VCB.[4]
Small-signal model
The Early effect can be accounted for in small-signal circuit models (such as the hybrid-pi model) as a resistor
defined as[5]
in parallel with the collector–emitter junction of the transistor. This resistor can thus account for the finite
output resistance of a simple current mirror or an actively loaded common-emitter amplifier.
In keeping with the model used in SPICE and as discussed above using VCB the resistance becomes:
which almost agrees with the textbook result. In either formulation, rO varies with DC reverse bias VCB, as is
observed in practice.[citation needed]
In the MOSFET the output resistance is given in Shichman–Hodges model[6] (accurate for very old technology)
as:
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Early effect - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Early_effect
where VDS = drain-to-source voltage, ID = drain current and λ = channel-length modulation parameter, usually
taken as inversely proportional to channel length L. Because of the resemblance to the bipolar result, the
terminology "Early effect" often is applied to the MOSFET as well.
References and notes
1. ^ R.C. Jaeger and T.N. Blalock (2004). Microelectronic Circuit Design (http://books.google.com
/books?id=u6vH4Gsrlf0C&pg=PA317&dq=early-effect+collector+depletion+collector-base&as_brr=3&ei=92gtR-
OaGKLstAOFn_SgCQ&sig=Tm2F-2TyuE-sePiaK1A-gdmpqtQ#PPA317,M1) . McGraw-Hill Professional. p. 317.
ISBN 0072505036. http://books.google.com/books?id=u6vH4Gsrlf0C&pg=PA317&dq=early-
effect+collector+depletion+collector-base&as_brr=3&ei=92gtR-OaGKLstAOFn_SgCQ&sig=Tm2F-2TyuE-
sePiaK1A-gdmpqtQ#PPA317,M1.
2. ^ Massimo Alioto and Gaetano Palumbo (2005). Model and Design of Bipolar and Mos Current-Mode Logic:
CML, ECL and SCL Digital Circuits (http://books.google.com/books?id=rv13_kMvjFEC&pg=PA12&dq=early-
effect+collector+depletion&as_brr=3&ei=QcMqR5ONOIfCtAOd05DXDA&
sig=gypONs7Y5uiXP4Mm3rXM1hE9M_4) . Springer. ISBN 1402028784. http://books.google.com
/books?id=rv13_kMvjFEC&pg=PA12&dq=early-effect+collector+depletion&as_brr=3&
ei=QcMqR5ONOIfCtAOd05DXDA&sig=gypONs7Y5uiXP4Mm3rXM1hE9M_4.
3. ^ Paolo Antognetti and Giuseppe Massobrio (1993). Semiconductor Device Modeling with Spice
(http://books.google.com/books?id=5IBYU9xrGaIC&pg=PA58&dq=early-effect+collector+depletion+collector-
base&as_brr=3&ei=92gtR-OaGKLstAOFn_SgCQ&sig=pyOokxyOJjfIqrHo6ItJZ-wLp74#PPA59,M1) .
McGraw-Hill Professional. ISBN 0071349553. http://books.google.com/books?id=5IBYU9xrGaIC&pg=PA58&
dq=early-effect+collector+depletion+collector-base&as_brr=3&ei=92gtR-OaGKLstAOFn_SgCQ&
sig=pyOokxyOJjfIqrHo6ItJZ-wLp74#PPA59,M1.
4. ^ Orcad PSpice Reference Manual named PSpcRef.pdf (http://people.clarkson.edu/~ortmeyer/ee211
/pspice%20files/pspcref.pdf) , p. 209. This manual is included with the free version of Orcad PSpice, but they do
not maintain a copy on line. If the link given here expires, try Googling PSpcRef.pdf.
5. ^ R.C. Jaeger and T.N. Blalock (2004). Microelectronic Circuit Design (http://worldcat.org/isbn/0072320990)
(Second Edition ed.). McGraw-Hill Professional. pp. Eq. 13.31, p. 891. ISBN 0-07-232099-0. http://worldcat.org
/isbn/0072320990.
6. ^ NanoDotTek Report NDT14-08-2007, 12 August 2007 (http://www.nanodottek.com/NDT14_08_2007.pdf)
See also
Small-signal model
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Categories: Transistor modeling
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