Early effect

The Early effect is the variation in the width of the base in a 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 base width is dark blue, and the depleted base regions are light blue. The neutral emitter and collector regions are dark red and the depleted regions pink. 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 emitter–base junction is unchanged because the emitter–base voltage is the same.

Base-narrowing has two consequences that affect the current:

*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 characteristics at large voltages extrapolate backward to intercept the voltage axis at a voltage called the Early voltage, often denoted by the symbol V_A.

Large-signal model

In the forward active region the Early effect modifies the collector current ($I\_mathrm\{C\}$) and the forward common-emitter current gain (), as typically described by the following equations: [cite book | title = Microelectronic Circuit Design | author =R.C. Jaeger and T.N. Blalock | publisher = McGraw-Hill Professional | year = 2004 |page=p. 317| isbn = 0072505036 | url = 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 ] [cite book | title = Model and Design of Bipolar and Mos Current-Mode Logic: CML, ECL and SCL Digital Circuits | author = Massimo Alioto and Gaetano Palumbo | publisher = Springer | year = 2005 | isbn = 1402028784 | url = http://books.google.com/books?id=rv13_kMvjFEC&pg=PA12&dq=early-effect+collector+depletion&as_brr=3&ei=QcMqR5ONOIfCtAOd05DXDA&sig=gypONs7Y5uiXP4Mm3rXM1hE9M_4 ]

:$I\_mathrm\{C\}\; =\; I\_mathrm\{S\}\; e^\{frac\{V\_mathrm\{BE\{V\_mathrm\{T\}\; left(1\; +\; frac\{V\_mathrm\{CE\{V\_mathrm\{A\; ight)$

:

Where
* $V\_mathrm\{CE\}$ is the collector–emitter voltage
* $V\_mathrm\{T\}$ is the thermal voltage $mathrm\{kT/q\}$; see thermal voltage:
* $V\_mathrm\{A\}$ is the Early voltage (typically 15 V to 150 V; smaller for smaller devices)
* is forward common-emitter current gain at zero bias.

Some models base the collector current correction factor on the collector–base voltage "V"_CB (as described in base-width modulation) instead of the collector–emitter voltage "V"_CE. [cite book | title = Semiconductor Device Modeling with Spice | author = Paolo Antognetti and Giuseppe Massobrio | publisher = McGraw-Hill Professional | year = 1993 | isbn = 0071349553 | url = 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 ] Using "V"_CB 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 "V"_CB. Computer models such as those used in PSPICE use the collector–base voltage "V"_CB. [ [http://people.clarkson.edu/~ortmeyer/ee211/pspice%20files/pspcref.pdf Orcad PSpice Reference Manual named 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.] .

mall-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 (see cite book | title = Microelectronic Circuit Design |author=R.C. Jaeger and T.N. Blalock |edition=Second Edition |publisher = McGraw-Hill Professional |year = 2004 |isbn =0-07-232099-0 |page=Eq. 13.31, p. 891 |url = http://worldcat.org/isbn/0072320990]

:$r\_O=frac\{V\_A+V\_\{CE\{I\_C\}\; approx\; frac\{V\_A\}\{I\_C\}$

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 $V\_\{CB\}$ the resistance becomes:

:$r\_O=frac\{V\_A\; +V\_\{CB\{I\_C\}$,

which almost agrees with the textbook result. In either formulation, $r\_O$ varies with DC reverse bias $V\_\{CB\}$, as is observed in practice.Fact|date=November 2007

In the MOSFET the output resistance is given in Shichman–Hodges model [ NanoDotTek Report NDT14-08-2007, 12 August 2007 [http://www.nanodottek.com/NDT14_08_2007.pdf] ] (accurate for very old technology) as::,

where $V\_\{DS\}$ = drain-to-source voltage, $I\_D$ = drain current and $lambda$ = 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

ee also

*Small-signal model

*