From: Jonathan Kirwan
Subject: Re: Ebers-Moll equation
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NNTP-Posting-Date: Fri, 29 Nov 2002 18:49:53 GMT
Organization: AT&T Broadband
Date: Fri, 29 Nov 2002 18:49:53 GMT
On Fri, 29 Nov 2002 16:12:19 -0000, "Kevin Aylward"
>> Paul Burridge wrote:
>>> Can some kind soul post the E-B equation that describes the behaviour
>>> of BJTs? Also, how accurate is this model and does it contain
>>> everything one needs to know about BJT behaviour in isolation?
>> Ic = Is ( exp(Vbe/Vt) - 1 )
>> Is = saturation current
>> Vbe = base-emitter voltage
>> Vt = thermal voltage = k (Boltzmann const) * T (Kelvin) / q (electron
>> The Ebers-Molls equation is almost completely useless, other than for
>> exploring "how transistors work". There is, for example, just one
>> parameter that defines the device, namely Is. No Ohmic resistances,
>> parasitic capacitances, parasitic diodes or parasitic pnp's are
>> simulated. You need to look at Gummel-Poon, or even Mextram models
>> for decent accuracy.
>This is not the Ebers-Molls equation. This is just the one diode
>equation. Ebers-Moll includes both diodes.
My reading doesn't include Mextram's models, but does include
some GP and three EM models.
In answer to the OP's question about 'how accurate':
EM1 is your basic transistor model, described originally by J.
J. Ebers and J. L. Moll in December 1954, "Large-Signal Behavior
of Junction Transistors," in Proceedings of the IRE, volume 42.
It's a non-linear DC model (no characterization of charge
storage.) The model happily covers all four VBE vs VBC regions;
saturation, inverse, off, and active. There are two versions,
the injection version and the transport version, which are
mathematically identical but the transport version puts all the
non-ideality in beta at low currents in the base currents.
Without temperature being a factor, only three model parameters
are needed -- the forward and reverse betas and the saturation
current. With temperature, the nominal temperature and the
effective energy gap are added and becomes part of the equation
describing the saturation current over temperature.
EM1 limitations are mainly due to neglecting transistor charge
storage and ohmic resistances. Those are included in the EM2
model, to a first-order. But EM1 isn't too bad for DC analysis
or in mentally viewing an 'ideal' transistor.
EM3 deals with second-order effects on the DC aspects of EM2,
better charge storage modeling and temperature performance. It
includes basewidth modulation (Early Effect) and variation of
beta over current and voltage; distributes the collector-base
junction capacitance across RB (base ohmic resistance); handles
the rise in the forward transit time at high currents; and deals
with the variation of more device parameters over temperature.
So when you say Ebers-Moll, which one?
Gummel-Poon was formulated in 1970 and is almost entirely
concerned with improved DC characterization of the EM3 model.
It provides a little better modeling of the Early Effect, if
memory serves, and a somewhat more mathematical approach which
makes it clearer how to improve the model when the underlying
assumptions are found incorrect.
The limitations are largely based on the 1D model assumed. They
ignore 3D effects, such as crowding phenomena for DC and AC.
Getting back to the EM1 model, even it needs an equation to
model the saturation current over temperature, which I see is
missing from Rick's post.
Perhaps Kevin will be kind enough to provide the full EM1 model,
in either injection, transport, or non-linear hybrid-pi form.