From: "John S. Dyson"
Subject: Re: Ebers-Moll equation
X-Newsreader: Microsoft Outlook Express 6.00.2800.1106
Date: Fri, 29 Nov 2002 16:09:13 -0500
NNTP-Posting-Date: Fri, 29 Nov 2002 16:01:34 EST
"Rick" wrote in message news:email@example.com...
> Paul Burridge wrote:
> > hi,.
> > 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 charge)
> The Ebers-Molls equation is almost completely useless, other than for
> exploring "how transistors work".
I THINK that I understand what you are trying to say, but it isn't really
completely useless. The equation (of the various forms) is really the first
start of the best way to understand how to apply the transistor in many
applications (after the initial Santa-Claus tale of the transistor being a
current controlled current source.)
Without the Ebers-Moll equation (and it's derivatives), a developer would
be stunted in being able to mathematically describe the operation of almost
any transistor circuit. There are some technologists approximations that
allow some modeling of a circuit without the Ebers-Moll concept, but the
breadth of innovative design ability would be limited.
If you look at the various physically relevent DC models of the transistor
(usually derivatives or variations on the Ebers-Moll theme), you'll find the
ability to deal with saturation, Early effect, and even dynamic characteristics
if you use the right derivation that starts with the Ebers-Moll concept.
As Kevin said, the equation above is only part of the Ebers-Moll equations, but
is sometimes informally given that name. As a first-start, the equation above
is a good place to base a flexible understanding of the BJT. After the first
few days of a 'Transistors 101' class, it would be better to present the
Ebers-Moll relationship as 'defining', rather than the often-misused Ic=B*Ib.
Even the most physically ideal transistor will have more complex relationships
than the version of Ebers-Moll stated above. However, that model will give
insight to future and more complete understanding. Beyond simple saturated
switch circuits, the Ebers-Moll equation will take you MUCH FURTHER than
the B=Ic/Ib relationship and misguided interpretations of it. (There is absolutely
NOTHING wrong with the B=Ic/Ib idea, but it isn't a very good general
model of the component, and unfortunately the often nearly linear relationship
leads to an incorrect notion that the 'Beta' is the most fundamental parameter
of the most fundamental model of the real component called a 'Bipolar Transistor.')
IMO, 'Beta' is of the same category as other parasitic measures
like rb, Cbc, etc. Unlike my initial (early teenage) understanding of transistors,
the Is (which isn't quite the same as leakage, but can look similar) is a basic
proportionality parameter that is used in the description of the transistor action
itself. My mistaken early understanding that Ge transistors had more leakage,
because Ge wasn't as 'good' was about as wrong as the transistor relation being
Ic=B * Ib. (You might want a low Is for biasing stability reasons at low current levels,
but a high Is could be interpreted as the ability to work more easily with lower
voltages also. That is, a higher Is would generally let a lower Vbe enable
Ic-Ie current flow.)