Reply-To: "Kevin Aylward"
From: "Kevin Aylward"
Subject: Re: Ebers-Moll equation
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Date: Sat, 30 Nov 2002 07:47:39 -0000
NNTP-Posting-Date: Sat, 30 Nov 2002 07:47:44 GMT
Jonathan Kirwan wrote:
> On Fri, 29 Nov 2002 16:12:19 -0000, "Kevin Aylward"
>> Rick wrote:
>>> 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
>>> 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". 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.
Its a matter of getting round to type it in. I hazad a guess that a web
page alrady has it....
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