The suggestion that the physical reality compels us to model a BJT
as a voltage controlled current source is not as certain as it may
seem. In fact, neither the CCCS nor the VCCS model account for all
the situations that a circuit designer will face.
In particular, while many simulators use the voltage controlled model
as their basis, the fundamental operation of the device depends on the
injection of minority carriers into the base region. This
charge-controlled model correctly explains two important phenomena:
1. In many optocouplers, there is no base terminal in the output
transistor. The base region is exposed to the photo diode where the
light impinging on the base region creates free minority carriers in
the base. These carriers create the path for the collector-emitter
current.
2. In bulk CMOS processes the N well diffusion (created to hold the
P-FET) combined with the P doped substrate, and a nearby N diffusion
for a source/drain terminal for a neighboring N-FET can form a
parasitic NPN transistor. It is possible to turn this transistor on
(and create a short between Vdd and Vss!) by injecting electrons into
the sliver of P material between the well and the source. This charge
can come from a number of sources that include:
- Current pumped out of a nearby on-chip decoupling capacitor. (We
used to make these out of N devices where the gate was connected to
Vdd and and the source and drain both connected to Vss. Works great
unless the poly gate is too big and acts as a charge pump...) - Current dumped into the substrate when an I/O pin falls below
ground or rises above Vdd.
The VCCS model doesn't do a good job of accounting for either effect.
I'm not arguing that there are no models that can legitimately relate
Ic to Vbe. In fact, they're pretty useful even on the
back-of-an-envelope if you want to deal with q/kT variation with
temperature.
The Wikipedia article makes your point in support of the VCCS
model. But it presents without support the contention that (in their
words) "to accurately and reliably design production BJT circuits, the
voltage-control (for example, Ebers–Moll) model is required." Yes,
SPICE and other simulators use models that often have VCCS components,
but that doesn't mean their models mimic the physics -- they just
account for the effects sufficiently to justify their costs. In fact,
I think it goes too far. I don't believe that such models are
required for the design synthesis process, but they are warranted as a
validation/verification step.
The graph cited above presents a <relation> between Vbe and Ic. There
are many such relations. The length of my morning commute is related
to the number of pizzas sold in a given year. The existence of the
relation does not prove causality. Further, the graph correctly shows
an exponential relation between Ic and Vbe, but if you had chosen the
graph of Ic vs. Ib, the plot would have been largely linear. Which
would you rather reason with?
My biggest problem with the Ic vs. Vbe graph is that it suggests Ic is
the "output" from some function that takes Vbe as an input. This
notion of a function (as a thing that operates on an independent
variable and produces a value of a dependent variable) is a trap.
These expressions are <relations> that the physics tells us must hold
true.
As an example, consider a diode connected to a stiff voltage source.
Ramp the source from 0 to 0.7 V and measure the current. Clearly Id
will be proportional to exp(Vd * q / kT). So, we have a case where Id
is determined by Vd.
Now let's put a current source across the diode. Ramp the current
from 0 to 5mA. What do you see? Of course Vd = k * ln(Id/Is) So we
have a case where Vd is determined by Id.
Both models are useful. Both reflect physics as well as we cared to.
Most of our readers are working to develop an intuitive understanding
of how circuits work. I've found that the h-parameter model relating
Ic to Ib has been the most useful over the years. The CCCS h-parameter
model is the clear choice when thinking about the classic
common-emitter or common-collector configurations.
But the VCCS model is pretty good at explaining how a current mirror
works. (and the CCCS model is singularly unhelpful for that). While
the transconductance model is at the heart of most simulation models,
it cannot account for charge injection modes. Further its awkward
dependence on the exponential relation makes it inconvenient as a
reasoning mechanism in initial design creation. The awkwardness is
such that the model is often linearized to make it useful.
On the other hand, the h-parameter model can tempt designers into
an unholy faith in hfe, and is useless for non-linear design like
oscillators (it can't predict the limiting amplitude, for instance)
or for predicting harmonic content of an amplifier output. (Though
it should be noted that the VCCS model handles this with the aid
of Mr. Bessel. For a real treat, take a look at the first chapter
of "Communication Circuits: Analysis and Design" by Clarke and Hess.
Their presentation of the non-linear analysis is a joy to read.)
Neither model does a very good job of handling the extremes.
Transconductance, alpha, and beta vary with temperature, frequency,
and current. The VCCS model probably comes out ahead in large signal
analysis, but datasheets are often pretty sparse when it comes to
things like gm.
In the end, the most powerful argument for the h-parameter model is
that there's a chance that you can find the parameters for "normal"
devices. The transconductance model suffers here. What is the gm for
a 2n3904? 2n2222? 2n5179? All specify at least their hfe, and I can
find specs for all four parameters for the first two devices.
So, I would suggest that there is no valid categorical claim that a
BJT must be modeled exclusively a transconductance device or that it
is a current controlled current source. If I am controlling terminal
voltages, then I think of it in terms of a VCCS. If I control
terminal currents, then my best bet is to treat it as a CCCS,
recognizing that the terminal voltages can become hard to treat if I
push the base too hard. If I'm ready to sharpen a pencil and crank
through the Bessel series approximations, I'm back to Ebers-Moll.
Finally, if my only control is over charge injection, I'm in the soup.
(Though there are simulators that deal with those effects.)
In any case, this has been a stimulating discussion. For the reader,
the points on both sides are non-trivial. These choices matter.
If there is a takeaway here, it is that all we have are "models" of the
reality, and our choice of models is influenced by where we've been
and where we are, and what we're give to work with.
For the vast majority of the problems that our fellow readers encounter,
Ic = hfe * Ib and Vbe = 0.6V will allow them to calculate the permissible
range of base resistors for that 2n3904 that is driving a LED, or
the emitter resistor to get 5x gain out of a single amplifier stage.
With luck they'll develop a style and habits that ensure the stuff works
when it gets cold, or when the batch of 1000 2n3904s from the
Semiconductor and Screen Door Company of Greater Guangzhou
turns out to have a beta of 20.
'73
Home
Help
Search
Login
Register
