Re: gEDA-user: ngspice shot noise

[John Doty <jpd@xxxxxxxxxxxxx>]

On Wed, 28 Sep 2005, Karel Kulhavy wrote:

> Does ngspice noise model also work for operation of BJT with extremely
> small collector current?

Should work just fine.

> I got an idea to make low-noise amplifier by taking some 25GHz
> transistor and powering it with so small collector current that its
> transition frequency would drop down to 300MHz and then using it in
> Ronja preamplifier instead of 2N3904. As second or even first stage
> of the preamp.

First stage looks at a photodiode, right? You'll generally find it better
to use a FET there: base current noise will kill you with a BJT. Get the
impedance down with a FET front end. Use a BJT for the second stage: a
well chosen BJT in a well designed circuit will generally be quieter than
a FET at moderate impedance. There's a good discussion of this in Horowitz
and Hill.

Your idea to use fast transistors to achieve low noise is good. For
interface to a capacitive sensor, a good procedure for choosing a front
end FET is to choose a transistor technology that maximizes sqrt(gm)/Cin,
and then choose a transistor whose input capacitance, Cin, matches the
sensor capactance This will generally get you close to optimum from a
noise perspective if you've done your homework on the rest of the circuit.

For the second stage, operating a BJT at low current density will minimize
noise due to parasitic resistances, but again you'll want a relatively
fast transistor to do this. There's a tradeoff though: high beta will
reduce base current noise, but really high beta transistors are generally
not really fast. So, there's some art here.

Always remember that noise is a system issue: choosing "low
noise" components is no guarantee that you'll wind up with a low noise
system. For a photoelectric detector, you probably want to start by
calculating the shot noise in the detector output current (dark current +
photocurrent): if the input-referred noise of your amplifier is more than
a factor of two or three lower there's little to be gained by sweating the
amplifier design.

> 
> How can one calculate shot noise in BJT?
> Some papers say that shot and thermal noise are the same phenomenon,
> some are talking about partition noise, some say that shot noise in
> base actually doesn't exist, some say that the shot noise is modelled
> as two independent noise currents, one for BC and other for BE junction,
> some say that the previous papers aren't true, and if I try to imagine
> a transistor, I have a feeling that there should be one shot noise
> current source connected with it's pins to B and E with
> DC current given by base current, and another between E and C with
> "steering" with DC current given by collector current.
> 
> I get crazy from that. Does anyone know the truth?

Start with an ideal semiconductor diode. I = Is*exp(V*q/(k*T)) - Is. Now
what, exactly, is that magic parameter Is? The diode junction represents a
potential barrier. Thermal energy will occasionally excite a charge
carrier over the barrier, at a rate given by Is. Since the excitation of a
carrier over the barrier is a random event, independent of other such
events, the result is shot noise.

At zero applied volts, the net current is zero (as thermodynamics
requires), but from a noise standpoint it actually makes more sense to
consider it as two currents, of magnitude Is, crossing the junction in
opposite directions.

For shot noise in a current I of charges of magnitude q measured over a
bandwidth B, the current variance In^2 = 2*q*I*B. Plug in 2*Is for the
current, you get 4*q*Is*B. But there's another point of view.

The conductance, g = dI/dV = Is*q/(k*T)*exp(V*q/(k*T)). For zero bias,
it's Is*q/(k*T). Now, the thermal (Johnson) noise current variance
associated with an ohmic conductange g is In^2 = 4*k*T*g*B: plug in the
above expression for g at zero bias, and you get 4*q*Is*B, the very same
result we got from shot noise! Again, thermodynamics requires
this: otherwise you could base a perpetual motion machine around a diode.

At nonzero bias, things are just a little more complicated. For I>>Is,
there's only significant noise current associated with the forward
current. The result is that the noise variance is half of the Johnson
noise for conductance g: the forward biased diode, as a noise source,
behaves as if it's at half its physical temperature. This isn't a problem
for thermodynamics as the bias supply is a source of free energy. Still,
the noise current variance scales with temperature at a fixed g, so one
might reasonably consider it thermal.

So, is diode current thermal or shot noise? Since the conduction mechanism
is thermal, but involves individual carriers, it's impossible to draw such
a distinction.

Of course a real diode also has parasitic resistances that make ordinary
thermal noise. Ngspice takes these into account. However ngspice computes
the junction noise as shot noise based on net current, which isn't right
around zero bias, but in most cases parasitic leakage dominates the noise
there anyway.

For a BJT, the base-emitter junction acts like a diode, with the same
noise current. The collector current follows a similar equation based on
the base-emitter voltage (at least away from saturation). A good model is
a  shot noise current based on the collector current, uncorrelated with
the base current noise. Alternatively, you can consider it Johnson noise
generated by the transconductance, but at half its physical temperature,
just like a diode.

Of course, the Johnson noise associated with parasitic resistances also
matters. Base "spreading" resistance is often an important noise source.

For situations where the emitter current is controlled externally (as in
the upper transistor of a cascode pair) it is sensible to consider the
noise as partition noise between the base and collector currents. Again,
however, this yields the same answers as the shot noise and thermal
approaches. The only advantage is computational: in the other models
emitter-base voltage fluctuations work through gm to cancel part of the
collector noise in this case, while the partition noise model doesn't
require you to consider them (as they don't, by definition, affect the
emitter current in this special case).

John Doty          "You can't confuse me, that's my job."
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