1.

Assume we have a battery with a resistor connected between the poles. Is

there a shot noise current flowing in the resistor?

No, and I believe that AofE (H&H) states this somewhere. Resistors do have

several other sources of noise, one of which operates without regard to the

fabrication itself and is tied directly to the resistance itself, Johnson noise.

AofE talks about this, too.

Is the battery a

potential barrier like the one mentioned by H&H?

I can't say there is no noise process in battery chemistry. But I don't believe

that any noise process in battery chemistry is similar to that across a PN

junction. If there is, I don't think it wouldn't be described by this same

equation. In the case of the PN junction, it's a statistical process where

electrons move from valence into the conduction band (and back) and there is a

small 'step' to it, in the neighborhood of 1+ eV, or so. Perhaps someone can be

more 'sure' about this or correct me.

My 'understanding' of shot noise is that it is always associated with cases

where discrete quanta of charge (e) or quanta of energy (hv) are emitted

randomly in time by some source. The 'independence' part that AofE talks about

here is that each of these individual, elemental 'emitters' do so (roughly)

independently of each other. If there's a large number of these emitters and

there is a very small probability of emission then the overall emission rate is

(or, at least, theoretically should be) Poisson distributed. It's this that is

talked about when saying 'shot noise,' I think.

2.

What about a (charged) capacitor discharging into a resistor? Shot noise

current flowing or not? The dielectric between the plates seems to be quite

a huge barrier, but there are no charge carriers crossing it; only a

displacement current is flowing?

The charge on the capacitor has an energy distribution that has to obey

Boltzmann statistics for the probability density.

There is some noise associated with capacitance, kT/C, based on Boltzman

statistics. In fact, from this you can derive the Johnson noise equation for

resistance. In Boltzmann's equipartition theorem, the mean internal energy

associated with each degree of freedom in a system is (1/2)kT (Joules.) In the

case of electrostatic energy in a capacitor, this becomes:

(1/2) C V^2 = (1/2) k T

or, the geometric mean of the V^2's is:

V^2 = kT/C

Or, another way... The energy distribution [E=(1/2)*C*V^2] must obey Boltmann

statistics for the probability density, such that:

p(E) = (1/(k*T))*e^(-E/(k*T))

Then, the probability density of V^2 is:

p(V^2) = p(E) * dE/d(V^2)

Since dE/d(V^2) of [E=(1/2)*C*V^2] is just (1/2)C, we can substitute for E and

for dE/d(V^2) to get:

p(V^2) = (C/(2kT))*e^(-CV^2/(2kT))

By this, you can arrive at the geometrical mean of <V^2> must be 0 or kT/C.

Or it can be taken from the point of view of a statistical thermodynamics

theorem from Einstein, which is that "every state function A that can be

expressed in terms of the system entropy S has a mean value <A> that is obtained

by finding the maximum of S, solving for dS/dA=0 (well, often the partials

instead of the derivatives.) By solving this, we also find that the variance is

again, kT/C.

In the case of an RC discharge, the noise is just Johnson and not shot. In

fact, it's the kT/C realization that generates the formula for Johnson noise, as

any stray capacitance C that is inevitably present across an R, gives a cutoff

frequency that is B=1/(2*PI*RC) and the voltage's spectral density must be:

Integral(Sv(f) df) = kT/C

substituting Sv(f) with Sv0/(1+(f/B)^2), where Sv0 is the DC value of spectral

density, we can then combine to yield:

kT/C = 2*Integ(Sv0/[1+(f/B)^2] df) = 2*Sv0*|atn(f/B)| at 0,B

or, kT/C = 2*(Sv0/(2*PI*RC))*(PI/4)

Solving for Sv0, we find that Sv0 = 4kTR!

3.

Assume a battery which is shorted for AC via a large capacitor, that means

that any shot noise current that the battery

assumes a fact not in evidence -- is there shot noise in batteries?

may produce runs through the

capacitor and not elsewhere. Across it is a resistor. Does it really depend

on the composition of this resistor (metallic conductor, i.e. metal film vs.

metal oxide, thick film etc.) if there is a shot noise current flowing or

not?

The composition of resistors does have an impact on 1/f noise (which is

sometimes called 'shot noise' in SPICE simulators, I gather), but the shot noise

I've been talking about is white, not 1/f. White shot noise doesn't depend on

the composition. But I'm not sure of your question.

4.

At the bottom of the first column of p.432, H&H mention that the standard

transistor current source runs quieter than shot-noise-limited. Anybody out

there who knows a little more (literature, math) about this?

Well, perhaps Win can answer what he meant here (more likely if you ask in

sci.electronics.design, I think.) But I'd imagine as a hobbyist-guess that the

"independence" mentioned earlier isn't entirely true for this case -- some of

the current is dependent in some way or the probability of emission is high, so

the integral over all the behavior is no longer quite Poisson.

Wish I could have done better. But that's all I can do without putting effort

in.

Might want to ask these questions in sci.electronics.design. I'm no expert, but

there are some over there.

Jon