Infinity - John Dunn, Consultant, Ambertec, P.E., P.C.

I usually think I know at least something about this or that blog topic, however blithe that notion may be, but not this time. Instead, I have a question to pose.

Consider some resistance value and call it "R". For that value of resistor, we have an associated noise voltage called Johnson noise of Erms noise = sqrt ( 4kTBR ) where k = Boltzmann's constant, T = temperature in degrees Kelvin, B = bandwidth in Hz and R = resistance in ohms. By comparison however, I have never heard of, nor have I ever read of, anything like Johnson noise being associated with inductance or capacitance. Reactive elements, so far as I have long thought, have always been considered noiseless but I have begun to have my doubts about that.

Please consider an idealized transmission line of infinite length for which the circuit model is an infinitely long cascade of inductance per unit length elements "L" and capacitance per unit length elements "C". 

The characteristic impedance of this model will be Z = sqrt (L/C) where Z will look resistive. This Z will look like an R, because any energy that we send into the cable in the process of measuring the input impedance will go traveling away from the observer and never come back again.

The inductances and the capacitances are all ideal. There are no resistive attributes to either of those reactances. Therefore, neither the L or the C elements should generate any noise, so I have long thought, as they would not have Johnson noise properties.

However, if these lossless and noiseless elements combine in this model to present a resistive input impedance, R, at the one end of that infinitely long transmission line, does that presented R exhibit Johnson noise?

If so where is that Johnson noise coming from given that all of the circuit elements in this model are supposedly lossless and noiseless?

I'm starting to think that L and C elements must make noise after all, but I've never read, or heard, of any such thing. Have you??

Comments invited.

Comments

[TOny Stewart]

Many many times.

Ceramic is microphonic

Oil insulators in transformers can generate impulse ticks of PD from charge accumulation and breakdown of a microvoid from contaminants.
Similar with dry insulation.

Magnetics are microphonic if they move.....

[John Dunn]

Hi, Tony.

A number of answers have been offered, but like these, they relate to real world parts that can have parasitic effects from various causes.

The issue at hand is that the L and C elements in this model are all absolutely ideal. They have no contaminants, no stray L or C elements, no leakage and so forth.

Even so, even though the L and C elements are perfectly free of every anomaly imaginable, the circuit model yields a resistive input impedance which, in looking like an R, ought to have Johnson noise, but where would that Johnson noise come from?

I have no explanation for that at all.

[Tony Stewart near Toronto, EE since 1975]

I remember hearing running water coming out of my Buck Regulator choke 100uH epoxy sealed. It was PWM mode, but part of the load was boost regulator for biasing a Kopin LCD and driving the analog amps.

Evidently what I heard was a mathematical metastable condition call CHAOS and the microphonics in the coil.

A bigger Cap with lower ESR Fixed it.

[Tony Stewart near Toronto, EE since 1975]

but I dont think the distributed impedance of reactive components generates thermionic brownian noise in an ideal transmission line.