Relationship between impedance, wire gauge, and noise to due radiation

[tree]

I came across a switched 3-phase motor controller app note. It had a very short section on choosing the proper wire gauge. It stated that as the wire diameter decreases, the impedance increases. As impedance increases, so does the noise radiated from this wire. I was wondering why this is so. My reasoning for this was that when impedance is lower, power would much rather be delivered to the load than simply radiated. Am I correct?

[T3sl4co1l]

That doesn't make sense.  The increase in impedance, in lumped terms, is due to the inductance provided by the close-in magnetic field, since the field at a given diameter is free around a small wire (r > R), but shorted out by a fat wire (r < R).  A thin wire has more inductance, but the fields causing that inductance are specifically close-in, not distant and radiating.

Subsequent things may have an effect, like winding capacitance ringing with wire inductance, and snubbing (if any).  But in and of itself, I don't think so.

An equivalent way to ask the question: does an antenna work better with larger or smaller wire?  The answer is, larger: larger wires give lower Q (higher bandwidth), essentially because the radiation resistance (the part that's coupling the electrical circuit to the field) dominates more.

And of course, in the same way, you can put whatever combination of tuning components into the antenna to tune one of arbitrary length to almost any frequency: though the bandwidth and efficiency may be dreadful at certain combinations.

If this is like VFD applications we're talking about, it's best practice anyway to put the leads inside conduit (flexible or rigid), where they can't radiate, or induce magnetic fields (at line frequency or otherwise) or start fires.

Tim

[tree]

What did you mean by "free around a small wire"? Do you mean that the magnetic field is not contained within the wire, but rather in free air?

I figured it had to do with the inductance of the wire. So a thicker wire has lower inductance, thus it will radiate less noise?

The words that the app note used are : "Higher impedance wire will broadcast more noise than lower impedance wire"

[T3sl4co1l]

Yes, the field that's not within the wire.  Suppose you have a straight, infinite wire with radius R1; the magnetic field which contributes to its inductance extends from R1 to infinity (and a little bit less than R1 due to skin effect, but suppose we count that as zero for now).  Now consider a thinner wire of radius R2 < R1.  At a given current, the magnetic field from R1 to infinity is exactly the same -- Ampere's law states this.  The field only from R2 to R1 -- which by definition is not part of infinity -- is exactly the field which causes this thinner wire to have a higher inductance (or impedance).

Now, it's worth noting that wires don't go for infinity anyway; infinity is a rather poor conductor.  So suppose you have a pair of wires.  Now you have the capacitance between them, as well as the inductance between them; and this defines an impedance.  A pair of wires very close together has low L high C; since Z = sqrt(L/C) the impedance is low.  The stray field is also low because what little field contributes to the inductance is mostly between the wires (for a separation D, you'll find very little beyond 3*D or so in any direction; though it is never zero, so does extend to infinity).  In this sense, "higher impedance [transmission line] will broadcast more noise..".

But that's still not accurate, because there are many configurations of transmission line.  A coax cable is self-shielding and radiates nothing, regardless of impedance.  A parallel-plate or ladder line will radiate as a dipole.  Twisted pair radiates as a dipole if the twist is unlucky, but that occurs for few frequencies, so it can be assumed on the average to cancel out; it's not self shielding like coax, but it does a pretty good job for the most part.

So it would be more accurate still to say: "higher impedance, untwisted, parallel conductor type transmission lines will broadcast more noise..."

By the way, this assumes common mode is zero.  Any transmission line, driven common mode, reduces to the case of single-conductor-in-space, so it is not necessary to consider combinations.  Common mode noise is often the primary concern in switching circuits anyway, since that's the part that causes conducted emissions.

Tim

[tree]

Thanks, that makes sense. The app note doesn't go into too much detail explaining much, just has a rule of thumb.

When you place 2 wires close together (1 being signal and the other being the return path), their magnetic fields will tend to cancel (somewhat) on the exteriors of the wires leading to a lower inductance. I just hadn't considered the capacitance.

It's very strange that the app note only suggests that thicker wire be used and doesn't talk about keeping the wire close together.

[T3sl4co1l]

Rules of thumb are like that.  Lots of misinformation and incomplete statements out there.  Antialias filtering for ADC/DACs.  Minimize inductance in switching converters.  All sorts.  Sometimes from a theoretical basis that's not understood (even a theorem as simple as the Shannon-Nyquist sampling theorem is poorly known by the average EE), let alone applied correctly in a system design.  Sometimes a rule that someone discovered for a limited case ("minimize stray inductance!!!"), and spread without ever being understood for the general case.

The impedance of a parallel wire transmission line happens to be dependent on geometry, and is independent of scale.  Bigger wires, if the insulation is proportionally thicker, end up with exactly the same impedance!  Or perhaps it's higher (fatter insulation for more voltage rating?) or lower (same thickness for same voltage rating).  And anyway, radiation with respect to the impedance of a balanced transmission line is more-or-less first order with spacing, but it's already a -3rd order dipole, so it's not like you're talking big effects.

The real lesson to conclude with is, appnotes are written by people, who have imperfect knowledge like anyone else.  One should hope the manufacturers hold them to a higher standard, but reality says otherwise!

Tim

[tree]

More on this application and topic....

In this application, I have differential hall effect sensor feedback signals in a shielded twisted pair. Do I connect the shield to earth ground, or circuit common which is NOT connected to earth ground?

Suppose instead of differential, I had single ended, where one wire would be the signal and the other wire would be circuit common. Where would I connect to the shield to in this case?

[T3sl4co1l]

Hmm, I'd have to see more of the circuit.

Why isn't circuit ground common?  Or do you mean protective earth ground versus circuit common (which is often isolated to avoid ground loops)?  Is circuit common at line potential (which would be a galvanic isolation hazard)?  Does the signal have to be safety grounded?  Is this an internal signal only (in which case the concern is mainly signal quality and noise), or is it user accessible?

As for differential versus single ended, you don't magically gain anything from physics; it's largely the same as two single ended signals.  The advantage is having better transceivers.  Common mode errors are still present at full strength, so, you can't just run diff pair through a noisy field and expect it to behave, not without better termination or coupling or isolation.

[tree]

Circuit ground is common to the circuit, but PE is connected to the chassis. I think the true nature of my question lies in a new thread I created called "Shielding".