Resistance, capacitance, inductance of a real wire

[crashcat]

Two different projects require me to understand the behavior of a basic signal wire at 20-100 kHz and also at 1.7-2.1 MHz. So I tried to go to basics and take, as a starting model, a single real wire say 18 AWG of pure Cu to make it simple and understand the frequency dependent impedance including the resistance, tiny capacitance, and tiny inductance.

I've found some "answers" but it's always just some handbook equations and not a real answer from basic principles. I am just struggling to find a source that actually derives it even though, practically, you would have to measure your wire at some point and can't derive the whole thing from first principles.

What even is the cause of straight wire capacitance? Some models act like it is a shunt to ground which means it should depend on how you install the wire, but that's usually called parasitic capacitance and is at least an order of magnitude smaller than typical wire capacitance. Do charges get trapped at grain boundaries inside the wire, or the weak dipole moment of some impurities or vacancies, or anyway it's something intrinsic to the wire? Or is it purely related to conduction and the real time delay of signals making it appear to have capacitance at higher frequencies? I can't even find basic stuff like this. Just some equivalent circuits with ESR and IR and this and that which aren't given on wire data sheets anyway so how do you build and understand the model?

 

[DaveE]

which means it should depend on how you install the wire

For something like this you can't really separate the wire from it's environment. Everything else is an approximation.

called parasitic capacitance and is at least an order of magnitude smaller than typical wire capacitance.

It's all the same thing. Capacitance must be defined between two conductors (one could, theoretically, be the rest of the universe, I guess).

What even is the cause of straight wire capacitance?

You'll need to take a college level E&M class to learn this. Maxwell's Equations etc.

 

[berkeman]

Resistance, capacitance, inductance of a real wire

Since the wire has a resistivity in Ohms/length, you can calculate the resistance of an isolated length of wire.

Capacitance is defined between two conductors, so you need to know the geometry of the wire and whatever the 2nd conductor is (another wire, a ground plane, other metal objects nearby, etc.) in order to calculate the capacitance of the wire to that other metal object(s). To calculate the capacitance C between two conductors, you solve the equation $Q=CV$, and in more complex geometries this involves integration. Search on calculating capacitance of a conductor geometry for more info.

Inductance is defined for a full current path, so you need to know how the return current flows for your wire segment. Usually inductance only makes sense for a wire pair or at least a loop of wire. Calculating the inductance of a conductor geometry (parallel wire TL or coaxial TL or wire loop, or inductor with a return wire, etc.) involves the concepts of flux linkages and the magnetic permeability $\mu$. Search on calculating inductance of a conductor geometry for more info.