I feel like I've seen several different papers say that ohmic losses in metals become very large at: low frequency, high frequency, and at plasmonic resonances.
Are all of these true, or am I misremembering what I've read?
Ohmic losses are worse at high frequencies. There are at least two things at work here. First is the skin effect where at high frequencies not all of a conductor is utilized. This gives the conductor an effectively smaller cross sectional area that raises resistance and increases ohmic loss. Second, as frequency increases, the electric response weakens allowing more of a wave to penetrate the metal and experience the loss. At low frequencies, loss in the metal is so high that waves reflect and do not experience as much of the loss.
Thanks for the detailed response! Unfortunately, I still have the same basic confusion. You've said that losses are high at low and high frequency.
At high frequency, should I be thinking about the electron dynamics (current cross section) and wave dynamics separately? You say that electrons are confined to the surface, but the E field can pass into the bulk.
At low frequency, the losses are so high that the wave simply doesn't interact with the media? So this means that losses are strong at both low and high frequency, and RF is a nice low-loss frequency range for electronics?
Thanks again.
Up to microwave and millimetre frequencies the resistivity and conductivity of metals is similar to what it is at DC. If a wire is thin compared to a skin depth, then its resistance will not change with frequency. The main effect of frequency is the skin depth. This is a few cm at 50 Hz, and a few microns at microwave frequencies (in copper, silver or aluminium for instance). It scales as the inverse square root of frequency. In good conductors most of the current flows only in a layer a few skin-depths deep at the surface, so the resistance at microwave frequencies is not determined by the thickness of the metal, unless it is very thin, but by the skin depth. For the same reason very thick mains cables aren't used, as the middle would be wasted as far as conducting electricity is concerned. The surface resistance increases as the frequency increases, because the thickness of the layer carrying the current gets thinner.
Something different, but related, is that because metals have such a different conductivity to air, electromagnetic waves (microwaves, VHF, radio waves) mostly reflect off the surface and not much gets inside. For this reason metals tend to be reflective and don't absorb much radio signal.
The conductivity of metals changes a lot around the frequency of light (1000 THz) and above so the above does not necessarily apply there.
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