# Skin effect for pulse current

I've just bought some 6mm^2 copper wire for my project where I will have large pulse currents - ~500A peak (driving very large Xenon flash bulbs, 1000J pulse in 2ms).

But I know that skin effect make it useless to use thick wires on high frequency, but does it apply to sharp fronts? Is that correct that having multiple non-isolated wires make it even worse? (mine cable have about 20 tiny 'wires')

• Somewhat a nitpick, but the skin effect does not mean that thick wires are useless at high frequencies, rather it means that the interior of the wire is not useful. There's still more conductor in the skin deep circumferential ring of a large wire than that of a small one. Tubing is sometimes used in high power transmitters. Feb 8 '11 at 5:19

## You should use the finest magnet wire with many multiple strands or LITZ WIRE to improve L/R time constant and peak current for lowest loss cable. Your discharge rise time will then drop to xx picoseconds. But for conductor pairs use twisted pair Litz wire to reduce CM emissions.

Otherwise, you can jam many radios/mobiles with high rep rates of > 1pps affecting AGC. !!

In most conductors R(f) rises fast and L(f) drops slow from skin effect. This R effect increases more with iron content since it is from Eddy Currents. In DSL and cable modem skin effects change Zo, phase shift and group delay.... Tony

## ref wiki

Although the geometry is different, a twisted pair used in telephone lines is similarly affected: at higher frequencies the inductance decreases by more than 20% as can be seen in the following table.

Characteristics of telephone cable as a function of frequency
Representative parameter data for 24 gauge PIC telephone cable at 21 °C (70 °F).

   (Hz) R (Ω/km)    L (mH/km)   G (μS/km) C (nF/km)
1    172.24    0.6129      0.000      51.57
1k    172.28    0.6125      0.072      51.57
10k    172.70    0.6099      0.531      51.57
100k    191.63    0.5807      3.327      51.57
1M    463.59    0.5062     29.111      51.57
2M    643.14    0.4862     53.205      51.57
5M    999.41    0.4675    118.074      51.57


The spectrum of your pulse is not at all like a square wave, since it is not repetitive over a small interval. It is a continuous spectrum rolling off similar to The null of 2nd harmonics of the equivalent pulse of a "square" wave and then rolling off above the 0.35Tr rise time. So resonant frequency and group delay calculations of pulses is very poor and affected by skin effects, even in controlled impedances, making Baseband communication much worse than the discrete equalized channel's of a modem for thruput in bps/Hz .....Tony

However hollow copper tubing with interior flash gold plating works wonders in microwave as does ENIG on stripline and gold-plated aluminum cases for RF circuits and enclosures for microwave. I saw this in '77.

Here is a different skin effect from UV on dielectrics (human skin) and how Sodium Bicarbonate helps prevent cancer. ( also reduce causes/reactions of itching). https://www.cancertutor.com/simoncini/. :):)

For 6mm2 copper (~1.4mm radius), the skin effect impacts the wire at ~2.5kHz.

Your 2ms pulse is equivalent to a 0.25kHz square wave. Mathematically, that square wave is a sum of all the odd-multiple sine waves (0.25kHz, 0.75khz, 1.25khz, etc). Since the skin effect drastically reduces frequencies above 2.5khz (more as the frequency goes higher), you're creating an imperfect square wave (aka slowing down the ramp-up and ramp-down times of your pulse).

So, the rise-time on an "ideal" 2ms pulse will get slowed to maybe 80uS. This assumes you're able to generate 500A pulses with very high rise times in the first place.

And yes, having stranded cable (20 tiny wires), does make this a small bit worse, but not much. As one other poster suggested, litz wire (http://en.wikipedia.org/wiki/Litz_wire) helps for 100kHz+ applications by providing many insulated tiny wires.

Ref: http://www.marcspages.co.uk/pq/3250.htm (Skin Depth Tables) http://www.nessengr.com/techdata/skin/skindepth.html

• Wouldn't stranded be a bit better? Feb 7 '11 at 6:31
• If it's Litz wire (which has each strand insulated), yes. But for regular stranded wire it's worse for a given (overall) wire diameter because the stranded wire still has some gaps between the wires, meaning you have less overall copper. The strands all short to each other, so its effectively a big wire with some holes in it as far as skin effect is concerned. Feb 8 '11 at 7:33
• solid thin hollow copper tubing is best for microwave "semi-rigid" copper coax, while braid improves coax but greatly depends on weave pattern and is improved with alum foil with double shields May 20 '17 at 13:54

skin effect do affect pulse dc, since electrons must move to compensate the introduction of e-field. The surface electrons respond very fast to the introduce e-field whereas the interior electrons warms up to join in the in the race due to the metallic bonding between metallic atoms forming the conductor.