# Skin effect in 1 milliOhm resistor?

#### eem2am

Aug 3, 2009
429
I have an 11 Amp RMS current flowing in a one milliOhm sense resistor (1%).
(its a 1210 size chip resistor)

...this current is amplified by a differential amplifier with a gain of 100, and there are filter capacitors incorporated in the differential amplifier (using OPA335 op amp which has low Vos) so that the amplified output voltage is DC.....(and then this DC output of the opamp is read by an ADC on a microcontroller)

......The 11 Amps current waveshape is of the form of a full wave rectified 50Khz sinusoidal current waveform....so it has a frequency of 100KHz.

.....Do you think skin effect issues will be at large here?......will the 1 MilliOhm resistor act like its a lot more than 1 MilliOhm?

#### davenn

Moderator
Sep 5, 2009
14,011
hi ya

Im not a total expert here, But I understand that skin effect doesnt really become a critical factor till the frequency is well in excess of 1MHz

I have seen a skin effect calculator online, doing a google search will probably find it for you

Dave

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,505
Traps for young players.

The wires, traces, and solder joints may each contribute more than 0.001 ohms of resistance.

In particular, the solder joints are going to be in series with your resistor no matter how careful you are with having separate traces to carry the 11A and the voltage signal from the resistor.

The skin thickness at 50Hz is likely to be multiple times the size of your component.

#### eem2am

Aug 3, 2009
429
Thanks, however Steve, its 50KHz, and not 50Hz.

I appreciate you'd think 50Hz as thats mains...but this is 50KHz.

#### davenn

Moderator
Sep 5, 2009
14,011
Thanks, however Steve, its 50KHz, and not 50Hz.

I appreciate you'd think 50Hz as thats mains...but this is 50KHz.

as I said above skin effect isnt really likely to become a factor till much higher freq

did you bother to do as I suggested and google an online skin effect calculator ??

Dave

#### eem2am

Aug 3, 2009
429
Yes thanks

http://chemandy.com/calculators/skin-effect-calculator.htm

....told me at 100KHz its 206um, so i suspect my resistor is not going to suffer skin effect...although i dont know because the resistor is thicker than 200um

I have been trying to find a calculator that gives the ratio of DC to skin effected resistance........i used to have that in the back of my Marty Brown book, but it went walkies............

However, This site appears to give the ratio....

http://daycounter.com/Calculators/SkinEffect/Skin-Effect-Calculator.phtml

...and putting in 500um as the "r" value (thickness of chip resistor) makes the ratio 1.42.....which i take as bad news because it means the 1mR reistor will look like 1.42mR ....?

....it was a little confusing because the equation was for a round wire, wheras i wanted it for a chip resistor.

#### davenn

Moderator
Sep 5, 2009
14,011
plus you are talking about a carbon resistor a few mm long and not a metallic conductor that can be any length or diameter which has a huge effect

I still think you are panicing about nothing

Dave

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,505
...and putting in 500um as the "r" value (thickness of chip resistor) makes the ratio 1.42.....which i take as bad news because it means the 1mR reistor will look like 1.42mR ....?

How are you correcting for the resistance (and hence voltage drop across) the solder joints and possibly in the traces leading to it?

Is this a 4 terminal resistor? Do you have separate traces for the current and the sense connections? Are they connected to the same pad, or have you split the pad too?

What size is this resistor? It may be 200uM thick, but if it is much wider, there is more skin available.

Resistance (distinct from reactance) increases with frequency due to the skin effect, the self-induced eddy-current effect within a conductor. Above a frequency at which the effective depth of current penetration into the conductive material is reduced, resistance increases. Thin-film resistors suffer this effect at relatively higher frequencies than bulk resistors because skin depth exceeds their thin conductive dimension at lower frequencies, causing no change in their effective resistance.
http://www.innovatia.com/Design_Center/Making Sense of Sense Resistors 2a.htm

Are you using something like this? It doesn't have any graphs to describe response vs frequency But it does suggest it work up to 50MHz, although I expect that is the point at which inductive and/or capacitive effects start to dominate the reactance.

#### Laplace

Apr 4, 2010
1,252
Wikipedia gives a formula for skin depth as a function of the frequency, relative permeability and resistivity of the medium. It is likely that the relative permeability of the material comprising the sense resistor is 1, while the resitivity is somewhat higher than copper. A high restivity material will give a greater skin depth, making the skin effect less of a problem. That would leave you with the problem of estimating what the restivity of the sense material is.

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