Hello,

I'm using an Agilent 4263B, and I'm trying to understand the relationship between different measurement parameters.

I'm measuring an air core inductor and these are the results I get at 100kHz:

Lp = 9.97 uH

R = 0.968 X = 7.63

|Z| = 7.689 Theta = 82.77

When I measure Rdc I get: .087 ohms

My first question is, why dont R and Rdc match? Z = R + jX = |Z|< theta... shouldnt Rdc = R??

Second question: can someone explain the difference between Lp and Ls?

Thanks.

 

Are you aware of the skin effect?

 

Nope, that's new to me

 

Nope, that's new to me

Did you read the wiki? Do you understand it?

 

Yes, its interesting and it makes sense to me. According to the page, in copper at 100 kHz, the skin depth is 210 um and at 60 Hz its 0.8mm. My wire diameter is .9mm.

So by my calculations:

Rdc = .087 ohms
R_real_100k = .968 ohms

DC Conductance = 1/.087 = 11.236
Skin Effect at 60 Hz relative to DC: .8/.9 = .88
Skin Effect at 100 kHz relative to 60 Hz: .210/.8 = .236

Conductance at 60 Hz: 11.236*.88 = 9.88
Conductance at 100 kHz: 9.88*.236 = 2.306

==> Expected resistance at 100k: 1/2.306 = .433 ohms. I measured .968.

Thoughts?

Thanks!

 

The relationship between DC resistance and that due to the skin effect is not the simple ratio that you used. The "skin" is the distance into the surface of the wire so it forms a cylinder equal to the thickness of the skin.

Thus for a skin depth of 0.8mm the cylinder would extend 0.8mm into the wire on all sides, which is greater than your wire radius of 0.45mm. Thus there is no significant skin effect at 60Hz for that wire's resistance.

At higher frequencies you need to use the formula given in the "Resistance" paragraph in the Wikipedia article that Ron referenced.