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DC resistance v.s. AC resistance

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don_quixote

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ac resistance vs dc resistance

Hello everyone,

I'm using Ansoft Q3D to do some extraction tasks and found out that Q3D gives lower AC resistance value than DC resistance value. This really confused me because all what i learned tell me that the resistance of a conductor @ high frequency is going to increase due to the skin effect and/or proximitty effect (like what's being said in Howard Johnson's HSSP book). If it does not increase (e.g. the wire cross section is smaller than the skin depth) at lease it shouldn't decrease.

I searched on the internet and found this on Ansoft HF forum:

DC Resistance versus AC Resistance in Q3D
by: eustacec
email: eustacec@nus.edu.sg
12/17/2002 5:55A
Hello, I have a question on quick3d. I have run a simulation which shows that the DC resistance value is HIGHER than the AC resistance. Can this happen? and Why. Theoretically, the AC resistance is due to the skin effect, and it will always be bigger than DC. 2nd situation where I have 2 different conductors in series. Copper + Solder. How does this impact on the DC and AC? Your reply is appreciated. Thank you. Cheers.

Re: DC Resistance versus AC Resistance in Q3D
by: Richard Remski
email: remski@ansoft.com
3/3/2003 11:41A
The AC solver doesn't 'know' what skin depth is, so it assumes that the current is in the 'surface' of the conductor only. This curve is valid for frequencies up where the skin depth is less than the real conductor thickness, but is going to be incorrect at really really low frequencies. The DC solution on the other hand does assume currents thru the whole thickness, so its answer is more 'valid' for those very, very low frequencies. So no, higher AC than DC resistance shouldn't happen in real life....if you see it that's an indication that for the frequency you're looking at is in that transition region where the AC assumptions are breaking down. RTR
Click to expand...

Now i'm even more confused because Richard from Ansoft says "higher AC than DC resistance shouldn't happen in real life....". Since this is so a fundamental issue i guess many of you can help me.

Any input is appreciated.

Thank you,
don_quixote
 

dc resistance vs ac resistance

hi,

I also do think that the AC resitance should be larger than the DC resistance for a conductor. However, this is for the case where the capacitance and inductance of the line is neglected, and the propagation characteristics are neglected. However, if you are using e.g. the Y-matrix to find the resistance and neglecting the parasitics, then i think that this will give you a wrong answer.

I think what Mr. Richard just misstyped the word.

br
adel
 

ac resistance dc resistance

Hi Don -- I agree, Richard just made a typing mistake. AC resistance is always higher than DC resistance, no exceptions. In fact there are two transition frequencies that you must go through before you get to skin effect loss. The multi-sheet model gets these transitions with no problem. It is detailed in our paper:

James C. Rautio and Veysel Demir, "Microstrip Conductor Loss Models for Electromagnetic Analysis," IEEE Transactions on Microwave Theory and Techniques, Vol. 51, No. 3, March 2003, pp. 915 - 921.

You can use the multi-sheet model in any EM analysis, but it is much much more efficient in a planar EM analysis. In Sonnet (I work for Sonnet), the multi-sheet model is automated, all you have to do is to type in the number of sheets.

One most amazing conclusion in the above paper is that there is a thickness for minimum loss. Thicker or thinner results in higher loss.

You might also want to view the following topic in this forum:



where low frequency inductance is discussed as well. The inductance determines the first loss transition frequency.
 

effect of resistance in ac

Dear all:

I've ever encountered the same problem long time ago when I used the Q3D version 5 to extract RLC of a 3D structure. It gives me Rac<Rdc which is physically not true. Till today, I still can not understand why is that so if it's not a bug of the software. Can anyone here has a "reasonable" explanation if its not a bug?

One of the explanation I've heard is that: it's because the way Q3D report the value of "AC resistance" is different. The conventional definition for "AC resistance" is a measure that how effective the object "impedes the current flowing inside it" and is usually "Rdc + Rac" where the Rac is the frequency dependet effect(such as skin effect). What the Q3D reports is only the second part of the conventional definition: the Rac part. I always think it is not so convencing. But at least it's a good explanation if this is really the case of Q3D and the developers of this tool not consider it as a BUG. :)

Regards,
 

dc resistance + ac resistance

thx
 

will the ac resistance is smaller than dc?

Hi Smithchart -- R total is most definately not Rdc + Rac. When it transitions from low frequency to skin effect, Rdc dissappears and Rac appears. Except when in transition, it is all Rdc or all Rac. Please read the paper I referenced above for details.
 

ac resistance vs dc resistance copper

don_quixote shalom,

Have you upgraded to Q3D version 7?

It allows you to export S-parameters which should take into account the transition of the resistance from DC into AC gradually. The Z-parameters =R+j(wL-1/wC) should give you a good indication.

Regards,
Itai
 

pure ac resistance

Hi, Rautio:

I totally agree with you that the real-life(phycially true) R(ac) is not separable for a specified object. The reason I quote "Rdc+Rac" considered as R(ac) by someone is only a way to facilitate the understanding from a pure "mathmatica" point of view. Just like magnetic dipole is not physically exist but people still use this conception to explain and understand some EM phenomena.

As I stated before, Rac of "Rdc+Rac" represents the contributions "mathmatically" from frequency-dependent effects. Put it another way, if R(ac) considered as R(ac)=R(dc)*sqrt(freq), Rac is the value of R(dc)*(sqrt(freq)-1) which is only the contributions from the frequency-dependent effects.

Using the above-mentioned "definition", it is understandable that Q3D reports an AC resistance less than its DC value if it reports the Rac, rather than R(ac).

BTW: please be careful that I used Rac stands for pure frequency-dependent effects which is mathmatically true and R(ac) represents the real-life AC resistance which is physically true.
 

resistance in ac

Hi Smithchart -- I guess it is always possible that what you suggest is the case. Seems like if it were, Itaifrenkel would have stated that instead of suggesting that you try the latest release. In addition, the documentation should also carefully point out this non-standard way of looking at it. I tend to think it might be more likely that it is just simply an oversight in the software. It might be related to the fact that if you just take skin effect loss into consideration, and do not include the transition to low frequency loss (as is very very common in most circuit theory based tools), then the loss goes to zero at zero frequency. In this case, if you look at the skin effect loss at a frequency that is below the transition frequency, you will get skin effect loss lower than the DC resistance of the line. This is necessarily incorrect, and can serve as an indication that you are below the skin effet-to-DC transistion frequency. In this case, a quick email to support should generate a thank you and a very simple modification to the software completely removing the problem.
 

skin effect rdc

Hi, rautio:

Yeah! I do agree with you that this kind of explanation is kind of "unconventional" if it is really the case and the developer of this tool do not consider it as a "bug". Actually I contacted their support engineer and they do not give me a good answer at that time. Anyway, I didn't use that tool for a long time and do not have access to it now. It's just a past story. If anyone here have the lastest version, please try a simple case to see if Ansoft did something to change this or not. Really appreciate if you can share with me the results.

BTW: I don't want to look at the Z as was suggested. I only want to look at R which is the real part of Z and considered as the LOSS. This is also the starting point of this post try to discuss. :)

Best regards,
 

dc vs ac resistance

Hi Smithchart -- If what you want are the R, L, G, and C per unit length, download free SonnetLite www.sonnetsoftware.com (I work for Sonnet). Install (about 5 minutes), go through the Help->Tutorial (about 45 minutes), then read chapter 22 in the manual (esp. the N-coupled line section). With a few seconds of analysis time you will have your numbers to within a percent or so. And R will be strictly lower bounded by the DC value.
 

same thing happens in Q3d version10, but in lower frequencies only.
@ freq=1MHz, Rac < Rdc.
but @ freq=100MHz, Rac > Rdc.

i think in Q3d, the real Rac is the measured Rdc+Rac.
just a thought.

:cool:
 

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