dc resistance of EM simulated inductor

I simulated a spiral inductor with ADS EM Momentum and would like to look for its dc resistance.

Can I get the dc resistance of this EM-simulated-inductor from its S2P file?

Or since I have the EM model, could I set up a simple circuit as blow to get dc resistance? With a dc source Vdc and a current probe, can I do Rdc=Vdc/I?

Does anyone have suggestions?

Extracting DC resistance from EM model may be erroneous.Because even though EM simulator covers 0 Hz ( DC ) in fact the simulator starts from very low frequency but not exactly 0 Hz.
Your method will not work-absolutely..
Extrapolation ( down to DC ) may work but it can also not give the "exact" resistance, just approximated value can be obtained..
The better way is to calculate DC resistance by well known method.( Sheet resistance technique )

Yes, it works and you can get accurate results when using Momentum RF mode. I use this all the time for RFIC inductor work.

For evaluation, you can use your circuit, or you can calculate series resistance in the data display from Z-parameters using equations. Below are equations that evaluate the path between port 1 and port 2 (differential operation).

Thanks for the information! I tried your equations, it gave same result as using the circuit. Your mentioned that I can get accurate results from Momentum RF mode, how about Microwave mode? Would be result be similar?

Also, you might can help me with this... The EM simulated indcutor seems to have much lower R_dc compared to schematic one, do you know why that's the case?



Hi BigBoss, do you have a reference about calculating DC resistance? In a spiral inductor, the dc resistance mainly depends on the width of lines, right? I know the thickness and rho resistance of the metal.

I have used RF mode extensively for RFIC inductors, and that mode uses a special approach to cover low frequencies and DC. RF mode is valid as long as there is no relevant radiation and no multimode propagation, so I also use it from DC to 100GHz in some cases.

I have NOT tested Microwave mode results down to DC much, but in theory there is a reason why Agilent/Keysight introduced RF mode for the low(er) frequency range. The usual formulation of MoM that Bigboss refers to breaks at DC due to singular matrix. EM tools like Sonnet use a "faked" DC point that really is a low RF frequency, low enough to be almost like DC, but high enough to give reliable results. I would expect that Momentum Microwave mode also breaks at DC, but I don't know if they internally switch to RF mode below a certain frequency.

For manual calculation of DC resistance, you just add all the metal sheet resistance * length / width and also add the via resistances. This is a good test to check EM solver results at DC.

That makes sense! Great helpful information!! I tried to run the inductor in Microwave mode, the DC point did failed off while everything else looked the same as in RF mode.

For calculation, I have the metal sheet resistance in ohm/square(which is equal to ohm right?). should I just use this number without unit conversion? and is length the total length of all sections? My calculated DC resistance is 1.8ohm compared to 0.7ohm in EM. and the schematic inductor gives 3.5ohm. that's a lot of difference. Any thoughts?

I assume you are also working on RFIC inductors, not PCB?

ohm/square is the resistance of a square segment. If that value is 10mOhm/square and your inductor turn length is 1000μm and width is 10μm, then resistance is 10mOhm * 1000/10
This calculation must be done for all the metal in the inductors current path.

You also need to include the vias. In the process spec, you find the resistance per via, and need to calculate the resistance of parallel vias in the via array. For Momentum, via array merging might result in a larger cross section of the merged via. Since ADS 2016, there are some advanced features to keep the area when doing via merging.

From my experience, Momentum DC results are very close to manually calculated data, so your difference is unexpected. Maybe your path length is wrong or the vias are missing or there is a mistake in the EM model. All values should agree much better.

Below I have attached an example what I get for measured vs. simulated in RF mode (2.8nH in IHP SG25H technology).

Yes, I am also working on RFIC inductors.

That's a great feature to know! Thanks! the via is Au(resistance should be minor right?). Just re-ran the inductor with your info, result looked similar but definitely not exact.

I recalculate the resistance and is still 1.3ohms. Here's what I did:

The drawing trace is the length I added up = 3200um. width of trace is 25um. and Rs=10mohm/sq. Without via resistance, I am still getting 10mOhm*3200/25=1.28ohm which is big compared to 0.65ohm result. Am I adding the path length correctly?

Your simulations look great comparing to measurement. Just not to be confused. The effective resistance in your graph is DC+AC resistance right?

I am also trying to understand the equations you provided. Why omega and Zdiff are needed? Would it be okay just use Z-parameters?

Sorry for all the questions and I sincerely appreciate your help!!! Thanks so much!

Sounds like some III-V technology? I am working on SiGe/CMOS technologies where via resistance can be very significant for narrow lines where the via array is small.

Looks ok for the coil layer, to be accurate we need to add the bridge and the via (which results in even larger value then). Double check the material properties and metal thickness in your EM simulation!

The shape of your simulation result, with the drop below 2GHz, looks a bit unusual. I would rather expect the curve to flatten towards lower frequencies. Can you copy this model into a new workspace, and upload it here?

Yes, correct. This is the total resistance measured/simulated across the inductor.

You are correct for data that comes from schematics. I want my equations to also work with imported S-params, where the dataset does not include "freq" variable and Z-parameters. That's why I get the frequency as indep(S) and create Z-params from the S-params.

Yes, I am working on GaAs technologies. - still learning :(


I double checked the metal thickness and its resistivity. They seem reasonable. I have so many things in the workspace, and I am trying to look for a way to simplify it! I exported .gds and its substrate. Need a way to put in material definitions.


I am trying couple ways at this point. I tried Zin from s-parameters to get its real part at DC, but doesn't seem working. The dc resistance does not match to you method. I also tried simulate Z-parameters, but I do need your Zdiff equation. Could you please explain Zdiff and why it should be used?
Thanks!!

The Momentum stackup consists of two files that reside in the library directory: *.subst and materials.matdb
You can copy these two to other libraries. The layers in these files are references by ADS layer number.

Zin should be the inductor in series with the 50 Ohm at port 2.

I was about to explain that in my last post, but then left it out to keep the post short. In RFIC on silicon (my stuff) most circuits are differential, and we are interested in the electrical parameter between the inductor terminals (between port 1 and 2), driven in a differential way.

If you look at my appnote here (section "Why are these results different?"), you will see that results are indeed different, because the parasitics from the substrate network have different effect.

For DC, results for single ended and differential R and L are the same. For RF frequencies, you might select single ended or differential parameters depending on your circuit use.

A lot of useful information in one post!!

I rechecked the design manual and realized that the inductor I simulated was double-metal (which was not visible in my previous picture), but the 10mOhm resistivity is for single metal only. For double-metal, the resistivity cut in half. In the newest calculation: 5mOhm*3200/25=0.64ohm (without airbridge and vis resistance), which is pretty close to 0.7 of my EM. That was my stupid mistake!! and thank you so much for all the trouble-shooting ideas!

Does it mean that R_dc = the DC point of Zin - 50ohm?

Thanks for the great resources! My inductor is no differential, but your equations work since I only care about the DC point. If I don't want to use differential parameters, is there anyway I can reconstruct the equations?

P.S. There are lots of useful information in your website, which are helpful for building my ADS skills(as a beginner)!!

Great, that's what I expected: there must be some reason for the difference. The solvers are usually accurate if the model itself is accurate.

I haven't tried, but from my understand that should be it. I don't use that because from EM simulation you don't get Zin (it's not in the dataset by default).

Regarding equations and the single ended/differential topic: due to the shunt parasitics, "the inductance" and "the resistance" of our inductor can be interpreted in different ways. There is not one unique value for all configurations, so all these values are correct for their specific circuit configuration.

My differential evaluation from Zdiff gives you the values across the inductor, including the shunt elements => this is what we are interested in for series configuration. I would also use that for your series inductors in GaAs, if you want an effective value of R and L to represent the inductor at one frequency.

If for component modelling purposes you want to know the series element only, excluding the effect from shunt path parasitics, you would calculate that as R=real(1/-Y21). I use that for extracting equivalent circuit models from inductors, where I model separate elements for series and shunt path.

And if you want to know the value for the inductor grounded on one side, you can simply use R=real(1/Y11).

1/Y11 is the impedance into port 1, with all others port shorted (V=0). If you evaluate Z11 instead, you get the impedance into port 1 with all other ports open (I=0). What I do is really to take a piece of paper and write down the equations for current and voltage using Y params and Z params. It's not complicated.