Replies: 7 comments 9 replies
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I'm glad to see that my original one-post suggestion of using "Djordjevic-Sarkar model with numerical curve fitting into the Lorentz model" has not only been implemented in code but is being verified experimentally, with the limitations highlighted. The progress is truly impressive. Thanks for your contribution to the entire community. If I read this report correctly, preliminary results are:
I'd like to add another separate point that was previously reported to me:
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Impressive work on wideband dielectric loss and excellent presentation of results, Tobias, congratulations!!! I want to comment on one error source for conductor loss when simulating it as zero thickness sheet in EM. Conductor loss for thin sheet model uses a frequency dependent surface impedance calculated from effective cross section in the skin effect regime. However, in the real thick conductor current can flow on the top side, or bottom side, or a mixture of both. This makes it difficult to estimate the effective current cross section in skin regime.
For a stripline with grounds above and below, we have a symmetric case with equal "skin sheets" on top and bottom, resulting in twice the skin thickness for the thin sheet model. For microstrip, most current is on the bottom of the conductor only, so that the resulting thin sheet model is more accurate when using only one skin depth for the loss calculation. The difficulty here is that the thin sheet EM solution does not solve for top and bottom side separately, so this "current ratio" is only an estimate. For thin sheet conductors in the Sonnet EM solver, this current ratio is actually a user defined parameter, with default set to the "pessimistic" case of single sided current flow. For OpenEMS I don't know what the underlying calculation assumes, one or two skin depths. I wanted to simulate your testcase in Sonnet today, to compare the optimistic (2 skin sheets) and pessimistic (1 skin sheet) case, but my license expired a few days ago and I need to wait for license renewal. Maybe we can then add a separate topic on conductor loss modelling, so that we don't disctract from your great progress in dielectric loss modelling presented here! |
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openEMS's lossy conducting sheet model is basically just a Lorentz material with 30-pole parameters, defined in the following code: These material parameters are generated by the script The model appears to be a rather basic one, defined mainly by these equations: Before they're used as input to the underlying Lorentz material code, these Lorentz material parameters are further modified by a scale factor calculated according to simulation conditions such as conductivity and thickness in operator_ext_conductingsheet.cpp. It should not be difficult to check the underlying assumptions of the current model by reviewing the code involved. It should also be possible to create a better lossy conductor model without major changes to the engine if it can be expressed in terms of a set of Drude/Lorentz/Debye material parameters. |
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Here is a small addition to @biergaizi's information. In FDTD/extensions/operator_ext_conductingsheet.h is a link to the paper used for the conducting sheet model. |
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Thanks for pointing it out! I've completely missed this comment in spite of working with the codebase for several months... |
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Can this disparity be entirely attributed to surface roughness, or are we also missing something else? Have you tried to check the agreement between openEMS with another model (simple equations, analytical models, 2D models like Si9000, or another full-wave model) by modeling the same fixture, but with the copper's surface roughness turned off? |
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In the meantime I simulated Tobias model in a commercial FDTD solver. I used the STL data exported from AppCSXCAD and thin sheet metal model, with loss calculation set to wideband lossy for metal and dielectric, no conductor roughness. Result for insertion loss agrees very well with openEMS calculation shown by Tobias, I get -1.3dB @ 20 GHz. My conclusion is that Tobias did an excellent job with his math and model, and the extra loss in measurement is indeed some additional effect not included in the model. |
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I was hoping that someone with access to commercial software can verify the results. Awesome that Volker was able to do so! Unfortunately, the tolerance range for tand is quite high for the FR4 material used. It may be that the real tand value is slightly higer. So, some uncertainty exists in this parameter.
No, I have not done this yet. I will request further information from Aisler maybe they can provide some information about the used copper foil to get data for copper roughness. A simulation with metal losses in a commercial software would also be appreciated (Does Sonnet have copper roughness models?). Thanks again, for the time you spent in the forum. I have learned quite a lot here! Regards, |
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I could not check in Sonnet yet (waiting for license file), but verified results including surface roughness using two other commercial solvers, one FDTD and one Method of Moments solver. Insertion loss without roughness is 1.3dB at 20 GHz (FDTD) and 1.35 dB (MoM), using the same assumptions that you used for your model (thin sheet metal model). This confirms your model and results. When I include a (large!) roughness value of 6um using the Hammerstad-Jensen model, the additional insertion loss is 0.1dB in both solvers. Not sure what a realistic roughness value is, but I guess my 6um is already pessimistic. [1] Hammerstad and Jensen, “Accurate models for microstrip computer aided design,” in IEEE MTT-S Int. Microw. Symp. Dig., pp. 407–409, May 1980 |
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Update: Using the metal roughness modell in Sonnet, the effect is much larger than seen with the other solvers: S21 = -2.1dB @ 20 GHz with 6um roughness, -1.4dB @ 20 GHz without roughness. I can't explain why that is so much larger effect compared to the other solvers. In the manual they link this reference:
Note that the 6um roughness value in my tests is just a guess, most likely a very pessimistic guess. Tobias, could you find out what roughness Aisler specifies? |
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Hey Volker, The used stack up is - most certainly - not optimized for RF. It was, for me, just very cost-effective to source. The copper roughness value may indeed be high value. In PCB manufacturing, high surface roughness on the dielectric side is preferred to strengthen the bond between the copper foil and the dielectric. It increases the immunity against delamination. Aisler had most certainly no RF applications in mind and optimized for durability. A Google search returned 6um for "standard copper foil". However, the source does not look trustworthy to me :). I did even ask ChatGPT :)
I have noticed that models for conductor loss can produce significantly different outputs. Especially, the Hammerstad-Jensen model has some terms in it that saturate at higher frequencies. This prevents the loss term from growing. However, the loss in real models does indeed grow. The Hammerstad-Jensen model underestimates' conductor loss for higher frequencies significantly. I think the CST help recommends this model only up to 5 GHz, or so? I have to check.. Getting the metal losses right will be another hard to solve task... Verify using WCALCI have now verified the results above using an equation-based microstirp analysis tool. WCALC is a great tool. It provides references to all the equations used. It is also free. It is supplied as a web calculator and also in binary form to be installed on a computer. https://wcalc.sourceforge.net/about.html It uses the Hammerstad-Jensen model where the saturation effect can be observed. The loss value does not change much for higher frequencies and higher roughness values. Substrate losses only
The two dielectrics I have simulated above have different values of tand (I guessed the core metal to have a loss tangent around 0.02). I went simply with the mean value of the two tand=0,0165. As the core is thicker, I think the effective loss tangent will be slightly higher. Wcalc reports a loss value of 1.18dB for the substrate losses only case. This is very close to my simulated 1.22dB loss. I think the substrate losses are treated correctly Substrate and metal losses (Hammerstad-Jensen with saturation effect)
The metal losses do not change the result significantly. Here is a link to the used models of WCALC. Maybe it is a good idea to open a new discussion thread for metal losses to separate this discussion from the substate losses, as suggested by Volker earlier. Regards! |
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I just noticed the PCB has gold plating. Thus, another source of error is the losses from gold plating. Losses from the ENIG surface finish has a magnitude comparable to surface roughness due to the use of nickel and gold. Let's continue this discussion at #161 (comment) instead. |
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I'm now trying to model this PCB using Si9000 for comparison. But I have find it's difficult to understand the PCB layout and what exactly are simulated and measured. Could you please clarify these details: Which layer is the signal layer? Which layer is the ground layer? How long is the line (after de-embedding)? What happened to the unused layers (Which layer is removed? Which layer is via-stiched to the ground layer)? Since you've mentioned that both prepreg and core are included in the dielectric, my guess is that the signal layer is layer 1, the ground layer is layer 3, meanwhile the layer 2 copper under the trace is removed, and all the other unused layer in via-stitched to layer 2? Thus, this test fixture can be modeled as a PCB with two metal layers and two dielectric layers? Is that correct? |
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Line length to be simulated is 23.5mm, width = 0.65mm, gap from line to side ground = 1.225mm Signal + side grounds on layer 1 The vias connect side grounds to the bottom ground, diameter 0.3mm, distance from side ground edge to via center 0.3mm |
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As proposed, I've opened a new thread: Conductor loss for wideband models to separate further discussion about conductor loss modeling from dielectric modeling. |
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Comparison with Si9000Polar Instrument's Si9000 is a transmission line calculator widely used by printed circuit board manufacturer. It's primarily an impedance calculator based on a 2D MoM electromagnetic field solver, but new versions also support frequency-dependent analysis, including S-parameter analysis, substrate εr extrapolation via Svensson-Djordjevic model, and surface roughness modeling using Hammerstad, Groisse, Huray, and Cannonball-Huray models. Dielectric Loss OnlyHere's a comparison of openEMS (Djordjevic) and Si9000's dielectric loss calculation. To eliminate conductor loss, an extremely high, unphysically value is used as the metal conductivity in Si9000. To extrapolate dielectric's εr, the prepreg and core meterial's dielectric constant and loss tangent are specified at and only at 6 GHz. Internally, Si9000 uses the Svensson-Djordjevic model to approximate the wideband material property. This is similar to the Djordjevic-Sarkar model used in the original openEMS simulation. As one can see, both models are indistinguishable.
Dielectric Loss + Smooth Metal LossThe following is a comparison of openEMS (Djordjevic + CondSheet) with Si9000, with both dielectric loss and smooth metal loss. As one can see, the agreement is still respectable to 0.1 dB at 20 GHz.
Rough SurfaceNext, two different surface roughness models - Hammerstad and Cannonball-Huray - are compared with the results from smooth conductor. In this comparison, the worst preset value from Si9000 is used. In the Hammerstad model, the roughness on both sides of the copper foil is set to Rq = 8.25 µm RMS. In the Cannonball-Huray model, the roughness on both sides is set to Rz = 7.5 µm. Since I've already explained the assumption, properties and application of each model and parameter in a separate thread, Conductor loss for wideband models, so it will not be repeated here.
As one can see, Cannonball-Huray predicts a worse attenuation than Hammerstad, as expected, since it's widely accepted that Hammerstad underestimates losses (but do note that these two models use different paramaters so they're technically not directly comparable). However, even with the assumption of Rz = 7.5 µm, a pretty bad roughness value, the simulated result is still 0.3 dB away from measurement. Thus, there are three possible explanations for this disparity:
I suspect it's a combination of these three factors. Input Parameters Used for CalculationLossless Calculation
Frequency-Dependent Calculation
Causally Extrapolate Substrate Data (Svensson-Djordjevic)
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Hello,
in the last weeks I took a closer look at substrate losses. More specifically the Debye and Djordjevic-Sarkar [1] models. I think this is a good point to share the results I have so far.
The Djordjevic-Sarkar model was suggested by @biergaizi in the context of my Microstrip to SMA transition model. @VolkerMuehlhaus has opened a discussion thread for wideband dielectric models where he published some simulations in Sonnet for comparison to openEMS.
The Djordjevic-Sarkar was originally developed for FR4-type materials based on measured data. The idea is to have epsilon'' (imaginary part) approximately constant between two corner frequencies$\omega_1 = 10^{m_1}$ (lower limit) and $\omega_2 = 10^{m_2}$ (upper limit). With this assumption it is possible to create a wide band model with only one epsilonR, tand pair at a single frequency. The model is implemented in several commercial simulators (CST, HFSS, Simberian). According to multiple sources this model works well for materials with an almost constant loss tangent (very common for PCB materials). The Djordjevic model is roughly speaking a Debye model with an infinite number of terms, but it can be approximated by a finite number of poles. With some math it is possible to solve for the unknowns by choosing an appropriate number of Terms. In a second step the Debye model can be (approximately) converted into the openEMS Lorentz model as defined in openEMS
Motivation
Currently I am working on a openSource tunable band pass filter. The plan is to make a co-simulation of QUCS (models for lumped elements and the varactor) and openEMS (for the passive filter structure). To achieve a close agreement between measured and simulated results it is critical to get all losses right. In the passive structures as well as in the lumped component models. This is why I started to look into the substrate losses.
The DUT (Device Under Test)
The low cost Rosenberger 32K242-40ML5 connector combined with my wide band transition is an enabler for accurate de-embedding using the IEEEP370 open source 2xThrough method. Accurate wide band de-embedding can be achieved. From the two projects I have two calibration lines of different lengths (See Figure below). By de-embedding the half sections of the short transmission line from the longer one connector effects are removed. The length difference is 23.5mm.
Both are fabricated on the Aisler 6Layer HD stackup. To get a reasonable substrate thickness for RF (filter) design the upper prepreg and core have to be combined. This is bad for the insertion loss due to the lossy core martial. However, this is the price to pay when using an ultra low cost PCB.
The material parameters are taken from the substrate datasheets (min./max values) linked by Aisler and the Panasonic datasheet.
The maximum value for the laminate is a very high tand=0.035 value. Typical values in the datasheet are around 0.013 (a very low value for an FR4 laminate). These datasheet values are known to be very optimistic. Are these values trustworthy? The span between typical and max. is a too high in my opinion. Therefore, I went with a typical value for FR4 of tand=0.02. For the prepreg the datasheet typical value form the datasheet was taken.
The figure below shows a de-embedded VNA measurement of the transmission line.
OpenEMS Simulation Model
A openEMS simulation model was written to recreate the DUT from above with a length of 23.5mm.
Four test cases were simulated
The current result of my work is a function
AddDjordjevicSarkarMaterial()that calculates a multi term wide band material model. In short - without providing too much details - the following steps are performed:Example call:
Here are debug plots that show the model fit of multi term Debye and Lortentz model in linear and logarithmic scale
The "abuse" of the Lorentz model comes with some stability problems. In the time domain the frequency dependent material properties are handled by an equivalent circuit approach. My function basically forces the equivalent circuit of the Lorentz model to be equal to the Debye one. Maybe here some instability occurs.
In its current state I would not consider
AddDjordjevicSarkarMaterial()to be save to use. The cleanest way would be to add the Debye model into openEMS along with the Lorentz model (This is certainly a topic of discussion). However, I consider this is a long term project. If anybody needs a wide band dielectric model desperately (like me :).:AddDjordjevicSarkarMaterial()can be used at own risk.Results
The simulation model's outputs for the four test cases can be plotted on a single graph, following the standard practice for these types of comparison. Transmission losses in the lossless case are almost zero. I noticed that at these low attenuation values even the PML boundary thickness has an influence.
The substrate and conductor losses were added sequentially. For comparison the measured transmission is also included. We can see, that the simulation has too low losses. Even when conductor losses are considered by
AddCondSheet()and a wide band model for the substrates. I think that the conductor losses are probably not treated well. Copper roughness is not included. This is in my experience required. What do you think?It would be nice to have a simulation of a commercial simulator for comparison. The results of the Djordjevic-Sarkar model agree with Sonnet (see here]. But this simulation is without conductor losses.
For completeness here is the plot for S11.
Problems
AddCondSheet()model. The filter is highly sensitive to coupling effects between transmission lines. I must model the traces with their proper thickness. To my knowledge there is no way to treat metal losses of volumetric shapes without a very fine mesh to capture the skin effekt?References
[1] Djordjevic, Antonije R., et al. "Wideband frequency-domain characterization of FR-4 and time-domain causality." IEEE Transactions on electromagnetic compatibility 43.4 (2001): 662-667.
Link to model
Please find the code and measured touchstone files in my repository:
https://github.com/toammann/OpenEMS_MultiTermDebyeExperiments
Any comments or suggestions are welcome.
Regards,
Tobias
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