How to plot S-parameters for Coil Inductor - FEKO

In FEKO, I have created a wire helix with diameter of 4 inches and 5 turns (1 inch per turn). I want to plot the S-parameters for this simple inductor, but everytime I plot them, S1,1 is 0 dB or slightly positive at 1 dB. I have added straight lines to each end of the helix coil and made these lines each a port. This is all I should need to do, but the S-Parameter plot shows nothing is getting through the coil with S1,1 at 0.
Ive tried adding a box of free space around the coil, but same results. I have unioned the coil and two straight lines but still get the same results. Both ports active when setting up the s parameters.
Please assist.

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Accepted answers

Jaehoon

Hello Daniel,

Let me give my answers to your questions.

Q1) So all I really needed to do was add a wire port connecting the ends of my coil to the closest/adjacent box face?

→ Yes, because this structure is measured by VNA, the two ports are associated with the ports of the VNA (Vector Network Analyzer).

This is similar to using a wire port located between the end of the monopole wire and a ground plane, which simulates the monopole antenna fed by a coaxial cable.

Q2) shouldn't S1,1 be zero for DC & low freq then drop off, allowing signal though at higher frequencies?

→ S1,1 (dB) = 0 (in other words, reflection coefficient =1) means that all the input power reflects back to the source (VNA's input port).

Q3) If you could help me troubleshoot this last small issue, I would really appreciate it.

→ Please see the new attached models.

Q4) Shouldn't the S-parameter plot look something like the image below?

→ Please see the new attached models.

2. Let me simplify your model again. (to reduce the computational cost ( for speedy simulation.)

2.1)Here I replaced the 3D coil with a 1 D coil with radius of 0.38 inch (the radius is in the modify mesh.)

and activated "Double precision" under Solver setting > General.

3d-coil-in-a-box-upload_simple.zip

2.2) Since a resonance is observed around 90 MHz, I changed the frequency setting and gave finer meshes.

3d-coil-in-a-box-upload_simple_1.zip

So, to get more exact results, please use finer simulation frequency step and mesh size.

Best regards,

Jaehoon

PS) I think that the characteristic of the coil inside a metallic box is similar to rectangular cavity resonator, whose size determines the resonating frequency.

https://learnemc.com/ext/calculators/cavity_resonance/rect-res.html

(There are so many resonant frequencies as below.)

Additionally, the behavior of the coil depending on the frequency affects the total S11 and S21, too.

Jaehoon

MY QUESTION: how to allow the skin effect to be simulated on this geometry (relatively small coil: 4" diameter made of tubing with OD = .625 inches) without having solid models and without getting errors for wire radius to segment length? Do I only need to lower the segment length like you have done to 0.8 or lower to avoid this error?

→ Please know that implementing a solid (3D) wire with a segment (1D) wire is based on thin wire approximation. (Please search for this for more information.)

If the radius of the original 3D wire is too thick, there is no way (I mean invalid) to replace a 3D wire (solid) with a 1D wire (segment), This becomes worse as the simulation frequency increases, because the 1D mesh size (length) should be at least 5 times bigger than its radius. If this condition is not met, Feko generates the error message.

Additionally, the segment length (1D mesh size) of the helix is much shorter than a normal straight line, because of its curvature.

Therefore, if you keep having the same error, I'd recommend you to return to the 3D wire construction.

Or, please use an acceptable maximum radius of the 1D wire, if the wire's radius is not that important for your simulation result. (as you asked..)

Best regards,

Jaehoon

PS) Please check/modify the 1D wire dimension and shape, if you want to use the simplified model.

All comments

Jaehoon

Hello @DanielPerk,

I guess (based on the following theory); since the coil is not long enough to resonate at the operating frequency, the S11 is 0 dB (= 1).

"The reflection coefficient of a coil measures how much incident radio-frequency (RF) energy is reflected due to impedance mismatch, typically ranging from 0 (perfectly matched) to 1 (totally reflected). Ideally, a pure, lossless inductor presents a purely reactive impedance (jwL)
), resulting in a reflection coefficient of 1, placing it on the outer edge of a Smith chart."

Reflection coefficient of a coil = (jwL-Zo)/(jwL+Zo).

If you share your Feko model (.cfx), I will investigate more.

Best regards,

Jaehoon

DanielPerk

Coil in a Box_UPLOAD.cfx

Jaehoon,

Thank you for your response. I have a small understanding of the physics, but not the networking (so schematics and how a port should actually be added). I come from CFD, where one only needs to add boundary conditions on a single entity. I have since learned ports need to be connected between two conductors. I might be saying this incorrectly—I'm new to EM.

Nonetheless, I have uploaded the requested .cfx file. It is very basic, but I'm not asking FEKO to do much. The overall goal is to put the inductor into a box and optimize the size of the box to push any resonance away from certain frequencies. Sizing the box is not an issue, nor is optimizing it, but plotting S-Parameters has stopped me in my tracks.

Thanks again for your time & assistance.

Jaehoon

Hello @DanielPerk,

I can open your model with higher Feko version than yours (2024.1) and modify your model.

I attached here, but you cannot open my modified model, because you are using the lower version.

Please use 2025 version or higher version to open it.

coil-in-a-box-upload_mod.zip

So I explain below what I modified in your model.

The wire port should be located in the middle of the line (not at the end of the line).

1.Please delete one out of two wire ports. (One wire port is enough.)

2. Create a Polyline to connect two ends of the helix.

3. locate the wire port in the middle of the Polyline.

4. After applying "Seperate" for Union1, I delete the Cuboid1.

6. Union all the geometry.

7. Modify the frequency setting.

8. Run the Feko solver and check the result.

Best regards,

Jaehoon

DanielPerk

Jaehoon,

This was a very detailed answer and I appreciate the time you put into creating it. I was able to recreate your approach in 2024.1 and sweep across 1 MHz - 800 MHz (for a smoother plot). With only one port, I am only able to plot one S-Param, and although I only mentioned S1,1 in my earlier

3D_Coil in a Box_UPLOAD.cfx

post, I am interested in both. You got me half way there—thank you.

I have attached the actual model I need to run. The wires were meant for self training. The attached is basically the same model, but with an imported step file and solid geometry. As it was earlier, my goal is to plot the S-parameters (S1,1 & S2,1) with the coil inside of a box. I'm not sure i simply connecting the ends of the coil would be sufficient for this model, as the Box is ground and the coil is the center conductor. Perhaps just completing the circuit with a polyline is the way to go about this, but if so, I'm not sure how to add a second port for insertion losses (S2,1).

The attached model is a 3d coil inside a 3d box. there are two hole in each end of the box where straight sections of the coil ends terminate. I assume I need to add ports here, so I included small doughnut shaped cylinders and put them between the coil ends and the box holes—these are dielectric. Ive tried all types of ports, but can only get waveguide ports to take. If you could please put me on the correct course for this model—using two ports—I would greatly appreciate it. A few of the attempts I've made with this 3D model have resulted in errors saying something about "…metallic triangles", which I remedied by removing teflon from the dielectric body—but again, I'm trowing darts in the dark at this point.

Thanks in advance for your help!

Daniel

Jaehoon

Hello @DanielPerk,

I got your Feko model and read your question. However, I can't do any thing without fully understanding your simulation geometry and goal.

In your Feko model, there are one helix inside a box and two cylindric dielectrics at the two ends of the helix.

It seems that you want add two ports to the ends of the helix for S11 and S21 calculation.

Here are some questions.

Q1) Helix: As I mentioned in the previous reply, the coil (inductor) needs a return path. Even if the coil is multi-turned (as below), two ends should be connected for source connection.

Normally, S21 is defined to calculate a coupling between two coils.

Why do you need two ports for one coil? (You want to know input power and loss power between two ends?)

What about using the metallic box' wall as a voltage reference (0V) of the port?

Q2) Box: what material fills the box? what is the material of the 6 faces of the box, metal or not metal?

Q3) Dielectric: What is the role of the two dielectric at the ends of the coil?

I think modeling a coil with 3D needs more computation resources. Instead of using the imported step CAD (Triangular mesh), we'd better use a helix wire (line mesh) with some thickness definition.

Best regards,

Jaehoon

DanielPerk

Hello Jaehoon,

Thanks for you quick response.

Using the box, which is made of aluminum (and is ground in my physical system) is perfect. The box is simply filled with air at ambient temperature and pressure. Future thermal calcs/sims will be conducted based on future EM simulations if I can use FEKO to excite the coil and heat up, but that is not the goal of this study. The goal here is to see what effect the box has on resonance throughout the freq sweep of 1 MHz - 800MHz. The box shields interference, but might also cause downstream signal issues, so I will be simulating different sized boxes—the one in the model is the first of 3 sizes to simulate.

I added the two dielectric cylinders because some types of ports require non-PEC boundaries. the dielectric cylinders are not in the physical "box with coil", but I added them so I could try to properly apply a port/s. If they are not needed, that's great—two less bodies to mesh! I tried to connect the ends of the coil to the hole in the box, but the port i attempted to use said i needed to have a dielectric (microstrip port). Why did I try to use a microstrip port??? I don't really know—I just need a port and I tried them all.

As far as computational resources, I don't have super-computer but do have a high-end chip and GPU (not sure if FEKO allows GPU to help solve or not). I'm fully prepared for simulations to take hours to solve, but if I can preserve fidelity by modeling the coil with wire and assigning thickness, that would also be preferrable. Does FEKO simulate skin effect on wires with thickness?

The reason I believe I need two ports: when I re-created the first setup you helped me with, I was only able to plot one S-parameter. I assume I need an in and an out port to plot both S1,1 & S2,1.

In short:

Q1) Im looking for S2,1 in addition to reflection. I'd like to see whats coming out the other side as well as whats bouncing back. This geometry is just a fraction of the entire system—If I can get this small sub-section going, I shouldn't need help with the larger simulation.

Q2) The box is a 6-sided aluminum box filled with air.

Q3) The dielectric was only put in the model to satisfy port definitions. if ports can be added without the dielectric cylinders, that would be great

Thank you for your continued assistance,

Daniel

DanielPerk

Quick follow-up:

I've swept the actual box and coil on a VNA and we saw higher harmonic spikes—somewhere between 550MHz and 700MHz depending on the coil. I want to use FEKO to determine the optimal box size with a given coil, to push these spikes out and away from harmonic freqs. If I can accurately simulate this, I do not need to build the boxes and hook the box+coil combo up to a VNA—I can just use FEKO and save mfg time and money.

DanielPerk

Jaehoon,

One impt. geometrical detail—the coil is not solid copper at 16mm diameter, but rather its made of copper tubing with OD = 16 mm, ID = 12 mm.
I modeled it solid as I assumed that solid coil vs tubing would not make a difference for this simulation.

Jaehoon

Hello @DanielPerk,

Please open the attached model perpared with the Feko 2024.1 version (I just installed).

3d-coil-in-a-box-upload_mod.zip

In the model, I re-drew the box, deleted the dielectric plug, and a little moved/translate the coil.

(I didn't change the 3D coil to a 1D coil, but I just adjusted the mesh setting to reduce the simulation time.)

Port: Two wire ports were defined at the wires between the coil and the box wall.
Box: was constructed by Cuboid which was filled with air and whose faces were Al with thickness.
S parameter configuration: Port 1 (active) and Port 2 (passive) lead to S11 and S21.
EM solver: MoM (default)

Simulation result: S11 and S21 were displaced in the rectangular plot as below.

Please check the dimensions, since I am not sure everything is correct.

Please also give more points to the frequency setting in your simulation.

Best regards,

Jaehoon

DanielPerk

Jaehoon,

So all I really needed to do was add a wire port connecting the ends of my coil to the closest/adjacent box face? It appears you selected mesh nodes for the line's endpoints. I was able to re-run this setup with more points and get the same plot as you. I have a question regarding the plot because it looks like other plots I have gotten, where nothing is getting through the coil regardless of frequency.

-Below is my plot with more points between 1e6 - 8e8 Hz. I changed the quantity (y-axis) to dB.

-Please correct me if I am wrong but shouldn't S1,1 be zero for DC & low freq then drop off, allowing signal though at higher frequencies? If I am interpreting this plot correctly, this looks like an "open" circuit, per se—like nothing is getting though the inductor coil.

I activated both ports and re-ran to see if that would affect the plot and hopefully give me something that looks different, but the graphs looked the same as with only one port active. I'll try to move the ports around and re-run—maybe a wire isn't exactly where it needs to be. If you could help me troubleshoot this last small issue, I would really appreciate it.

-Shouldn't the S-parameter plot look something like the image below? You are the expert, so I am asking more than anything if a single inductor would also look somewhat like this plot:

Thank you for your patience Jaehoon,

Daniel

Jaehoon

Hello Daniel,

Let me give my answers to your questions.

Q1) So all I really needed to do was add a wire port connecting the ends of my coil to the closest/adjacent box face?

→ Yes, because this structure is measured by VNA, the two ports are associated with the ports of the VNA (Vector Network Analyzer).

This is similar to using a wire port located between the end of the monopole wire and a ground plane, which simulates the monopole antenna fed by a coaxial cable.

Q2) shouldn't S1,1 be zero for DC & low freq then drop off, allowing signal though at higher frequencies?

→ S1,1 (dB) = 0 (in other words, reflection coefficient =1) means that all the input power reflects back to the source (VNA's input port).

Q3) If you could help me troubleshoot this last small issue, I would really appreciate it.

→ Please see the new attached models.

Q4) Shouldn't the S-parameter plot look something like the image below?

→ Please see the new attached models.

2. Let me simplify your model again. (to reduce the computational cost ( for speedy simulation.)

2.1)Here I replaced the 3D coil with a 1 D coil with radius of 0.38 inch (the radius is in the modify mesh.)

and activated "Double precision" under Solver setting > General.

3d-coil-in-a-box-upload_simple.zip

2.2) Since a resonance is observed around 90 MHz, I changed the frequency setting and gave finer meshes.

3d-coil-in-a-box-upload_simple_1.zip

So, to get more exact results, please use finer simulation frequency step and mesh size.

Best regards,

Jaehoon

PS) I think that the characteristic of the coil inside a metallic box is similar to rectangular cavity resonator, whose size determines the resonating frequency.

https://learnemc.com/ext/calculators/cavity_resonance/rect-res.html

(There are so many resonant frequencies as below.)

Additionally, the behavior of the coil depending on the frequency affects the total S11 and S21, too.

DanielPerk

Jaehoon,

This has to be the best continued assistance I've received—so thank you for your help & for answering my questions—I realize in my first question, I meant S2,1 should be zero (or close to it) at low freq, and S1,1 should be very negative.

Before getting to your latest response, I should admit something: I had actually set up and run this simulation correctly several times—I just didn’t realize it. I kept chasing what I thought a “proper” inductor S‑param plot should look like. Every time I plotted my results, S11 showed up as a positive value (around 1–3 dB), so I assumed my setup was wrong.

Turns out the issue was how I was plotting it. When I dragged a second S‑parameter onto the Cartesian plot and changed it to S21, I would click “dB” for that trace. What I didn’t realize was that I also needed to select the first trace, S11, and apply the dB scale to that as well—even though the y‑axis already said dB. Once I did that, S11 looked correct: very negative at low frequency and rising with frequency.

So basically, I had been plotting S21 in dB, but not S11.

Now that I've learned how to display S-params on the same scale as one another, I can actually make progress correcting real mistakes instead of chasing an error I wasn't making.

____________________________________________________________________________Concerning your #2 above: I have attempted to use a helix and give the wire a radius, but I would get an error which states the wire radius to segment length is too big. I would need to keep reducing this radius and found that the biggest I could make the wire is 0.1 inches. Anything bigger would result in an error and the simulation would stop. Eventually, if not now for this simulation, I will need to take the skin effect into account. I'd prefer using wire bodies, but the radius to segment length has forced me to import/or model in CADFEKO 3D sweeps. These sims take so long to run! MY QUESTION: how to allow the skin effect to be simulated on this geometry (relatively small coil: 4" diameter made of tubing with OD = .625 inches) without having solid models and without getting errors for wire radius to segment length? Do I only need to lower the segment length like you have done to 0.8 or lower to avoid this error?I will go through the example you have provided now.Thank you for your help with this.

Jaehoon

→ Please know that implementing a solid (3D) wire with a segment (1D) wire is based on thin wire approximation. (Please search for this for more information.)

Additionally, the segment length (1D mesh size) of the helix is much shorter than a normal straight line, because of its curvature.

Therefore, if you keep having the same error, I'd recommend you to return to the 3D wire construction.

Or, please use an acceptable maximum radius of the 1D wire, if the wire's radius is not that important for your simulation result. (as you asked..)

Best regards,

Jaehoon

PS) Please check/modify the 1D wire dimension and shape, if you want to use the simplified model.

DanielPerk

Jaehoon,

Concerning the size of this geometry, importing the 3D geometry appears to be the only way I can simulate the coil while maintaining its actual size. This is what I have been doing, and although each solve takes about 20 min, I'm getting good results.

Thank you for your help with this case.

Daniel