In electrical circuits, AC resistances are not equivalent to their DC counterparts, especially at higher frequencies. Ansys Maxwell can be used to calculate the AC resistance of a conductor in multiple ways, but the main two would be through an impedance matrix in the eddy current solver or through a series of field calculations in the magnetic transient solver. The eddy current case is easier to setup, but there are some assumptions present in that solver that don’t work for every problem; the excitations in the eddy current solver are always pure sinusoids, and the value of resistance is the peak resistance seen during the excitation. But there are times where it is important to see how the impedance of a conductor evolves due to a high frequency pulse or non-sinusoidal waveform – this is where the magnetic transient solver comes in!

Time-Varying Resistance

In order to calculate the AC resistance, we’re going to need to utilize the Field Calculator. Because the typical expression of the current-voltage relationship, V=IR, is for DC resistance because it assumes R is constant, we need another expression to calculate the time-varying resistance. For that, we can use the ohmic loss density and the current flowing through the conductor to calculate the time-varying impedance using the relationship between power and current:

P = I²R

With the definitions out of the way we can now begin to set up the simulation, starting with our sample geometry of a simple cylindrical wire.

Example Geometry

The geometry in this example is a cylinder of copper with a radius of 2 mm and a height of 10 mm, surrounded by vacuum. A sinusoidal current is assigned to the coil (although any waveform can be represented in the transient solver) with an amplitude of 100 A and a DC offset of 200 A – this is to prevent large impedance spikes at zero-crossings in this simple model.

We have our geometry now, so we can start the process of setting up the field calculator equations we need. The first step is to get the current flowing through the conductor from the electromagnetic field definitions – this process is described in this blog post about Amperian Loops, but the calculator steps are slightly different in a transient simulation compared to the eddy current/frequency domain simulation discussed in that blog. The process of creating the loop line to use in our field definitions remains the same as in the previous case, so review that blog if you are unfamiliar with these steps. Don’t worry, we’ll still tell you the updated calculator steps for a transient amperian loop in this post.

The Field Calculator and You

After creating the loop for the Amperian Loop calculation (in this example, its name is AmpLoop), you’ll need to perform the following operations in the field calculator to get the current through the conductor in a transient magnetic model:

Because there’s a field representation of the current flowing through the conductor of interest, we can use the field calculator again to create a calculation of the time-varying resistance. Because the default ohmic loss definition in Ansys Maxwell is the ohmic loss density, we need to make sure to integrate that value over the volume of interest – in the example project, the volume is simply called Cylinder1. The field calculator steps are as follows:

Solution Setup

In this example, we parameterized the excitation frequency when setting up our current excitations through the wire to allow for investigating the AC resistance at multiple frequency points. We want to simulate over 2 frequency periods and have 30 steps per period (which are also a parameterized variable).

When defining the solution setup, we use these variables to set out stop time and step size so as to not have too large of time steps for the high frequency simulations, or way too small of steps for the low frequencies. To get our 2 periods we set the stop time to “2/Frequency,” and our time step size to “1/Frequency/Steps” to give us 30 steps per period for each of our frequencies.

It is also important to ensure that we are saving the fields during the time our simulation is running, since those results are needed to use the field calculator. We can also use our variables there, so that they adapt to the changing time scales as the different frequencies are simulated.

Once our field calculator equations and solver settings are finished being set up, we can run the simulation and plot the corresponding results.

Temporal Resistance at Different Frequencies

To plot these quantities, we need to use a Fields Report, rather than a transient report, since we are plotting field calculator values.

Because we simulated across a wide range of frequencies, the time scale for each of these simulations will be drastically different and make it difficult to plot them all on the same graph for comparison if we were to simply plot them directly. But because we have parameterized our excitation frequency, we can instead plot the resistance over Normalized Time, allowing us to see the resistance over the two periods of the waveform for each of our frequencies. We’ll need to uncheck the “Default” box next to the X-axis definition, and replace “Time” with “Time/(1/Frequency).”

Because these are field calculator values, there are no units assigned automatically. It will also initially plot both of the waveforms on the same y-axis and plot the current waveforms at each frequency over the normalized time (all of the current waveforms are identical when normalized over time like that). There are a few steps we can take to clean up the waveforms – we can plot the current at just one frequency, move the current to its own axis, and set the units of the AC_Resistance axis to µ in order to get the results below:

Conclusion

From the example model here, we can see how the AC resistance changes over time as higher and higher excitation frequencies are applied. At low frequencies, the wire still behaves close to the DC case, with little variation over the sinusoid. But as the frequency increases, the resistance can spike to values over 5 times larger than the baseline! If you would like to learn more about Ansys Maxwell or other simulation tools and services we offer here at PADT, you can do so on our website here.

Have other questions or looking for a quote? Contact us or call (480) 813-4884 to get in touch with one of our engineering experts today.

In the 2024R1 release of Ansys Maxwell, a new feature was introduced to allow for a twisting factor to be included in Litz Wire models. This allows for a more robust solution that includes the increase in total wire length that occurs when twisting the bundles together. This article will detail how to set up the material properties and calculate the twisting length factor, and then show a simple Helmholtz coil model and the difference in results between a solid wire, stranded wire, and litz wire model.

Defining the Material

In the toolbar at the top, navigate to “Tools -> Edit Libraries -> Materials… “ Search for ‘copper’ (do NOT press Enter or it will close the window) and then select “Clone Material(s)” with copper selected.

This will bring up the View/Edit Material window for our copy of copper, which will be the basis for our litz wire. The first step is to change the Composition of the material from Solid to Litz Wire, which will allow us to put information such as the number of strands in the litz bundle, the individual wire diameter, and the twisting length factor.

For this example, our litz wire is 64 strands of Round 38 AWG wire, which is .1007 mm in diameter for each strand; this comes to a total wire size of 20 AWG. Twisted Length Factor is the new feature introduced into Ansys 2024R1 that accounts for the increase in total strand length due to the wires being twisted together to calculate the DC resistance more accurately. Twisted Length Factor (TLF) is the ratio between the twisted-strand length and the overall bundle length and is a value greater than or equal to 1. To calculate the twisted length factor, the following equation, derived in Appendix I of [1], can be used:

Where n is the number of strands, d_s is the strand diameter, p is the pitch length, and K_a is the packing factor. The packing factor is found by dividing the sum of the cross sectional areas of all strands by the overall bundle area; this comes to approximately 3.93 for the chosen wire. The pitch for this wire is given as 12 twists-per-foot, which translates to a pitch of 1 inch, or 25.4 mm. For this example, the TLF is calculated to be 1.000632.

Example Helmholtz Case Study

Now we want to see the effects of setting up this litz wire material. To do that, a simple Helmholtz coil model was created, with two 10 mm radius loops separated by 10 mm, with the current flowing in the same direction. We’re going to set up three different versions of this model, varying the wire composition. The three models will be the default solid and stranded models using copper as the material, and the final will be using our new copper_litz material with a stranded model. We’ll run each of these models, using the default solution setup, and compare the losses in the wires.

Loss Comparison

After the simulations complete, we can examine the coil impedance and the wire losses that Maxwell reports and see if they correspond to our earlier hypothesis. First, we’ll look at the wire losses for the litz wire case (both DC and Eddy current), the ideal stranded wire case, and the solid wire case.

We can see that the solid wire has the greatest losses and the ideal stranded wire has the lowest losses, both of which are in agreement with our hypothesis. The litz wire has two values associated with it – we’ve computed both the DC loss and the total loss. The DC loss is close to that of the ideal stranded wire, just slightly higher due to the twisted length factor we added in earlier. Since the DC loss report doesn’t include eddy effects, and neither does the ideal stranded wire, this result also agrees with our ideas. The total litz wire loss sits in-between the DC loss and Solid Loss, which is our expected outcome. Solid wires have the highest impedance and therefore the highest loss, especially when excited with higher frequency currents, like the 500 kHz we used in this example.

Conclusion

We have successfully demonstrated how to set up the new Litz Wire model that includes the Twisting Length Factor for accurate determination of DC resistance and shown how this impacts the ohmic losses and resistance of the wire. The litz wire feature, combined with the twisting length factor addition in Ansys Maxwell 24R1, allows for more robust simulations that can include the eddy current effects on stranded windings without having to model every wire individually.

References

[1] – Tang, Xu, and Charles R. Sullivan. “Stranded wire with uninsulated strands as a low-cost alternative to litz wire.” IEEE 34th Annual Conference on Power Electronics Specialist, 2003. PESC’03.. Vol. 1. IEEE, 2003.

These solutions help you solve any electromagnetic, temperature, SI, PI, parasitic, cabling and vibration challenges in your designs.

In 2024 R1, Ansys Electronics delivers capabilities that speed time to results, enable new functionalities, and expand interoperability with other Ansys products for multiphysics and multiscale solutions.

Join PADT’s Application Engineer and LF expert Tyler Buntin for a look at what’s new for the low-frequency tool set in Ansys 2024 R1.

This presentation focuses on updates regarding the following:

• Maxwell
• Motor-CAD
• Symmetry Mesh
• And much more

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When doing electromagnetic simulations, we often want to know what current is flowing through an object other than the one we are exciting – eddy currents. There’s a lot going on within Maxwell’s equations related to this topic, but we’re going to focus on one simple equation:

∮H∙dl=I_enc

Which is the integral form of Ampere’s Circuital Law, and we’ll show how you can use the field calculator to find that enclosed current using the fields that Maxwell calculates for you! For this example, we are going to be using a simple case of two adjacent copper wires – the one on the left is excited with a 100 Amp current coming out of the screen (+Z), and the other is not excited at all.

Measurement Setup

The first step is to make a closed loop around the object of interest – we’ll be doing this by drawing a 2D circle that fully surrounds our non-excited wire. There isn’t an exact diameter value, we just need to make sure the circle fully surrounds a cross section of just the wire.

And now we have a circle, and we need to convert it to a closed loop that doesn’t have a covered face. To do this, we select our circle, right click, and navigate to Extend Selection -> All Object Edges. This will select just the edge of our circle, which we will then turn into a unique object using either Modeler -> Edge -> Create Object from Edge in the menus on the top bar, or select it from the Draw ribbon:

The circle can be deleted now, we just wanted the edges (kind of like when eating homemade brownies). The edge will have a ridiculously long name – by default something like “Circle1_ObjectFromEdge1.” Feel free to rename it to anything you desire, just remember what it is when going through the field calculator. In this example, it was named “Current_Sense_Eddy.”

Field Calculator

or, How I Learned to Love Reverse Polish Notation

The easiest way to open the fields calculator is to right click on “Field Overlays” in the project manager and select the “Calculator” option. This will open the fields calculator, which we will use to generate our expressions for current.

Below is a table showing the calculator operations, and what the stack will look like after each step – handy for following along.

And then we have our final expression – that whole mess of words represents the same equation as we showed before, where the contour that is being integrated over is the edge of the circle we drew! We can save this value as a Named Expression, and then use it in future reports – we’ll call ours Hdot_dL_Eddy.

The same process can be used to create a measurement loop around the excited wire (with a new circle) so we can verify we’re getting the right current. We’ll name that expression Hdot_dL_Exc, so now we have an expression for the Amperian loop current in both our excited wire and the one that we want to extract eddy currents from. We’ll create a data table of our two calculated currents and see how they change with frequency.

Results

Our excited wire is measuring around 100 Amps – a positive sign since that is what we set it to be! The other wire’s current increases with frequency and is negative, both of which make sense from Maxwell’s equations – another positive sign. Our Amperian loop is accurately measuring the current in our two wires! This method can be done with any closed loop, in both 2D and 3D solvers, if it is a line object that completely encapsulates a cross-sectional area where current is flowing.

A Few Final Words

Now we all have a handy method of measuring current in eddy current solutions, and all we needed was a couple circles and a little bit of Reverse Polish Notation from our fields calculator!

The Ansys Electronics Desktop environment (referred to hereafter as AEDT) is a familiar place to users of Ansys Maxwell or HFSS, among other tools. And within the AEDT environment, it is easy to set up a parametric analysis, allowing a designer to quickly see results from different design variations. For example, examining how changing the thickness of a conductor or the diameter of a permanent magnet can affect the results of a simulation. Setting up a sweep of a numerical parameters is quick and easy, and a user can also sweep multiple variables at the same time – changing both the magnet diameter and the conductor thickness and seeing which combination yields the best results.

But what if the user wanted to compare different magnet or conductor materials? Materials in AEDT are stored as strings such as “iron” or “NdFe30,” and the sweep setup window doesn’t have a way to change strings. Luckily for us, there is a solution – arrays. Material names can be stored in an array variable and then indexed by an integer variable, which will be the value that we adjust through the parametric sweep!

Basic Setup

For this example, we are going to use a very basic example of a metal plate and a magnet, 1 mm away from one another. The magnet will be an NdFe30 permanent magnet and the metal plate, or target, will have its material swept between iron, 1010 steel, and copper.

Array Setup

The first thing that needs to be done is to create the list of materials that we want to include in our sweep and set up the array. To set up an array, first we right click on the project name and then click Design Properties. This will open a new window that shows all of the local variables in the project, the properties window. Once we get to the properties window, there’s a handy “Add Array…” button that we will be clicking. We need to define a name for our array (we’ll call it “MaterialArray1”), and then all our values with their indices.

Two important things to note: string arrays require entries to be in double quotes (“”) and entries aren’t case-sensitive. No need worry about leaving caps-lock on, just make sure you spell “IRON” correctly. Now we have our handy material array – but it doesn’t do anything on its own, we must find a way to access the data values. This is where a second variable comes in, which can be added from the properties window as well by clicking the “Add…” button. We’ll name this new variable MatID1.

Indexing Arrays

A unitless value is all that’s needed for the material ID, it just needs to be a number, preferably with a nominal value of zero (0) – arrays in AEDT are zero-indexed, so the first entry in our array corresponds to an ID of 0. Once we have our material array and the ID to select which array value we want, we need to tell our object what it’s made of. Select the object we want to change the material of and go to its properties. In the material section, we need to edit it to delete whatever was there before and tell it that it’s now made of MaterialArray1[MatID1], the array name followed by the index value inside of square brackets. Then if we check the “evaluated value” column of our material, we can see that it corresponds to the first value in our array if MatID1 is equal to 0.

If we change the value of MatID1 to 1, we end up with Steel_1010 as our material – all is working as it should. But we don’t want to have to manually change the value of MatID1 before each of our simulations; that would be time consuming, especially if we have a wider range of materials we want to compare. This is where we utilize the parametric sweep we looked at earlier.

Setting Up a Sweep Analysis

First, right click on the “Optimetrics” category in the project explorer, then navigate to “Add > Parametric…” This will open the “Setup Sweep Analysis” window; we will then click “Add…” and add our sweep. We select MatID1 from the drop down, set the process to a Linear step, and set up out parameter sweep – starting from 0 and ending at 2 in steps of 1.

By adding a sweep of our index, MatId1, we now have an object with parameterized materials and a sweep setup that will allow us to run simulations with all the materials in our array, and we don’t have to change the index manually every time. Before we close this window, we want to make sure we head over to the “Options” page and check the box next to “Save Fields and Mesh” – this will allow us to visualize the fields for all of our material variations. After running the simulation, we can investigate the results of the force on the metal plate from our magnet. Remember, our order of materials was Iron, 1010 Steel, and then Copper. As we look at the graph, we see the force from the magnet drop down to 0 when the target is non-magnetic copper – exactly what we expected!

A Few Final Words

Parameterizing materials is a powerful tool for our belts, allowing us to easily investigate and compare the answers to questions such as “What if I made this wire aluminum?” or “How does a Samarium Cobalt magnet compare here?” to name but a few. And with that, I am out of words now.

Automatically generate nonlinear equivalent circuits and frequency-dependent state-space models from field parameters that may be further used in system and circuit simulation to achieve the highest possible fidelity on SIL (software-in-the-loop) and HIL (hardware-in-the-loop) systems.

Ansys simulation technology enables you to predict with confidence that your products will thrive in the real world.

Join PADT’s Application Engineer and Maxwell expert Tyler Buntin for a look at the latest advancements for Maxwell in Ansys 2023 R2. 

This presentation focuses on updates regarding the following:

• Mesh Technology

• Workflow Enhancements

• HPC

• ECAD Integration

• And much more

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Published on:	April 4th, 2022
With:	Eric Miller & Aleksandr Gafarov
Description:	In this episode your host and Co-Founder of PADT, Eric Miller is joined by PADT’s electromagnetics expert Aleksandr Gafarov to discuss what’s new for HFSS and Maxwell in the latest release of Ansys. If you have any questions, comments, or would like to suggest a topic for the next episode, shoot us an email at podcast@padtinc.com we would love to hear from you!
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If you are interested in learning more about any aspect of Ansys Maxwell, have a consulting project that involves electromagnetic components, or want to learn more about Ansys in general, please contact us.

Or

“Failover feature ‘HFSS solver’ specified in license preferences is not available. Request name hfss_solve does not exist in the licensing pool. Feature has expired.”

Thankfully, as long as the new PPE licenses are installed and present on your license server, the fix is very simple. With Electronics Desktop open, simply navigate through Tools > Options > General Options from the top ribbon menu:

Then, under the General > Desktop Configuration section, make sure to enable ‘Use Electronics Pro, Premium, Enterprise product licensing.’

This tells any program run through Electronics Desktop to look for the new PPE licensing iterations rather than the older legacy format and is remembered across sessions. This change will need to be made once for each installation of the 2020R1, 2020R2, and 2021R1 versions of the electronics software, and has now been made the default setting for versions 2021R2+.

PADT’s Kang Li shows how Ansys Maxwell can be driven by Ansys OptiSLang to optimize the design of a magnetic gear. This is a great example of connecting an Ansys solver to OptiSLang.