Inductors are used in many applications such as low-pass, high-pass,
band-pass filters or antennas. In particular for low-pass filters, an
inductor is combined with a capacitor to block high frequencies to avoid
interference in communication systems.
In antennas, inductors are used to match impedances to ensure the
maximum power transfer with minimal losses. This is due to the ’Maximum
Power Transfer Theorem’. This theorem says, the maximum power transfer
takes place, when the impedance of the load equals the impedance of the
source. Deviations lead to reflections resulting in losses. The
frequency range starts at near 0 Hz and ends with several MHz (At high
frequencies the HF-Extension is necessary).
Analytic formulas are very simplified, so that a simulation is
necessary. An analytic approach would be: \[Z_L = j \cdot \omega \cdot L\]
with:
\(Z_L\) is the
impedance,
\(j\) is the imaginary
unit,
\(\omega\) is the circuit
frequency,
\(L\) is the inductivity of the
coil.
The inductivity L must be calculated by the characteristics of the
coil and over a range of frequencies from 1MHz to 10MHz. But an analytic
calculation ignores special effects resulting from high frequency
calculations. This makes the analytic calculation inacurate and
simplified.
In this example the inductor consists of a copper coil and a magnetic
core, which is described with a conductivity of zero to prevent eddy
currents. In reality, the core would be laminated. The core increases
the inductivity and reduces the electromagnetic interference with other
electromagnetic devices. The load is divided and applied to the two
surfaces of the coil. The goal of the simulation is to simulate the
inductor over a range of frequencies, then plot the impedance graph.
Unzip the archive. There will be one folder ’start’ and one
’complete’.
Start the Program Simcenter3D (or NX). Use Version 12 or
higher.
In Simcenter, click Open and navigate to folder ’start’. Select
the file ’inductor.prt’ and click OK. (Maybe you must set the file
filter to ’prt’)
Start the application Pre/Post.
Create a New Fem and Sim. Set the solver to ’MAGNETICS and choose
if possible ’Non-Manifold’. Click OK.
Hint: Depending on the used NX Version, the ’Non-Manifold’ feature is
available. Alternatively ’Mesh-Mating Conditions’ and a boolean
substract must be used. For more details, see document ’Tutorials
EM-Basic’, chapter ’Recommended Settings’, subchapter
’Non-Manifold’.
Start meshing the components. Mesh the coil, use tetra elements
and half of the recommended element size.
Edit the coil mesh collector, change the name to ’Coil’ and click
’edit’.
Click ’Choose Material’, use ’Copper simple’ from the MAGNETICS
Library, in your MANETICS installation folder.
Mesh the core also using tetra elements and half of the
recommended element size.
Edit the mesh collector of the core and name it ’Core’. Edit the
physical porperties and click ’choose material’. Right click ’copper
simple’ and click ’Clone’. Name the material ’Core’ and edit the
properties like shown in the picture below.
Now mesh the air using tetra elements. Divide the automatic
element size by 2. In the mesh collector change to ’FluidPhysical’ and
use ’air’ for material.
We are ready to go in the sim part.
Significance of the
High-Frequency Extension
To demonstrate the significance of the high-frequency extension, we
will first simulate using the magnetodynamic frequency solution and then
compare the results with the full wave solution. This comparison will
highlight the limitations of the magnetodynamic approach in handling
high-frequency scenarios.
Create a solution of type ’Magnetodynamic Frequency’.
In ’Output Requests’, ’Plot’, click ’Magnetic Fluxdensity’,
’Current Density’ and ’Electric Potential (phi-Pot). In ’Table’ activate
the ’Ohm Resistance’ and ’Inductivity’ checkbox.
In ’Frequency’, click ’edit’ to create a frequency sweep. Set the
properties like shown in the picture below.
Next create a constraint of type ’Flux Tangent(zero a-pot)’ and
select all ten outside faces.
Next we will create the load. Click ’Load Type’, ’Current
Harmonic’ and choose ’On Solid Face’. For ’Select Object’, select the
right coil face. In ’Electric Current Amplitude’ type ’0.5’A. Create a
second load with an amplitude of ’-0.5’A on the left coil face.
Hint: In high-frequency simulations, it is crucial to apply the load
evenly to ensure a symmetric potential on both sides of the coil. This
creates a balanced electric field, which is essential for producing
accurate results. If the load is applied asymmetrically, the resonant
frequency of the coil could shift due to the resulting asymmetric
electric field. Alternativly, a circuit load can be used, that
distributes the potential evenly by default. However, in low-frequency
simulations, this symmetry has little to no effect on the outcome, as
the frequency is not high enough for the asymmetry to significantly
impact the system’s behavior.
Now solve the solution. This will take a few minutes.
The visible plots display the AFU graphs of resistance and inductance
from the magnetodynamic solution. However, these results are of poor
quality because the magnetodynamic solution is not well-suited for
handling high-frequency scenarios. To address this limitation, the
HF-extension is necessary. This add-on accurately simulates
high-frequency conditions by coupling the electric field to the magnetic
field, ensuring more reliable and precise results for high-frequency
simulations.
Setup
of the High-Frequency Solution
Create a new simulation of type ’Full Wave Frequency’. In
’Frequency’, select the already created frequency sweep. In the ’Output
Requests’, click ’Current Density’, ’Electric Potential’, ’Ohm
Resistance’ and ’Inductivity’. Create the Solution.
Drag and drop the load and the outside constraint from the first
solution in the new one.
Solve the new solution.
Post Processing the
High-Frequency Solution
Open the ’Post Processing Navigator’, plot the afu graphs of
resistance and inductivity. They should look like the pictures below.
The left graph shows the magnitude of the resistance, the right graph
the coil inductance. Due to the high frequency, the skin effect (Picture
3) intensifies and modifies the current distribution. The result is an
increase of the resistance, which peaks at the resonance
frequency.
In the inductance graph, we observe a distinct change in the inductor’s
properties as it approaches its resonance frequency at 5.75 MHz. Beyond
this point, the inductive behavior of the coil diminishes, and
capacitive effects begin to dominate. As a result, the coil transitions
from behaving like an inductor to acting more like a capacitor.
This behavior is typical in high-frequency circuits where inductive
components experience a transition in their behavior due to the
interplay of inductance and capacitance at resonance.
