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comsol螺旋线圈建模
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更新于2023-03-16
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Models of such spiral inductors can become quite large as the number of turns increases. This example demonstrates how to exploit the near-symmetry of the structure to greatly reduce the model size. A ten-turn octagonal spiral coil is modeled via the usage of a Single Turn Coil boundary condition, with Floating Potential boundary conditions to enforce continuity of the current between the disjoint turns of the coil.
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Solved with COMSOL Multiphysics 5.2
1 | MODELING A SPIRAL INDUCTOR COIL
Modeling a Spiral Inductor Coil
Introduction
Spiral inductor coils are attractive because they can be integrated easily while
electroplating other printed circuits and provide robust inductance values.
Models of such spiral inductors can become quite large as the number of turns
increases. This example demonstrates how to exploit the near-symmetry of the
structure to greatly reduce the model size. A ten-turn octagonal spiral coil is modeled
via the usage of a Single Turn Coil boundary condition, with Floating Potential
boundary conditions to enforce continuity of the current between the disjoint turns of
the coil.
The approach used in this example is valid when the operating frequency is sufficiently
below the resonance of the inductor such that the capacitive coupling between the
turns is negligible.
Model Definition
An octagonal spiral coil is patterned on a 300 μm silicon wafer. The electroplated metal
traces are 1 μm thick, and at the operating frequency of 13.56 MHz the thickness of
these traces is much smaller than the skin depth.
Solved with COMSOL Multiphysics 5.2
2 |
MODELING A SPIRAL INDUCTOR COIL
Although the actual structure does not have any true symmetry, it is very nearly
symmetric, and can be reasonably approximated as shown in Figure 1.
Figure 1: A slice showing 1/16 of the entire coil.
Since the thickness of the traces is much less than the skin depth, it is reasonable to
assume that the current and voltage distribution is uniform through the thickness of
the trace material. Under this assumption, it is reasonable to use the Single Turn Coil
Boundary Condition. This boundary condition will introduce an additional governing
equation into the model which solves for the voltage field on the boundaries defining
the coil. Edge conditions representing a voltage source and a ground are applied at one
edge on the inside and outside turn of the coil. Additional floating potential conditions
are used on pairs of edges on either side of the model (Figure 2). These floating
potential conditions fix the potential to be the same, unknown, voltage on both edges
and also enforces that the current flowing into one edge equals the current flowing out
of the other edge in the same floating potential condition.
Air
Silicon wafer
Air
Electroplated copper traces
modeled as a single-turn coil
Solved with COMSOL Multiphysics 5.2
3 | MODELING A SPIRAL INDUCTOR COIL
Schematically, we can visualize this as:
Figure 2: Configuration of the Single Turn Coil boundary
Results and Discussion
Since we are only solve 1/16 of the entire model, we must scale up the computed
inductance accordingly. We can visualize the magnetic fields and the current flowing
along the surface of the coil. The skin effect does drive the current to the outer edges
Ground
Boundary feed 1 V
Floating potential pairs
Solved with COMSOL Multiphysics 5.2
4 |
MODELING A SPIRAL INDUCTOR COIL
of each turn of the coil. Such a model provides a quick approximation of more complex
structures.
Figure 3: The magnetic flux density (blue arrows), and surface current density (black
arrows) over the surface current density norm distribution of the coil are shown.
Model Library path: ACDC_Module/Inductive_Devices_and_Coils/
octagonal_surface_coil
Modeling Instructions
From the File menu, choose New.
NEW
1 In the New window, click Model Wizard.
MODEL WIZARD
1 In the Model Wizard window, click 3D.
2 In the Select physics tree, select AC/DC>Magnetic Fields (mf).
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