This paper investigates the possibilities of using carbon fiber as an inductor material by analyzing its inductive properties. Various shapes such as rectangular, spiral, helical, and cylindrical line structures have been simulated under various constraints using simulation software. Hardware implementations were also tested and both simulation and hardware results show that carbon fibers have the potential to replace copper inductor lines. The implemented spiral inductor produced a quality factor of 40 while producing an inductance of 4 nH at 1.2 GHz frequency.
Inductor, a critical passive circuit element, is extensively used in analog signal processing circuits. Inductors designed using copper wires are found to be bulky in nature and also result in significant losses. With the recent advancement in MEMS technology, the size and performance of inductors have become a major factor in analyzing the efficiency of low-power, high frequency circuits. This calls the need for realization of inductors of very small sizes [
Inductors are one of the bulk devices which limit the performance in most of the electronic circuits. During the 19th century micro-electro-mechanical inductors played an important role in replacing conventional copper inductors, since the power consumption of the later is higher due to the high current density. As an example the maximum current density of twenty turns of 16 AWG (American Wire Gauge) inductor with 26 mm2 diameter will be about 275 A/cm2.
Microscale inductors have been investigated by several researchers, and it has been proved that they can be superior to conventional copper inductors [
Carbon fibers are strands of conductor embedded in a nonconductive epoxy. This configuration nearly eliminates eddy currents, which otherwise would reduce conductivity limiting it to the surface, thus making it highly conductive at high frequencies. Without eddy currents, the area available for conduction in carbon fiber is much thicker than for a similar amount of copper. The reason for high conductivity of carbon fibers is due to large skin depth. Carbon fibers have ultra high modulus around 1000 GPa and low mass. It offers great flexibility in terms of tuning thermal and mechanical properties through the orientation and number of layups of the fibers. It has many outstanding properties such as high intensity, high modulus, high heat endurance, creep resistance, fatigue endurance, corrosion resistance, and small coefficient of thermal expansion. The internal structure of carbon fiber can be changed by processing under different temperatures so as to change its thermal conduction, thus making it a suitable material for use in aviation and aerospace [
Highly conductive metal materials are the best shielding materials for reflecting and absorbing electromagnetic waves. But they are bulky in nature, difficult to process, expensive and have a tendency to corrode. In contrast, light-weight and anticorrosive properties of polymer materials are extremely suitable for electronic equipment. However, most current polymer materials are not conductive and have no electromagnetic shielding effectiveness. The addition of a conductive filling to polymer material increases the load transfer ability, so that the material can rapidly conduct a load and provide the shielding ability against electromagnetic waves [
A design methodology has been developed to analyze the various properties of carbon fiber inductors using existing simulation software—COMSOL Multiphysics and High Frequency Structural Simulator (HFSS). A spiral inductor formed using carbon fiber has been implemented in resonant and amplifier circuits. Practical measurement of inductance was carried out by extracting “
Inductor and inductive devices formed of a conductive loaded resin-based material is a combination of conductive fibers (nickel plated carbon fiber, silver, or copper) and micron conductive powders (carbon or graphite) [
The study of properties of carbon fiber reinforces that inductor design using carbon fiber is found to be more efficient than copper. This can be inferred from the properties listed in Table
Comparison of properties between copper and carbon fiber.
Properties | Copper | Carbon fiber |
---|---|---|
Density (Kg/m3) |
|
|
Electrical conductivity (Kg/m3) |
|
|
Coefficient of thermal expansion (1/K) |
|
|
Heat capacitance at constant pressure (J/kg·K) |
|
|
Electron mobility (m2/V·s) |
|
|
Thermal conductivity (W/m·K) |
|
|
Poisson’s ratio |
|
|
Young’s modulus (Pa) |
|
|
Resistivity (Ωm) |
|
|
The small signal analysis of an inductor is based on the principle that if an inductor’s magnetic material is nonlinear, then the inductance depends upon the current passing through it [
Geometry profile of the inductor which is used to study the small signal analysis where the domain radius is 3 cm, inductor length is 2 cm, core radius is 5 mm, coil outer radius is 10.5 mm, and the coil inner radius is 7.5 mm; 1 represents the air domain; 2 and 3 represent the magnetic core and thickness of the coil, respectively.
The module used is 2D axisymmetric space dimension—AC/DC module. The geometry consists of a magnetic iron core with carbon fibers wound over it. The operating frequency is set at 10 kHz.
The small signal inductance is plotted versus the DC bias current and is shown in Figure
Plot of DC current bias versus coil inductance.
Relative permeability distribution.
The mutual inductance between a primary and secondary single turn carbon fiber coil in a concentric coplanar arrangement is computed using a DC (steady-state) model [
A current of 1 Ampere flows through a single turn coil of radius
Concentric coplanar arrangement.
In the limit as
The two concentric coils are modeled in a 2D axisymmetric sense, as shown schematically in Figure
A schematic representation of the 2D axisymmetric model of the concentric coils.
The modeling domain is surrounded by a region of infinite elements, which is a way to truncate a domain which stretches to infinity. Although the thickness of the infinite element domain is finite, it can be thought of as a domain of infinite extent. The coils are both modeled using the Single Turn Coil Domain feature, which can be thought of as introducing an infinitesimal slit in an otherwise continuous torus. The Single Turn Coil feature can be used to excite the coil, to represent the open circuit case and the closed torus case, and to model an external load. The primary coil is excited by specifying 1 A of current.
The DC magnetic flux is plotted in Figure
Magnetic flux density distribution.
For the AC case, a 1 kHz sinusoidal time-varying current drives the primary coil. This can either induce currents in the secondary coil or induce a voltage difference if the coil is modeled as an open circuit. The secondary coil domain uses the Single Turn Coil Domain to model both the open circuit and the closed circuit case.
To model the open circuit case, the current through the coil is specified to be 0 A, which specifies that there is no current flowing through the coil. The Single Turn Coil Domain feature will introduce a coil voltage that causes no current to flow. The average of the induced currents over the cross section is zero; that is, there is no net current flow through the coil. Since the Single Turn Coil Domain computes the loop potential, this voltage induced across the coil can be used to compute the mutual inductance which is given as follows:
The computed mutual inductance is found to be
Induced currents in the coil for open circuit case.
On the other hand, to model the closed circuit case, the voltage drop across the coil is fixed at 0 V. Although this seems to imply a short circuit, the reactance of the copper coil is inherently included, so the case being modeled is analogous to a closed continuous loop of wire.
The skin effect is clearly visible; the current is being driven to the boundaries of the domain. The total induced current around the secondary coil is
Induced currents in the coil for the closed circuit case.
In this analysis, COMSOL Multiphysics is used to solve the magnetic fields surrounding the coil that is placed in electrical circuit and calculate the inductance of the coil. In some cases the analytic approach could be difficult and with increasing complexity of geometries of some coils these are sometimes quite difficult to calculate [
Number of turns is
Geometry of this study is created in 2D axisymmetric space dimension—AC/DC module. For simplicity and initial testing a circular spiral coil is considered. Figures
Spiral coil topology.
Simplified model of coil, (a) 2D and (b) 3D representation.
Because the coil is created in 2D axisymmetric space dimension, the model is simplified and the coil is created with nine circles. Geometry consists of 10 domains, one air domain surrounding the coil and the remaining are coil domains.
The coil material is selected as carbon fiber with conductivity
Total magnetic energy
Figure
Magnetic flux density—surface.
Magnetic flux density—contour.
For the final implementation a rectangular spiral inductor has been selected since it is a well studied topology and most of the on-chip applications use the rectangular spiral inductor. As a first step a spiral inductor model has been considered for analysis using HFSS in order to determine the value of inductance and
A spiral carbon fiber coil of 2.5 turns is modeled using HFSS with thickness of 2
Model illustrating spiral coil embedded on a silicon base.
Inductor model with radiation boundary.
Model illustrating wave port excitation.
Wave port with mode lines.
The simulation of the spiral inductor model has been carried out in the frequency range of 1–5 GHz. The sweep type is chosen as discreet and the frequency sweep type that is selected is linear step.
The quality factor of the inductor is simulated with respect to the frequency and is plotted in Figure
Plot of Quality Factor versus frequency.
The proposed model is based on using the silicon wafer as an on-wafer test-fixture with the carbon fiber embedded on it using the adhesive silver paste. Silver paste is a conductive solder paste which has excellent resistivity, good soldering ability and adhesion strength. The paste has good adhesion to glass, plastics, and dielectrics. The spherical ultra fine silver powder is readily dispersible in multiple base formulations. Inductor model has been designed by using silver paste as an adhesive to implant the fiber on the wafer. But the binding of the fiber on the base material was not strong enough which ruled out the possibility of using silver paste to design the inductor. The authors have used silver paste to make the fabrication as cost effective. The intention of this research was to test whether the fiber material could be used for inductors. The nickel coated flexible fibre bundle with the diameter 0.15 mm has been used in this fabrication where the diameter of each strand was 150 um. The fabricated low cost inductor is shown in Figure
Image of implemented low cost carbon fiber inductor.
The
Inductance and quality factor measurements of low cost inductor.
Frequency (GHz) | Inductance |
|
---|---|---|
0.544 | 10.153 | 30.0 |
0.630 | 12.947 | 31.9 |
0.700 | 9.452 | 32.3 |
0.772 | 5.249 | 30.4 |
0.945 | 4.290 | 29.5 |
1.000 | 3.328 | 26.8 |
1.100 | 3.437 | 36.0 |
1.200 | 2.271 | 40.5 |
1.350 | 4.189 | 35.9 |
1.400 | 5.310 | 36.3 |
1.500 | 5.224 | 3.5 |
In this paper we proposed a low cost carbon fiber inductor. The spiral inductor designed by embedding the carbon fiber on a silicon wafer has been fabricated and tested. The device is fabricated with ultra low cost since carbon fiber material is much cheaper. In addition to this a low cost fabrication is also employed in this work. The fabricated device produces a maximum
The authors declare that there is no conflict of interests regarding the publication of this paper.