air core

Voice Coil 2009 1

The Audio TechnologyAuthority

Article prepared for www.audioXpress.com

Almost Air Core By Steve Mowry

The steel, iron, or other ferromagnetic material within the tweeter’s motor assembly is a source of dynamic

nonlinearity. These materials conduct both electricity and magnetic flux. AC eddy current within the ferro-magnetic material results in skin effect losses, inductance, flux modulation, and heat. B&W silver-plates some of its tweeters’ pole pieces to keep eddy current within the steel at a minimum, while most other hi-fi tweeters uti-lize copper shorting rings and others have also laminated copper steel, and so on in place of the motor assembly steel parts.

Although these design techniques are effective in reduc-ing nonlinearity, they are really just bandages compared to air-core motor topology. The permeability of steel and iron just cannot be made linear. Air and rare-earth magnets within their respective operating temperatures are linear with regard to their magnetic B and H field relationships. The DC permeability of the magnets and air is a constant, µ0. The electrical conductivity of air is zero and, NdFeB magnets are poor conductors, less than 10% the conductiv-ity of steel.

Most polymers have electromagnetic material properties that are approximately that of air. It is possible to imple-ment a high-performance tweeter assembly that utilizes no ferromagnetic or electrically conductive materials and approaches an air-core AC electromagnetic environment for the voice coil. A simple design example is presented that should be suitable for the audio “purist.”

INTRODUCTION Audiophile DIY hobbyists would not think of using

iron-core inductors in their passive crossover networks. Much has been written about “saturation” and the nonlin-ear characteristics of ferrite core inductors. This is admi-rable, but the transducers in the system most likely contain ferrous cores or pot topologies anyway.

I don’t want to say too much for fear that “speaker cable” people may complain. OK, I have steel-core mov-ing coil transducers, and some would argue that air-core inductors do not significantly improve the sound quality of the loudspeaker. However, suppose the transducers were somehow approximately air core—are they still comfortable with that argument? All the concerns regard-ing iron-core inductors and more apply to steel-core and/

or steel potted transducers.There is no known insulator of magnetic flux. Flux den-

sity and magnetic field strength are linearly related within air, which is insensitive to temperature changes but con-ducts flux poorly. Air and nonferrous material permeability is linear and constant.

Figure 1 plots the BH curves of air and steel on the same axes. You can see that steel conducts flux very well up to a 1.5T density; above that the nonlinear permeability transitions to the permeability of air. Notice the curves become parallel. Equation 1 shows that the permeability, µ, is then the instantaneous slope of the BH curve of that material. µ = Tm/A (1)

Figure 2 illustrates the nonlinear dynamic permeability of steel, and equation 2 summarizes the relationship.

µ(Tm, I) = Tm/A (2)

where Tm is the temperature of the magnet and I is the current amplitude.

FIGURE 1: BH curves for 1010 steel at room tem-perature and air.

FIGURE 2: Example of dynamic perme-ability, DC + AC, for the nonlinear ferromagnetic materials including steel.

2 Voice Coil 2009 www.audioXpress .com

With regard to the magnets, there are only two suitable types for air-core applications: samarium cobalt, Sm2Co17, and neodymium iron boron, NdFeB. Sm2Co17 is available with a room temperature 30-31 MGOe energy product, BHmax, but the cost is high. NdFeB is available with a room tempera-ture 33 and 38 MGOe energy product in high-temperature grades N33UH and N38SH. Their respective temperature-dependent BH curves are illustrated in Figs. 3a and 3b.

Figure 3b depicts the temperature-dependent BH char-acteristics of an N38SH magnet. These characteristics are linear up to 120° C at any permeance. This magnet is suit-able for an air-core application. Figure 3a illustrates the temperature-dependent BH characteristics of an N33UH magnet. These characteristics are linear up to 135° C at any permeance.

Despite that, the two limitations that I see with typical pole or potted moving coil transducer motor assemblies are the steel and the single-ended asymmetric drive typol-ogy. Figure 4 shows a simple but high-performance motor assembly that offers a solution to those limita-tions.

Figure 4 also illustrates the magnets’ orientation within the motor assembly. The motor topology is dual concentric complementary STEALLUS that implements a symmetrical push-pull magnetic circuit with annular radial gap contain-ing no steel whatsoever. The magnet spacer rings and the back plate are nonferrous and nonconductive materials.

DC MAGNETIC FEA Figure 5 contains the model of the voice coil that is used

in the DC and AC simulations.Figure 6 displays the simulation of the magnitude of the

DC flux density. You can see that the peak flux in the mag-netic gap is greater than 1.5T. This is quite high and higher than peak flux density within the magnets themselves.

Figure 7 includes the simulation of the DC flux distri-bution. There is significant flux leakage from the motor OD similar to larger ferrite magnet topologies.

Figure 8 depicts the simulation of the DC mag-netic field strength. You can see that the ratio of B to H is approximately µ0. This relationship is illustrated in Fig 9. Although the contour coloring is different, the value of relative permeability contour in Fig. 9 is approximately one everywhere.

Figure 10 displays the far-field simulation of |B|. The flux leakage at the enclosure boundaries for multimedia application should be less than 2.0 G at 1.0cm.

Figure 11 shows the simulation of BETA, Bl, and Re versus the voice coil position. Notice that the variation in Bl from –Xmax to Xmax is less than 2%, such that B1(±Xmax) > 0.98B1(0).

RESTART AC ELECTROMAGNETIC FEA Electrodynamic transducers have two sources of mag-

netic flux, the permanent DC magnet(s) and the AC current within the voice coil.

FIGURE 3A: Temperature-dependent BH curves of N33UH magnet.

FIGURE 3B: Temperature-dependent BH curves of N38SH magnet.

FIGURE 4: Illustration of the air core motor assembly with magnet orientation indicated.

FIGURE 5: Voice coil model.

Voice Coil 2009 3

Equation 3 shows an approximation of the skin depth, d, where σe is the electrical conductivity of the material, 1/(Ωm). See Table 1 for conductivity values.

d ≈ m (3)

Simplifying equation 3 for an approximation of the skin depth of steel for AC current and thus AC flux, the result follows (steel skins). Skin effect causes the appar-ent resistance of a material to increase and thus losses to increase.

ds ≈ m

Now for the N33EH magnet, the result follows.

dm ≈ m

Then ds ≈ 0.006dm, less than 1% the skin depth of the magnets as a result of the high magnetic permeability and moderate electrical conductivity of steel.

Notice that for air, d ≈ 1/0 and tends to infinity for any frequency, d → ∞. There can be no skin effect within the

audio bandwidth within materials with σe ≈ 0. Materials such as the magnet have µ = µ0 and have a low conductiv-ity and will exhibit very little if any skin effect within the audio bandwidth.

The properties listed in Table 1 are utilized in the elec-tromagnetic and thermal finite element analysis and simu-lations. Within the AC electromagnetic simulation actual air-core simulations are also presented as a reference for the motor assembly contour plot evaluations. I performed the motor assembly simulations at 1.0kHz and 10kHz,

Table 1 Common Electromagnetic Material Properties

Thermal Electrical MagneticMaterial conductivity conductivity permeability τ W/(° C m) σe 1/(µm) µ Tm/AAir 0.026 0 µ0

1010 steel* 47 0.7 × 107 2750µ0 (H dependent)aluminum 200 3.6 × 107 µ0

nylon 0.25 ~0 µ0

kapton 0.12 ~0 µ0

magnet 8.9 6.7 × 105 ~µ0(high temperature limited)glass fiber 0.040 ~0 µ0

*Steel is also subject to the skin effect electromagnetic phenomenon.

FIGURE 6: Contour plot of the simula-tion of the mag-nitude of the DC flux density, B.

FIGURE 7: Contour plot of the simula-tion of the DC flux distribution.

FIGURE 8: Contour plot of the simulation of the magnitude of the DC magnetic field strength, H.

FIGURE 11: Quasi-dynamic DC simu-lation of BETA, B1, and Re vs. voice coil position.

FIGURE 10: Contour plot of the simulation of the far-field, B, ~3G at 6cm from the transducer.

FIGURE 9: Contour plot of the simula-tion of the relative DC permeability, µ ≈ µ0.


whereas only the 1.0kHz free-air voice coil simulations are presented. The 1.0kHz and 10kHz free-air simulations are identical. The absence of any frequency modulation is a characteristic of air core coils.

Current density, J, is defined by equation 4, where SV is the cross sectional area of the voice coil, 2.8 × 10-6 m2 and i is the current, A.

(4)i/√2 ≈ ARMS

Figure 12 shows the input current density to the AC prob-

lems, 0.5 × 106 A/m2. Notice there is no negative current den-sity. Eddy current is indicated by a minus sign and opposes the direction of the input current. Figure 13 illustrates that there is some eddy current within the magnets at 1.0kHz.

With respect to AC electromagnetics, it is desirable to use polymers for the faceplate, back plate, and chamber. Aluminum has high thermal conductivity but is also a good electrical conductor. The objective is air core and polymers have electromagnetic properties that are essentially equiva-lent to air and thus the recommendation is to avoid alumi-num parts. However, the need for heat dissipation should be evaluated on case-by-case basis design requirements. Aluminum and/or copper could be utilized for heatsink parts with interfacing on the magnet ID and/or magnet OD and as a back plate, and/or faceplate material.

Figures 14 and 15 are plot contours of the current den-sity excluding the voice coil at 1.0kHz and 10kHz. There is some eddy current density within the magnets that increases with increasing frequency. However, there is no visible skin effect even at 10kHz, and, with respect to equation 3, the magnet electrical conductivity is small and the permeability is approximately that of air. This small eddy current density will result in some heating of the magnets and a small per-

turbation from the free-air AC B and H field distributions.Figures 16 through 24 illustrate the AC magnetic fields

for the voice coil in free air and with the voice coil within the motor assembly. The results for the simulations of the motor assembly are “almost air core.” The differences in both the fields and the distributions are small.

The AC H field simulations in Figs. 23 and 24 show that the H field within the magnet will cause changes in the BH curve from DC by ±B = ±Hµ0. The dynamic perme-ability of the magnets is still µ0. The AC quantities of B and H within the magnet are small, while the DC B and H within the magnet are very large. Then Figs. 16 and 22 show that the simulations in free-air result in comparable values of B and H to simulations of the voice coil within the

FIGURE 12: Contour plot of the simulation of the amplitude of the AC current density, J, with the voice coil in free-air.

FIGURE 13: Contour plot of the simulation of the amplitude of the AC current density, J, with the voice coil within the motor assembly.

FIGURE 17: Contour plot of the simulation of the magnitude of the AC flux density, B, with the voice coil within the motor assem-bly at 1.0kHz.

FIGURE 16: Contour plot of the simulation of the magnitude of the AC flux density, B, with the voice coil in free-air at 1.0kHz.

FIGURE 15: Contour plot of the simulation of the amplitude of the AC current density, J, within the magnets only at 10kHz.

FIGURE 14: Contour plot of the simulation of the amplitude of the AC current density, J, within the magnets only at 1.0kHz.

Voice Coil 2009 5

motor assembly. Thus, the AC perturbations of the magnets’ operating points on the DC BH curves are relatively very small and linear (Figs. 6 and 8). The voice coil is trying to magnetize (+) and demagnetize (-) the magnets.

Figure 25 contains a plot of the simulation of induc-tance, Le, versus the voice coil position with approximately 1A RMS current input.

Equation 5 shows the total Bl product from the magnet and from the voice coil.

Bl(x,i) = Bl(x) + Bl(x, i), the DC and AC components of the Bl product, Tm (5)

Equation 6 relates the inductance, Le, to the AC Bl with respect to the change in voice coil position. Figure 26 is a plot of the simulated AC Bl product. Without ferromagnetic material around the voice coil, these quantities are small. Inductance tends to be linear.

Le(x) = (6)

It then follows in equation 7 that the AC Bl product is the change in the AC flux linkage with respect to the voice coil position.

FIGURE 18: Contour plot of the simulation of the magnitude of the AC flux density, B, with the voice coil within the motor assem-bly at 10kHz.

FIGURE 19: Contour plot of the simulation of the AC flux distribu-tion with the voice coil in free-air at 1.0kHz.

FIGURE 20: Contour plot of the simulation of the AC flux distribu-tion with the voice coil within the motor assembly at 1.0kHz.

FIGURE 21: Contour plot of the simulation of the AC flux distribu-tion with the voice coil within the motor assembly at 10kHz.

FIGURE 22: Contour plot of the simulation of the magnitude of the AC field strength, H, with the voice coil in free-air at 1.0kHz.

FIGURE 23: Contour plot of the simulation of the magnitude of the AC field strength, H, with the voice coil within the motor assem-bly at 1.0kHz.

FIGURE 24: Contour plot of the simulation of the magnitude of the AC field strength, H, with the voice coil within the motor assem-bly at 10kHz.

FIGURE 25: Quasi-dynamic simula-tion of the induc-tance, Le(x).


Bl(x, I) = ,The peak AC Bl product, Tm (7)

THERMAL FEA The DC resistance of the voice coil increases with tem-

perature. Figure 27 illustrates this relationship between temperature and resistance.

The heat transfer coefficient of air has mildly nonlinear velocity dependence (Fig. 28). The magnitude of the veloc-ity, the speed of the voice coil, is given by equation 8.

x = 2πf • x m/s (8)

Figure 29 displays the simulation of the temperature of the motor assembly with the voice coil at steady-state of 200° C but ignoring eddy current. The voice coil heats the magnets, which are quite thick, so high temperature grades are utilized, N33UH on the ID and N38SH on the OD. You can substitute N30EH or even Sm2Co17 magnets for an even more robust implementation. However, there will be a reduction in Bl and BETA due to the lower energy products. Simply using larger magnets can then increase Bl and BETA, but there will be an increase in cost and package size.

MECHANICAL FEA I selected Hytrel 5555HS for the surround/suspension.

Hytrel is a medium modulus thermo-ester-ether-elastomer (TEEE) with a nominal hardness of 55D. I discussed this material in the January 2006 issue of Voice Coil1. The method of manufacture is molding. Hytrel is typically sold as plastic pellets.

The surround mesh is incrementally displaced ±0.5mm and the reaction force is evaluated at each increment. The positive and negative displaced mesh shapes are illustrated in Figs. 30 and 31, respectively.

Figure 32 shows the simulated buckling displaced shape

at greater than 18 PSI. The modulus of the Hytrel is high relative to rubber. The result is a robust surround/suspen-sion.

Equation 9 defines the force and stiffness relationship. Equation 10 defines the stiffness as the change in force with respect to change in position. The simulated force, F(x), is plotted in Fig. 33, and the simulated stiffness, Kms(x), is then plotted and shown in Fig. 34.

F(x) = Kms(x)x N (9)

FIGURE 28: Plot of the heat transfer coefficient of air vs. velocity.

FIGURE 27: Plot of the DC resistance of the aluminum voice coil vs. tem-perature.

FIGURE 26: Quasi-dynamic simula-tion of the AC B1(x, 1.0A RMS).

FIGURE 29: Contour plot of the simulation of temperature with the voice coil tem-perature fixed at TV = 200° C.

FIGURE 30: Simulation of the surround static and displaced shape at 0.5mm.

FIGURE 31: Simulation of the surround static and displaced shape at –0.5mm.

FIGURE 32: Simulation of the buckling mode shape at 18.1 PSI.

Voice Coil 2009 7

Kms(x) = N/m (10)

The simulated compliance is then just the reciprocal of the stiffness. This relationship is shown in equation 11 and the results plotted in Fig. 35.

Cms(x) = (11)

NATURAL FREQUENCY FEA With regard to selection of diaphragm material, there are

several choices. I discussed this topic in the March 2006 issue of Voice Coil2. 1. CVD diamond—highest performance but highest cost and limitation on geometry, particularly height of the dome. 2. Beryllium—very high performance with very high cost. 3. AlBeMet—high performance with high cost. 4. Keronite treated light alloy—high performance with moderate cost. I selected material 4, Keronite treated light alloy, which is inherently a sandwich composite. My material of choice for the Keronite treatment substrate is magnesium, which has low mass with a reasonably high speed of sound. The Keronite treated magnesium dome is environmentally robust with excellent adhesive bonding characteristics.

Figures 36 through 40 depict the simulation of the natural frequencies of the diaphragm. The results are sum-marized in Table 3. The simulation requires composite finite elements that allow a thickness for each layer of mate-rial. Lumped boundary conditions of a spring and mass ele-ments are utilized to simulate the stiffness and mass of the entire moving assembly, dome, surround, and voice coil.

Figures 41 and 42 display the geometry and frequency response simulation. The FINECone simulations did not reveal any significant in-band resonances and/or bend-ing modes. The modulus of the sandwich composite diaphragm, Keronite/Mg/Keronite, is unknown and is an effective quantity that is simulated using composite finite elements. However, the first bending frequency is known. The modulus property input within FINECone is then adjusted such that the onset of bending is at 19kHz.

Table 2 Common Mechanical Material Properties

Material Density Modulus √E/ρ (m/s) Damping Poisson’s ρ (kg/m3) E (N/m2) δ RatioHytrel 5555HS 1,190 1.84 × 109 1,243 0.010 0.3magnesium 1,740 44.0 × 109 5,029 0.005 0.3keronite 3,580 275 × 109 8,764 0.005 0.3aluminum 2,699 68.0 × 109 5,019 0.005 0.3AlBeMet 2,071 193 × 109 9,654 0.005 0.2Beryllium 1,844 303 × 109 12,819 0.005 0.1CVD Diamond 3,500 >1,000 × 109 >1,700 0.005 0.3Kapton NH 1,420 15.4 × 109 3,293 0.020 0.3

FIGURE 33: Quasi-dynamic simulation of the surround reaction force.

FIGURE 34: Quasi-dynamic simulation of the surround stiffness, Kms(x) vs. voice coil position.

FIGURE 35: Quasi-dynamic Simulation of the Surround Compliance, Cms(x) vs. Voice Coil Position.

FIGURE 36: Simulation of the diaphragm piston natural frequency, f0 = 718Hz.

FIGURE 37: Simulation of the diaphragm first bending natural frequency, f1 = 19,971Hz.

FIGURE 38: Simulation of the diaphragm second bending natural frequency, f2 = 20,664Hz.


LINEAR PARAMETER MODEL I produced a linear parameter model using the simulated

parameter quantities (Fig. 43). Figure 44 contains a plot of the simulation of the infinite baffle frequency response at 1.0m on-axis with 2.83V input. Finally, Fig. 45 contains an illustration of the simulated high-frequency transducer assembly.

ENGINEER’S COMMENTS Figure 46 shows a highly symmetrical but lossy radial

flux motor with a peak radial flux density in the gap of greater than 1.5T. The transducer concept is a serious attempt to design out nonlinearity, while maintaining reasonable cost. Steel within the magnetic circuit allows for efficient use of magnets; however, this comes at the price of inherent nonlinearity. The transducer designer must then concentrate on designs that minimize the effects of steel within the limitations of the typical efficient topology.

Table 3. Natural Frequency FEA Results Summary

MODE NO. FREQUENCY (Hz) MASS (g) δ f0 718 0.82 0.001 f1 18,971 0.005 f2 20,664 0.005 f3 22,397 0.005 f4 24,657 0.005

FIGURE 39: Simulation of the diaphragm third bending natural frequency, f3 = 22,398HZ.

FIGURE 40: Simulation of the diaphragm third bending natural frequency, f4 = 24,657Hz.

FIGURE 41: Moving assembly simulation at 20kHz.

FIGURE 42: Simulation of the frequency response at 1.0m, 0 to 45° off-axis.

FIGURE 43: Simulation of the target linear parameters.

FIGURE 44: Linear simulation of infinite baffle fre-quency response with 2.93V RMS input at 1.0m.

FIGURE 45: 2d illustrations of a 30mm air core high frequency trans-ducer assembly.

FIGURE 46: Contour plot of the simulation of the radial component of the DC flux den-sity, BR with the DC flux distribu-tion overdrawn.

Voice Coil 2009 9

Due to the flux leakage at the magnets’ OD interface, this transducer is not magnetically shielded and thus may not be suitable for small multimedia loudspeaker applica-tions using CRT video monitors. However, the transducer is robust with a Keronite treated light alloy diaphragm, a Hytrel surround, nickel-plated magnets, and assorted poly-mer parts. These materials are commonly used within the automotive industry. Along with a reasonable size package, this transducer is well-suited for both car audio and hi-fi.

The air-core motor topology does present a paradox. The input current heats the voice coil, which heats the magnets; however, heat transfer from the voice coil is desirable. Thus, it is then desirable to heat the magnets in this implementation—well, no; but if the temperature is kept within linear operating limits, then the magnets just become effectively smaller. This is not a new situation; it’s just more apparent in this case. The magnets are kept quite large, and only high-temperature materials should be utilized. A small consolation is that the magnets will become less electrically conductive as their temperature increases and thus give a better approximation of the properties of air.

The intended assembly procedure utilizes one hard part (gap) gauge and either a soft part (coil) gauge for bottom-up assembly or a butterfly diaphragm subassembly that locates from the outside magnet OD. Magnet annular tolerance can be held to ±0.10mm or better with ring magnets such as these. Due to opposing direction, magnets must be magnetized prior to assembly. Magnets and spacers are assembled into STEALLUS subassemblies using align-ment fixtures and then subsequently bonded to the back plate while gauged. Assembly methodology is similar to push-pull planar magnetic transducers but much simplified due to the limited number of parts and/or subassemblies; however, size does matter and could pose some assembly challenges.

An industry colleague interviewed me for a job in 1999. I was asked a technical question: What was the function of shorting rings within motor assemblies? My answer was that

the shorting rings’ function was to make the motor look like air core to the voice coil. My interviewer told me that I was incorrect and that the function of the shorting rings was to reduce distortion.

I have studied this topic and stand by my answer and add a followup comment: A shorting ring will not reduce distor-tion in this case. The results are just another perturbation of air-core characteristics along with the heating of the high conductivity-shorting ring with eddy current. It looks like “less is more” again this time. VC

REFERENCES 1. www.klippel.de/pubs/Klippel%20papers/Loudspeaker%20Nonlinearities–

Causes,Parameters,Symptoms_06.pdf. 2. www.audioxpress.com/magsdirx/voxcoil/addenda/media/mowry1107.pdf. 3. www.audioxpress.com/magsdirx/voxcoil/addenda/media/mowry108.pdf. 4. www.audioxpress.com/magsdirx/voxcoil/addenda/media/mowry907.pdf.

Steve Mowry is president of S. M. Audio Engineering. He has a BS degree in Business Administration from Bryant College and BS and MS degrees in Electrical Engineering with highest distinction from the University of Rhode Island. He has worked in loudspeaker R&D at BOSE, TC Sounds, EASTECH, and P.Audio Systems. He was responsible for the design and development of BOSE’s 2¾″ plastic bas-ket multimedia AM5/Lifestyle “cube” transducer in 1997-1998, “Hotshot.” This in raw quantity is the single largest-selling electrodynamic audio transducer of all time and is still being manufactured today. Steve is currently an independent researcher, lecturer, and consultant in transducer/loudspeaker system design and new product development along with being a frequent contributor to Voice Coil and Multi Media Manufacturer.

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