Practical Finite Difference Time Domain (FDTD) Shielding Analysis of Thin Coatings and Shield Bonding Methods

John G. Kraemer Rockwell Collins, Inc.

Cedar Rapids, IA 52498

Absiraci: Thin coatings such as Indium Tin Oxide (ITO) or gold splatter on glass are often used on electronic display enclosures for shielding to allow compliance with radiated emissions standards while allowing optical transmission. The thin coatings are often bonded to the display enclosure to allow realization of the maximum shielding. The bonding is often accomplished by the use of a conductive gasket that mates with a buss bar on one or more edges of the thin coating. Shielding effectiveness of the coating and gasket configuration is very difficult to predict using traditional shielding effectiveness equations. This paper shows how 3-dimensional(3D) Finite Difference Time Domain (FDTD) simulation and analysis are used to examine trends in shielding effectiveness with respect to gasket characteristics, thin coating characteristics (thickness and conductivity), and bonding methods. Practical simulation and model setup methods are presented. Results are provided for common configurations.

BACKGROUND

Thin conductive coatings are often used on displays and viewing glass to reduce radiated emissions by providing electromagnetic shielding. The coating is characterized by its thickness (Th) and conductivity (03. Just as important as the conductive coating is the quality of the coating’s bond to the rest of the conductive enclosure. The bonding is most often implemented with conductive fingers or a conductive EM1 gasket. When conductive fingers are used, the main area of concern is the space between the bonds, as the conductivity of the bond is often not the limiting factor of shielding: the spacing between the bonds may limit high frequency performance. When ease of fabrication and costs are considered, along with high frequency emissions control, bonding is routinely implemented using a conductive elastromer gasket. Because of this, our focus will be limited to conductive gaskets that provide a continuous bond between one or more of the edges of the thin coating and host enclosure.

As thin conductive coatings on viewing surfaces may carry a significant cost as well as have a notable effect on optical qualities, it is important to be able to understand exactly what a particular type of thin shield will provide for radiated emissions control. It is also important to understand the resulting shielding quality as a function of EM1 gasket type and the number of edges (amount of coating perimeter) used for bonding the coating to the rest of the enclosure, as this too may have notable impact on product cost and climatics/dynamics performance.

In general, it is usually known that a certain amount of shielding, as a function of frequency will be needed on a display. This is best determined early in the design cycle by evaluating the emissions of display assemblies against the products emissions requirements.

Shielding effectiveness of materials can be computed using well- known relationships based on wave impedance, material properties (thickness, conductivity, permeability, and permittivity), and field type. Empirical methods exist to computing shielding when apertures are present. However, it is often difficult to adapt these

methods to a particular situation where shield dimensions, source dimensions, shield to field measurement point, and aperture arrangement fall outside of the often simplistic geometry and assumptions made with these methods. This is especially true when one considers the 3-dimensional nature of most EM1 problems and instances when electromagnetic waves encounter a shield or boundary at angles other than 90 degrees and significant internal scattering and reflections are involved.

Recent advances in computing hardware have brought the capability of 3-D Finite Difference Time Domain (FDTD) EMC analysis involving “real-world” structures to the practicing EMI/EMC engineer. As computing hardware capabilities continue to grow, 3-D FDTD EMC analysis will become even more useful in accelerating design and development cycles. For the practicing EMC engineer, 3-D FDTD analysis is most useful in examining shielding, radiation, and field-wire coupling trends. A Fourier transform of the time domain output quickly yields a response across a wide frequency range. From conceptual and mathematical standpoints, 3-D FDTD electromagnetic analysis has been quite mature for some time, and details regarding the algorithms and implementation of various formalisms to improve computational efficiency, such as thin wires, thin slots, and thin surfaces are provided in [I] and [2]. Reference [3] provides an excellent summary of the FDTD method.

An example of how the FDTD method can be used to analyze shielding trends with respect to radiated emissions E-field for a conductive enclosure with thin shield bonded to the enclosure with conductive gaskets is shown below. The key properties and considerations of each model feature type are discussed. Finally, trends seen from the simulation are presented and compared to test results. The reader is assumed to be familiar with the basics of FDTD analysis for electromagnetics, and is directed to references [l] through [4] if additional background is needed.

GENERALPROBLEMSETUP

Figure 1 shows the dimensions of the enclosure subject to analysis. Note that the lightly shaded surface is the thin shield. The darker area around it is a model of the EMI gasket that bonds the thin shield to the conductive (aluminum) enclosure, and, as discussed below, this placement and modeling as such is only valid under specific conditions. Also, note that the enclosure’s two sides, top, and back contain a layer of nonmetallic material, which will be used to absorb reflections. Figure 1 also shows the ground plane that would be present in a military or avionics equipment EMI radiated emissions test setup. Also shown is the wire loop radiator that will model the source. Note that the source wire is near the thin shield and has a run close to the length of the shield. This is purposely set up as such to mimic dimensions, principally loop size and distance to the shield, of the most suspect source of emissions involved with the situation being analyzed.

Not shown in Figure 1 is the field measurement point. The measurement point is 30 cm above the ground plane and 1 meter in

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Figure 1. 3-D FDTD Model Setup of Enclosure with a Thin Coating Shield and EMI Gasket

tknt of the front face of the enclosure. Several E-field “probes” were placed in that general area, with the measurements being derived from a full tield integration over a surface around the model space using the free-space Green function with the Lorentz condition (gauge). This allows results at a desired distance and point without significantly increasing computational volume and yet providing results consistent with what would he seen if tbe whole volume out to the measurement point was meshed.

Tbe end objective is to determine wire currenf-to-E-$eMtmnsfer functions (in the frequency domain) for an enclosure without a front shield and for tbe enclosure with various typa front shields. Shielding effectiveness is defmed as the difference in the transfer functions. Although not a standard definition, this definition is most practical in that it tells the engineer specifically what a shielding wntigumtion will provide for the given situation: given a set of radiated emissions measurement data from an enclosure without a shield, tbe analysis will allow quick determination as to whether or not the shielding will provide adequate emissions suppression.

Furthermore, if tbe source used in the FDTD analysis accurately lrprcscnts the worst case radiating source, the result may also yield expected field strengths in absolute terms at the point of meas”remnt.

Finite Dlflerence Cell Size and The Domain Step Size

Since special formalisms exist to model thin wires, thin slots, and thin surfaces (with thin referring to feature size << I cell dimension), the smallest resolvable feature is generally a matter of taste and consideration of the geometrical coarzzness effects that will be present after the problem space is meshed into cells. A 0.5 cm cell size in all three directions was thus chosen for tbe subject problem with this in mind. As FDTD analysis involves diswetization and sampling in the spatial domain as well as the time domain, bandwidth will be limited by tbe cell size. References [I], [Z], and [4] state that tbe upper frequency components present in sources should he limited such that

whereficmr ranges from 5 to 20.

Note that the wavelmgtb will be shorter in dielectrics than in air by the square mot of the relative permittivity.

For a 0.5 cm cell size, and using a factor of IO, our highest fnquency of use will be 6 GHz in air, and about 2 GHz in dielectric with a relative pem&tivity of IO. The energy in tbe sources must bc limited accordingly. However, a cursory/logical analysis would show that error due to spatial discretization in dielectrics is less severe if the dielectric is lossy and thus a 3 GHz upper frequency bound is acceptable for this analysis.

Of significant impact ta simulation practicality using desktop computing resowces is the Finite Difference cell size and hence the total number of cells in tbe meshed model. The cell size is determined by the smallest feature desired to be resolved and the highest frequency of interest.

The time step used must he small enough to satisfy the Cowant m nt”R oe small mougn lo smsly ute LO”ram Stability Condition and must also he small enough to satisfy the ion and must also he small enough to satisfy the Nyquist condition for tbe highest &equency of interest. m for tbe highest &equency of interest. The Cowant The Cowant Stability Condition is: 10n is:

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(2)

However, when thin wire formalisms are used, the Courant Condition is often inadequate and thus the time step may have to be made 10 to 30% less to ensure numerical stability. For the above mentioned 0.5 cm (all three directions) cell size, the Courant Stability Condition would dictate a maximum time step of 9.6 pS. Since thin wires will be used in the problem, the time step was decreased to 8 pS to yield a stable simulation. Per the Nyquist sampling criteria, a 8 pS time step would yield a highest resolvable frequency of 62.5 GHz, which is beyond the highest frequency of interest for this problem, 3 GHz. A time step of only 166 pS is needed to resolve 3 GHz, hence the data from only every 20” point needs to be written to the time domain output files. This conserves disk space and makes the Fast Fourier Transform (FFT) more practical when a long simulation is required.

Modeling “Standard” Materials The ground plane and enclosure shell shown in Figure 1 were modeled using a perfectly conductive metal surface/boundary (tangential E-field components are zero), as the actual enclosure and ground plane are very good conductors.

It is readily discemable that if the shield (gasket and thin coating combination) on the enclosure front is of good quality, excessive ringing will occur in the enclosure, making the simulation almost impossible to complete in reasonable time. To reduce reflections, a 2-cell thick (1 cm) body of lossy material was placed on the top, sides, and back surfaces of the enclosure. The intent is to moderately minimize reflection and maximize absorption of non-reflected components. Since reflection is dependant upon angle of incidence, polarization, and field type [5], it becomes difficult to compute the optimal material type for this function. Hence it is often best determined by trial and error and observing how material characteristic impedance, 17, and wave attenuation constant, a, as shown in equations (3) and (4), are affected by material conductivity, permittivity, and permeability. Providing too much minimization of reflection reduces insight to the shielding and scattering trends caused by the enclosure shape itself, especially if multiple openings are involved. Providing too little absorption will cause notable re-reflections at the enclosure wall - dielectric boundary: the additional scattering provided by this effect may excessively distort results.

(3)

For the subject example problem, an absorbing material with a conductivity of 5800 S/m, a relative permittivity of 10, and a relative permeability of 1000 was used. For shield compositions that yielded high effectiveness (and thus required a high number of time steps to produce a settled response), this material provided a notable decrease in the required simulation time steps while affecting shielding effectiveness results less than 2 dB. It is important to note that the

same lossy material must be used for the simulations with and without the shields of interest.

Thin Wires The radiator is modeled using a thin wire formalism. Common to most practical FDTD codes, this formalism allows transport of charge from one location to another while considering wire resistance, inductance, and capacitance when the wire radius is much less than a cell’s dimension and thus too small to be directly gridded in a finite difference mesh. Modeling the wire as having a diameter of approximately one cell dimension would require either a cell size that is too small to be practical for most applications or an oversized representation of the wire which would result in much less inductance and much more capacitance than what would be characteristic of the real wire. Thus thin wires are modeled as transmission lines driven by the mesh electric field components tangential to it that couple back a current density into these same field components. For this problem, the radiating thin wire (actually three segments) is terminated with 50 ohms on each end and driven by a voltage source (gaussian pulse) near one end. Wire current is probed at the source node to allow computation of a wire current-to-E-field transfer function. As noted above, shielding effectiveness is the difference between transfer functions with and without the shield of interest in place.

EMI Gasket Analysis and Modeling The EM1 gasket can be modeled as a l-cell wide isotropic surface since radiation effects due to gasket inadequacies at the gasket location will be driven by the length (long dimension) of the resulting “slot.” However, inaccuracy could result from macroscopic frequency dependence if the gasket cross-section is notably smaller than the cell dimensions and the material conductivity is low, thus warranting consideration and examination. Aside from macroscopic frequency dependence, the important focus is to understand how the FDTD algorithm handles input parameters to the “surface” formalism. The FDTD code used for this problem handled isotropic surfaces as being l-cell deep: the input conductivity, permittivity, and permeability are applied against a l-cell thickness.

It is best, and usually quite simple, to measure the gasket conductivity on the host product as opposed to using a vendor’s data, as the end product’s gasket pressure, mounting, etc., often yield dramatically different results. For the example problem, the “installed” gasket conductivity was determined by taping over all the gasket material with very thin tape, except for a 1 cm length, and measuring the resistance across the joint when that product area was assembled. To facilitate measurement, the coated glass was replaced with an aluminum plate of the same thickness. The measurement showed 0.72 ohms. Noting that:

R = Length /

ohms ug . Cross-section-area (5)

we can compute that the gasket material model conductivity, os, and find that it must be equal to 139 S/m for a 1 cell (0.005 m) long bond with a cross-section area of 1 cm x 1 cell.

Thin Shield Analysis and Modeling As with the EM1 gasket, the conductivity of the thin shield coating can be measured from actual samples. However, surface resistance, the common measurement and specification item for thin coatings, is expressed in ohms per square and computations in FDTD analysis are

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based on a material conductivity. Thus coating thickness must by considered. For the problem shown here, the surface resistance of the thin shield was 9 ohms per square and the coating was 1400 Angstroms (1400 x 10-i’ meters) thick. Assuming uniformity, this equates to a material conductivity of 0.79 x lo6 S/m.

Simulation using FDTD with the thin surface requires special attention, especially if the thin surface is very thin and/or a poor conductor, where the cell dimension is much less than its skin depth over the frequency range of interest. However, the cell dimension (0.005 meters) is larger than the skin depth of the above mentioned material, over the frequency range of interest. Noting that skin depth, and more importantly, absorption, reflection, and re-reflection vary as complex functions of conductivity, it is not simple to model the thin surface as a standard l-cell thick isotropic finite difference surface. However, special formalisms for FDTD that have evolved for thin composite materials work well in allowing the coating thickness to be considered and thus simplify problem setup and increase accuracy. The thin/composite surface FDTD modeling methodology used for this analysis is described in [6].

Field Probing Integration using the free-space Green function with the Lorentz condition (gauge) to determine E-field (or H-field) strength, yields a vector quantity. Because of the scattering involved for a particular configuration, the dominate field component varies as a function of frequency. In most military and aerospace EM1 emissions compliance measurement setups, the environment is not free space and thus reflections from the EMI shield room will influence the dominate field component/polarization seen at the measurement point. Variation will be a function for frequency. Thus analysis results (shielding effectiveness and/or absolute field strength) addressing each component individually may be cumbersome and have little practical use for the EMI-compliance situation. This is especially true under the MIL-STD-461D and DO-160D conditions where peak detection is required and compliance must be present under both horizontal and vertical polarizations. If a mode stirred or mode tuned chamber is used for emissions measurement, polarization information is altogether lost. Thus shielding effectiveness and field strength results were based on the vector sum of all three components in the frequency domain. This especially works well since the thrust of the analysis/simulation is to determine trends.

Overall Model Space and Computation Parameters The subject problem, which included the metal surface ground plane, shown in Figure 1, was meshed in rectangular coordinates using 0.5 cm cells in all three dimensions. The far-field integration surface was located 10 cells from the bounds of the modeled objects. The start of an S-layer Perfectly Matched Linear (PML) boundary was placed five cells out from the far-field integration surface. Not counting the PML boundary, the problem space was 171 x 117 x 93 cells (1.86 x lo6 cells total). The time step was set to 8 pS, with each simulation completed to 12,500 steps (100 nS), as this provided at least 70 dB of difference in the peak time domain responses between the early part of the simulation and the late part of the simulation. As good practice, the models with the best shielding were run out to 25,000 steps to assess the frequency domain effects from time domain waveform truncation (none were noted greater than 1 dB).

Using a moderately loaded HP C 180 workstation with 500 MB of RAM, runtime for a 12,500 step simulation varied between 20 and 26 hours, depending on other concurrent CPU and memory loading on the workstation. RAM usage for the FDTD simulation was 286 MB.

SIMULATIONRESULTS

The shielding effectiveness of the 23 cm wide x 24 cm high x 6 cm deep enclosure, as shown in Figurel, was determined using 3-D FDTD simulation for conditions shown in Table 1.

IIDI DescriDtion Cl2 139 S/m* gasket on 4 sides, 1460 A, 9-ohrn/sq IT0 Cl3 Copper (5.8 x IO-’ S/m*) gasket. on 4 sides, 1400 A,

9-ohrn/sq IT0 Cl4 139 S/m* gasket on top, bottom, left side, 1400 A,

9-ohm/sq IT0 Cl5 0.139 S/m* gasket on 4 sides, 1400 A, 9-ohm/sq IT0 Cl6 139 S/m* gasket on 4 sides. 1400 A. 2X-ohm/sa IT0

1 Cl7 1139 S/m* gasket on left & right sides, 1400 A, 1 9-ohm/sqITO

Cl8 139 S/m* gasket on top & bottom sides, 1400 A, 9-ohrn/sq IT0

* Cell property translated from material measured or property.

Table 1. Configurations Analyzed

The overall E-field shielding effectiveness results are shown in Figure 2. Figure 3 shows the wire current-to-E-)eld transfer function for contiguration C12. Most notable from Figure 2 is the fact that little shielding was seen between 10 and 50 MHz, and that the “weak link” in providing good high-frequency shielding was the display coating, not the continuous EMI gasket. This was observed in radiated emissions testing of an enclosure with these features. Although the thin coating was shown to be the most notable degrading aspect of high frequency shielding effectiveness when a continuous gasket is used, it is seen that removing the bond from the sides of the coating causes notable shielding degradation due to slot radiation. Also, as shown in Figure 2, increasing the conductivity of the thin coating notably increased shielding at frequencies above 20 MHz. For frequencies above 100 MHz, the configuration with a typical military/air transport environment silver-filled elastromer EMI gasket (i.e. configuration C12), a 10 dB increase of shielding was seen for a 10 dB increase in the conductivity of the thin coating.

Figures 4 and 5 show actual test results, with Figure 4 showing radiated emissions results for the unshielded configuration and Figure 5 showing emissions for the shielded configuration. Note from these plots that not all the emissions are from the front area of the enclosure. At 200 kHz, the analysis predicts about 35 dB of shielding, and as shown in Figures 4 and 5, this is adequate to bring the emissions that were approx. 20 dB above the limit, to at least 10 dB below the limit. At 25 MHz, we see an actual shielding of about 4 dB, as predicted by the simulation.

We can use the wire-to-field transfer function data to compute the field strength at 1 meter from a 25 MHz, 0 to 5 volt, 50 ohm signal being driven through the radiator into a 50 ohm load. This is representative of the situation illustrated in Figure 1 where a signal is routed on a ribbon cable without a controlled return conductor or integral return plane. As shown in Figure 3, the transfer function is -32 dBV/m per Ampere of wire current. Thus if the 25 MHz signal has a 2.5 Volt DC component (-6 dB), we would predict a field strength of: -32 dBV/m per Ampere + 2OZog(5 volts / 109 ohms) - 6 dB + 120 dBuV/m - dBV/m = 55 dBuV/m. (From Figure 6, we see that the loaded radiator impedance is 109 ohms at 25 MHz.) The actual

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shielded enclosure that was the base for model configuration Cl2 showed test results (see Figure 5) of 52 dBvV/m at 25 MHz,

which is only 3 dB from the predicted value.

Overell E-field Shielding Effectiveness

1 .E+O5 1 .E+O6 l.EW7 1 .E+O8

Frequency (Hz)

1 .E+O9 l.E+lO

Figure 2. Overall E-field Shielding Effectiveness

_ _ _ _ Comp. A - Comp. B - Comp. C -+- Xkr Sum 1

40 I I l/llllI I I IIIIIII I I llllllI I III

9” E-field Trensfer Function for Configuration 12, Pt 50 * L”

0

-20

-40

-60

-60 ~

-100 i-titilll I IllrI~ -5, 1 .E+O5 1 .E+OB l.E+07 1 .E+O8 1 .E+O9 1 .E+lO

Frequency (Hz)

Figure 3. Wire Current to E-field Transfer Function for Configuration 12

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RAOIATED EM1 (150kHz-1.215GHz) NARROWBAND RADIATED EM1 (150kHz-1.215GHz) NARROWBANO

Figure 4. Radiated Emissions -No front Shield Figure 5. Radiated Emissicks - Cl2 Front Shield Added me *-

8 800 5 w 600

g E

400

200

1 1 Source Wire Impedance’- Configuration Cli

l.BO6 l&O7 Is308 lx+09 l.E+lO Frequency (Hz)

Figure 6. Source Wire Impedance for Configuration Cl2

CONCLUSION

In summary, we have shown how 3-dimensional FDTD analysis and simulation can be set up and used to examine trends in shielding effectiveness of enclosures that use thin shields and EM1 gaskets. The ever increasing capability of desktop computing resources now allows the practicing EMI/EMC engineer to use FDTD analysis to focus in on product compliance. Additionally, it was shown that not only can FDTD analysis lend insight to radiation and shielding trends: it can also yield quantitative results close to measured values.

REFERENCES

[l] A. Taflove, Ed., Finite Difference Time Domain Methods for Electrodynamic Analysis, Artech House, NY, 1995.

[2] K. Kunz and R. Luebbers, The Finite Difference Time Domain Methodfor Electromagnetics, CRC Publications, Inc., Boca Raton, FL, 1993.

[3] S. D. Gedney, “ The Application of the Finite-Difference Time- Domain Method to EMC Analysis”, Symposium Record, IEEE 1996 International Symposium on Electromagnetic Compatibility, Santa Clara, CA, August 19 - 23,1996.

[4] R. A. Perala, T. H. Rudolph, P. M. McKenna, Application of the Time Domain Three Dimensional Finite Difference Method to a Wide Variety of EMC Problems, Proceedings of 1992 Regional Symposium on Electromagnetic Compatibility, Tel Aviv, Israel, November 1992.

[5] D. T. Paris, F. K. Hurd, “‘Basic Electromagnetic Theory”, McGraw-Hill Book Company, New York, 1969.

[6] P. M. McKenna, T. H. Rudolph, R. A. Perala, A Time Domain Representation of Surface and Transfer Impedances Useful for Analysis ofAdvanced Composite Aircraft, Proceeding of International Aerospace and Ground Conference and Static Electricity, June 1984, Orlando, FL.

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