Proc. of the 2014 International Symposium on Electromagnetic Compatibility (EMC Europe 2014), Gothenburg, Sweden, September 1-4, 2014
A fast method for estimating shielding effectiveness of an enclosure with apertures Ali Shourvarzi and Mojtaba Joodaki Department of Electrical Engineering Ferdowsi University of Mashhad Mashhad, Iran
[email protected],
[email protected] shielding (e.g. absorption, reflection, etc). This method is mostly in use for the enclosures without apertures. It shows that for the metal enclosures especially at the higher frequencies, SE is normally in an appropriate range.
Abstract—A new and fast method to determine the shielding effectiveness (SE) of an enclosure with aperture is proposed. This method is based on the Z-parameter analysis combined with a circuit theory to define which configuration of the apertures can result in the optimum SE. The method is based on the fact that an aperture with the least destruction in the current flow due the incident field will have most effective canceling field. To show the effectiveness of the method and its excellent capability in estimating SE two examples, which have been numerically investigated in recent literatures, are solved. The simulation results of this fast and simple technique fit very well with those of the complex and time consuming numerical approaches. Furthermore, using this method the designer is able to recognize the problematic points and easily can optimize the shielding geometry.
Another approach in defining SE (especially for enclosures with apertures) is followed through circuit theory. As a matter of fact at higher frequencies, the effect of apertures is of the major importance comparing to the effect of the geometry or shield material [5]. In the rest of this paper these issues will be discussed: The principle of operation and the circuit theory approach will be presented in section 2. In section 3, a brief introduction to Zparameters will be presented and consequently the new method for estimating SE will be proposed. In section 3, two examples will be simulated through the proposed method. In these examples, it is tried to determine the preferred aperture size and the number of apertures which results in the optimum SE. Both of the examples have been analyzed recently utilizing numerical methods [7]. In the final section, a conclusion of the whole previous sections will be discussed. All simulations implemented here to show the effectiveness of the new approach utilize a commercial 3D full-wave electromagnetic simulator (CST 2013).
Index Terms—shielding effectiveness; enclosure with aperture; Z-parameters; S-parameters; circuit theory
I.
INTRODUCTION
The trend to increase the frequency and integration density in the electrical equipment has made the electromagnetic compatibility (EMC) a considerable issue. In this regard, shielding is one of the most remarkable EMC procedures. There are two general methods for electromagnetic shielding: shielding the source and shielding the victim. An enclosure can be utilized for both methods. Designing an enclosure with its apertures is an attractive subject in EMC studies in recent years [1-4].
II.
To estimate the effect of aperture on SE three parameters are of the major importance:
While handling the EMC issues, the best strategy which reduces the costs and increases the performance of the system, is to determine the major parameters before the fabrication, especially in the design level [5]. These primary tests and considerations can be accomplished through different approaches, e.g. numerical/analytical simulations, modeling, experimental simulations (i.e. experiments in lower levels and sizes), and etc.
9
The maximum linear dimension,
9
The wave impedance,
9
The frequency [5].
The circuit theory can be utilized to modify the maximum linear dimension effect. Through this theory, it can be mentioned that: an incident electromagnetic field can lead to flow a current on the enclosure. This current will results in additional fields. Some of these additional fields are able to oppose and cancel the primary incident field. This mechanism is shown in Fig.1. The aperture can ruin the optimum path for this current and destroy the opposing filed and as a result reduce the cancellation of the incident field. So, the mission is now obvious: design the aperture in a way that results in the
Considering figures of merit to estimate the efficiency of the shielding, shielding effectiveness (SE) is a major parameter. There are several approaches that can be utilized to initialize SE. One of these approaches is introduced by Schelknoff [6] which considers initializing SE through a transmission line approach. In this regard, it divides the measurements to different mechanisms that can participate in
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PRINCIPLES OF OPERATION
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Proc. of the 2014 International Symposium on Electromagnetic Compatibility (EMC Europe 2014), Gothenburg, Sweden, September 1-4, 2014
IV.
SOLVING SOME EXAMPLES BY THE PROPOSED METHOD
A. Finding the optimum aperture sizes Suppose that the area of a rectangular aperture is known and the lengths of its dimensions are free to choose. The aim here is to choose the best lengths for the sides to have the optimum SE. In an article it was shown by Method of Moments (MoM) that the optimum SE can be achieved by a square aperture [7]. This issue is now simulated through the proposed method in this research (calculating Z-parameters). The test structure for this simulation is shown in Fig.2. As it can be seen, two discrete ports are placed at the top and bottom of the aperture and a perfect electric conductor (PEC) is utilized as the common terminal of the ports. Simulation results for the z-parameters, for three different sizes of the aperture with constant area, are shown in Fig.3. As it can be seen, the square aperture has the least Z12. In another simulation the electric field inside the enclosure, after applying a TEM wave to the enclosure is measured for all three cases of the aperture sizes. The results are shown in Fig.4. There is a conventional definition of SE in the literature:
Figure 1. The circuit theory approach to explain the shielding mechanism for enclosures.
least destruction in the flowed current. So the opposing field can cancel the incident field better and less internal field will be detectable in the middle of the enclosure. The final achievement will be the optimum SE.
III.
SE
THE PROPOSED METHOD
The main idea in this research is to utilize Z and Sparameters in finding the best aperture designation through the circuit theory approach.
Z 21
0
Contemplating the relationship between Z-parameters and S-parameters in (4), (5), and (6), it will be concluded that Z11 (or Z22) is an expression of reflection. So, the greater Z11 (or Z22) shows the better SE. In the next simulation, Z11 (or Z22) is shown in Fig.5 to discuss about. As it can be seen for the square aperture, the Z11 (or Z22) is of the greater value which results in better SE. Again, it shows the justifiable performance of the proposed method.
(1)
where V2 is the voltage of port 2 and I1 is the current in port 1 when the current in port 2 (I2) is equal to zero (port 2 is opencircuited). The idea of this paper originates from this fact that the greater V2 due to I1 (in other words greater Z21), results in the worse path for the current. Comparing this fact with the circuit theory approach discussed in introduction, it can be concluded that less Z21 leads to the better SE. From the other point of view, Z12also can be mentioned (2). The greater current in port 2 (I2) as a result of a constant voltage in port 1 (V1), the better SE can be achieved. This shows the inverse relation between Z12 and SE.
Z12
V1 I 2 I1
0
(3)
Where Eout is the incident field which is outside of the enclosure and Ein is the internal field which is inside the enclosure.Based on (3), the lower this internal field results in the higher SE. A comparison between Fig.3 and Fig.4 indicates that lower Z12 is consistent to the lower internal electric field and consequently greater SE. For the square aperture the least Z12 is the case of the least internal electric field and the best SE. These results prove the efficiency of the proposed method.
Z-parameters (impedance parameters) are suitable symbols to define the electrical behavior of linear networks in electrical engineering. Each parameter is the result of a voltage over a current due to its subscript. In a 2 port system, Z21 is defined as:
V2 I1 I 2
Eout Ein
Z11
((1 S11 )(1 S 22 ) S12 S 21 ) Z0 's
(2)
These facts result in this idea: the aperture designation is more suitable that causes less destruction in impedance integrity. In the other words, if the aperture size and the number of apertures have been chosen in a way that causes less Z12 (or Z21), this is the case that leads to the optimum SE.
Figure 2. The simulation set up (the enclosure dimensions are 300mm×120mm×300mm)
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Proc. of the 2014 International Symposium on Electromagnetic Compatibility (EMC Europe 2014), Gothenburg, Sweden, September 1-4, 2014
Fig.6 shows the S-parameters in all three different aperture sizes. Fig. 6-a shows the analogy of the S11 and SE (like Z11 and SE) as it was expected. The relationship between S21 and Z21 shows that they are proportional and this proportionality can be seen in Fig.6-b, too. In other words, less S12 leads in better SE. So another way to optimize the aperture size is to minimize S12. B. Finding the more appropriatenumber of apertures Suppose that the area in need for the aperture on the enclosure is fixed, but you can fulfill this area by one or two aperture. In this section, it will be discussed that which way leads to a better SE. In the same article that was mentioned in the previous example, it has also been derived that an enclosure with two apertures has better SE comparing with an enclosure with one aperture but with the same area [7]. In this subsection, the same issue will be investigated, utilizing the new proposed method. Fig. 7 shows the enclosure with two apertures. In Fig.8, the Z21 parameter of this enclosure will be compared with the Z21 of an enclosure with one aperture but with the same total area. It can be observed that if the area in need, divided between two apertures, the SE will be promoted. It is the same result that the mentioned article have been acquired utilizing MOM.
Figure 3. Z21 parameter for different aperture sizes: Solid (red/circle): 4cm×4cm, Dashed (blue/triangle): 2cm×8cm, Dotted (green/cross): 1cm×16cm
Figure 4. The inner electric field { dBV/m) of the enclosure for different aperture sizes: Solid (red/circle): 4cm×4cm, Dashed (blue/triangle): 2cm×8cm Dotted (green/cross): 1cm×16cm
Figure 5. Z11 parameter for different aperture sizes: Solid (red/circle): 4cm×4cm, Dashed (blue/triangle): 2cm×8cm, Dotted (green/cross): 1cm×16cm
Z 21
2S 21 Z0 's
(5)
where Z0 is the characteristic impedance and 's can be defined as follows:
's (1 S11)(1 S22 ) S12 S21
Figure 6. (a) S11 parameter, and (b) S21 parameter for different aperture sizes: Solid (red/circle): 4cm×4cm, Dashed (blue/triangle): 2cm×8cm, Dotted (green/cross): 1cm×16cm
(6)
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Proc. of the 2014 International Symposium on Electromagnetic Compatibility (EMC Europe 2014), Gothenburg, Sweden, September 1-4, 2014
a more destruction in the induced current. This destruction will decrease the opposing field and pull down the cancelation of the incident field and finally the SE will be reduced. These issues were tested and simulated in two examples. In the first example, the best aperture sizes for a rectangular aperture, with fixed area, were estimated. It was shown by the new method that for a square aperture the best SE will be obtained which is in adoption with the literature and previous studies. In the second example the preferred number of apertures for a specified aperture area was predicted by the proposed method. It was proved that two apertures with the same total area results in a better SE than that of with one aperture. These results have excellent agreements with the literature and previous researches. Consistency of these examples with the science shows the efficiency of the proposed method. In addition, the method is considerably simpler and more time consuming comparing to the conventional methods.
Figure 7. The enclosure with two apertures with the same area of one aperture. The material properties of the enclosure are also available in this figure.
REFERENCES [1]
[2]
[3] 2
Figure 8. Z21 parameter for an enclosure with aperture area of 16 cm : Solid (red/circle): one 2cm×8cm aperture, Dashed (green/cross): two 2cm×4cm apertures
V.
[4]
CONCLUSIONS [5]
A new and fast method for estimating SE of the enclosures was proposed. This method can be utilized to find the suitable geometrical parameters to have the optimum SE. The method is based on a circuit theory approach which discusses about the induced current of the incident field and the induced opposing filed of this current. This method in based on Z-parameter analysis of several ports on the shield. The greater Z21 results in
[6] [7]
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