The main parameter to determine the influence of the metal sheath on EMF is SE related to the ratio of the incident and transmitted electric (magnetic) intensities, which are given as (ref. [11] and ref. [14] ):

S E e = 20 lg | E i E t | (1)

S E h = 20 lg | H i H t | (2)

where E i , E t ( H i , H t ) are the incident and transmitted electric (magnetic) intensities, respectively.

Beyond Equation (1) and Equation (2) given above, as shown in Figure 1 the SE can be formed as the sum of the reflection, R [dB], absorption, A [dB] and re-reflection (multiple-reflection), B [dB] which are given follows:

S E [ dB ] = R [ dB ] + A [ dB ] + B [ dB ] (3)

where,

R dB = 168 + 10 log 10 ( σ r / μ r f ) (4)

is the reflection in far field (ref. [14] ),

R e , dB = 322 + 10 log 10 ( σ r / μ r f 3 r 2 ) (5)

R m , dB = 14.57 + 10 log 10 ( f r 2 σ r / μ r ) (6)

are the reflections of electric and magnetic sources in near field, respectively (ref. [14] ),

A dB = 20 log 10 e t / δ = 20 t δ log 10 e = 1.314 t f μ r σ r (7)

is the absorption (ref. [14] ),

B = 20 lg ( 1 − e − 2 t / δ ) , (8)

is the re-reflection (ref. [15] ), δ = ( π f μ σ ) − 1 is the skin depth of the material. μ r is the reversible permeability relative to air. σ r is the conductivity relative to copper. μ is the magnetic permeability of material. σ is the conductivity

of material. t [ cm ] is the thicknees of material. r [ cm ] is the distance between radiation source and metal sheath. The re-reflection B will be meaningful if A ≤ 15 [ dB ] (ref. [14] ), only, consequently it is always really ignored, since A > 15 [ dB ] .

All the results above show that the metal shielding is easy to design, but it needs to eliminate slits and to choose suitable size of holes if they are that depends on technology. So to enhance or perfectly guarantee EMC it is necessary to use distance estimation between RE modules or units combined to metal shielding. As know, the EMF changes with propagation distance, but differently for near and far fields. For the far field, Inverse Distance Method (ref. [15] ) is used to determine radiation noice at distance R and R' (Figure 2), which is given as follows:

E ( R ′ ) [ dB ] = E ( R ) [ dB ] + 20 lg ( R / R ′ ) (9)

The near field is more complex than far field. The field parts change inversely not linear to distance as 1 / r , but nonlinear as 1 / r 2   or   1 / r 3 (Figure 3).

The boundary between near and far fields is where the ratio E / H = Z w called wave impedance is approximately equal to internal impedance of free space η 0 (ref. [15] ).

Consider an aluminium (Al) sheathed box (ASB) with size of 16 × 10 × 3   cm and thickness of sheath of 2 cm (Figure 4). The coaxial cable with copper core of 0.16 cm diameter and impedance of 50 Ω is used to put a radiation source placed inside ASB so that the radiation distribution in the upper space around it is homogeneous (ref. [10] ).

A second ASB with size of 10 × 10 × 3   cm is placed in distance of d from the first one. The CST will be used to evaluate SE for different cases as: single ASB, single ASB with holes in the sheath, two ASBs with different distance one from other. The EMC will be simulated and evaluated at frequency changing from 1 MHz to 1 GHz. Beside using CST to evaluate the SE of proposed solution, the oscillation circuits and power supply with output voltage of 5V is experimentally evaluated using measurement equipment EMxpertEHX consisting from EMxpert software and EMSCAN scanner (Figure 5).

Using Equation (3) and aluminium sheath with t = 0.2 [ cm ] , μ r = 1 and σ r = 0.61 at frequency from 500 kHz (ref. [15] ) the SE-frequency characteristic is calculated and presented in Figure 6. The distribution of electric field inside ASB is simulated and shown in Figure 7.

From Figure 6, we can see that in the frequency band from 30 MHz to 1 GHz of CISPR-22 standard (ref. [6] ), the SE speedily increases, event till 1000 dB. It results that any part of electric field (EF) transmitted outside ASB as shown in Figure 7.

However, the ASB is not always closed tight; instead, there are slits or small holes and apertures used for air ventilation or for cable installation, really. If the slits and holes are not suitble designed, the radiation signal leakage may overcome the standard limit as of CISPR-22 then causes inexpectant effects. Figure 8 and Figure 9 are the distribution of the electric field around the ASB with aperture of 1 × 0.5   cm size. It is clear that with hole there is the leakage outside of radiation signal (Figure 8). The minimum inside electric intensity is about 100 dBμV/m while outside electric intensity is lower than 80 dBμV/m. Specially, the electric intensity at aperture is equivalent to that inside ASB, meanwhile, it is only about 20 - 60 dBμV/m otherwhere (Figure 9).

Figure 10 presents EMC test is measured at distance 3 m followed to CISPR-22 standard (ref. [6] ). Consider that there is a unshielding signal overcomes limit line of EMC standard (dark line). In the case of closed tight ASB, the EF intensity is very small about −200 dB which is the minimum value of simulation.

For the case of ASB with three apertures of different size of 3 × 1.5   cm , 2 × 1.0   cm and 1 × 0.5   cm the EF intensity decreases about 23.1 dB, 48.2 dB and 57.3 dB in comparison to that of inshielding case measured at 500 MHz frequency. This situation is similar to the case measured at a distance of 2 cm (Figure 11).

Using Equation (9) and what described in Figure 2 and Figure 3, the field distribution around the ASB is simulated and presented in Figure 12 and the EF intensity-frequency characteristics at different distances are presented in Figure 13.

From Figure 13, we can see that the electric intensity decreases with the increase of distance till 10 cm at wide frequency range to 1 GHz, but nonlinear if distance is longer than 10 cm. In the distance longer than 10 cm, the electric intensity increases with the increase of frequency. This situation is absolutely similar to that shown in Figure 10 and Figure 11. We can say that the results obtained in Figure 13 are too high, because they are measured in free space. It means the receiver is not EMC guaranteed. The situation will be different for the EMC guaranteed ASB.

Let a second ASB with size of 10 × 10 × 3   cm is placed in distance of d from the first one. The distribution of the EF around both ASBs is simulated and illustrated in Figure 14. It is clear that the EF generated from the radiation source inside the first ASB overlaps a part of the space around the second ASB. Changing

the distance between two ASBs, the EF intensity inside second ASB-frequency characteristics with different distances are simulated and illustrated in Figure 15. From Figure 15, we can see that the EF intensity reduces significantly by shielding and linearly decreases with the increase of distance between ASBs, and consequently the metal shielding, as well as the distance estimation, affects directly on the EMC guarantee.

Although EF intensity decreases with the increase of distance, but it does not reject the influence one on other if both of ASBs are in operation regime. This phenomenon is proved when observing the power supply is placed close to the oscillator circuit without shielding (Figure 16).

From the EF distribution in the plane of scanner (Figure 17), we can see the

EF intensity is relatively hight and unhomogeneous depending on the circuit power of the individual electronic elements. At some positions, it rises to 90 dBuV.

However, the EF intensity reduces significantly when both units are metal sheilded and placed in distance of 10 cm one from other, i.e. is under the EMC guarantee (Figure 18).

From Figure 19 illustrated EF distribution in scanner plane, we see that the EF attenuation is about (25 - 30) dB in comparison to that without EMC guarantee.

It is clear that the electromagnetic noises from radio-electronic units should not act one on other, means the EMC is guaranteed when they are shielded with high SE and placed in a suitable distance.