A. Radiation of the Reference Board
Fig. 6 shows the simulated and measured EMI at 3m for the reference board, which configuration is shown in Fig. 2(a), with the excitation being located at (6cm, 6cm). The geometrical parameters of the reference board are cm, h = 1.6mm, and the dielectric constant ε
10 a b= =
r of the embedded substrate is 4.3. The CW exciting source of 20mV is swept in frequency from 200MHz to 2GHz. The agreement between the measurement and simulation is in generally good and can assure both the accuracy of our FDTD modeling approach and the correctness of the EMI measurement setup. It can be seen that the ignorance of the conductor loss in the numerical modeling results in higher peaks at resonance than in the experimental results, but the frequency variations are the same. As shown in this figure, the radiated emission is increased significantly at the resonant frequencies 0.72GHz, 1.05GHz, 1.45GHz, and 1.65GHz because the power planes act like a patch antenna and radiate effectively the at these frequencies. These resonant frequencies fmn can be predicted by the cavity model [23] of the microstrip antenna with
(8)
2 εr a b
2 2
( ) ( )
mn
c m n
f = +
where c is the light speed and (m, n) is the mode numbers of TMmn mode. The corresponding mode numbers of these resonant frequencies are denoted in this figure.
Because the tested board is geometrical symmetry with a b= , TM10 and TM01 modes are degenerate with the same resonant frequency and so do TM20 and TM02 modes and TM21 and TM12 modes. The resonant frequencies both estimated by the cavity model
and calculated by our FDTD approach are listed in Table I and compared with the measurement results. It is seen that they are quite consistent. The resonant behavior can also be seen in the measurement of S21. Fig. 7 shows the calculated and measured with the exciting and receiving port being located at (5cm, 4cm) and (4cm, 8cm), respectively. The agreements between the measured and simulated results are also favorably good. It is clearly found that significant power is transferred to the receiving port at those resonant frequencies 0.72GHz, 1.45GHz, and 1.65GHz. The TM
| S |21
11 mode at 1.05GHz is not excited due to the excitation in on the centerline of the tested board.
B. Isolation Effect on Radiation
To eliminate the radiation problems caused by the GBN on the reference planes, an intuitive way in practical PCB is isolating the noise source by a surrounding etched slit (or called moat). The effect of the isolation moat on the radiated emission caused by the GBN is discussed in this section. The EMI behavior of an isolated board, which configuration is shown in Fig. 2(b), with the moat of cm being located at the center of the PCB board are both simulated and measured and presented in Fig. 8. The slit width is set to s = 1mm. The slit, which is narrower than the cell size, is modeled by the contour integral interpretation in our FDTD approach [24].
Compared with the EMI of the reference board, it is seen that the radiation at the resonant frequencies 0.72, 1.05, 1.45, and 1.65GHz are significantly reduced about 20 to 30dB by the etched slit. Because the cavity resonance structure is destroyed by the moat and the GBN is completely isolated inside the etched slit, the resonant conditions for those resonant modes appearing in the reference board are no longer satisfied in the isolated board and, thus, the resonant modes can not be excited to radiate efficiently through the isolated board structure. However, significant radiation can be found at frequency near 1.74GHz for simulation and near 1.77GHz for measurement. This phenomenon is resulted from a new resonant TM
4 c d= =
10 mode excited in the smaller cavity (4cm × 4cm) formed by the slits. The discrepancy of the
resonance frequency between the calculation and the measurement may be caused by the non-equivalence of the dimensions between the experimental board and the numerical model due to the machinery tolerance. The appearance of this mode can also be verified by the measurement of S21 of the isolated board. Fig. 9 shows the calculated and measured up to 3GHz with the excited and receiving locations being (5cm, 4cm) and (6cm, 6cm) respectively, where both ports are inside the moat.
The resonance behavior inside the smaller cavity at 1.74GHz is obviously seen. It could be found that completely isolating the switching noises by the etched slit is an effective way to eliminate the EMI problems caused by the SSN for frequency below the fundamental resonant frequency of the smaller cavity formed by the moat.
| S |21
C. Bridging Effect on Radiation
However, connections bridging the two sides of the slits may be necessary for the equal potential DC reference or for supplying the RF return current for signal traces crossing the moat. Therefore, we next discuss the EMI behavior of the bridged board, which configuration is shown in Fig. 2(c), with the bridge being located at the center of the right-side slit and the bridge width w = 6mm. The other geometrical parameters are the same as those in the previous case, i.e., a b= =10cm and h = 1.6mm, cm, and s = 1mm. The exciting noise is at (6cm, 6cm). Fig. 10 demonstrates the simulated and measured EMI strength at 3m for the bridged board.
The consistency between the modeling and measurement is in generally good. The calculated radiation of the isolated board is also plotted in this figure for comparison.
It can be clearly found that the bridge electrically connecting two sides of the slit significantly degrade the EMI performance of the isolated board. Compared with the EMI of the isolated board, relatively strong radiation for the bridged board can be seen at the frequencies near 0.44GHz, 0.69GHz, 1.02GHz, and 1.29GHz. It is evident that the moat is no longer effective in isolating the switching noise at those resonant frequencies if a bridge is built on the moat either to supply a return path for high frequency signals or to supply same voltage potential between two sides of the moat.
4 c d= =
The corresponding mode numbers of those resonant frequencies are denoted in Fig.
10. At higher frequency near 1.78GHz, it is seen that both the isolated and bridged boards behave significant radiation due to the TM mode of the smaller cavity formed by the square 4cm × 4cm moat. An interesting point that is worth noting is that there is an additional resonance mode with the resonant frequency being lower than that of the fundamental mode. This new resonant mode, hereafter called -like mode, behaves strong radiation at about 0.44GHz and does not appear on the reference board. The new resonant mode can also be seen both in the simulation and measurement of | for the bridged board at frequency below 1GHz. As shown in Fig. 11, significant power is transferred from the excitation port at (6cm, 6cm) to the receiving port at (1cm, 9cm) at the resonant frequencies of the mode and -like mode. The calculated of the isolated board is also plotted in this figure and we can obviously find the isolation effect is significantly degraded about 40dB by the connection bridge at the frequency near resonance and about 20-30dB in between the resonant frequencies. The vectorial plots of the current distribution, solved by the 3D-FDTD modeling approach, on the power plane of the bridged board could help us understanding the radiation mechanism of these two resonant modes. Fig. 12(a) and 12(b) show the current patterns of the -like modeand mode, respectively. It is obviously seen that the currents flowing on the power plan inside and outside the moat have the same direction for the mode, but have opposite direction for the -like mode. This current distribution could imply that the TM mode and -like mode seem operating in the resonant cavity with different effective length equal to the length of the dashed line shown in Fig. 12. It can be found that the TM -like mode operates in the effective cavity with longer l than the TM mode does and this phenomenon could explain why the -like mode has the resonance frequency lower than of the
mode. The resonant frequency of the -like mode could be estimated by the concept of the cavity model and is expressed as
10
(9)
f0 = c
2leff εr
, which is obtained from (8) with (m, n) = (1, 0) and the real cavity length a being replaced by the effective cavity length . For the previous case of the bridged board, the effective length of -like mode is about 17.5cm and the corresponding resonant frequency is about 0.42GHz by (9), which is very close to the simulated and measured value of 0.44GHz.
leff 10
leff TM
Often the partially partitioned board configuration, as shown in Fig. 2(d), is employed in the layout of high-speed PCB circuits. The bridge is connected on the ground plane for the same ground reference and the complete isolation by slit is etched on the power plane for different DC power level considerations. Fig. 13 presents the calculated and measured EMI at 3m distance for the partially bridged board with the bridge width w = 6mm. The geometrical dimensions of the partially bridged board is the same with those of the bridged board in the previous case, i.e.,
cm and h = 1.6mm,
10
a b= = c d= =4cm, and s = 1mm. The excitation noise is also positioned at (6cm, 6cm). Strong radiations can be seen at the frequencies near 0.56GHz, 0.69GHz, 1.02GHz, which is corresponding to the resonant modes of -like, , modes, respectively. The resonant mode of is not excited in the configuration of the partially bridged board and significant radiated emission can also be seen at the frequency near 1.71GHz due to the mode in the smaller cavity surrounded by the moat. As shown in Fig. 13, the -like mode is also excited in the partially bridged board with resonant frequency about 0.56GHz.
The agreement between the calculation and measurement implies that a bridge just connecting on one of the power/ground planes will not only significantly reduce the isolation ability of the etched slit, but also excite an additional resonant -like mode with strong radiations at the frequency lower than that of the fundamental
mode.
TM10
TM10
TM10 TM11 TM20
TM10 10
TM TM
10
Next we numerically discuss the bridge designs and their influence on the EMI behavior of the bridged board. Fig. 14 shows the effect of different locations of the bridges on the radiations of the bridged board. As shown in the inset of this figure, the bridge of case A, B, and C are positioned at near (7cm, 5cm), (7cm, 7cm), and (7cm, 6cm), respectively. It can be seen that both the radiation strength and the resonant frequency for - like, , and smaller cavity modes behave little difference between those three cases, but significant difference in the radiation intensity can be found for and TM modes. For case B the mode is not excited and the mode appears with strong EMI, but for case A, opposite to case B, the TM mode is excited with strong radiation and the TM mode behaves relatively weak emission. This impact of the bridge position on the radiation behavior of these two higher order modes could be explained by their corresponding current patterns. Fig. 15(a) and 15(b) plot the current distributions of the mode in case B and modes in case A, respectively. As shown in Fig. 15(a), the mode could be well excited in case B because the bridge located at the corner of the moat supply a current path which is consistent (or parallel) with the current distribution of the mode near the bridge, but the mode could not be easily excited since the direction the current distribution of the mode near the bridge is orthogonal to the direction of the current supplied by the bridge. As shown in Fig. 15(b), the reason that the mode behaves relatively stronger radiation than the mode in case A could be the same with that in case B. The measured EMI strength of these two higher-order modes for case A and case B, whish are presented in Table II, support the previous explanations. It is seen that the radiation strength of the mode for the bridge positioned at the corner (case B) is about 6dB higher than that for case A, and the strength of the mode for case A is about 8dB higher that that for case B. The bridge could be considered as an excitation path for the resonant modes of the 10cm × 10cm board cavity. Changing the bridge locations may excite different higher-order modes with different EMI behavior, but it could be emphasized again that the radiation behavior of fundamental - like and
TM10
TM modes are relatively less sensitive to positions of the bridges. Finally, the 10
bridge width effect on the radiation behavior of the bridged board is discussed. Fig. 16 shows the EMI behavior of three different bridge width, 2mm, 6mm, and 10mm. The bridge is positioned at (7cm, 5cm). The influence of the bridge width on EMI behavior is in generally not significant for the - like, modes, and TM modes in the smaller cavity, but it can be seen that the resonant frequencies of - like and TM modes are slightly shifted to lower range as the bridge width is decreased. Significant differences of the radiation behavior are for the case of narrower bridge 2mm. It can be found that the radiation strength of the mode and the mode is relatively weaker for 2mm bridge than the other cases of wider bridges. The bridge can be modeled as a lumped inductor. The inductance (L) increased as the bridge width is decreased. For higher-order modes with higher resonant frequencies, the impedance (
TM10 TM10 10
TM10 10
TM20
TM11
j Lω
= ) of the narrower bridge becomes significant to isolate the noise from coupling to the outside of the moat and, thus, cause lower EMI strength. According the above discussions, it may be summarized that the EMI behavior of the - like and modes are less sensitive to the variation of the bridge location or bridge width, but the radiation behavior of higher order modes, such as TM and modes, are more sensitive to those geometrical parameters.
TM10
TM10
TM10
11 TM20
10