Fast Calculation of Radiated Emissions fromArbitrarily Shaped PCB with IC/LSI

Masahiro Nishida*, Yoshitaka Toyota*, Kengo Iokibe*, Ryuji Koga*, Osami Wada** *Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530 Japan

**Graduate School of Engineering, Kyoto University, Kyoto 615-8510 Japan

Abstract: This paper describes fast calculation of radiated emissions from an arbitrarily shaped printed circuit board (PCB). The radiated emissions from the PCB edge are calculated by taking into account magnetic surface current based on the field equivalent principle. The electric field at the PCB edge is provided by a fast algorithm the authors have proposed for power-bus resonance in the PCB. The calculation of radiated emission was completed within a few minutes and in good agreement with Finite Difference Time Domain (FDTD) calculation. In addition, an EMI simulation was demonstrated by using a linear macro model of IC/LSI. The calculation results were found to be in good agreement with the measurements. Keywords: PCB, power-bus resonance, cavity-mode resonator model, segmentation method, magnetic current, radiated emissions, EMI simulation

1 Introduction

In the viewpoint of electromagnetic compatibility (EMC) design, it is important to evaluate and control radiated emissions from a printed circuit board (PCB) before production. Therefore, it is required to develop a tool to simulate the emissions quickly and accurately to assist the PCB design.

Recent digital devices densely pack a number of ICs/LSIs, which also behave as a high-frequency (RF) noise source. The electromagnetic noise due to the source is difficult to estimate by characterizing an entire PCB together with such ICs/LSIs. In general, fullwave simulation of the entire PCB requires extremely high calculation cost. Another possible way to simulate electromagnetic emissions from PCB is to divide the PCB into subcomponents and simulate each of them with the most appropriate method in the terms of calculation cost.

Figure 1 shows that electromagnetic interference (EMI) can be characterized by three factors: noise source, transmission path, and antenna. Let us see an

example of radiated emissions due to power-bus resonance in a PCB.

The power-bus resonance is a severe EMI problem because it causes electromagnetic radiation at resonant frequencies. A pair of a power plane and a ground plane, or a “power bus” acts as a parallel plate resonator. At the edge of the power bus, furthermore, electromagnetic radiation occurs. It is an emission antenna. In the actual PCB, the resonance is caused by RF current through IC/LSI power supply terminal due to simultaneous switching noise. In the power-bus noise problem, the noise-source factor corresponds to power supply terminal current of IC/LSI. On the other hand, power-bus structure in PCB plays roles of a transmission path and an antenna.

In order to characterize the power-bus resonance quickly, we have developed a fast algorithm based on a cavity-mode resonator model with segmentation method [1-3]. As a result, the power-bus resonance of an arbitrarily shaped power/ground plane pair is able to be calculated within minutes. The calculation also provides the electric field at the edge of the power-bus.

This paper examines radiated emissions from an arbitrary shaped PCB by taking into account magnetic surface current along the edge of the board according to the field equivalent principle [4]. The calculation result is evaluated by comparison of finite difference time domain (FDTD) calculation.

In the last section, we demonstrate an EMI simulation of electromagnetic radiation from a PCB on which an IC module is mounted. For the simulation, a simulator HISES (High-speed EMI simulator) under development was used with a linear macro model to

EMI AntennaTransmissionpath

NoiseSource=

Figure 1 Characterization of EMI. 1-4244-1372-9/07/$25.00 ©2007 IEEE

describe power supply terminal current of IC/LSI called LECCS (linear equivalent circuit and current source) [5, 6] as a noise source. The EMI simulation is evaluated by the measurement in a semi-anechoic chamber.

2 Radiated Emissions from Arbitrarily Shaped PCB

2.1 Calculation models

Figure 2 (a) illustrates an example of a non-rectangular PCB with IC/LSI. As shown in Fig. 2 (b), the PCB can be rewritten using a cavity-mode resonator model with segmentation method. At the edge of the PCB, there exists a magnetic current model for radiation. The following describes that these models are applied to calculation of radiated emissions from the arbitrarily shaped PCB.

Cavity-mode resonator model An electrically thin rectangular power-bus structure

in PCB is modeled as a parallel plate resonator by using Green’s function to obtain closed-form expression for the impedance Z-matrix [7]. The fast algorithm based on the cavity-mode resonator model was obtained by reducing the original double infinite series to a single infinite series and convergence

acceleration [2]. The additional arrangements enable the power-bus resonance calculation within minutes.

Segmentation method The algorithm based on the cavity-mode resonator

model is available for not only a rectangle but an isosceles right-angled triangle [3]. Segmentation method was applied to arbitrarily shaped PCBs [3, 7]. In Fig. 2, for example, the parallel plate resonator is divided into two rectangular segments. Both segments are connected by virtual ports at their interface, where Kirchhoff’s law must be satisfied. Thereby, Z-matrix of overall segments is generated and expresses the resonance characteristics.

Radiated-emission calculation by magnetic current

The power-bus resonance of arbitrarily shaped PCB is calculated as described above. According to [4], radiated emissions from a rectangular power-bus are calculated by applying the field equivalence principle to the boundary surface of power-bus. This paper examines that radiated emissions from an arbitrary shaped PCB are calculated by combining these models.

Based on the field equivalence principle, magnetic surface currents as radiation source are placed on the side edges of power-bus [4]. As shown in Fig. 3, magnetic current vector on the edge is given by

EnMS , (1)where MS, n, and E are a magnetic current, a normal unit vector on the boundary surface, and the tangential component of the electric field, respectively. Then, the amplitude of magnetic current is given by

hIZhVEM z // noiseedgeedgeS , (2)where Vedge and Zedge are the voltage between two plates and transfer impedance from noise source at the edge, respectively. In addition, Inoise and h are an RF current of the noise source and a thickness of the power-bus, respectively.

In the end, the radiated emissions from the PCB are obtained by integrating radiation from all the magnetic currents along the edge. According to (2), an EMI

RadiatedEmission

IC/LSI:Noise Source

Power-bus Structure:Transmission path, Antenna

High FrequencyCurrent

(a) Schematic diagram of PCB.

Cavity-moderesonator model

Segmentationmethod

Magnetic current loopas radiation source

High FrequencyCurrent

(b) Application of calculation models. Figure 2 Actual structure and model of PCB with IC/LSI.

MS En

Figure 3 Notation of vectors at the edge of parallel plate

simulation due to power-bus resonance will be able to be carried out if an RF power current is given.

2.2 Model Validation

For model validation, resonance characteristics and radiated emissions were examined in comparison with Finite Difference Time Domain (FDTD) method.

Figure 4 shows the test board used for validation. The board consists of two parallel copper plates and a dielectric with a relative dielectric constant of 4.3 and a loss tangent of 0.02. The copper conductivity used for calculation was 710765. S/m. The feeding point on the board is port 1 in Fig. 4.

Figure 5 shows calculation results for comparison. A personal computer (3.2 GHz Pentium 4, 1 GB RAM) was used for calculation. The calculation time of the proposed method was 20 seconds, whereas the FDTD simulation took several tens of hours. This indicates the advantage of the proposed method.

Figure 5 (a) shows reflection characteristics S11 .The characteristics from both methods are in good agreement. Furthermore, Figs 5 (b) and (c) show radiation characteristics, when a voltage of 1 V is given at port 1. Figure 5 (b) shows radiation spectra in the xdirection and Fig. 5 (c) shows radiation patterns in the xy plane at 440 MHz (TM20) where the radiation intensity is a maximum. They are in good agreement within the difference of 5 dB. Thus, the proposed method is found to be applied to non-rectangular PCB.

3 EMI Simulation for PCB with IC

In this section, an EMI simulation for an arbitrarily PCB on which an IC module is mounted is demonstrated.

In the actual PCBs, high-frequency noise currents come from ICs/LSIs. The authors have proposed a frequency-domain model of RF power supply terminal current, LECCS [5, 6]. In this study, the LECCS model was used for the EMI simulation.

The LECCS model, which was applied to EMI simulation and decoupling simulation [5, 6], consists of a linear equivalent circuit and an equivalent internal current source. Model parameters can be determined by measurement of the device because the LECCS model does not have intrinsic design parameters.

In the experiment, an IC module was installed to the board shown in Fig. 4 and connected at port 1. Figure 6 shows the circuit diagram of the IC module, which consists of a CMOS 6-inverter IC (74LVC04)

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Figure 4 Test board with a square hole.

and a 20-MHz crystal oscillator on a 1-inch square four-layer PCB with several passive components. Five inverters were connected in parallel to increase switching noise current.

The equivalent circuit diagram of the LECCS model for the IC module and current spectrum Ii are shown in Fig. 7. The model parameters are derived by measurement and are summarized in Table 1. In the simulation, an additional inductance Lpin+wire of 6 nH is taken into account.

The measurement was performed in a semi-anechoic chamber. The test board and a receiving antenna were set 1 m off the ground and their distance was 3 m. Vertical polarization was measured in eight directions. In calculation, reflection on the floor was taken into account. The calculation of 30 frequencies took 5 seconds on the PC described earlier.

Figure 8 shows a comparison of radiation spectra in the x direction. Both spectra agree within 5 dB in the case of high S/N ratio. Thus, EMI simulation was demonstrated by the proposed method with the LECCS model.

4 Conclusion

This paper described fast calculation of radiated emissions from an arbitrarily shaped PCB. The radiated emissions are calculated using magnetic surface current provided by a fast algorithm the authors have proposed for power-bus resonance in the PCB. We also demonstrated fast calculation of radiated emissions from PCB with IC module. The simulation by the proposed method was in good agreement with the FDTD simulation and the measurement.

References

[1] Z. L. Wang, et al., in Proc. Symp. Electromagn. Theory, EMT-00-68, pp. 17-23, Toyama, Japan, Oct. 2000.

[2] Z. L. Wang, et al., IEEE Trans. Electromagn. Compat., vol. 47, no.1, pp.2-9. Feb. 2005.

[3] Z. L. Wang, et al., in Proc. 3rd Asia-Pacific Conf. Environ. Electromagn., Hangzhou, China, pp. 73-76, Nov. 2003.

[4] M. Leone, et al., IEEE Trans. Electromagn. Compat., vol.45, no. 3, pp.486-492, Aug. 2003.

[5] O. Wada, 17th Int. Zurich Symp. Electromagn. Compat., Singapore, T3-ICPK-1-5, March 2006.

[6] K. Takayama, et al., IEICE Trans. Electron., vol.J86-B, no.2, pp.226-235, 2003 (in Japanese).

[7] T. Okoshi, “Planar Circuits for Microwaves and Lightwaves”, Springer-Verlag, 1985.

FiveInverters

IC

1 5R1(1M)

R2(470)C2(5p)

C1(5p)

TP1

Vcc

GNDFB(Ferrite Beads)

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Figure 6 Circuit diagram of IC module.

Lpin + wireIv

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Figure 7 LECCS model and current spectrum.

Table 1 Model parameters. i Ri ( ) Li (nH) Ci (pF) 1 1.99 7.7 7.5 2 6.7 9.0 3.7 3 0.38 0.75 19

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Figure 8 Comparison of radiation spectra in the x direction