An improved model for estimating radiated emissions from a PCB with attached cable.
Cable attached on a PCB is a well-known source of unintentional radiated emissions due to its large dimension relative to the PCB . The study on this kind of structure has gained a lot of interest as it is one of the most commonly seen setup of electronic equipment. There are a few recent papers on the study of EMC effect of attached cable and simplified models are proposed to estimate radiated emission from such structure [1-7]. These studies showed that the electromagnetic field coupling of noise sources from PCB traces to the attached cable can be modelled as an equivalent board-cable model driven by a common-mode source. Shim and Hubing showed that the magnitude of this common-mode noise source generated through voltage-driven mechanism was related to the capacitance of the PCB trace and signal return plane . Based on this, Deng et al. proposed that if the magnitude of the common-mode voltage source of such model was known, a closed-from equation can be used to estimate the maximum radiated E field at resonant frequency of such model . Similar approach was taken by Wang et al. to investigate the maximum radiated E field of PCB with attached cable whereby the PCB was shielded with a conducting enclosure . The enclosure and attached cable were modelled as an asymmetrical dipole instead of a monopole as in Deng's method. However, the noise coupling mechanism in an actual product is usually too complicated to be described by a simple equation due to multiple noise sources and coupling paths. Park et al. presented an alternative to circumvent this problem by combining the measured common-mode current on the attached cable and simulation of the Radiation Transfer Function to predict the radiated emission of a box-source-cable model .
In a typical board-source-cable model, unintentional radiated emissions are usually caused by common-mode current induced on the cables by differential mode sources located on the PCB. There are two mechanisms by which this common mode current can be induced on the cable: current-driven (magnetic field coupling) and voltagedriven (electric field coupling) . The current-driven mechanism is associated with the magnetic field that wraps around the finite width of the signal return plane (e.g., ground plane). An effective voltage drop exists across the signal return plane due to its finite impedance and this drives a common-mode current on the cable. This mechanism can be a source of radiated emissions if the impedance of the signal return path is significant; i.e., the width of the signal return path is narrow or the signal frequency is very high .
The voltage-driven mechanism is due to electric field coupling directly from the PCB trace to the attached cable, thus induces a common mode current on the cable. The magnitude of common-mode current induced is directly proportional to the magnitude of the differential-mode voltage source that drives the PCB trace. Referring to the model in Figure 1, it can be seen that the voltage-driven model drives a current through objects referenced to ground against the load connected to the PCB trace. This implies that the voltage-driven emissions can be significantly large when the signal trace capacitively couples to other large conductive object, such as heat sink. When there is no large ungrounded object on the PCB, the voltage-driven emission is less apparent and hence little attention is given to the study of this mechanism. However, Shim and Hubing showed that voltage-driven mechanism can be a significant source of radiated emissions when a cable is attached to the PCB, and a model for estimating voltage driven common-mode current was developed . It was further proved that the voltage-driven mechanism is significant even for the case where the PCB trace is terminated by a matched load. The work of Kayano et al. also showed that even with a terminating load of 49 Q, the coupling mechanism is predominantly voltage-driven type at lower frequency .
The board-cable model driven by a common-mode source developed by Shim and Hubing  has a limitation that the estimated radiated emission is only valid at frequencies below 300 MHz. The attached cable was modelled as a wire antenna and its radiation characteristics with respect to frequencies were considered but the influence of the varying antenna driving point impedances on the magnitude of the induced common-mode voltage was neglected. As a consequence, the common-mode voltage was assumed to be constant over all frequencies and its magnitude was only affected by the PCB board size. This paper is set out to correct this shortcoming and extend the applicability of the board-source-cable model to higher frequencies and yield better accuracy in estimating the EMC radiated emissions. This paper is organized as follows. Section 2 examines the voltage-driven mechanism and limitation of the simplified board-source-cable model introduced by Shim and Hubing. Section 3 introduces an improved method to model the voltage-driven mechanism and shows the derivation of the formula. In Section 4, validations are made to show the improved accuracy in estimating the radiated emission compared with Shim and Hubing method. Section 5 examines the relationship between PCB board area, length of attached cable and the resulting wire antenna driving point impedance, [Z.sub.drive]. A simple equation to approximate the value of antenna driving point impedance is developed by mean of a curve-fitting method using the simulation results of [Z.sub.drive] under different board areas and cable lengths. Section 6 shows the validation of the approximation equation under different conditions. Lastly, some conclusions are made in Section 7.
2. VOLTAGE DRIVEN SOURCE MODEL
Shim and Hubing proposed that a voltage-driven coupling to an attached cable can be represented as an equivalent wire antenna model where the differential-mode voltage source driving the PCB trace (as shown in Figure 2(a)) was converted to an equivalent commonmode voltage source connected between the attached cable and the ground plane (as shown in Figure 2(b)). Based on this model, the relationship between the differential-mode voltage source and the equivalent common-mode voltage source was developed by assuming the charge induced on the attached cable in both cases were the same. The resulting equation was expressed as 
[V.sub.CM] = [[C.sub.t-c]/[C.sub.in]][V.sub.DM] (1)
where [C.sub.t-c] represents the effective mutual capacitance between the trace and the attached cable and [C.sub.in] the input capacitance of the wire antenna model. The equation can be further simplified if the cable length is much longer than the board dimension. The input capacitance of the wire antenna model is approximated as predominantly the self-capacitance of the PCB board, [C.sub.board]. Also, the effective mutual capacitance, [C.sub.t-c] is approximated as predominantly the self-capacitance of the signal trace, [C.sub.trace]. Hence, the simplified equation is expressed as
[V.sub.CM] = [[C.sub.trace]/[C.sub.Board]][V.sub.DM] (2)
However, there is one drawback with this method, i.e., it models the driving point impedance of the wire antenna as a purely capacitive one. This is relatively accurate when the wire antenna is being driven at the frequencies lower than its first resonant frequency. When the frequency increases beyond the resonant frequency, the driving point impedance will start to shift due to the inductance of the antenna, as shown in Figure 3. The simulated [Z.sub.drive] is obtained by running a CST Microwave Studio simulation on a 10 cm x 8 cm board attached with a 6 m cable.
It is noted that although the calculated antenna input reactance based on [C.sub.board] does not exhibit the sinusoidal oscillation characteristic of the CST simulated [Z.sub.drive], its value is close to the average value of the simulated [Z.sub.drive] from 50 MHz to about 200 MHz. Beyond 200 MHz, error in the calculated input reactance starts to increase gradually with frequency. This same characteristic is evidenced in the error between the radiated E-field from CST simulation and the E-field estimated using Shim and Hubing method which will be shown in Section 4. Nevertheless, the varying [Z.sub.drive] suggests that the equivalent common-mode voltage will not be a constant over all frequencies. Instead, it shall oscillate with the similar pattern as [Z.sub.drive].
3. IMPROVED VOLTAGE-DRIVEN SOURCE MODEL
An improved equation is proposed in this paper, taking into account the said characteristic of [Z.sub.drive]. Referring to Figure 2, we shall expect that the common-mode currents induced on the cable [I.sub.CM], for both cases, are the same. In the actual circuit of Figure 2(a), [I.sub.CM] can be expressed as
[absolute value of [I.sub.CM]] = 2[pi]f[C.sub.t-c][absolute value of [V.sub.DM]] (3)
In the equivalent wire antenna model, with [Z.sub.drive] replacing 1/[omega][C.sub.in], [I.sub.CM] can be expressed as
[absolute value of [I.sub.CM]] = [absolute value of [V.sub.CM]]/[absolute value of [Z.sub.drive]] (4)
By equating (3) and (4), the induced common-mode voltage source, [V.sub.CM], can be expressed in term of the differential-mode voltage source, [V.sub.DM] as
[absolute value of [V.sub.CM]] = [omega][C.sub.t-c] [absolute value of [Z.sub.drive]] [absolute value of [V.sub.DM]] (5)
where [omega] = 2[pi]f. If the cable length is much longer than the board dimension, [C.sub.t-c] can be approximated as the self-capacitance of the signal trace, [C.sub.trace]. Hence,
[absolute value of [V.sub.CM]] = [omega][C.sub.trace] [absolute value of [Z.sub.drive]] [absolute value of [V.sub.DM]] (6)
Previous study showed that the self-capacitance of the signal trace can be approximated using a close-formed equation . Thus, the only unknown parameter left in (6) would be the antenna driving point impedance, [Z.sub.drive]. The wire antenna model is essentially an asymmetrical dipole where the cable is driven by a common-mode voltage source against the signal return plane . Ostadzadeh et al. has suggested a method to compute the driving point impedance of an isolated dipole antenna using fuzzy model . However, the same method cannot be applied here as the structure of interest is an asymmetrical dipole. For the asymmetrical dipole, its driving point impedance can be computed from CST simulation.
4. VALIDATION OF THE MODEL
Figure 4 shows a model comprising a conductive ground plane that is 8 cm x 10 cm with a signal trace on top of it. The trace is 5 cm long, 1 mm wide, and 1 mm above the ground plane. The substrate between the signal trace and ground plane is air. One end of the trace is connected to the voltage source, [V.sub.DM] and the other end that is adjacent to the attached cable is terminated with an open circuit. A 6 m cable with a radius of 0.1 mm is attached to the board.
To validate the model, simulation is done using CST Microwave Studio to compute the driving point impedance of the wire antenna model, [Z.sub.drive]. This [Z.sub.drive] is used in (6) to find the corresponding [V.sub.CM] when the model in Figure 4(a) is driven by a 1-V [V.sub.DM]. The [C.sub.trace] in (6) is calculated using the closed-form equation of  and its value is 0.025 pF. The maximum E-field of the wire antenna model at a distance of 3 m is simulated and compared with the one from the original configuration.
Figure 5 shows that the E-field simulated using Shim and Hubing method is reasonably close to the E-field simulated using the original configuration only at low frequencies. Beyond 200 MHz, the error starts to increase with frequency. At 400 MHz, the error of Shim and Hubing method is about 7dB. At 700 MHz, the error increases to about 12 dB.
Using the improved method proposed in this paper, a good match is achieved throughout the frequencies. The error is within 2 dB from 400 MHz to 700 MHz.
5. MODELLING [Z.sub.drive] OF WIRE ANTENNA
From the simulated result, it is observed that the driving point impedance of the wire antenna, [Z.sub.drive] is related to the board area, [A.sub.board] and cable length, [l.sub.cable]. For the ease of curve fitting, [Z.sub.drive] is multiplied with the angular frequency, [omega] to avoid infinitely large value of [Z.sub.drive] at low frequency, i.e., at dc. Figure 6 and Figure 7 show the effect of different board sizes and cable lengths on [omega][Z.sub.drive].
Figure 6 shows that the oscillation magnitude of [omega][Z.sub.drive] reduces significantly with the increase of cable length. Since the magnitude of induced common mode voltage is directly proportional to [omega][Z.sub.drive], as suggested in Equation (6), the effect of the cable length cannot be neglected. Longer cable also gives rise to lower resonant frequency and closer spacing between subsequent harmonics.
Figure 7 shows that the board size can lower the resonant frequency but the effect is not very significant. Larger board area increases the shunt capacitance and reduces the driving point impedance.
In addition to the results in Figure 6 and Figure 7, a large number of simulations are performed to evaluate the effects of different board sizes and cable lengths on [omega][Z.sub.drive]. A curve-fitting method is used to consolidate the various results. A simple closed-form expression that fits the data collected is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
where [f.sub.resonant] is the first resonance frequency of the cable plus board capacitance, in MHz. [f.sub.MHz] is the frequency of interest in MHz. [l.sub.cable] is the length of the cable in meter and [A.sub.board] the area of the board in [m.sup.2]. Since the wire antenna is similar to a half-wave dipole and the cable in a typical setup usually much longer than the board size, the effective length of the wire antenna can be approximated as the cable length, [l.sub.cable]. For a half-wave dipole, the length of the dipole is equal to half the free space wavelength multiply with an adjustment factor, k (l = [1/2]k[lambda]0). The adjustment factor is to compensate for propagation speed somewhat less than the speed of light and its value is typically around 0.95. For simplicity, k is assumed to be 1. Hence,
[f.sub.resonant] = 1/2 x C/[l.sub.cable] x [10.sup.-6] (8)
The cos term in the square bracket of Equation (7) provides an oscillatory pattern which matches the resonant and harmonic characteristics of half-wave dipole as seen in Figure 6. The shorter is the cable, the higher is the resonance frequency, and the wider is the spacing between subsequent harmonics. The magnitude of oscillation in the curve of [omega][Z.sub.drive] decreases with cable length, especially at the higher harmonic numbers. For the same length of cable, the resonant and harmonic characteristics are only slightly affected by the PCB board area as seen in Figure 7. The exponential term in Equation (7) accounts for the gradually increasing [omega][Z.sub.drive] with respect to frequency in which the rate of increase dependens on the PCB board area.
6. EVALUATION OF CLOSED-FORM EXPRESSION
Table 1 shows the comparison between the error in dB of the maximum E-field estimated by Shim and Hubing method and that by the improved method. The error is the difference between the maximum radiated E-field from simulation of the actual circuit and that radiated from the wire antenna models. For the Shim and Hubing model, [V.sub.CM] is a constant as given by (2). For the improved model, [V.sub.CM] varies with frequencies and its values are given by (6) and (7). It is noted that in the six cases that were tested, all of them show much lesser error for the improved method. The improved method has a much better accuracy than Shim and Hubing method, especially at the higher frequency range.
The radiated E-field is related to the induced common-mode current on the wire antenna. A 1.6-mm thick FR4 substrate PCB with conductive ground plane of 8cm x 10cm is built. The signal trace on the top of it is 5 cm long and 1 mm wide. A 1-m long wire is attached to the ground plane in a similar configuration as shown in Figure 4(a). The induced common-mode current [I.sub.CM] on the wire, near the edge of the PCB, is measured using a 9119-1N RFI current probe from Solar Electronics Co. and a spectrum analyzer. RF signal is fed to the PCB trace through an SMA connector. The RF voltage is measured using an RF active probe and a LeCroy 6Zi Digital Oscilloscope. The measured common-mode current [I.sub.CM] is then normalized to a 1 V RF source voltage. The measurement results compared with the simulation results are shown in Figure 8. A good match is achieved throughout the frequencies, although there are small discrepancies due to calibration accuracy of the measurement instruments and sensitivity of the measured common-mode current near the resonance frequency of the open-circuited PCB trace around 800 MHz. Hence, the approximate model developed through EM simulation proposed in this paper for estimating radiated emissions from a PCB with attached cable is experimentally validated.
An improved wire antenna model for estimating EMC radiated emission from a PCB with attached cable due to voltage-driven mechanism is developed and validated. The magnitude of the equivalent common-mode voltage source that drives the wire antenna is expressed in term of the self-capacitance of the signal trace and the driving point impedance of the wire antenna. The self-capacitance of the signal trace can be obtained using the closed-form equation of . The driving point impedance of the wire antenna can be approximated using the closed-form equation developed in Section 5 of this paper. Simulation results show that the maximum radiated E-field from this improved model matches well with the simulation results of the actual circuit. It has a much improved accuracy compared with Shim and Hubing model and can be used to estimate maximum radiated E-field across a wider range of frequency, well beyond the first resonance of the attached cable.
This project is partially sponsored by Intel MSC Sdn Bhd.
[1.] Hockanson, D., J. Drewniak, T. Hubing, T. van Doren, F. Sha, and M. Wilhelm, "Investigation of fundamental EMI source mechanisms driving common-mode radiation from printed circuit boards with attached cables," IEEE Trans. Electromagn. Compact., Vol. 38, No. 4, 557-566, Nov. 1996.
[2.] Shim, H. W. and T. Hubing, "Model for estimating radiated emissions from a printed circuit boards with attached cables due to voltage driven sources," IEEE Trans. Electromagn. Compat., Vol. 47, No. 4, 899-907, Nov. 2005.
[3.] Deng, S., T. Hubing, and D. Beetner, "Estimating maximum radiated emissions from printed circuit boards with an attached cable," IEEE Trans. Electromagn. Compat., Vol. 50, No. 1, 215-218, Feb. 2008.
[4.] Wang, J., O. Fujiwara, and K. Sasabe, "A simple method for predicting common mode radiation from a cable attached to a conducting enclosure," Proc. 2001 APMC, 1119-1122, Taipei, Taiwan, 2001.
[5.] Kayano, Y., M. Tanaka, and H. Inoue, "Radiated emission from a PCB with an attached cable resulting from a nonzero ground plane impedance," Proc. IEEE Int. Symp. Electromagn. Compat. , 955-960, Aug. 2005.
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[8.] Park, H. H., H. Park, and H. S. Lee, "A simple method of estimating the radiated emission from a cable attached to a mobile device," IEEE Trans. Electromagn. Compat., Vol. 55, No. 2, 257-264, Apr. 2013.
[9.] Cooray, G. and V. Cooray, "Electromagnetic fields of a short electric dipole in free space--Revisited," Progress In Electromagnetics Research, Vol. 131, 357-373, 2012.
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Jia-Haw Goh, Boon-Kuan Chung *, Eng-Hock Lim, and Sheng-Chyan Lee
Universiti Tunku Abdul Rahman, Malaysia
Received 11 June 2013, Accepted 7 September 2013, Scheduled 13 September 2013
* Corresponding author: Boon-Kuan Chung (firstname.lastname@example.org).
Table 1. Comparison between the Shim and Hubing method and improved method ([C.sub.trace] = 0.025 pF; [V.sub.DM] = 1V). Board Size Cable Error in Max E-Field (dB) Length Shim and Improved Method Hubing Method 400 MHz 700 MHz 400 MHz 700 MHz 10 cm x 8 cm 3m 2.64 5.69 0.12 0.95 10 cm x 16 cm 3m 10.97 17.79 0.22 1.59 10 cm x 8 cm 6 m 6.79 12.17 0.89 1.07 10 cm x 16 cm 6 m 9.67 16.91 1.87 0.68 10 cm x 8 cm 10m 2.80 5.45 0.36 0.39 10 cm x 16 cm 10m 9.17 15.13 1.11 0.17
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|Title Annotation:||printed circuit board|
|Author:||Goh, Jia-Haw; Chung, Boon-Kuan; Lim, Eng-Hock; Lee, Sheng-Chyan|
|Publication:||Progress In Electromagnetics Research M|
|Date:||Jun 1, 2013|
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