Input Differential-Mode EMI of CRM Boost PFC Converter - IEEE Xplore

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 3, MARCH 2013

1177

Input Differential-Mode EMI of CRM Boost PFC Converter Fei Yang, Student Member, IEEE, Xinbo Ruan, Senior Member, IEEE, Qing Ji, and Zhihong Ye, Member, IEEE

Abstract—In this paper, the differential-mode (DM) electromagnetic interference (EMI) noise of a single-phase boost power factor correction converter operating in critical current mode was analyzed. The DM noise spectra are calculated based on the mathematical model of EMI receiver and the required corner frequencies of DM filter are obtained. It can be seen that the minimum corner frequencies are determined by the maximum noises at 150 kHz. With the relation between the magnitude of the inductor current ripple and the DM noise, the characteristics of noise at 150 kHz are obtained by analyzing the current ripple magnitude at 150 kHz; thus, the worst conditions which have the maximum noise value are figured out. Meanwhile, the maximum noises at 150 kHz for different input voltages are identical, so the DM filter can be designed based on one worst spectrum at one input voltage without testing the spectra in other conditions. Index Terms—Boost converter, critical current mode (CRM), differential mode (DM), electromagnetic interference (EMI), power factor correction (PFC).

I. INTRODUCTION OWER factor correction (PFC) converters have been widely used in ac–dc power conversions to achieve high power factor (PF) and low harmonic distortion. The boost converter is one of the preferred topologies for PFC converter because the boost inductor is in series with the line which leads to low input current ripple. When operating in critical current mode (CRM), the boost PFC converter features high PF, lower inductance compared with continuous current mode (CCM), lower peak inductor current compared with discontinuous current mode (DCM), zero-current turn-on for the power switch and no reverse recovery of the diode [1], [2], and it is suitable for low- and medium-power applications. Electromagnetic interference (EMI) filter is necessary to be added in the switching-mode power supplies to comply with the standards, such as EN55022. Since the input current ripple of the CRM boost PFC converter is relatively high, in addition to common-mode filter, differential-mode (DM) filter is needed.

P

The design of the DM filter is based on its minimum corner frequency, which can be obtained according to the noise at the critical frequency in the worst noise spectrum [3]. Unlike the constant-frequency operation manner of the boost PFC converter in CCM or DCM, where the noises just exist at the switching frequency and the multiples of switching frequency, and their maximum values normally happen at the low line with full load [4]–[7], the CRM boost PFC converter operates with variable frequency, and the noise spectrum is continuous and varies in a complicated manner [1], [8]. Thus, it is not easy to figure out the condition of the worst spectrum. Moreover, due to the special signal processing of the EMI receiver, the harmonics in the inductor current obtained simply from Fourier transform or fast Fourier transform cannot be used directly as EMI noise. This necessitates significant simulations and experimental tests for designing the DM filter. Recently, the mathematical modeling of EMI receiver has been developed in [8]–[10], and the noise spectrum can be calculated, making it possible to calculate the noise spectra for analyzing and predicting the worst conditions of the spectrum. The objective of this paper is to investigate the characteristics of conducted DM noises of a single-phase CRM boost PFC converter. Section II introduces the inductor current ripple magnitude and the switching frequency, and analyzes the characteristics of the harmonics magnitude of the inductor current ripple. Section III calculates the noise spectra based on the EMI receiver model and derives the required corner frequencies of the DM filter under different conditions. It can be seen that the minimum corner frequencies are determined by the maximum DM noises at 150 kHz. In Section IV, based on the similar variation trend between DM noise and their current ripple magnitude, the conditions of worst spectra are obtained by analyzing the current ripple at 150 kHz. Section V provides the experimental results of a 80-W prototype. Finally, Section VI concludes this paper.

II. RIPPLE AND HARMONICS OF THE INDUCTOR CURRENT Manuscript received February 28, 2012; revised May 3, 2012; accepted June 20, 2012. Date of current version October 12, 2012. This work was supported by the LiteOn Technology Corporation, Nanjing, China. Recommended for publication by Associate Editor D. Maksimovic. F. Yang, X. Ruan, and Q. Ji are with the Aero-Power Sci-Tech Center, College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China (e-mail: [email protected]; [email protected]; [email protected]). Z. Ye is with the Lite-On Technology Power SBG ATD-NJ R&D Center, Nanjing 210019, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2012.2206612

A. Ripple Magnitude and Switching Frequency of Inductor Current Fig. 1 shows the boost PFC converter, where Q is the power switch, D is the diode, L is the boost inductor, Co is the output filter capacitor, and Cx is an input capacitor for filtering high-frequency ripple current. The input voltage is defined as √ vin = 2Vin sin ωt, where Vin is the rms value of input voltage, and ω is the line angular frequency. The rectified input volt√ age is vg = |vin | = 2Vin |sin ωt|. When the boost converter

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From Fig. 2(a), the peak inductor current can be presented as vg (4) iL pk = dts L where ts is the switching period. Substituting (2) and vg = √ 2Vin |sin ωt| into (4), the switching frequency fs can be derived as Fig. 1.

Single-phase boost PFC converter.

fs =

1 Vin2 d. = ts 2Pin L

(5)

B. Harmonics of the Inductor Current Ripple

Fig. 2. Inductor current iL and the drive signal of switch v g s in (a) a switching cycle and (b) a half-line cycle.

operates in CRM, the duty cycle of the power switch is vg =1− d=1− Vo

√ 2Vin |sin ωt| Vo

(1)

where Vo is the output voltage. As seen, the duty cycle in √ varies a half-line cycle. Its minimum value dm in = 1 − 2Vin Vo occurs at sin ωt = 1, and the maximum value dm ax = 1 at sin ωt = 0. Fig. 2 depicts the waveform of the inductor current in a switching cycle and a half-line cycle when the boost PFC converter operates in CRM. It can be seen that the peak inductor current iL pk is twice its average value iL avg , and the ripple magnitude of the inductor current ΔiL pp equals iL pk . Assuming that PF is unity, ΔiL pp in a half-line cycle can be expressed as

ΔiL

pp

= iL

pk

= 2iL

avg

√ Pin =2 2 |sin ωt| Vin

(2)

where Pin is the input power. According to (1) and (2), we have ΔiL

pp

=2

Pin Vo (1 − d) . Vin2

(3)

Equation (3) shows the relation between the ripple magnitude and duty cycle.

According to Fig. 2, the inductor current consists of a twice line-frequency component, i.e., average inductor current iL avg , and a switching-frequency component, i.e., inductor ripple current, and the latter is mainly attributed to the DM noises. Since the switching frequency is much higher than the twice line frequency, any time point in a half-line cycle can be well approximated as a switching cycle [11], the inductor current ripple in a switching cycle can be expressed as ⎧ ΔiL pp ΔiL pp ⎪ ⎪ , (0 ≤ t < dts ) t− ⎨ dts 2 ΔiL (t) = ΔiL pp ΔiL pp ⎪ ⎪ ⎩ − (t − dts ) , (dts ≤ t ≤ ts ) 2 (1 − d) ts (6) where ΔiL pp and ts are functions of d and they are constants as d is fixed in a switching period. Considering the triangle waveform as a periodic function, the harmonic magnitude at nfs , |cn (d, nfs )|, can be obtained by Fourier analysis [8], [12] as 1 sin(nπd) (7) |cn (d, nfs )| = ΔiL pp · πn nπd(1 − d) where n is the harmonic order (n = 1, 2, 3. . .). Actually, the switching frequency is modulated with twice the line frequency (100 Hz for the grid voltage with 50 Hz), which causes sideband harmonics. In practical tests with an EMI receiver [13], the noise at a frequency is obtained from the total noise energy in the resolution bandwidth (RBW). Since the modulation frequency (such as 100 Hz) is much smaller than the RBW (9 kHz), the sideband harmonics will not appear in the measured spectrum and the effects of frequency modulation on the final EMI measured results are indistinguishable [14]–[16]. So, only the noise currents at switching frequencies and their harmonics are calculated as the DM noise current in this paper. As seen in (7), the harmonic magnitudes are proportional to the inductor current ripple ΔiL pp . The values of |cn (d, nfs )|/ΔiL pp over the whole duty cycle range [0, 1] calculated by MathCAD are shown in Fig. 3. As seen, the values of fundamental component (n = 1), which are higher than those of the high-order cases, vary in a limited range [0.318, 0.405]. Substituting (1) into (7), the duty cycle d, |cn (d, nfs ) |/ΔiL pp , ΔiL pp and its fundamental |c1 (d, fs ) | in a halfline cycle at 85 and 265 V are depicted in Fig. 4 (Pin = 80 W, Vo = 380 V). It is noticed that ΔiL pp and |c1 (d, fs )| at 85 V have similar profile due to the relatively narrow variation range of duty cycle, while those of the 265 V case are different. The maximum difference ratio is about (0.405−0.318)/0.318 = 27%,

YANG et al.: INPUT DIFFERENTIAL-MODE EMI OF CRM BOOST PFC CONVERTER

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1 Vo d −1 f 10−6 Lπ sin 2P LV 2 · πf in in + 20 log . (9) 2Pin L Vin2 · πf

|cn (d, f )| = 20 log 20 log 10−6

Fig. 3. orders.

Values of |cn (d, nfs )|/ΔiL

pp

vary with d for different harmonic

Fig. 4. Duty cycle d, |cn (d, nfs )|/ΔiL p p , ΔiL p p and its fundamental component |c1 (d, fs )| in a half-line cycle for given input voltage and input power (80 W).

√ and it mainly happens at high line (Vin ≥Vo 2 2 ) while ΔiL pp is reduced with the increment of input voltage, so the absolute value of deviation is not very high. Hence, it can be concluded that ΔiL pp can be used to represent the variation profile of their fundamental harmonic. In order to analyze the harmonics magnitude in the frequency domain, the harmonics at nfs (n = 1, 2, 3. . .) can be changed to a continuous envelop by substituting n = f/fs , (3) and (5), into (7) [12] and simplified as 1 sin (f πd/fs ) |cn (d, f )| = ΔiL pp · f π/fs f πd (1 − d)/fs

Vo d sin 2Pin L Vin2 · πf = Lπf 2Pin L Vin2 · πf

(8)

where f is a continuous variable. The envelope of the harmonics in dBμA form can be expressed as

When Vin , Vo , Pin , and d are given, the first part of (9) is a line with a −20 dBμA/dec slope and the second part is a typical form as 20 log|(sinx)/x|, of which the asymptote is nearly 0 dBμA/dec for small x and −20 dBμA/dec for large x [12] andthe two asymptotes converge at x = 1 which derive f = Vin2 (2Pin Lπ) = fs /(dπ) from (9). Thus, the harmonics envelope also has two parts: when f < fs /(dπ), the envelope has a asymptote of −20 dBμA/dec slope; when f > fs /(dπ), the envelope has a asymptote of −40 dBμA/dec slope. On the other hand, when the harmonics frequencies satisfy nfs < fs /(dπ), which leads to d < 1/(nπ), the harmonics envelope varies with −20 dBμA/dec, while the rest high-order harmonics varies √ with −40 dBμA/dec. That means when Vin < (π − 1)Vo π 2 (devary rived based on dm in >1/π), all the harmonicsenvelopes √ with −40 dBμA/dec; When Vin ≥ (π − 1)Vo π 2, the harmonics envelope of which the duty cycle d ≤ 1/nπ may vary with −20 dBμA/dec initially and then with −40 dBμA/dec, which mainly happen nearly at the peak instantaneous input voltage with low switching frequency, and the cases with d >1/π just vary with −40 dBμA/dec, which happen at low instantaneous input voltage with high switching frequency. For Vo = 380 V, Pin = Po = 80 W (assuming √that the efficiency is 100%) and L = 790 μH, (π − 1)380 π 2 = 183 V. Two envelopes are taken as examples and shown in Fig. 5, which include their asymptotes (dashed line) and the harmonics magnitude at nfs (empty circles). As seen, for 85 V and d = dm in = 0.684, since dm in >1/π, all the switching-frequency harmonics envelopes, of which the duty cycles are larger than dm in , vary with −40 dBμA/dec as shown in Fig. 5(a). For 265 V and d = 0.1 case, since 0.11/π, (b) d ≤ 1/π.

Fig. 6.

(a) DM noise test diagram including LISNs and DM noise separator and (b) its simplified circuit.

that is fairly constant. The 50 Ω resistors represent the standard 50-Ω input impedance to the EMI receiver, and the DM noise voltages on the receiver impedance RLISN are directly related to the noise current ΔiL [12]. So, Fig. 6(a) can be simplified as Fig. 6(b), where ΔiL is treated as a current source. Since the DM noise voltages caused by ΔiL are much higher than the maximum voltage limit of the EMI receiver used in practical tests (130 dBμV) and there is not a fixed attenuator on hand, an input capacitor Cx is added here to attenuate the noise to a lower value. The value and position of Cx are quite important on the line current spectrum, but it is not in the scope of this paper. The effects of Cx on the final calculation results are analyzed later. According to Fig. 6(b), the DM noise voltage vDM (d, f) can be calculated as RLISN . (10) vDM (d, f ) = |cn (d, f )| 1 + j2RLISN CX (2πf ) The gain of LISN without/with Cx in decibel form is shown in Fig. 7. In the test frequency range, 150 kHz–30 MHz, the impedance is just RLISN (50 Ω) without Cx , and the main effects of Cx on vDM are a constant level reduction and an attenuation of −20 dB/dec slope. Meanwhile, a lower capacitance leads to a smaller level reduction value, and the phase shift of the linefrequency input current to input voltage, which is caused by Cx , is also low when the capacitance is small [17]. Thus, Cx = 0.47 μF is selected to provide a big enough noise attenuation and a limited current phase shifting.

Fig. 7.

Gain of LISN with/without considering the effects of C x .

Based on the EMI receiver model proposed in [8], Fig. 8 shows a diagram to explain how to calculate the DM noise and spectrum from the inductor current ripple. The detail mathematic expressions of the EMI receiver are as follows. First, the intermediate frequency (IF) filter selects the noises around the intermediate frequency fIF with different attenuations. The resulting output signals of this filter are [8] vDM (d, nfs , fIF ) = vDM (d, nfs )|GIF (nfs , fIF )| where |GIF (nfs , fIF )| is

−

|GIF (nfs , fIF )| = e

n f s −f I F √ 4 . 5 ×1 0 3 / l n 2

(11)

2 .

(12)


Fig. 8.

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EMI receiver model diagram.

At last, all the signals in the time domain will be processed separately by a peak value (PK) detector, average value (AV) detector, and quasi-peak value (QP) detector to get the DM noise at fIF . Since the noise envelope for a specific fIF is discrete pulses in a half-line cycle, QP is of more importance due to its higher value than AV [8]. And, PK is close to QP and it is easy to be obtained; here, PK is chosen to be the DM noise at fIF which can be expressed as vPK (fIF ) = max[vDM

Fig. 9.

Gain of the IF filter

The IF filter is a bandpass filter with a 9-kHz RBW at −6 dB, and its gain in decibel form, 20 log[|GIF (nfs , fIF )|], is shown in Fig. 9. It can be noticed that the closer the nfs to fIF , the lower the attenuation. Second, with the time changed in a half-line, the noise envelope at fIF is obtained from an envelope detector. Substituting (1) into (11), the noise envelopes at fIF in a half-line cycle at different orders, of which the frequencies satisfy nfs = fIF , are obtained. Since the pulses are generally discrete for CRM, the final result of this filter can be expressed as vDM

env (t,

fIF ) =

N

vDM (t, nfs , fIF )

(13)

n =1

where N is the largest integer that is smaller than the value of fIF /fs m in , so that all the situations of nfs = fIF are considered. Take fIF = 150 kHz as an example (see Fig. 8); if 150, 75, or 50 kHz exists in a half-line cycle, the noise envelopes caused by the fundamental of 150 kHz, the second-order harmonic of 75 kHz, and the third-order harmonic of 50 kHz will be calculated in (13).

env (t, fIF )].

(14)

Generally, the DM noises are mainly attributed to the noise at low-frequency side of the standard frequency range [3], so fIF sweeps from 100 kHz to 1 MHz in the following calculations. For a given input voltage and input power, when fIF equals 100 kHz, 110 kHz, 120 kHz,. . . , 1 MHz (mass fIF points is preferred at the expense of more time consuming in calculation), the corresponding DM noises can be calculated from (1), (3), (5), (7), and (10)–(14), and the noise spectra are obtained by depicting the noises points in a Bode diagram. B. DM Noise Spectra and the Required Corner Frequency of DM Filter According to (5), the maximum and minimum switching fre √ 2Vin Vo , quencies, occurring at dm ax = 1 and dm in = 1 − respectively, can be expressed as ⎧ Vin2 ⎪ ⎪ ⎨ fs m ax = 2P L in (15) √ 2 ⎪ ⎪ ⎩ fs m in = Vin Vo − 2Vin . 2Pin L Vo Since the fundamental of the switching-frequency current is normally larger than their high-order harmonics, the noise spectrum in the switching-frequency range, i.e., fs m in ≤ f ≤ fs m ax , is mainly caused by the fundamental, and the spectrum in the multiples of switching-frequency range, i.e., f > 2fs m in ,

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Fig. 10.


Calculated noise spectra with varied input powers when (a) V in = 110 V and (b) V in = 220 V.

is caused by the high-order harmonics. With varied Vin and Pin (the output voltage is constant), the variation range of switching frequency can be classified into two cases. 1) When the switching-frequency range is relatively narrow and satisfies fs m in < fs m ax < 2fs m in , the spectra have two parts and are not totally continuous. 2) When the variation range is wide, which satisfies fs m ax ≥ 2fs m in , the spectra are totally continuous. From (15) and fs m ax = 2fs m in , the boundary √input voltage of the two cases can be derived as Vin = Vo 2 2 . Thus, the √ spectra are not totally continuous when Vin < Vo 2 2 , and √ totally continuous when Vin ≥ Vo 2 2 . For Vo = 380 V, L = 790 μH, and the rated output power Po rated = 80 W (assuming that the efficiency is 100%), the noise spectra at 110 and 220 V with different input powers are calculated as two examples for illustration in Fig. 10. Since the switching-frequency harmonics spectra of inductor currents have an asymptote of −40 dBμV/dec or −20 dBμV/dec slope (see Fig. 5) and Cx provides an attenuation of −20 dB/dec (see Fig. 7), the envelope of the noise spectrum decreases with an asymptote of approximately −60 [see Fig. 10(a)] or −40 dBμV/dec slope [see Fig. 10(b)]. The limit of EN55022 Class B has a slope of −20 dBμV/dec at the low-frequency band, 150–500 kHz [13], so the required attenuation of EMI filter needs at least −40 or −20 dBμV/dec slope. Normally, the single-stage or two-stage filter has a positive attenuation slope, so the key for the filter design is to figure out ⎧ ⎪ ⎪ fs m in ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ 150 kHz or 2 fs fcrit =

⎪ ⎪ ⎪ ⎪ 2fs m in ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ 150 kHz

m in

its minimum corner frequency based on the noise at the critical frequency fcrit in worst spectra [7], [18]. For a fixed input voltage, with the input power increasing, the switching frequency decreases (5); thus, the whole spectrum shifts to a low frequency; meanwhile, the current ripple magnitude increases (3), which lead to an increased noise envelop. When the input power is very low (20 W in Fig. 10), the DM noise initially appears at fs m in that is higher than 150 kHz, i.e., fs m in ≥ 150 kHz, so fcrit is at fs m in . When the input power increases further, crit varies with different conditions. f√ For Vin . 300 × 103 L Vo The corner frequency of EMI filter can be calculated as [18] −6

fcor = 10log(f c r i t )−[20 log (v P K (f c r i t ) /10 )−Lim it ]/slop e

(18)

where “Limit” is the limit value at fcrit stated in the standard [13], and “slope” is the attenuation asymptote of the EMI filter (for a single-stage LC filter, slope =40 dBμV/dec). From (16)–(18), the corner frequencies varying with input powers and input voltages are calculated as shown in Fig. 11, where slope = 40 dBμV/dec, and the dashed lines represent the corner frequencies calculated just based on the noises at 150 kHz. As seen, the minimum corner frequencies (empty circles) are determined by the noises at 150 kHz and their values are identical for different input voltages. If the corresponding input powers of the minimum corner frequencies are known, the worst spectra for DM filter design can be obtained by calculation or experimental tests. Hence, the following sections will focus on the analysis of the conditions under which the noises at 150 kHz reach the maximum value. IV. WORST CONDITIONS PREDICTION The earlier corner frequencies are calculated point by point without a general analytic expression, so identifying the minimum values is not straightforward, especially when the specification of the prototype and the test conditions are changed [8]. If the relations between the noise at 150 kHz and input powers as well as input voltage are obtained, the worst condition can be found directly without the exhausting and time-consuming process. The current ripple magnitude can represent the variation of its fundamental harmonic as stated in Section II-B, and the maximum DM noise at 150 kHz is mainly caused by the fundamental (see Fig. 10), so it is possible to predict the maximum DM noise based on the current ripple magnitude. Two examples

Fig. 12. Switching frequency and magnitude of inductor current, the fundamental noise, and the noise envelope at specific fIF for (a) V in = 110 V, P in = 40 W, and (b) V in = 220 V, P in = 80 W.

are shown in Fig. 12, where ΔiL pp , fs , the DM noise voltage caused by the fundamental vDM (n = 1), and the noise envelopes vDM env (t, fIF ) for different fIF in a half-line cycle are depicted together. As seen, although the envelope of vDM (n = 1) has some difference caused by Cx (much more attenuation for high-frequency harmonics as shown in Fig. 7), its variation trend is still similar to that of ΔiL pp , and the PK DM noises (empty circles) generally equal the fundamental vDM (n = 1). In Fig. 12(b), the second-order harmonics of 100 and 75 kHz lead to noise pulses in the noise envelop of fIF = 200 kHz and fIF = 150 kHz, respectively, but the PK noises of fIF = 200 kHz and fIF = 150 kHz are still determined by their fundamental noise voltage vDM (n = 1). Thus, PK noise variation can be represented qualitatively by the corresponding current ripple magnitude (black dots), so the following parts will just analyze the inductor current ripple at 150 kHz for simplicity. From (3) and (5), the ripple magnitude of the inductor current at fcrit can be expressed as ΔiL

pp f c r i t

= (1 − df c r i t )Vo · 1−

df c r i t 1 · fcrit L

2Vin ≤ df c r i t ≤ 1 Vo

√

(19)

where df crit is the corresponding duty cycle. The maximum ripple magnitude, which occurs at df crit = 0.5, can be expressed as ΔiL

pp f c r i t m ax

=

Vo 4Lfcrit

(20)

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and its value is independent of the input voltage and input power. The duty cycle at fcrit can be solved from (3) as df c r i t =

2fcrit LPin . Vin2

(21)

Substituting (21) into (19) yields the ripple magnitude at fcrit varying with the input power and input voltage as 2Vo 2fcrit L 2 Δiin pp f c r i t = 2 Pin − · Pin Vin Vin2 √ Vin2 Vo 2Vin Vin2 ≤ Pin ≤ . (22) Vo 2fcrit L 2fcrit L For the maximum ripple magnitude at fcrit , the corresponding input power can be derived from (21) for df crit = 0.5 as Pin

worst =

Vin2 . 4Lfcrit

(23)

For fcrit = 150 kHz, the ripple magnitudes at 150 kHz that vary with input powers for different input voltages are calculated from (22) as shown in Fig. 13, where Vo = 380 V and L = 790 μH. For the input power which is so light that all the frequencies are higher than 150 kHz or so heavy that all the frequencies are lower than 150 kHz, the corresponding input powers are beyond the range in (22), so the ripple magnitude values are set at 0. For the whole duty cycle range, i.e., df crit ∈ [0, 1], all the mathematical ripple magnitudes at fcrit are calculated from (22), with corresponding Pin ∈ [0, Vin2 (2fcrit L)], and representedby√ thegray dotted lines in Fig. 13. √ For Vin √ 4fcrit LPo rated , such as 220, 240, and 260 V, df crit over the whole power range [0 W, 80 W] are lower than 0.5, so the ripple magnitudes increase with the increment of input powers [see Fig. 13(c)]. Actually, the maximum ripple magnitudes also happen at input powers (23) higher than Po rated . The DM noises at 150 kHz that vary with input powers at different input voltages are calculated in (1), (3), (5), (7), and (10)–(14) for fIF = 150 kHz and depicted in Fig. 14. As seen, the noise variation is similar to that of the ripple magnitude in Fig. √ 13. The noises appearing at high powers for Vin

4fc rit LP o

ra te d .

at 150 kHz]. Since the maximum ripple magnitudes (empty circles) at 150 kHz for different input voltages are identical (20) with a fixed duty cycle (d = 0.5), the corresponding fundamental (7) and DM noises in those conditions are identical and almost reach the maximum values. That is why the minimum corner frequencies for different input voltages in Fig. 11 are identical. Hence, input powers calculated in (23), which derive the maximum ripple magnitudes and DM noise at fcrit , can be seen as the worst conditions.


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Fig. 15. Calculated DM noise spectra under the worst conditions that the current ripple magnitudes at 150 kHz reach the maximum value.

Fig. 14. Calculated DM noises at 150 kHz varying with input powers when √ √ (a) V in < V o /(2 2), (b) V o /(2 2) ≤ V in ≤ 4fc rit LP o ra te d , and (c) V in >

4fc rit LP o

ra te d .

Fig. 16.

Four DM noise spectra under worst conditions are calculated as shown in Fig. 15. Apparently, the worst spectra for different input voltages are nearly overlapped for fIF ≥ 150 kHz, and the noises at 150 kHz are identical (111.16 dBμV). In this manner, the DM EMI filter can be designed based on the spectrum under one worst condition, which can save the calculations and tests under other worst conditions.

(a) Test equipments and (b) the schematic diagram.

V. EXPERIMENTAL RESULTS In order to verify the aforementioned analysis, an 80-W prototype of single-phase CRM boost PFC converter is fabricated and tested in the lab.

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Fig. 17. Experimental results of the DM noise spectra varied with output powers when (a) V in = 134 V, (b) V in = 180 V, and (c) V in = 240 V.

The specifications of the prototype are as follows: 1) input voltage vin : 85∼265 Vac / 50 Hz; 2) output voltage Vo : 380 Vdc ; 3) rated output power Po rated : 80 W. The components of the prototype are as follows: 1) boost power switch: FQP8N60 C (600 V, 8 A); 2) boost diode: MUR460 (600 V, 4 A); 3) boost inductor: L = 797 μH; 4) control IC: L6561 (STMicroelectronics). Fig. 16 shows the photos and diagram of the EMI test equipments. In the practical test, two LISNs are adopted to test the noises from the line and neutral, respectively, and a noise sepa-

Fig. 18. DM noise at 150 kHz varied with input powers when (a) √ √ V in < V o /(2 2), (b) V o /(2 2) ≤ V in ≤ 4fc rit LP o ra te d , and (c) V in >

4fc rit LP o

ra te d .

rator is used to get the DM noise voltages. Then, the DM noises were sent to the EMI receiver to obtain the DM noise spectra. Three test results √of PK DM √noise spectra √ taken as exam(2 (2 2), V 2)≤ V ≤ 4fcrit LPo rated , ples for Vin 4fcrit LPo rated with varied output powers are provided in Fig. 17. As seen, with the output power increasing, the whole spectra are moving up and to the lowfrequency side, and their spectra initially follow an asymptote of


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be obtained noise spectra at one proper input voltage √ by testing√ (Vo (2 2) ≤ Vin ≤ 4fcrit LPo rated ), while the tests under other input voltages and input powers are saved. VI. CONCLUSION

Fig. 19. PK and QP noise spectra under the conditions which the noises at 150 kHz reach the maximum value.

−60 or√−40 dBμV/dec slope as analyzed previously. For Vin ≤ Vo (2 2) such as 134 V [see Fig. 17(a)], with the output power increasing from 10 to 50 W, the noises at 150 kHz rise initially and then drop, and at higher output powers, the noises at 150 kHz rise again that are mainly attributed to the high-order harmon √ √ ics. For Vo (2 2) ≤ Vin ≤ 4fcrit LPo rated such as 180 V [see Fig. 17(b)], the noises at 150 kHz are very small at low output powers, such as 10 W, and for the output power higher than √ 30 W, their noises initially rise and then drop. For Vin > 4fcrit LPo rated such as 240 V [see Fig. 17(c)], when the output power is higher than 10 W, the noises at 150 kHz rise with the increment of output power. Actually, the inductor current ripple magnitude and switching frequency are determined by the input power that is different to the output power considering the conversion efficiency. We have tested nine input voltages from 100 to 260 V, and for each input voltage, eight output power points evenly distributed from 10 to 80 W are tested. Thus, the spectra as well as corresponding input powers are all obtained. The noises at 150 kHz that vary with input powers at different input voltages are depicted in Fig. 18, where the points are linked by straight lines. As seen, the variation waveforms are similar to the calculated cases in Fig. 14. The maximum noises at 150 kHz for different input voltages are 111.12 (134 V, 35 W), 111.11 (160 V, 45 W), 111.32 (180 V, 55 W), and 111.19 dBμV (200 V, 76 W). They are nearly the same and close to the calculated cases 111.16 dBμV in Fig. 15. In addition, the calculated input powers (see Fig. 15) basically match the experimental results. Thus, if the specifications and parameters used in calculations are close to those in practical tests, the maximum PK DM noise at 150 kHz can be obtained directly through the calculations provided in this paper. Fig. 19 shows the PK and QP noise spectra under the conditions in which the PK noises at 150 kHz reach their maximum value. As seen, the values of PK and QP are close and the QP noises at 150 kHz are also basically the same. The test results are similar to the calculated cases in Fig. 15, especially 160, 180, and 200 V cases that are nearly overlapped. Therefore, if we think that the calculated worst condition is not precise enough, the worst spectrum that has the maximum noise at 150 kHz can

With the mathematical modeling of the EMI receiver, the noise spectra of a single-phase CRM boost PFC converter can be calculated. Based on the analysis of characteristics of the spectra varied with input voltages and input powers, their required corner frequency of the DM filter can be obtained. It is found that the minimum corner frequencies are determined by the maximum noises at 150 kHz. Moreover, the similar variation trend between the PK DM noise and its current ripple magnitudes, the conditions of the maximum noise at 150 kHz, is predicted by analyzing their maximum inductor current ripples. For a specific input voltage, the worst spectrum happens at the input power when the current ripple magnitude at 150 kHz reaches its maximum value. Besides, as the maximum current ripple magnitudes at 150 kHz are a constant value with fixed duty cycle, the DM noises at 150 kHz generally reach the maximum value and they are also the same. Therefore, the DM filter can be designed based on the spectrum under one of worst conditions, and substantial repeated tests under other conditions can be saved. The validity of the analysis is verified by the experimental results, and the calculated maximum noises at 150 kHz match the experimental results very well. This method can be used for the converters that feature variable frequency input current ripple, such as interleaved CRM boost PFC converter which will be analyzed in the future work. REFERENCES [1] J. S. Lai and D Chen, “Design consideration for power factor correction boost converter operating at the boundary of continuous conduction mode and discontinuous conduction mode,” in Proc. IEEE Appl. Power Electr. Conf. Expo., Mar. 1993, pp. 267–273. [2] J. Zhang, J. Shao, P. Xu, F. C. Lee, and M. M. Jovanović, “Evaluation of input current in the critical mode boost PFC converter for distributed power systems,” in Proc. IEEE Appl. Power Electr. Conf. Expo., Anaheim, CA, Mar. 2001, pp. 130–136. [3] F. Y. Shih, D. Y. Chen, Y. P. Wu, and Y. T. Chen, “A procedure for designing EMI filters for AC line applications,” IEEE Trans. Power Electron., vol. 11, no. 1, pp. 170–181, Jan. 1996. [4] W. Zhang, M. T. Zhang, F. C. Lee, J. Roudet, and E. Clavel, “Conducted EMI analysis of a boost PFC circuit,” in Proc. IEEE Appl. Power Electron. Conf., Feb. 1997, pp. 223–229. [5] L. Yang, B. Lu, W. Dong, Z. Lu, M. Xu, F. C. Lee, and W. G. Odendaal, “Modeling and characterization of a 1 kW CCM PFC converter for conducted EMI prediction,” in Proc. 19th Annu. IEEE Appl. Power Electr. Conf. Expo., 2004, pp. 763–769. [6] B. Lu, W. Dong, S. Wang, and F. C. Lee, “High frequency investigation of single-switch CCM power factor correction converter,” in Proc. IEEE Appl. Power Electr. Conf. Expo., 2004, pp. 1481–1487. [7] K. Mainali and R. Oruganti, “Simple analytical models to predict conducted EMI noise in a power electronic converter,” in Proc. IEEE Ind. Electron. Soc. Conf., Nov. 2007, pp. 1930–1936. [8] Z. Wang, S. Wang, C. Wang, F. C. Lee, and P. Kong, “DM EMI noise prediction for constant on-time, critical mode power factor correction converters,” IEEE Trans. Power Electron., vol. 27, no. 7, pp. 3150–3157, Jul. 2012. [9] T. Nussbaumer, M. L. Heldwein, and J. W. Kolar, “Differential mode input filter design for a three-phase buck-type PWM rectifier based on modeling of the EMC test receiver,” IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 1649–1661, Oct. 2006.

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Fei Yang (S’10) was born in Shanxi, China, in 1983. He received the B.S. degree in electrical engineering and automation from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2006, where he is currently working toward the Ph.D. degree in electrical engineering. His main research interests include power factor correction converters, electromagnetic interference filter design, and dc/dc converters.

Xinbo Ruan (M’97–SM’02) was born in Hubei, China, in 1970. He received the B.S. and Ph.D. degrees in electrical engineering from the Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 1991 and 1996, respectively. In 1996, he joined the Faculty of Electrical Engineering Teaching and Research Division, NUAA, where he became a Professor in the College of Automation Engineering in 2002, and has been involved in teaching and research in the field of power electronics. From August to October 2007, he was a Research Fellow in the Department of Electronics and Information Engineering, Hong Kong Polytechnic University, Hong Kong. Since March 2008, he has been also with the College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China. He has published more than 100 technical papers in journals and conferences and also published three books. He is a Guest Professor at Beijing Jiaotong University, Beijing, China, and the Hefei University of Technology, Hefei, China. His main research interests include soft-switching dc/dc converters, soft-switching inverters, power factor correction converters, modeling the converters, power electronics system integration, and renewable energy generation system. Dr. Ruan was awarded the Delta Scholar by the Delta Environment and Education Fund in 2003, and was awarded the Special Appointed Professor of the Chang Jiang Scholars Program by the Ministry of Education, China, in 2007. Since 2005, he has been serving as the Vice President of the China Power Supply Society, and since 2008, he has been a member of the Technical Committee on Renewable Energy Systems within the IEEE Industrial Electronics Society. Since 2011, he has been an Associate Editor for the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS. He is a senior member of the IEEE Power Electronics Society and the IEEE Industrial Electronics Society.

Qing Ji was born in Jiangsu, China, in 1984. He received the B.S. degree in electrical engineering and automation from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2006, where he is currently working toward the Ph.D. degree in electrical engineering. His main research interests include electromagnetic interference (EMI) filter design and conducted EMI of switched mode power supply.

Zhihong Ye (M’00) was born in Zhejiang, China, in 1969. He received the B.S. and M.S. degrees in electrical engineering from Tsinghua University, Beijing, China, in 1992 and 1994, respectively, and the Ph.D. degree from the Bradley Department of Electrical and Computing Engineering, Virginia Polytechnic Institute and State University, Blacksburg, in 2000. From 2000 to 2005, he was with General Electric Global Research Center, Niskayuna, NY, as an Electrical Engineer. From 2005 to 2006, he was with Dell Inc., as a Commodity Quality Manager. Since 2006, he has been with LiteOn Technology Power SBG ATD-NJ R&D Center, Nanjing, China, as the Director of Research and Development. He holds seven U.S. patents, and has published more than 30 technical papers in transactions and international conferences. His research interests include high-density, high-efficiency power supply for computing, communication, and consumer electronics applications, digital control, power converter topologies and controls, soft-switching techniques, etc.