Common Mode EMI Reduction Technique for Interleaved MHz Critical Mode PFC Converter with Coupled Inductor Yuchen Yang, Mingkai Mu, Zhengyang Liu, Fred C. Lee and Qiang Li Center for Power Electronics Systems The Bradley Department of Electrical and Computer Engineering Virginia Tech, Blacksburg, VA 24061 USA
[email protected] Abstract— Coupled inductor has been widely adopted in VR applications for many years because of its benefits such as reducing current ripple and improving transient performance. In this presentation, coupled inductor concept is applied to interleaved MHz totem-pole CRM PFC converter with GaN devices. The coupled inductor in CRM PFC converter can reduce switching frequency variation, help achieving ZVS and reduce circulating energy. Therefore the coupled inductor can improve the efficiency of PFC converter. In addition, balance technique is applied to help minimize CM noise. This paper will introduce how to achieve balance with coupled inductor. The novel PCB winding inductor design will be provided. The PCB winding coupled inductor will have similar loss with litz wire inductor but much less labor in manufacture.
I.
Fig. 1 Switching frequency variation during half line cycle
recovery is not a problem anymore. Hence, totem-pole PFC converter is becoming more and more popular. However, the CRM totem-pole PFC converter has its own limitations. The first one is large variation of switching frequency. The operation principle of CRM PFC converter is well known. When the inductor current touches zero, the switch turns on. After a fixed on-time, the switch turns off. Hence, the peak current of inductor follows the equation below. = (1) As long as Ton is fixed, the peak current of inductor follows Vin. Theoretically, the waveform of inductor current is a series of triangle waveform with maximum value described in Equation (1) and minimum value as zero. The switching frequency can be calculated.
INTRODUCTION
Power factor correction (PFC) converter is a very essential component of power supply. In commercial products, the switching frequency of PFC converter is usually lower than hundreds of kHz. PFC converter consumes approximately one third volume of power supply. Increasing the switching frequency can reduce the volume of PFC converter. Furthermore, increasing the switching frequency to MHz can greatly raising the corner frequency of EMI filter and reduce the filter size. Thus, the power density of power supply can be increased a lot. However, MHz switching frequency can introduce great amount of switching loss. In order to overcome the high turnon loss of cascade GaN device, critical conduction mode (CRM) is a preferred control method. In addition, CRM boost PFC converter can eliminate the reverse recovery loss of power diode with ZCS. The other advantages of CRM boost PFC converter are high power factor and smaller peak inductor current [1-3].
( )=
√
(
))
(2)
Fig. 1 shows the switching frequency variation during half line cycle. It can be seen that with minimum switching frequency at 1MHz, the converter can have switching frequency as high as 2~3MHz. This high switching frequency will cause more loss. The second issue is that the CRM PFC converter cannot achieve zero voltage switching (ZVS) all the time. When inductor current drops to zero, the inductor will oscillate with the junction capacitors. The peak-to-peak oscillation amplitude of the device voltage is 2(Vo-Vin). Hence, when
Totem-pole PFC converter, compared with boost PFC converter and other bridgeless PFC converter, is the simplest topology. However, due to the reverse-recovery performance of the body diodes of switches, totem-pole PFC converter was not a practical topology [4]. With GaN devices, the reverseThis work was supported by Power Management Consortium (PMC) and High Density Integration (HDI) in Center for Power Electronics Systems (CPES), Virginia Tech.
978-1-4673-7151-3/15/$31.00 ©2015 IEEE
(
233
Fig. 2 Interleaved totem-pole PFC converter with coupled inductor
Fig. 4 Steady-state inductance variance during half line cycle
(a) Fig. 5 Switching frequency variance during half line cycle
II.
COUPLED INDUCTOR IN MHZ CRM PFC CONVERTER
Fig. 2 shows the interleaved totem-pole PFC converter with coupled inductor. Inductor L1 and L2 are inverse coupled. Fig. 3 shows the typical waveforms for different duty-cycle. In [5], the derivation of equivalent inductance Leq1, Leq2 and Leq3 is provided. The expression of Leq1, Leq2 and Leq3 is listed below.
(b) Fig. 3 Inductor current waveforms of coupled inductor. (a) D0.5
input voltage is larger than 0.5Vo, the switch can only achieve valley switching instead of ZVS. This will bring a lot extra switching loss for high switching frequency converters. On the contrary, when input voltage is smaller than 0.5Vo, the voltage oscillation amplitude is larger than the device voltage Vo. This will cause extra circulating energy during resonant period. This extra circulating energy will increase the loss significantly at high switching frequency. The concept of coupled inductor has been widely applied in multi-phase VRM to reduce loss and improve transient performance [5]. In [6], coupled inductor has been evaluated in interleaved CRM boost PFC converter. In [7], the impact of coupled inductor during the resonant period has been analyzed. All these analysis shows that coupled inductor is a promising technique for high frequency CRM PFC converters. In this paper, coupled inductor is applied to interleaved MHz CRM totem-pole PFC converter. The impact of coupled inductor on converter performance is analyzed. In addition, balance technique is introduced and applied to reduce the common mode (CM) noise. The calculation of equivalent inductance of coupled inductor with balance technique is provided. The analysis is verified by simulation.
=
− +
,
=
+
,
=
− +
When input voltage is high, the duty-cycle is smaller than 0.5, Leq1 determines the phase current ripple. Hence, Leq1 can be considered as steady state inductance when duty-cycle is smaller than 0.5. When input voltage is low, the duty-cycle is larger than 0.5, Leq3 determines the phase current ripple. Hence, Leq3 is the steady state inductance when duty-cycle is larger than 0.5. Therefore, for CRM PFC converter with coupled inductor, the steady state inductance is changing with input voltage during a half line cycle, as shown in Fig. 4. If the same steady state inductance is kept for non-coupled inductor and coupled inductor at Tline/4, the coupled inductor has larger steady state inductance when duty-cycle is approaching 0.5. Because of this, the on-time also need to change during half line cycle in order to still achieve unity power factor. Thus, the switching frequency variation with coupled inductor during half line cycle is different from the non-coupled case. Fig. 5 shows the switching frequency during half line cycle with different coupling coefficient. With the same switching frequency at 1MHz on T line/4, the coupled inductor CRM PFC converter has much lower switching frequency than the non-coupled case, except for the zero-crossing area. Thus, the coupled inductor can reduce the
234
Fig. 9 Balance technique for interleaved totem-pole PFC converter with coupled inductor
(a)
(a) (b) Fig. 10 (a) CM noise model; (b) effect of one voltage source
smaller than the inductance of original non-coupled inductor. The input current ripple for the coupled inductor is larger and hence the DM noise is larger. In order to keep the same filter configuration, the switching frequency needs to be slightly raised. As shown in Fig 8 (a), same two stage filter is kept for different coupling coefficient. In Fig 8 (b), it can be seen that the switching frequency of coupled inductor is slightly higher at the center region. However, for the other region, the switching frequency of coupled inductor is much lower than the non-coupled case. Thus, the average switching frequency is lower for coupled inductor case. Hence, this provide us the chance to reduce loss for PFC converter.
(b) Fig. 8 Coupled inductor impact on DM noise. (a) Calculated DM noise; (b) Switching frequency variation
average switching frequency of CRM PFC converter. And this can improve the converter efficiency. As analyzed in [7], the equivalent inductance during resonant period is Leq4. The expression of Leq4 is shown in (3). It can be seen that Leq4 is smaller than non-coupled inductor. Hence the resonant period with coupled inductor is shorter than non-coupled case. Shorter resonant period means larger portion of energy transferring time. Thus, the conduction loss is smaller. =
−
III.
BALANCE TECHNIQUE FOR COUPLED INDUCTOR
In [8], balance technique is introduced for interleaved boost PFC converter to reduce CM noise. Balance technique can also be applied to interleaved totem-pole PFC converter with coupled inductor. As shown in Fig. 9 an extra inductor is added to achieve balance. The CM noise model is shown in Fig. 10(a). The dv/dts of active devices are the dominant CM noise sources. Hence they are modeled as two voltage sources VN1 and VN2. Cb is the parasitic capacitance between output trace and ground. Cd is the drain-to-ground capacitance. According to the superposition theory, the two independent noise sources can be studied separately. Fig. 10(b) shows the CM noise model of source VN1. Here, VN2 is short circuit. The balance condition for this circuit is + = (4)
(3)
In [7], coupled inductor is proved to have the ability to help achieving ZVS when duty-cycle is smaller than 0.5. This is a great benefit for CRM PFC converter. In CRM PFC converter, when input voltage is higher than 0.5Vo, the devices cannot achieve ZVS but only valley switching. However, coupled inductor can help achieving ZVS during this time period. The coupled inductor can help reduce this non-ZVS loss by 50%. Coupled inductor can also reduce circulating energy when duty-cycle is larger than 0.5 [7]. This characterize of coupled inductor can help improving the performance of CRM PFC converter. When input voltage is low, the converter will have extra circulating energy. The coupled inductor can reduce circulating energy during this time period. Thus the coupled inductor can reduce conduction loss for CRM PFC converter. However, for the interleaved PFC converter with coupled inductor, the input current ripple is determined by Leq2, which is the leakage inductance of the coupled inductor. The input current ripple will impact the DM noise of PFC converter. Since the leakage inductance of the coupled inductor is
In order to get the balance equation, the ratio of Za/Zb needs to be calculated first. From the circuit we can get the following equations.
235
(a)
(a)
(b) Fig. 11 Improved balance technique for interleaved totem-pole PFC converter with coupled inductor. (a) circuit structure; (b) magnetic structure
(b) Fig. 12 (a) CM noise model; (b) effect of one voltage source
⎧ ⎪ ⎨ ⎪ ⎩
=
+
=
+ =
( + )
=
(9)
=−
⎨ ⎪ ⎪ ⎩
(5)
( − )
Then the ratio of Za/Zb can be derived from (5). / + = = / Thus the balance equation can be derived as:
=
⎧ ⎪ ⎪
( + )
+
= =
Then the ratio of Za/Zb can be derived from (9). =
(6)
/ /
=
+
(10)
Thus, the balance condition for source V1 is =
(7)
(11)
Similarly, the balance condition for noise source VN2 is also (11). The CM noise of this PFC converter can be minimized as long as this balance condition is achieved.
It can be derived that the balance condition for noise source VN2 is also (7). It can be seen that for the coupled inductor, the mutual inductance does not impact the balance condition. In [8], it is analyzed that in order to achieve better balance at high frequency, the balance inductor Lb should be coupled with the original inductor. Hence, for the coupled inductor, two inductor L3 and L4 are applied to achieve better balance and coupled with L1 and L2. Fig. 11 shows the circuit topology and magnetic structure. The CM noise model is shown in Fig. 12(a). According to the superposition theory, the model of noise source VN1 is shown in Fig. 12(b). The balance condition for this circuit is + = (8)
IV.
EQUIVALENT INDUCTANCE WITH BALANCE TECHNIQUE
In the analysis of section II, there are two inductors in the coupled inductor structure. And Leq1, Leq2, Leq3 and Leq4 is derived based on that structure. Then, the circuit performance can by analyzed by using these four equivalent inductance. However, with the balance technique, there are four inductors coupled together. In order to analyze the performance of this circuit, we need to derive the new Leq1, Leq2, Leq3 and Leq4. In order to do that, the inductance matrix need to be derived first. Fig. 13 shows the magnetic circuit. From the magnetic circuit, the inductance matrix can be derived as
Still, the ratio of Za/Zb needs to be calculated first. It is assumed that L1 and L3 are perfectly coupled, L2 and L4 are perfectly coupled. The number of turns of L1 and L2 is N1. The number of turns of L3 and L4 is N2. Thus, we have the equations shown below.
=
236
⎡ 1 ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
1
⎤ ⎥ ⎥ ⎥⎡ ⎥⎢ ⎥⎢ ⎥⎣ ⎥ ⎥ ⎦
⁄ ⁄ ⁄ ⁄
⎤ ⎥ ⎥ ⎦
(12)
Fig. 13 Magnetic circuit
(a) (b) Fig. 15 Current waveform. (a) non-balanced; (b) balanced
Fig. 14 Equivalent circuit
The circuit in Fig. 11(a) can be transformed in to Fig. 14. Then the equation of Veq1 and Veq2 can be derived. = + + (13) = + + From (12) and (13), we can get ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩
+ 2(1 + )
= 1 1(
+ 2(1 + )
1(
+ 2(1 + )
+ 2(1 + )
If we assume: = 1 = 1
+ 2(1 + )
+ 2(1 + )
= 1
2 1
2 1
Fig. 16 CM noise reduction
+ 2(1 + )
1
2
V. (14)
+
∙ )∙
+ 2(1 + )
2 2
Table 1. Loss breakdown for non-coupled inductor
2 1
+ 2(1 + )
1 2 2 1
+ 2(1 + )
2 2
INDUCTOR DESIGN
Previously, the two phase PFC converter has two independent non-coupled inductors. Table 1 shows the loss breakdown for two non-coupled inductors. The non-coupled inductor uses two ER23 core. The winding is 250/46 litz wire with 10 turns for each inductor.
)∙
+ 2(1 + ) + 2(1 + )
+
∙
(15)
Then the four inductor circuit in Fig. 11(a) can be simplified as two inductor circuit structure as Fig. 2. The selfinductance is equal to Leq, and the mutual inductance is equal to Meq. Hence, the new expression of Leq1, Leq2, Leq3 and Leq4 can be expressed using Leq and Meq. In order to verify this theory, a simulation model is build that Leq and Meq of the balanced circuit is equal to L and M of the non-balanced circuit. From Fig. 15, it can be seen that the balanced circuit and non-balanced circuit have identical current waveform. Fig. 16 shows the simulated CM noise. It can be seen that CM noise can have a 30dB reduction with balance technique.
DC W. Loss/W
AC W. Loss/W
Core Loss/W
Total Loss/W
0.7
1.6
2.3
4.6
The non-coupled inductor design provided a baseline of inductor size and loss. The design of coupled inductor is shown below. Based on the previous analysis, in order to reduce the average switching frequency, strong coupling is preferred. In this paper, α = -0.7 is chosen. However, the typical EI core structure cannot achieve such high coupling coefficient. Therefore the first attempt is UI core (Structure I). PCB winding has been used in many applications because it is easy to manufacture and easy to control the parasitic. Fig. 17 shows the structure of coupled inductor with PCB winding in a UI core. L1 is winded on the left leg with 5-layer PCB, each layer has 2 turns. L2 is winded on the right leg with 10 turns PCB winding. Table 2 shows the simulated loss breakdown of this coupled inductor in UI core structure. It can be seen that this coupled inductor has much higher AC
237
Fig. 20 Coupled inductor Structure III
Fig. 17 Coupled inductor in UI core
Fig. 21 Flux simulation result of left leg Fig. 18 Coupled inductor with interleaving
Fig. 19 Flux simulation result of left leg
Fig. 20 Coupled inductor with balance
Table 2. Loss breakdown for coupled inductor Structure I
DC W. Loss/W
AC W. Loss/W
Core Loss/W
Total Loss/W
0.5
6.2
1.3
8.0
Table 4. Loss breakdown for coupled inductor Structure III
winding loss than the non-coupled inductor. Therefore the total loss of this coupled inductor is much higher than the noncoupled inductor. This is because of the large eddy current loss in the PCB winding. In order to reduce the winding loss, a new structure of coupled inductor is developed (Structure II). As shown in Fig 18, the core structure is EI core. In addition, the interleave concept is applied to this structure. Instead of winding L1 only on left leg and L2 only on right leg, L1 and L2 have switched on the third layer. Now there are 8 turns of L1 and 2 turns of L2 on the left leg, 8 turns of L2 and 2 turns of L1 on the right leg. Table 3 shows the simulated loss breakdown of this new inductor structure. With interleaving effect, the AC winding loss has been greatly reduced. However, the total loss of this coupled inductor is still higher than the non-coupled inductor. FEA simulation is conducted to study that. Fig. 19 shows the FEA simulation result of left leg. It can be seen that there is strong fringing flux near the air gap, which will cause large loss on the winding.
AC W. Loss/W
Core Loss/W
Total Loss/W
0.5
2.6
1.9
5.0
AC W. Loss/W
Core Loss/W
Total Loss/W
0.5
1.9
1.9
4.3
According to [9], the winding can be cut to avoid fringing flux. Fig.20 shows the new winding structure to further reduce the winding loss (Structure III). In this structure, there is total 6 layers of PCB winding. The bottom two layers has only one turn. The winding on forth layer has been cut to avoid the fringing flux. Table 4 shows the simulated loss breakdown of inductor Structure III. With the new structure, the AC winding loss has been further reduced. Fig. 21 shows the FEA simulation result of left leg. It can be seen that the winding has avoid the fringing flux. The total loss of coupled inductor Structure III is smaller than the non-coupled inductor. The result shows that for coupled inductor, a good PCB winding structure can achieve similar loss as litz wire. With the PCB winding, a great amount of labor work can be removed in manufacture. Table 5. Loss breakdown for coupled inductor with balance
Table 3. Loss breakdown for coupled inductor Structure II
DC W. Loss/W
DC W. Loss/W
DC W. Loss/W
AC W. Loss/W
Core Loss/W
Total Loss/W
0.6
2.1
1.9
4.6
In section III, balance technique is applied to reduce CM noise. It can be easily implemented by replace the bottom layer of Structure III with the balance inductor L3 and L4, as shown in Fig. 22. Table 5 shows the simulated loss breakdown
238
of this coupled inductor with balance technique. The total loss is similar as the non-coupled inductor with litz wire. VI.
[3]
CONCLUSION
The major contribution of this paper is analyzing the impact of coupled inductor on MHz CRM PFC converter. The coupled inductor can help reducing the average switching frequency to reduce loss. With the coupled inductor, the ZVS range of CRM PFC converter is extended and the circulating energy is reduced. In addition, this paper introduces the balance technique for coupled inductor and analyzes the equivalent inductance of the new structure with balance technique. The balance technique can effectively reduce CM noise. Furthermore, a novel interleaved PCB winding coupled inductor structure is proposed. With this new structure, the boost inductor can be built with PCB winding with similar loss as the litz wire inductor.
[4]
[5]
[6]
REFERENCES
[7]
Jih-Sheng Lai; Chen, D., "Design consideration for power factor correction boost converter operating at the boundary of continuous conduction mode and discontinuous conduction mode," Applied Power Electronics Conference and Exposition, 1993. APEC '93. Conference Proceedings 1993., Eighth Annual , vol., no., pp.267,273, 7-11 Mar 1993 [2] Sebastian, J.; Cobos, J.A.; Lopera, J.M.; Uceda, J., "The determination of the boundaries between continuous and discontinuous conduction modes in PWM DC-to-DC converters used as power factor preregulators," Power Electronics, IEEE Transactions on , vol.10, no.5, pp.574,582, Sep 1995 [1]
[8]
[9]
239
Jindong Zhang; Shao, J.; Peng Xu; Lee, F.C.; Jovanovic, M.M., "Evaluation of input current in the critical mode boost PFC converter for distributed power systems," Applied Power Electronics Conference and Exposition, 2001. APEC 2001. Sixteenth Annual IEEE , vol.1, no., pp.130,136 vol.1, 2001 Laszol Huber, Yungtaek Jang, Milan M. Jovanonic, Performance Evaluation of Bridgeless PFC Boost Rectifiers, IEEE Transcation on Power Electronics, May 2008 P. Wong, P. Xu, P. Yang, and F. C. Lee, “Performance improvements of interleaving VRMs with coupling inductors,” IEEE Trans. Power Electron., vol. 16, no. 4, pp. 499–507, Jul. 2001. Fei Yang; Xinbo Ruan; Yang Yang; Zhihong Ye, "Interleaved Critical Current Mode Boost PFC Converter With Coupled Inductor," Power Electronics, IEEE Transactions on , vol.26, no.9, pp.2404,2413, Sept. 2011 Xiucheng Huang; Lee, F.C.; Qiang Li; Weijing Du, "MHz GaN-based interleaved CRM bi-directional buck/boost converter with coupled inductor," Applied Power Electronics Conference and Exposition (APEC), 2015 IEEE , vol., no., pp.2075,2082, 15-19 March 2015 Pengju Kong; Shuo Wang; Lee, F.C.; Chuanyun Wang, "Common-Mode EMI Study and Reduction Technique for the Interleaved Multichannel PFC Converter," Power Electronics, IEEE Transactions on , vol.23, no.5, pp.2576,2584, Sept. 2008 Dianbo Fu; Lee, F.C.; Shuo Wang, "Investigation on transformer design of high frequency high efficiency dcdc converters," Applied Power Electronics Conference and Exposition (APEC), 2010 Twenty-Fifth Annual IEEE , vol., no., pp.940,947, 21-25 Feb. 2010
