Parasitic Capacitance Cancellation Technique by Using Mutual Inductance and Magnetic Coupling

Abdulrhman Alshaabani Bingsen Wang Electrical and Computer Engineering Electrical and Computer Engineering Michigan State University Michigan State University East Lansing, USA East Lansing, USA [email protected] [email protected]

Abstract—This paper presents a technique for improving the |Z| performance of inductor at high-frequency through mitigating Cp the effects caused by the parasitic capacitance. This technique adds a small capacitor to the coupled windings of the inductor to cancel the parasitic capacitance of the inductor. This technique Frequency can also be used to improve the coupled windings with leakage L Rp inductance. The relationship between the parasitic capacitance, (a) (b) magnetic coupling coefficient, and the small capacitor is intro- duced. The method to determine the value of the small capacitor is described in this paper. The results of applying this technique Fig. 1. (a) Inductor model of parasitics (b) The impedance curve of an with different value of magnetic coupling coefficient k show that inductor versus frequency. an improvement of the inductor impedance by around 20-45 dB depending on k. MATLAB software is used to verify the technique. parasitic capacitance of an inductor [4]–[6], [8]. The third Index Terms—Parasitic capacitance cancellation, boost con- approach is adding a small magnetic components or radio verter, magnetic component. frequency to the inductor in order to improve its performance and cancel the parasitic capacitance [1]. I.INTRODUCTION If the magnetic coupling changes, then the inductor value Inductors and common-mode chokes have inherent resis- will change too, therefore it is necessary to calculate the small tance and capacitance parasitics which can affect their per- capacitor to generate an appropriate value of the negative formance. The parasitic resistance can be caused by winding capacitance. The calculation method of the additional capacitor resistance and core loss. The parasitic capacitance exists due should be based on the magnetic coupling coefficient to to capacitances between turn to turn and layer to layer of the improve the efficiency of the inductor. This paper introduces a winding, also from capacitance between winding and core. technique that calculates the additional capacitor by the value The parasitic components of an inductor can be represented of magnetic coupling. by lumped parameters as shown in Fig. 1 (a) [1]–[3]. Adding a capacitor to an inductor has been previously At high frequency, the inductor impedance is dominated done for EMI filters [1], [4]–[6]. The proposed approach for by parasitic capacitance, which can affect the impedance of parasitic capacitance cancellation determines the additional an inductor as shown in Fig. 1(b). The inductor impedance capacitance for different coupling coefficients. The proposed increases as frequency increases up to a certain extent. This approach enables for better inductor performance at frequen- phenomena occurs because of the limitation and geometry of cies up to 1 MHz. While the current EMI approaches suffer inductor material [1], [2], [4]. The performance of an inductor from bad performance at lower frequencies, the proposed can be measured by different methods such as the quality Q- technique achieves an enhancement up to 45 dB. The mutual factor method. inductance concept will be applied to an inductor with a new Several techniques have been proposed to improve inductor technique in order to improve its performance and eliminate performance at high frequencies [1], [4]–[7]. The techniques the parasitic capacitance. of parasitic capacitance cancellation can be divided into three The parasitic capacitance cancellation technique for an main approaches. Mutual capacitance in which the parasitic inductor based on the relationship between mutual inductance capacitance of an inductor is cancelled using the mutual model with magnetic coupling coefficient value is presented capacitance between two separate capacitors [5], [7]. Mutual in section II. In the section III, the simulation result of inductor in which the parasitic capacitance of an inductor is applying the new parasitic capacitance cancellation technique cancelled by adding a small capacitor with mutual inductor by MATLAB software is shown. Finally, the conclusion and model can generate a negative capacitor to eliminate the discussion are presented in section IV.

Ls Lv C

L1((a/2)-1) L1(1-(2/a))

C/(1+(2/a)) C/(1+(a/2))

Fig. 4. The π model of decoupled mutual inductance with k and the addition Fig. 2. The direct coupled windings with adding small capacitor. small capacitor.

As shown in Fig. 4, the effects of adding a small capacitor 2 2 to the coupled inductor with k 6= 1 are described by three 2L1 L1((1+k )/k ) different capacitors values. First capacitor Cv is in parallel with the parasitic capacitance and series with Ls. The other -L two capacitors are shunt capacitors with different values. The 1 parameters that are shown in the π model are equal to the following 1 + k2 a = (1) C k2 C C = (2) v −2a Lv = 2aL1 (3)

Fig. 3. The decoupled mutual inductance with magnetic coupling coefficient. Ls = (2 − a)L1 (4) where a is a simplified equation that is derived from the modeling of direct coupled windings when the number of turns II.CANCELLATION TECHNIQUEUSINGMUTUAL is chosen as N = L1 . The highest value of a is 2 when k = 1. INDUCTANCEANDMAGNETICCOUPLING M Cv has always a negative capacitance that can impact and The parasitic capacitance is modeled by the capacitor that eliminate the parasitic capacitance at any value of k. Lv which is connected between the terminals of winding as shown in is the inductance has a positive value at any the magnetic the Fig. 1 (a). In order to eliminate the parasitic capacitance coupling coefficient. of an inductor, generating a negative capacitance is one of the The value of both two inductors and two capacitors on the effective methods [4], [5], [7]. The cancellation parasitic ca- shunt sides depend on the value of k. The two shunt inductors pacitance method of two direct and indirect coupled windings can be positive or negative depending on k, while the shunt of an inductor has been proposed in [8]. This paper introduces capacitors are always positive with very small capacitance. a technique using two coupled windings as a relation to the The parameters for different magnetic coupling coefficient k magnetic coupling coefficient of the inductor. Fig 2. shows an are determined as follows: inductor that has direct coupled windings with an additional  small capacitance C. This coupled windings is assumed to Ls = 0  C C have two inductances with different values L1 and L2. The k = 1 ⇒ 1+ a = 1+ 2 = 0 coupling coefficient k of the two windings is not equal to  2 a L ( a − 1) = L (1 − 2 ) = 0 1. The additional capacitor with a small value, which is 1 2 1 a determined later on , is connected to the center tap of the  −20%L ≤ L < 0 inductor.  1 s  C C L1  a = = 50%C The number of turns can be chosen as N = where  1+ 1+ 2 M 0.9 ≤ k < 1 ⇒ 2 a M is the mutual inductance of the two windings. The two −11%L ≤ L ( a − 1) < 0  1 1 2 windings of the inductor can be decoupled by decoupling  2 L1(1 − ) ≤ 10%L1 network method. Fig. 3 depicts the decoupled inductor with a k 6= 1 N = L1  the magnetic coupling coefficient and M . In order −35%L ≤ L < 0  1 s to generate a negative capacitance that can cancel the effects of  C C  1+ a = 1+ 2 ≈ 50%C parasitic capacitance, Y − ∆ transformation theory is applied. 0.85 ≤ k ≤ 0.89 ⇒ 2 a a The equivalent circuit of applying Y −∆ transformation using 17%L1 = L1( − 1)  2 synthesis theory is represented in Fig. 4.  2 L1(1 − a ) ≤ 15%L1

1771  −55%L ≤ L < 0  1 s  C C L1 L2  1+ a ≈ 1+ 2 ≈ 50%C 0.8 ≤ k ≤ 0.85 ⇒ 2 a L ( a − 1) ≤ 28%L  1 2 1  2  V Voutput L1(1 − a ) ≤ 22%L1 input In the case of a coupled inductor when the magnetic coupling coefficient is in the range between 0.85 ≤ k < 1, the performance of the coupled is high and the losses are low. When the magnetic coupling coefficient k < 0.7, the losses of Fig. 5. The boost converter with mutual inductance. coupled inductor are increased and high. The effects of parasitic capacitance, as shown in Fig. 4, III.SIMULATION RESULTS will be on top side of the circuit which can be called Zc. The equivalent impedance equation of the parasitic capacitance In this section, the parasitic capacitance cancellation tech- with Zc is as follows nique using the mutual inductance and magnetic coupling coefficient for an inductor is applied on MATLAB software to s3L L C + s(L + L ) v s v v s verify the method. The parasitic capacitance of an inductor is Zceq = 4 2 (5) s LvLsCvCp + s (Lv + Ls)Cp + 1 calculated by using the analytical method in [2]. The inductor Zceq is the equivalent impedance of π model including the value is calculated to provide a load of 1 kW for a boost parasitic capacitance and the generated negative capacitance. converter as shown in Fig. 5. The input and output voltages The generated capacitance can be determined through (5) of the boost converter are 70 V and 200 V, respectively. The when the parasitic capacitance value is known. Cp can be inductor has 890 µH inductance while the parasitic capacitance determined by using the analytical method proposed by [2], or of the inductor is 17 pF . through finding the total impedance when frequency is applied Fig. 6 (a) shows the coupled inductor of two windings that with various values by experimental results as shown in [7]. includes the parasitic capacitance of the total inductor in the π In order to increase the efficiency of the inductor by model. The magnetic coupling coefficient k is included in the eliminating Cp, the capacitance C of the additional small model with various value of k. Fig. 6 (b) shows the coupled capacitor should be determined. C can be determined when the inductor of two windings with including the additional small magnetic coupling coefficient value changes. The following capacitor in π model where the magnetic coupling k is not equation is the equivalent impedance of the circuit including perfectly coupled. In order to test the technique of cancellation the parasitic capacitance and C to reach higher cancellation the parasitic capacitance of an inductor with different values of for the inductor. k, MATLAB software is applied. The results and performance s3L2C(2a − g) + (sL g) of the coupled inductor are tested with two different magnetic Z = 1 1 pc 4 2 2 (6) coupling coefficient k = 0.98 and k = 0.90. s L1CCp(2a − g) + s L1(gCp − C) + 1 The additional small capacitor C is calculated depending on g = a + 2 (7) k = 0.98 where C = 68.7pF . Hence, the generated negative The relationship between the parasitic capacitance, magnetic capacitance of the coupled inductor is Cv = −16.83pF . coupling coefficient, and the adding small capacitor can be The simulation result of cancellation the parasitic capacitance determined from (6). The following equation can determine technique is shown in Fig. 7. The inductance impedance is the appropriate value of the added small capacitance based improved by using the technique of cancellation Cp with on the different values of magnetic coupling and the parasitic appropriate value of C by around 45 dB. The impedance of capacitance. inductance has 8.23 dB but when the parasitic capacitance cancellation technique is applied, the impedance value is 2 3k + 1 improved to be 54.8 dB. This means the parasitic capacitance C = Cp (8) k2 is eliminated and the inductor can store more energy and has Equation (8) shows that the additional small capacitor value better performance Besides reducing the magnetic component is changed depending on the magnetic coupling coefficient. size at high frequency. When the magnetic coupling have k = 1, the small capacitor Fig. 8 presents of coupled inductor with and without adding value will be equal to four times the parasitic capacitance a small capacitor when the coefficient value of magnetic value. This result is same as the small capacitance value coupling is k = 0.90. The additional small capacitor is that was proposed in [4] for k = 1. C value is inversely calculated to be C = 71.99pF and the generated negative proportional to the square k. However, the significance of capacitance is Cv = −16.11pF . This technique shows good this technique is that the value of a small capacitor is deter- results even if the magnetic coupling value is low. The mined when the windings are not coupled perfectly. Therefore, performance of the inductor is enhanced by around 32 dB the cancellation of parasitic capacitance for an inductor can compared to the inductor without applying this technique. The achieve the higher elimination and improve its efficiency. impedance of inductance becomes 55.4 dB with applying the

1772 be inserted into the mutual coupling of the inductor. There

Cp is a leakage inductance due the two coupled windings of the Cp Cv

2L1(1-(a/2)) Ls Lv inductor. Therefore, this technique represents a π model for the coupled windings with leakage inductance. The technique L1((a/2)-1) L1(1-(2/a)) L1(1-(2/a)) L1((a/2)-1) adds an additional small capacitor in order to have the higher C/(1+(2/a)) C/(1+(a/2)) parasitic capacitance cancellation for the inductor. Another (a) (b) feature of this technique is the new method to calculate the value of the additional small capacitor based on the magnetic coupling coefficient of the inductor. This technique shows Fig. 6. (a) The mutual inductance and magnetic coupling coefficient with- improvement for inductor performance at frequencies below 1 out additional capacitor. (b) The mutual inductance and magnetic coupling coefficient with additional capacitor. MHz by increasing the value of inductance impedance between (20-45) dB depending on the magnetic coupling value. The impedance of the inductor increases at high frequencies when

200 k has a high value. The simulation results show that applying

100 this technique can improve the characteristics of the inductor.

) By using this technique, the inductor can be designed based

dB 0 ( on the magnetic coupling value besides the frequency and size

-100 to have a better performance. Magnitude -200 REFERENCES

-300 [1] T. C. Neugebauer and D. J. Perreault, “Parasitic capacitance cancellation 1 4 5 6 7 8 10 102 103 10 10 10 10 10 in filter inductors,” IEEE Transactions on Power Electronics, vol. 21, Frequency (rad/sec) no. 1, pp. 282–288, 2006. [2] A. Massarini and M. K. Kazimierczuk, “Self-capacitance of inductors,” IEEE transactions on power electronics, vol. 12, no. 4, pp. 671–676, Fig. 7. The bode diagram of comparison between with and without additional 1997. capacitor when k = 0.98 [3] A. Massarini, M. Kazimierczuk, and G. Grandi, “Lumped parameter models for single-and multiple-layer inductors,” in PESC Record. 27th Annual IEEE Power Electronics Specialists Conference, vol. 1. IEEE, 1996, pp. 295–301. technique while the impedance without parasitic capacitance [4] R. Chen, J. D. Van Wyk, S. Wang, and W. G. Odendaal, “Improving the cancellation technique is 23.1 dB. The best cancellation of characteristics of integrated emi filters by embedded conductive layers,” IEEE Transactions on Power Electronics, vol. 20, no. 3, pp. 611–619, parasitic capacitance is when the frequency that is applied 2005. on an inductor under 1 MHz. By choosing the value of [5] S. Wang and F. C. Lee, “Analysis and applications of parasitic capacitance small capacitor based on the magnetic coupling value, the cancellation techniques for emi suppression,” IEEE Transactions on Industrial Electronics, vol. 57, no. 9, pp. 3109–3117, 2010. cancellation of Cp will be more effective. Thus, the inductor [6] ——, “Common-mode noise reduction for power factor correction circuit can work with higher efficiency at high frequency. Also, the with parasitic capacitance cancellation,” IEEE Transactions on Electro- losses of an inductor are reduced. magnetic Compatibility, vol. 49, no. 3, pp. 537–542, 2007. [7] S. Wang, F. C. Lee, and J. D. Van Wyk, “Inductor winding capacitance cancellation using mutual capacitance concept for noise reduction ap- IV. CONCLUSION plication,” IEEE transactions on electromagnetic compatibility, vol. 48, no. 2, pp. 311–318, 2006. In this paper, a technique for improving the inductor per- [8] ——, “Design of inductor winding capacitance cancellation for emi formance at high frequency with imperfect coupled windings suppression,” IEEE Transactions on Power Electronics, vol. 21, no. 6, by eliminating the effects of parasitic capacitance has been pp. 1825–1832, 2006. proposed. This technique uses additional a small capacitor to

200

100 )

dB 0 (

-100 Magnitude Magnitude -200

-300 101 102 103 104 105 106 107 108 Frequency (rad/sec)

Fig. 8. The bode diagram of comparison between with and without additional capacitor when k = 0.90

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