Parasitic Capacitance Cancellation Technique byUsing Mutual Inductance and Magnetic Coupling

Abdulrhman AlshaabaniElectrical and Computer Engineering

Michigan State UniversityEast Lansing, USAalshaaba@msu.edu

Bingsen WangElectrical and Computer Engineering

Michigan State UniversityEast Lansing, USA

bingsen@egr.msu.edu

Abstract—This paper presents a technique for improving theperformance of inductor at high-frequency through mitigatingthe effects caused by the parasitic capacitance. This techniqueadds a small capacitor to the coupled windings of the inductor tocancel the parasitic capacitance of the inductor. This techniquecan also be used to improve the coupled windings with leakageinductance. The relationship between the parasitic capacitance,magnetic coupling coefficient, and the small capacitor is intro-duced. The method to determine the value of the small capacitoris described in this paper. The results of applying this techniquewith different value of magnetic coupling coefficient k show thatan improvement of the inductor impedance by around 20-45dB depending on k. MATLAB software is used to verify thetechnique.

Index Terms—Parasitic capacitance cancellation, boost con-verter, magnetic component.

I. INTRODUCTION

Inductors and common-mode chokes have inherent resis-tance and capacitance parasitics which can affect their per-formance. The parasitic resistance can be caused by windingresistance and core loss. The parasitic capacitance exists dueto capacitances between turn to turn and layer to layer of thewinding, also from capacitance between winding and core.The parasitic components of an inductor can be representedby lumped parameters as shown in Fig. 1 (a) [1]–[3].

At high frequency, the inductor impedance is dominatedby parasitic capacitance, which can affect the impedance ofan inductor as shown in Fig. 1(b). The inductor impedanceincreases as frequency increases up to a certain extent. Thisphenomena occurs because of the limitation and geometry ofinductor material [1], [2], [4]. The performance of an inductorcan be measured by different methods such as the quality Q-factor method.

Several techniques have been proposed to improve inductorperformance at high frequencies [1], [4]–[7]. The techniquesof parasitic capacitance cancellation can be divided into threemain approaches. Mutual capacitance in which the parasiticcapacitance of an inductor is cancelled using the mutualcapacitance between two separate capacitors [5], [7]. Mutualinductor in which the parasitic capacitance of an inductor iscancelled by adding a small capacitor with mutual inductormodel can generate a negative capacitor to eliminate the

L Rp

Cp |Z|

Frequency

(a) (b)

Fig. 1. (a) Inductor model of parasitics (b) The impedance curve of aninductor versus frequency.

parasitic capacitance of an inductor [4]–[6], [8]. The thirdapproach is adding a small magnetic components or radiofrequency to the inductor in order to improve its performanceand cancel the parasitic capacitance [1].

If the magnetic coupling changes, then the inductor valuewill change too, therefore it is necessary to calculate the smallcapacitor to generate an appropriate value of the negativecapacitance. The calculation method of the additional capacitorshould be based on the magnetic coupling coefficient toimprove the efficiency of the inductor. This paper introduces atechnique that calculates the additional capacitor by the valueof magnetic coupling.

Adding a capacitor to an inductor has been previouslydone for EMI filters [1], [4]–[6]. The proposed approach forparasitic capacitance cancellation determines the additionalcapacitance for different coupling coefficients. The proposedapproach enables for better inductor performance at frequen-cies up to 1 MHz. While the current EMI approaches sufferfrom bad performance at lower frequencies, the proposedtechnique achieves an enhancement up to 45 dB. The mutualinductance concept will be applied to an inductor with a newtechnique in order to improve its performance and eliminatethe parasitic capacitance.

The parasitic capacitance cancellation technique for aninductor based on the relationship between mutual inductancemodel with magnetic coupling coefficient value is presentedin section II. In the section III, the simulation result ofapplying the new parasitic capacitance cancellation techniqueby MATLAB software is shown. Finally, the conclusion anddiscussion are presented in section IV.

978-1-7281-4878-6/19/$31.00 ©2019 IEEE 1770

L1 L2

C

Fig. 2. The direct coupled windings with adding small capacitor.

2L1 L1((1+k2)/k2)

C

-L1

Fig. 3. The decoupled mutual inductance with magnetic coupling coefficient.

II. CANCELLATION TECHNIQUE USING MUTUALINDUCTANCE AND MAGNETIC COUPLING

The parasitic capacitance is modeled by the capacitor thatis connected between the terminals of winding as shown inthe Fig. 1 (a). In order to eliminate the parasitic capacitanceof an inductor, generating a negative capacitance is one of theeffective methods [4], [5], [7]. The cancellation parasitic ca-pacitance method of two direct and indirect coupled windingsof an inductor has been proposed in [8]. This paper introducesa technique using two coupled windings as a relation to themagnetic coupling coefficient of the inductor. Fig 2. shows aninductor that has direct coupled windings with an additionalsmall capacitance C. This coupled windings is assumed tohave two inductances with different values L1 and L2. Thecoupling coefficient k of the two windings is not equal to1. The additional capacitor with a small value, which isdetermined later on , is connected to the center tap of theinductor.

The number of turns can be chosen as N = L1

M whereM is the mutual inductance of the two windings. The twowindings of the inductor can be decoupled by decouplingnetwork method. Fig. 3 depicts the decoupled inductor withthe magnetic coupling coefficient k 6= 1 and N = L1

M . In orderto generate a negative capacitance that can cancel the effects ofparasitic capacitance, Y −∆ transformation theory is applied.The equivalent circuit of applying Y −∆ transformation usingsynthesis theory is represented in Fig. 4.

Cp Cv

Ls Lv

L1((a/2)-1)

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

L1(1-(2/a))

Fig. 4. The π model of decoupled mutual inductance with k and the additionsmall capacitor.

As shown in Fig. 4, the effects of adding a small capacitorto the coupled inductor with k 6= 1 are described by threedifferent capacitors values. First capacitor Cv is in parallelwith the parasitic capacitance and series with Ls. The othertwo capacitors are shunt capacitors with different values. Theparameters that are shown in the π model are equal to thefollowing

a =1 + k2

k2(1)

Cv =C

−2a(2)

Lv = 2aL1 (3)

Ls = (2− a)L1 (4)

where a is a simplified equation that is derived from themodeling of direct coupled windings when the number of turnsis chosen as N = L1

M . The highest value of a is 2 when k = 1.Cv has always a negative capacitance that can impact andeliminate the parasitic capacitance at any value of k. Lv whichis the inductance has a positive value at any the magneticcoupling coefficient.

The value of both two inductors and two capacitors on theshunt sides depend on the value of k. The two shunt inductorscan be positive or negative depending on k, while the shuntcapacitors are always positive with very small capacitance.The parameters for different magnetic coupling coefficient kare determined as follows:

k = 1⇒

Ls = 0C

1+ a2

= C1+ 2

a

= 0

L1(a2 − 1) = L1(1− 2

a ) = 0

0.9 ≤ k < 1⇒

−20%L1 ≤ Ls < 0C

1+ a2

= C1+ 2

a

= 50%C

−11%L1 ≤ L1(a2 − 1) < 0

L1(1− 2a ) ≤ 10%L1

0.85 ≤ k ≤ 0.89⇒

−35%L1 ≤ Ls < 0C

1+ a2

= C1+ 2

a

≈ 50%C

17%L1 = L1(a2 − 1)

L1(1− 2a ) ≤ 15%L1

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0.8 ≤ k ≤ 0.85⇒

−55%L1 ≤ Ls < 0C

1+ a2≈ C

1+ 2a

≈ 50%C

L1(a2 − 1) ≤ 28%L1

L1(1− 2a ) ≤ 22%L1

In the case of a coupled inductor when the magneticcoupling 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 ofcoupled inductor are increased and high.

The effects of parasitic capacitance, as shown in Fig. 4,will be on top side of the circuit which can be called Zc.The equivalent impedance equation of the parasitic capacitancewith Zc is as follows

Zceq =s3LvLsCv + s(Lv + Ls)

s4LvLsCvCp + s2(Lv + Ls)Cp + 1(5)

Zceq is the equivalent impedance of π model including theparasitic capacitance and the generated negative capacitance.The generated capacitance can be determined through (5)when the parasitic capacitance value is known. Cp can bedetermined by using the analytical method proposed by [2], orthrough finding the total impedance when frequency is appliedwith various values by experimental results as shown in [7].

In order to increase the efficiency of the inductor byeliminating Cp, the capacitance C of the additional smallcapacitor should be determined. C can be determined when themagnetic coupling coefficient value changes. The followingequation is the equivalent impedance of the circuit includingthe parasitic capacitance and C to reach higher cancellationfor the inductor.

Zpc =s3L2

1C(2a− g) + (sL1g)

s4L21CCp(2a− g) + s2L1(gCp − C) + 1

(6)

g = a+ 2 (7)

The relationship between the parasitic capacitance, magneticcoupling coefficient, and the adding small capacitor can bedetermined from (6). The following equation can determinethe appropriate value of the added small capacitance basedon the different values of magnetic coupling and the parasiticcapacitance.

C =3k2 + 1

k2Cp (8)

Equation (8) shows that the additional small capacitor valueis changed depending on the magnetic coupling coefficient.When the magnetic coupling have k = 1, the small capacitorvalue will be equal to four times the parasitic capacitancevalue. This result is same as the small capacitance valuethat was proposed in [4] for k = 1. C value is inverselyproportional to the square k. However, the significance ofthis technique is that the value of a small capacitor is deter-mined when the windings are not coupled perfectly. Therefore,the cancellation of parasitic capacitance for an inductor canachieve the higher elimination and improve its efficiency.

VinputVoutput

L1 L2

Fig. 5. The boost converter with mutual inductance.

III. SIMULATION RESULTS

In this section, the parasitic capacitance cancellation tech-nique using the mutual inductance and magnetic couplingcoefficient for an inductor is applied on MATLAB software toverify the method. The parasitic capacitance of an inductor iscalculated by using the analytical method in [2]. The inductorvalue is calculated to provide a load of 1 kW for a boostconverter as shown in Fig. 5. The input and output voltagesof the boost converter are 70 V and 200 V, respectively. Theinductor has 890 µH inductance while the parasitic capacitanceof the inductor is 17 pF .

Fig. 6 (a) shows the coupled inductor of two windings thatincludes the parasitic capacitance of the total inductor in the πmodel. The magnetic coupling coefficient k is included in themodel with various value of k. Fig. 6 (b) shows the coupledinductor of two windings with including the additional smallcapacitor in π model where the magnetic coupling k is notperfectly coupled. In order to test the technique of cancellationthe parasitic capacitance of an inductor with different values ofk, MATLAB software is applied. The results and performanceof the coupled inductor are tested with two different magneticcoupling coefficient k = 0.98 and k = 0.90.

The additional small capacitor C is calculated depending onk = 0.98 where C = 68.7pF . Hence, the generated negativecapacitance of the coupled inductor is Cv = −16.83pF .The simulation result of cancellation the parasitic capacitancetechnique is shown in Fig. 7. The inductance impedance isimproved by using the technique of cancellation Cp withappropriate value of C by around 45 dB. The impedance ofinductance has 8.23 dB but when the parasitic capacitancecancellation technique is applied, the impedance value isimproved to be 54.8 dB. This means the parasitic capacitanceis eliminated and the inductor can store more energy and hasbetter performance Besides reducing the magnetic componentsize at high frequency.

Fig. 8 presents of coupled inductor with and without addinga small capacitor when the coefficient value of magneticcoupling is k = 0.90. The additional small capacitor iscalculated to be C = 71.99pF and the generated negativecapacitance is Cv = −16.11pF . This technique shows goodresults even if the magnetic coupling value is low. Theperformance of the inductor is enhanced by around 32 dBcompared to the inductor without applying this technique. Theimpedance of inductance becomes 55.4 dB with applying the

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2L1(1-(a/2))

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

CpCp Cv

Ls Lv

L1((a/2)-1)

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

L1(1-(2/a))

(a) (b)

Fig. 6. (a) The mutual inductance and magnetic coupling coefficient with-out additional capacitor. (b) The mutual inductance and magnetic couplingcoefficient with additional capacitor.

Mag

nit

ud

e (d

B)

Frequency (rad/sec)

101102 103 104 105 106 107 108

0

100

200

-100

-300

-200

Fig. 7. The bode diagram of comparison between with and without additionalcapacitor when k = 0.98

technique while the impedance without parasitic capacitancecancellation technique is 23.1 dB. The best cancellation ofparasitic capacitance is when the frequency that is appliedon an inductor under 1 MHz. By choosing the value ofsmall capacitor based on the magnetic coupling value, thecancellation of Cp will be more effective. Thus, the inductorcan work with higher efficiency at high frequency. Also, thelosses of an inductor are reduced.

IV. CONCLUSION

In this paper, a technique for improving the inductor per-formance at high frequency with imperfect coupled windingsby eliminating the effects of parasitic capacitance has beenproposed. This technique uses additional a small capacitor to

Frequency (rad/sec)

Mag

nit

ud

e (d

B)

101 102 103 104 105 106 107 108-300

-200

-100

0

100

200

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

be inserted into the mutual coupling of the inductor. Thereis a leakage inductance due the two coupled windings of theinductor. Therefore, this technique represents a π model forthe coupled windings with leakage inductance. The techniqueadds an additional small capacitor in order to have the higherparasitic capacitance cancellation for the inductor. Anotherfeature of this technique is the new method to calculate thevalue of the additional small capacitor based on the magneticcoupling coefficient of the inductor. This technique showsimprovement for inductor performance at frequencies below 1MHz by increasing the value of inductance impedance between(20-45) dB depending on the magnetic coupling value. Theimpedance of the inductor increases at high frequencies whenk has a high value. The simulation results show that applyingthis technique can improve the characteristics of the inductor.By using this technique, the inductor can be designed basedon the magnetic coupling value besides the frequency and sizeto have a better performance.

REFERENCES

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[7] S. Wang, F. C. Lee, and J. D. Van Wyk, “Inductor winding capacitancecancellation using mutual capacitance concept for noise reduction ap-plication,” IEEE transactions on electromagnetic compatibility, vol. 48,no. 2, pp. 311–318, 2006.

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