An Alternative Method to Determine the Initial ... - IEEE Xplore

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 47, NO. 3, AUGUST 2005

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An Alternative Method to Determine the Initial Permeability of Ferrite Core Using Network Analyzer Jing Shenhui, Student Member, IEEE, and Jiang Quanxing

Abstract—A simple experimental method to determine the initial complex permeability of the toroidal type ferrite core using thoroughly designed fixtures is introduced. With the ferrite core installed in a shorted coaxial line, the fixture forms a one turn coil of inductor or a shorted transmission line with distributed parameters. The relative permeability of the ferrite can then be extracted from S11 of the coaxial test holder with the aid of a vector network analyzer. The “one turn coil” modeling method for radio frequencies (RF), and the transmission line modeling method for higher frequencies, are described. To improve the measurement accuracy of the test system, the subsidiary RF resistors and impedance matching circuits are integrated into the fixtures. Test results of the proposed methods achieve good agreement with the results of the traditional transmission/reflection method and the Agilent E4991A material analyzer. The influence of air gap on accuracy is discussed, as well as the upper frequency limit due to cavity resonance. Compared with some existing studies, this method achieves satisfactory accuracy and can be accomplished with normal instruments. Index Terms—Ferrites, impedance matching, magnetic cores, permeability measurement.

I. INTRODUCTION ERRITE core inductors play important roles in electromagnetic noise suppression. The inductor used for interference suppression typically consists of a round copper wire wound on slug type or toroidal type ferrite core. The inductance of the ferrite core inductors depends not only on the number or geometry of the winding wires, but also on the permeability of the ferrite core. In addition, ferrite tiles also find useful application as absorbers (combined with pyramid absorbers) in anechoic rooms. The permeability of ferrite versus frequency is important to the absorbing performance of ferrite tiles. The measurement of ferrite’s permeability is necessary for engineers to design and choose ferrite properly. At radio frequencies (RF), however, direct measurement of the permeability is difficult. Comprehensive reviews on the measurement techniques for RF material characterization are given in [1] and [2]. The commonly used methods for magnetic material evaluation are the transmission/reflection (T/R) method, equivalent circuit model method, resonant method, etc. [3], [4]. At RF, the ferrite core inductors can be described by a lumped parameter equivalent circuit, which consists of a series connected resistor R, an inductor L, and a parallel capacitor C.

F

Some existing methods ([5], [6]) to characterize the equivalent circuits of the inductors are not suitable for high frequencies because of the quasistatic assumptions used. In [7], the frequency dependent RLC equivalent circuit parameters, as well as the effective permeability of ferrite core, are extracted from the measured values, which are the impedance, the resonant frequency, the resonant impedance, and the quality factor of the RLC equivalent circuit. It is assumed that the capacitance of the equivalent circuit is invariant with frequency. The impedance measurement is accomplished using an impedance analyzer. Another extraction method, presented in [8], requires the assumption that the inductance of the equivalent circuit does not change significantly with frequency when the frequency is lower than the roll off frequency of core permeability. The equivalent circuit parameters of an inductor were then derived by measuring the resonant frequencies of two different inductor circuits whose resonant frequencies are close to each other. Due to the assumptions mentioned above, the upper frequency limitation of this method is the inductor’s self-resonant frequency. The measurements must be accomplished using both a network analyzer and an RF LCR meter. However, sometimes we need to determine the relative permeability of toroidal type ferrite core with the upper frequency extended to 1 GHz or even higher, and we are occasionally restricted to some common instruments such as a vector network analyzer (VNA). In this paper, a new technique for estimating the permeability of toroidal type ferrite core inserted in a coaxial holder using a VNA is described. Using the “one turn coil” modeling method and the transmission line modeling method, the test frequency band of the proposed technique can cover from 1 MHz up to 2 GHz, which is limited by the coaxial holder’s cavity resonance. The consistency between these two different modeling algorithms at RF and the accuracy of the method are well illustrated by the test result of a toroidal type Teflon sample. The test results of some ferrite samples, which are consistent with those obtained by the traditional T/R method and with an Agilent E4991A material analyzer, are also given to validate the study. The test uncertainties caused by the air gap between the sample and the holder are also discussed in detail. II. MEASUREMENT AND EXTRACTION METHODOLOGY

Manuscript received August 2, 2004; revised February 11, 2005. This work was supported in part by the National Natural Science Foundation of China (NSFC) under Contract 50277007. The authors are with the Electromagnetic Compatibility Laboratory, Southeast University, Nanjing 210096, China (e-mail: [email protected]). Digital Object Identifier 10.1109/TEMC.2005.853169

A. “One Turn Coil” Modeling Method We consider a toroidal type ferrite core installed in the end of a shorted coaxial line. As the shorted line provides the conducting path for the current, it forms a “one turn coil,” as shown in Fig. 1.

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Fig. 1.


Principles of one turn coil with ferrite core. Fig. 3.

Principles of transmission line modeling at higher frequencies.

The relative permeability of the ferrite core can then be derived from the measured impedance of the one turn coil. B. Transmission Line Modeling Method

Fig. 2.

Dimensional parameters of the coaxial test fixture.

The inductance of this one turn coil is defined as e h0 µ 1 dr dz. L= B dS = I 2πr a 0

(1)

According to the dimensional parameters of the test fixture shown in Fig. 2, we obtain the inductance as c h e h0 µ0 µ0 µr dr dz + dr dz L= 2πr 2πr c 0 b 0 b h0 c h0 µ0 µ0 dr dz + dr dz. (2) + 2πr 2πr b h a 0

Z0 = (4)

Where Lair is defined as the self-inductance of a one turn coil when the ferrite core is removed, which can be estimated as: µ0 e h0 ln . (5) Lair = 2π a Due to the loss of the ferrite core caused by alternating currents, the impedance of the one turn coil should be a complex value (Zˆ = jωL + R) rather than jωL. Thus, the selfinductance of this one turn coil, L in (4), should be expressed as a complex value ˆ ˆ= Z. L jω

(6)

Thus, (4) should be transformed as µ ˆr =

2π(Zˆ − jωLair ) + 1. jωµ0 h ln cb

ln

e c

2π · ε0 + ln ab +

1 εˆr

(3)

So 2π(L − Lair ) + 1. µr = µ0 h ln cb

Cˆm =

ln cb )

.

(10)

The characteristic impedances of these two sections of transmission lines are

Then we have

µ0 c e L= (µr − 1)h ln + h0 ln . 2π b a

When the frequency is so high that the wavelength is comparable with the dimensions of the holder, the fixture should not be considered as an inductor with lumped elements. Therefore, the coaxial fixture is modeled as a section of shorted transmission line with distributed parameters, as shown in Fig. 3. The distributed parameters of the upper shorted transmission line without the core are e µ0 e L0 = ln , C0 = 2π · ε0 / ln . (8) 2π a a And the distributed parameters of the other section of line with the core are defined as b µ0 c e ˆ Lm = ˆr ln ln + ln + µ (9) 2π c a b

(7)

L0 , C0

Zˆm =

ˆm L . Cˆm

(11)

Thus, the input impedance of this coaxial fixture is Zâir + j Zˆm tan(βˆm h) Zˆ = Zˆm · Zˆm + j Zâir tan(βˆm h)

(12)

where Zâir is the equivalent impedance of the upper section of transmission line without the sample, which acts as the load of the other section of transmission line below 2π · (h0 − h) Zâir = j · Z0 · tan (13) λ

ˆ m · Cˆm . (14) βˆm = 2π · f L Combining (8)–(14), the relative permeability of the ferrite core can then be derived from the measured input impedance of the transmission line. As the complex permittivity of the core is also unknown, several measurements under different conditions (such as altering the inner radius or the height of the fixture) are required in order to get enough equations for the final solutions.

SHENHUI AND QUANXING: AN ALTERNATIVE METHOD TO DETERMINE THE INITIAL PERMEABILITY

Fig. 4.

Fig. 5.

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Block diagram of low impedance matched circuit. Fig. 6.

Structure drawing of low impedance test fixture.

Fig. 7.

Measurement setup of the initial permeability.

Block diagram of high impedance matched circuit.

C. Matching Circuits for Impedance Measurement From the discussions above, it can be seen that both the “one turn coil” modeling and the transmission line modeling require accurate impedance measurement of the coaxial fixture to derive the permeability of the sample. Some specific impedance analyzers, for example the Agilent 4991A material and impedance analyzer, can provide accurate impedance measurements in a high dynamic range. Therefore, they are the recommended instruments for impedance measurement. Yet, in some circumstances, we are restricted to some common instruments such as a VNA to accomplish the measurements. The impedance should then be derived from S11 according to the following equation: ZˆL − ZˆC Sˆ11 = ZˆL + ZˆC

(15)

where ZˆL is the impedance loaded at the test head of VNA and ZˆC is the characteristic impedance of the transmission system, commonly 50 Ω. If ZˆL has a large deviation from ZˆC , the uncertainty of test system will be unacceptable. According to the relative permeability of typical ferrite cores [9], we estimated that the input impedance of the coaxial holder with ferrite core was in range of 0−200 Ω from 1 MHz to 2 GHz. This was proved by the following tests: in order to achieve acceptable accuracy, two appendix circuits were designed to make sure that ZˆL is close to 50 Ω. The block diagrams of these two circuits are shown in Figs. 4 and 5, respectively. The matching resistors in the diagrams were carbon filmed RF resistors with acceptable high frequency performance. Taking the low impedance matched circuit as an example, the simplified structure drawing of the test fixture is shown in Fig. 6. In Fig. 6, the 6-Ω resistor is in parallel with the ferrite core inductor, and the 47-Ω resistor is in series with the inductor. Under this circumstance, even when the input impedance of the coaxial holder with ferrite core in it was much lower than 50 Ω, the loaded impedance at the test head of VNA is still closely

matched with the measurement system. The input impedance of the holder [Zˆ in (7) and (12)] can then be derived from the measured impedance ZˆL according to (16). And the relative permeability of the ferrite core can finally be calculated according to the discussions in Section II-A and II-B. 6 × Zˆ ZˆL = 47 + . 6 + Zˆ

(16)

The similar derivation process for the high impedance case is omitted. As the residual resistance of the test fixture is also an important factor to decrease the accuracy of test system, we use an air loaded coil to compensate the error caused by the residual resistance. With the ferrite core removed from the one turn coil, the residual resistance of the test fixture can be obtained from S11 of the VNA. The detailed compensation process is similar to the method presented in [10]. III. EXPERIMENTAL VALIDATION Based on the measurement and extraction methodology described in Section II, two different series of test fixtures were thoroughly designed for various ferrite cores. The measurement system consists of an Agilent 8753ES vector network analyzer and the shorted coaxial fixture, as shown in Fig. 7. To validate the test accuracy and effectiveness of the proposed technique, a toroidal type Teflon sample (φ30 × φ7 × H30 mm)

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Fig. 8. The measured relative complex permeability of a toroidal type Teflon sample (φ30 × φ7 × H 30 mm) using “one turn coil” method and transmission line method from 1 MHz to 4 GHz.

Fig. 9.

Fig. 10. The measured relative complex permeability of a big ferrite core (TDK φ99 × φ64 × H 20 mm) using “one turn coil” method and transmission line method from 1 MHz to 4 GHz.

Typical SWR of the shorted coaxial fixture in [30 kHz, 4 GHz].

was measured using two different modeling methods, as shown in Fig. 8. It can be seen that both the “one turn coil” modeling method and the transmission line method achieve satisfactory accuracy below 600 MHz (∆µ /µ < 10%), and the test uncertainty increased to 40%–50% with the frequency going up to 1.5 GHz. When it is above 1.5 GHz, the results are unacceptable for both methods. And it can also be seen that the two modeling methods achieve good consistency up to 1.5 GHz, and show obvious divergence above this frequency. Fig. 9 shows a typical SWR (Standard Wave Ratio) of the shorted coaxial fixture without test sample. It demonstrates that the test system gets good impedance matching below 600 MHz (SWR < 1.5), and the SWR rises up to 3 when the frequency increases up to 1.5 GHz. When it is above 1.5 GHz, the test system shows dramatic mismatch due to the coaxial fixture’s cavity resonance. For different fixtures with different size or

Fig. 11. The measured relative permeability of a typical EMI suppression ferrite core (φ8.0 mm × φ16.0 mm × H 15.9 mm) from 1 MHz to 600 MHz using the proposed method (“one turn coil” modeling).

with various ferrite cores, the frequency points where the cavity resonance occurs differ. Thus the SWR characteristic of the shorted fixture and the test result of Teflon corroborate each other very well. Fig. 10 shows the test results of a big ferrite core (TDK φ99 × φ64 × H20 mm) in a specific large holder using those two modeling methods. It can be concluded that the “one turn coil” modeling method and transmission line method achieve good agreement up to 1.5 GHz, and leaps occur starting from 2 GHz due to the cavity resonance. Therefore, the proposed technique provides a practical way for the permeability measurement of big ferrite cores up to 2 GHz. Fig. 11 illustrates the test results of another typical ferrite core using “one turn coil” method in [1 MHz, 600 MHz].


Fig. 12. The comparison of the measured relative permeability of the same sample using T/R method and using the proposed method (“one turn coil” modeling).

In order to further demonstrate the validity of this method, some results were compared with those obtained from the traditional T/R method [11]. The tested core was φ8.0 × φ16.0 × H15.9 mm (FAI Electronics, FH-LG851-T), and the dimensions of the coaxial transmission line for T/R method were φ7 × φ16.0 × L100 mm. Because the sample cannot fully fill the space between the inner and outer conductors of the T/R holder, we have derived the intrinsic permeability of the core using static-like calculations according to (17) and (18). r2 r3 r3 (17) µequ = ln µins + ln µcore ln r1 r1 r2 r3 r2 r3 1 1 1 ln = ln + ln (18) r1 εequ r1 εins r2 εcore where r1 r2 r3 µequ µins µcore

inner diameter of the transmission line; inner diameter of the ferrite core under test; outer diameter of the transmission line; measured permeability in T/R coaxial line; permeability of the space filling between inner conductor and the ferrite core; corrected permeability of the ferrite core.

We set µins = 1, εins = 2.3 for the space filling (common paper), and the final results of µcore are presented and compared with that of the proposed method in Fig. 12. It can be seen that both the inductive and resistive permeability derived from two different measurement techniques achieve good agreement in trend. The best consistency between these two methods occurs from 1 MHz to 100 MHz, approximately. In Fig. 13, we have also presented the comparison of the relative permeability results extracted by the current method and the results measured using the Agilent E4991A RF impedance/material analyzer. The tested core was φ12.0 × φ6.5 × H6.28 mm and the high impedance fixture was used.

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Fig. 13. The comparison of the measured relative permeability of one ferrite core (φ12.0 × φ6.5 × H 6.28 mm) between current method (transmission line modeling) and Agilent E4991A.

The agreement between them again validates the proposed method. Using this technique, some Ni–Zn ferrite cores and iron power cores were also measured, and their distinct trend lines help us to choose the proper materials in various applications. IV. EFFECT OF AIR GAP IN THE COAXIAL FIXTURE There are several uncertainty factors in our test system, including the instrumental error, performance degradation of carbon filmed RF resistors at high frequencies, and the dimensional errors caused by the machining and the assembling of the fixtures. Therefore the coaxial fixtures claim strict requirements for the machining and assembling, as well as for RF resistors with stable high frequency performance. As the air gap between the magnetic core and the conductive walls of the coaxial fixture will also have some influence on the test accuracy due to the flux leakage, the test result of the same Teflon core (φ30 × φ7 × H30 mm) with different sample filling factors are given, as shown in Fig. 14. From Fig. 14, it can be concluded that the sample filling factor does have some influence on the test accuracy, and the larger the factor is, the more accurate the test results are. Fig. 15 is the measured permeability of the same ferrite core (φ8.0 × φ16.0 × H15.9 mm) with different sample filling factors. It can be seen that the deviation in permeability caused by small filling factors is relatively small compared with the large dynamic range of the relative permeability versus frequency. Nevertheless, it is still recommended that the test fixture should fit the sample under test dimensionally as much as possible to minimize the uncertainty of permeability caused by the air gap. The test results of the same ferrite sample using two different impedance matching schemes were also analyzed and it was found that there was no large deviation between them except the difference in accuracy.

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Fig. 14. The comparison of the measured relative permeability of Teflon core (φ30 × φ7 × H 30 mm) with different sample filling factors from 1 MHz to 1 GHz.

thoroughly designed test fixtures and a vector network analyzer. With the ferrite core installed in a shorted coaxial line, the fixture forms a one turn coil of inductor or a section of shorted transmission line. Using the “one turn coil” modeling method for RFs and the transmission line modeling method for higher frequencies, the relative permeability of the ferrite can finally be derived from the impedance at the test head of the coaxial holder. The consistency between these two different modeling algorithms at RFs and the accuracy of the method were well illustrated by the test result of a toroidal type Teflon sample. The subsidiary RF resistors and impedance matching circuits were integrated into the fixtures to improve the test accuracy. The test results of some ferrite samples were compared with those achieved by the traditional T/R method and those measured by the Agilent E4991A RF impedance/material analyzer. The consistency between them has also illustrated that the proposed method provides an alternative and practicable way to predict the permeability of toroidal type ferrite cores when there is no more sophisticated equipment available. The test uncertainty caused by the air gap between the sample and the holder was discussed, as well as the upper frequency limit of this technique due to the coaxial holder’s cavity resonance (about 2 GHz, and differs slightly for various samples and holders). In general, the technique proposed here can be used to estimate the permeability of toridial type ferrite core from 1 MHz up to 2 GHz with no need of some specific instruments. ACKNOWLEDGMENT The authors would like to thank Prof. W. Xingsong and W. Ruixin for their kindly help, and X. Xueshun for his help in the machining of test fixtures. The authors are also grateful to the reviewers for their careful review of the paper and for their very constructive suggestions for enhancements. REFERENCES

Fig. 15. The comparison of the measured relative permeability of a ferrite core (φ8.0 mm × φ16.0 mm × H 15.9 mm) with different sample filling factors from 1 MHz to 2 GHz.

Sometimes, it is a challenge to choose a proper matching scheme when the inductive characteristics of the ferrite core under test are totally unknown. The recommended procedure is to use both fixtures to predict the same sample, then evaluate the impedance of the one turn coil inductor Zˆ in (7) and (12), using the initial test results to choose the suitable fixture. It is emphasized that the impedance of the one turn coil varies with frequency. V. CONCLUSION A simple experimental method is proposed to determine the initial relative permeability of the toroidal type ferrite core using

[1] J. Baker-Jarvis, “RF materials characterization metrology at NBS/NIST: Past and recent work, future directions and challenges,” in 2001 Annu. Report, Conf. Electrical Insulation and Dielectric Phenomena, Kitchener, Ont., Canada, Oct. 2001, pp. 265–268. [2] Measurement Dielectric Constant With the HP 8510 Network Analyzerthe Measurement of Both Permittivity and Permeability of Solid Materials. Palo Alto, CA: Hewlett-Packard, Aug. 1986, Product Note: 8510–3. [3] J. Krupka, J. Rogowski, J. Baker-Jarvis, and R. G. Geyer, “Scalar permeability measurements of microwave ferrites using lumped circuit, coaxial line, and resonance techniques,” in MIKON’98 12th Int. Conf. on Microwaves and Radar, vol. 3, Krakow, Poland, May 1998, pp. 701–704. [4] C. F. Foo and D. M. Zhang, “A resonant method to construct core loss of magnetic materials using impedance analyzer,” in PESC 98 Record 29th Ann. IEEE Power Electronics Specialists Conf., vol. 2, Fukuoka, Japan, May 1998, pp. 1997–2002. [5] M. Bartoli, N. Noferi, A. Reatti, and M. K. Kazimierczuk, “Modeling winding losses in high-frequency power inductors,” J. Circuits, Systems and Computers, vol. 5, no. 4, pp. 607–626, 1995. [6] A. Massarini and M. K. Kazimierczuk, “Self-capacitance of inductors,” IEEE Trans. Power Electron., vol. 12, no. 4, pp. 671–676, 1997. [7] K. Naishadham, “A rigorous experimental characterization of ferrite inductors for RF noise suppression,” 1999 IEEE Radio and Wireless Conf., RAWCON 99, Denver, CO: Aug. 1999, pp. 271–274. [8] Q. Yu, T. W. Holmes, and K. Naishadham, “RF equivalent circuit modeling of ferrite-core inductors and characterization of core materials,” IEEE Trans. Electromagn. Compat., vol. 44, no. 1, pp. 258–262, Feb. 2002.


[9] Z. Zhigang, Ferrite Magnetic Materials. Beijing, China: Science Press, 1981, pp. 30–42. [10] “Agilent 16454A Magnetic Material Test Fixture Operation and Service Manual,” Agilent Technologies, Inc., Palo Alto, CA, 5th ed., Agilent Tech. Rep. No. 16454-90020, Jul. 2001. [11] J. Shenhui, D. Ding, and J. Quanxing, “Measurement of electromagnetic properties of materials using transmission/reflection method in coaxial line,” in Asia-Pacific Conf. Environmental Electromagnetics, CEEM 2003, Hangzhou, China, Nov. 2003, pp. 590–595. Jing Shenhui (S’04) was born in China in 1976. She received the B.E. and M.E. degrees in mechanical engineering from Southeast University, Nanjing, China, in 1998, and 2001, respectively. She is currently pursuing the Ph.D. degree at the same university, with her research focused on the conflict and coordination of EMC, and thermal design for improving the reliability of electronic equipment in coarse environments. Since 2001, she has been with Southeast University, Nanjing, China, where she is currently a Lecturer in the Mechanical Engineering Department. Her research interests concern EMI and thermal control for electronic equipment reliability.

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Jiang Quanxing was born in China in 1942. He received the graduate degree in radio engineering from the Southeast University (formerly Nanjing Institute of Technology), Nanjing, China, in 1965. Since 1978, he has been active in university teaching and research in EMC. He is a Full Professor of Electromagnetic Compatibility Research (since 1993), and Director of the Electromagnetic Compatibility Laboratory (since 1990) at Southeast University. He has been responsible for many large EMC research programs in China. He is a coauthor of books entitled Measurement Technologies for Electromagnetic Emission and Electromagnetic Susceptibility (Nanjing, China: Southeast Univ. Press, 1988), and Principles of Configuration Design for Electronic Equipments (Nanjing, China: Southeast Univ. Press, 1990). He has also published many articles, conference presentations, and reports in EMC issues. In addition to lecturing on basic electromagnetic theory, EMC principles, and EMC measurement technology, he has dedicated over 20 years to research activities on TEM, GTEM cell, TTEM cell, reverberation chambers, antenna design, and other EMC related topics. Prof. Jiang is very active in several EMC related national standardization committees. He is a main editor of many EMC related national and military standards in China, and a senior member of The International Special Committee on Radio Interference (CISPR) Branch-A in China.