Measurement of the Permeability in a Ferrite Core by Superimposing Bias Current

Transcription

1 Journal of International Council on Electrical Engineering Vol. 4, No. 1, pp.67~73, Measurement of the Permeability in a Ferrite Core by Superimposing Bias Current Kousuke Kikuchi*, Tomohiko Kanie** and Takashi Takeo Abstract In this study, we investigate measurement of the magnetic permeability in a ferrite core at RF frequencies when bias current is superimposed on an RF signal with a view to adaptively controlling performance of RF transformers using ferrite cores. A measurement arrangement used comprises a short microstrip line (MSL) circuit including a coaxial conductor (CC) structure consisting of an electrically grounded metal pipe, a center conductor and a sample between them. A bias tee network is incorporated into this MSL-CC circuit in order to superimpose direct current on an RF signal. Using this arrangement, a dependence of permeability on an amplitude of superimposed bias current was measured at frequencies of 10 MHz to 500 MHz. Reliability of the measurement results is discussed based on several experimental data, implying that the method has an accuracy less than 10 % at most of the above frequencies. Keywords: Bias current, Bias tee network, Ferrite, Permeability measurement 1. Introduction Ferrite is used in many RF devices, such as a transformer, and EMC components [1]-[]. For example, when designing an RF transformer, which is a typical RF device, engineers often select appropriate permeability or physical dimensions of a ferrite core to satisfy a specification designated for the device. Since this approach is costly and time-consuming with respect to manufacturing, the authors have proposed in a previous work [3] an adaptive method of controlling the permeability of a ferrite core of RF transformers by superimposing bias current on an RF signal. This proposed method provides us a means for a given ferrite core to vary its permeability and thus enables us to alleviate the above mentioned issue. In addition, this technique is beneficial when applied to compensation of temperature dependent nature of ferrite, for the permeability of a magnetic material is generally dependent on temperature [4]. However, how the permeability of a ferrite core changes when bias current is superimposed should be known or measured so as to actually implement the above mentioned adaptive control of RF device performance. In this study, we propose a relatively simple and practical measurement Corresponding Author: Graduate School of Engineering, Mie University, Japan (takeo@phen.mie-u.ac.jp) * Graduate School of Engineering, Mie University, Japan ** Kanie Professional Engineer Office, Japan (kanie@aioros.ocn.ne.jp) Received: December 5, 013; Accepted: January 6, 014 method employing a combined microstrip line-coaxial conductor (MSL-CC) circuit equipped with a bias tee network and report experimental results obtained with this method. Furthermore, the accuracy of the measurement is also discussed through several experiments and an electromagnetic simulation technique..1 Measurement Circuit. Measurement Procedure The arrangement used here to measure permeability when a bias current is superimposed on an RF signal is illustrated in Fig. 1. Fig. 1. Measurement circuit consisting of the combined microstrip line-coaxial conductor equipped with the bias tee network. In this circuit, a coaxial conductor (CC) structure 67

2 Measurement of the Permeability in a Ferrite Core by Superimposing Bias Current composed of a center conductor and an electrically grounded coaxial metal pipe is located at the end of microstrip lines each having a characteristic impedance of 50 ohms [5]. A measurement sample is housed between the center conductor and the pipe. In addition, a resistor (50 ohms) is connected to the MSLs for achieving better measurement accuracy. Furthermore, in front of the sample, a bias tee network is incorporated to superimpose bias current at the sample.. Equivalent Network We utilize an equivalent network as shown in Fig. for the above mentioned circuit so as to determine the permeability of a sample from the circuit impedance Z M. Here, the coaxial conductor structure is expressed as the L type network enclosed by the dotted rectangle, where circuit elements R m, L m, and C m are given as a function of parameters (sizes and permeability) of the sample and the coaxial conductor as described in the following. Namely, when electrical current flows through the center conductor and the metal pipe, inductance and resistance given by and L l s R R μ ln π R1R + μ ln ( R R ) m = / 3 R m (1) ω μ ls = ln( R3 / R ) () π are caused. Here, μ = μ jμ is the complex permeability of the sample, μ 0 is the permeability in vacuum, ω is the angular frequency, l s is the length of the sample, R 1 is the outer radius of the center conductor, R and R 3 are the inner and outer radii of the sample, respectively, and R 4 is the inner radius of the metal pipe. The equivalent network for the sample is expressed as a series connection of the resistance R m and inductance L m [6]. Furthermore, the two conductors (the center conductor and the electrically grounded pipe) generate a capacitive component C m, which is given by C m 1 = πl s (3) 1 R R4 1 ln + ln( R3 R ) ε 0 R1R 3 ε where ε and ε 0 are the permittivities of the sample and vacuum, respectively. Fig.. Equivalent network for the measurement circuit. If the impedance Z M of the coaxial conductor structure expressed by the L type network in Fig. is determined, one can calculate the permeability of the sample by a circuit analysis using eqs. (1) through (3) as will be described in the next subsection..3 Permeability Determination Procedure As mentioned in the previous subsection, the impedance Z M of the measurement portion indicated by the dotted rectangle in Fig. should be known in order to obtain the permeability of the sample. One of methods to accomplish this is to measure the impedance Z M of the whole measurement circuit and then remove contributions of the circuit components other than Z M, i.e. the load Z L, the bias tee network, etc. Following this procedure, the first step in the permeability determination procedure is subtraction of the impedance of the load Z L and the capacitor C 1 from the whole circuit impedance Z M obtained through measurement. Then, the effect of the components such as the choke coil connected in parallel with the sample was canceled by an elementary circuit analysis. In this way, we obtain the impedance Z M of the coaxial structure. This impedance value of the CC structure including the sample should be equal to the impedance enclosed by the dotted rectangle in Fig.. Namely, where Aωμ Z M = α1μ + β1μ + α1μ + γ 1 (4) α μ + β μ + α μ + γ + j α1μ + β1μ + α1μ + γ 1 68

3 Kousuke Kikuchi, Tomohiko Kanie and Takashi Takeo ls R A = ln π R ω C m A (5) α = (6) 1 m m β = ω C A( ω C B 1) (7) μ 0lS R R B = ln π R1R 1 = ( ω C m B 1) 4 3 (8) γ (9) 3 C m A α = ω (10) m B β = ωa(1 ω C ) (11) m B γ = ωb(1 ω C ) (1) Eq. (4) is a quadratic complex equation for unknown variables μ and μ. By solving this equation, we obtain the complex permeability. large at higher frequencies. Sample Metal pipe Bias-T network Fig. 3. Simulation model. 3. Electromagnetic Simulation We conducted an electromagnetic simulation based on a finite element method to check the validity of the procedure for determining the permeability of a ferrite sample described in the previous section. A measurement circuit model (referred to as C1 hereinafter) used in the simulation is shown in Fig. 3 and its major parameters are listed in Table 1. In the simulation, we employed results of impedance measurement for the choke coil in the bias tee network, which will be described in the next section. Namely, we used the measurement results for the impedance of the choke coil in the bias tee network. The electromagnetic simulation done in this way gives us the impedance Z M of the measurement circuit. Table 1. Parameters of the measurement circuit and the sample Initial core permeability Core length Core O.D. Core I.D. Metal pipe I.D. Center conductor O.D mm 3.5mm 0.7mm 5.0 mm 0.65 mm The value of Z M, which was obtained by removing the effect of the load Z L and the bias tee network was substituted into eq. (4) and the equation was solved with a Newton-Raphson method. The results are illustrated in Fig. 4. As can be seen, the values of the sample permeability obtained from the simulation are in agreement with the true values which are those used as the sample permeability in the simulation, indicating the validity of the present measurement procedure, though the error for μ is slightly Fig. 4. Results of an electromagnetic simulation for the permeability measurement. 4. Results of Permeability Measurement Before measuring the bias current dependence of the permeability in a ferrite core, we have experimentally 69

4 Measurement of the Permeability in a Ferrite Core by Superimposing Bias Current checked the cancellation procedure of the bias tee network. For that purpose, in addition to the circuit C1, we prepared another measurement circuit (Circuit C1 ) which is the same as C1 except that it does not have the bias tee network. for the circuit C1. In addition, with regard to the circuit C1, we subtracted the influence of the bias tee network, especially of the choke coil, from the measured circuit impedance Z M. As illustrated in Fig. 5, the measured impedance of the choke coil has a resonant nature in the frequency range of interest. Nevertheless, the difference between the impedance of C1 when I b = 0 and the effect of the bias tee network was canceled and that of C1 was less than a few percents as shown in Fig. 6, validating our procedure for measuring the dependence of permeability on the bias current. Fig. 5. Measurement results for the impedance of the choking coil. Fig. 7. Measurement results for the permeability by superimposing bias current: real and imaginary components. Fig. 6. Results of the effect of the choking coil cancellation. Then, the impedances of the two circuits were measured. In this measurement, the bias current I b was set to be zero After confirming the validity of our procedure experimentally in this way, we proceeded to permeability measurements by applying bias current. Ferrite samples having the parameters listed in Table 1 were purchased from Tomita Electric Co., Ltd. [7]. In the measurements, bias currents of up to 500 ma were superimposed on an RF signal from a network analyzer. Measurement results are illustrated in Fig. 7, indicating that both the real and 70

5 Kousuke Kikuchi, Tomohiko Kanie and Takashi Takeo imaginary components of the complex permeability vary significantly according to the bias current change especially at low frequencies. More specifically, when the bias current was varied from 0 ma to 500 ma, the real and imaginary components of permeability at a frequency of 10 MHz decrease from about 40 and 400 to about 135 and 100, respectively. 5. Accuracy Evaluation In order to check the measurement results in the previous section or examine the accuracy of the measurement, we prepared another circuit C which has the same sample as the circuit C1 but the inner diameter of the metal pipe is different (R = 3.5 mm) from C1. and 500 ma. Although the difference between the results for C1 and C is slightly large for the imaginary component in the case of I b = 100 ma, it is relatively small for the other conditions, and implying that the accuracy in this measurement is comparable to that with conventional methods [8], [9]. As another way to examine the accuracy in the permeability measurement or check the validity of the results for the permeability measurements obtained in the previous section, we measured transmission characteristics of the ferrite sample using a circuit shown in Fig. 9 and compared them to those predicted by simulation. Microstrip lines and a coaxial conductor in this circuit were designed in the same way as described in Fig. 1 and Fig., while another bias tee network is added after the sample so as to allow the bias current to flow to ground and the RF signal to flow to the output port, respectively. Fig. 9. Arrangement for measuring the transmission characteristics of the ferrite sample. Fig. 8. Comparison of the measurement results for circuit C1 and C: real and imaginary components. Since the samples of the two circuits (C1 and C) are the same, the permeability values measured for C1 and C should coincide. Permeability values obtained from C1 and C are given in Fig. 8 for bias currents of 100 ma, 300 ma Fig. 10. Comparison between the results of the experiments and the electromagnetic simulation for the transmission characteristics. Measured transmission S 1 is plotted in Fig. 10 for the bias currents of 0 ma to 500 ma. As can be seen, it monotonically increases with the bias current. In Fig. 10, 71

6 Measurement of the Permeability in a Ferrite Core by Superimposing Bias Current transmission characteristics predicted by an electromagnetic simulation using the permeability values of the sample obtained by the measurement in the previous section are also plotted. Although the difference between the measurement and the simulated results are slightly larger in the frequency range of 300 MHz to 500 MHz, it remains within 0.5 db in terms of S 1 at most frequencies. To examine how much this difference or error in S 1 can be in terms of permeability, S 1 was calculated by changing permeability values by 10 % to 30% from the measured one in the case of I b = 100 ma. Results are shown in Fig. 11, which indicates that the difference between the measurement and the simulation corresponds to about 10 % in terms of permeability. Fig. 11. Variation of the transmission characteristics S1 by changing the permeability value by 10% to 30%. 6. Conclusion Permeability measurement with bias current superimposed has been investigated at RF frequencies (10 MHz to 500 MHz) using the combined microstrip linecoaxial conductor arrangement equipped with a bias tee network. The experimental results show that the permeability of a ferrite core can vary significantly, e.g. from 50 to 140 for μ r and from 400 to 100 for μ r at a frequency of 10 MHz by applying a bias current of 500 ma. In order to check the validity of the results, two kinds of investigations were further made. Firstly, permeability measurement was conducted for two different circuits having the same sample on it and the results from each were compared. In the other investigation, transmission characteristics of a transformer having a ferrite sample as a core material were compared between experiments and an electromagnetic simulation. Both investigations for checking the validity of the permeability measurement indicate that the error remains within 10 % at most of the frequencies. The measurement technique presented in this study enables us to discuss performance of an RF transformer when bias current is superimposed on it. This is the subject of future study. Acknowledgements The authors would like to thank R. Goudy of Nissan Technical Center N.A. for his helpful comments. References [1] R. M. Bozorth, Ferromagnetism, IEEE Press, New York, 1993.MIT, 1981, p [] A. Goldman, Handbook of Modern Ferromagnetic Materials, Kluwer Academic Publishers, Norwell, [3] T. Aoyama, Y. Shibata, T. Kanie, and T. Takeo, Active Control of RF Splitter Isolation by Superimposing Bias Current, IEICE Trans. Electron., vol. E95-C, no.7, pp , July 01. [4] T. Aoyama, Y. Shibata, T. Kanie, Y. Noro, and T. Takeo, Adaptive Compensation Method for the Temperature Dependence of RF Transformer Isolation, Journal of ICEE, vol., no.4, pp , Oct., 01. [5] D. M. Pozar, Microwave Engineering, John Wiley & Sons, New Jersey, 005. [6] T. Aoyama, M. Katsuda, T. Kanie, and T. Takeo, Alternative Method for Determining Permeability of a Ferrite Core by Using a Combined Microstrip Line- Coaxial Conductor, IEICE, Vol.E95-C, No.11 (01) [7] Tomita Electric Co., Ltd., Homepage, [8] J. B. Jarvis, M. D. Janezic, J. H. Grosvenor, Jr., and R. G. Geyer, Transmission/Reflection and Sort-Circuit Line Methods for Measuring Permittivity and Permeability, Natl. Inst. Stand. Technol., Tech. Note 1355-R, December [9] J. B. Jarvis, M. D. Janezic, B. F. Riddle, R. T. Johnk, P. Kabos, C. L. Holloway, R. G. Geyer, and C. A. Grosvenor, Measuring the Permittivity and Permeability of Lossy Materials: Solids, Liquids, Metals, Building Materials, and Negative-Index Materials, Natl. Inst. Stand. Technol., Tech. Note 1356, February

7 Kousuke Kikuchi, Tomohiko Kanie and Takashi Takeo Kousuke Kikuchi received a B.E. in physics engineering from Mie University in 01, where he is currently engaged in research on an electromagnetic simulation of R devices in the master s program at the Department of Physics Engineering. Tomohiko Kanie received a B.E. in electrical engineering from Meijo University in 1985, an M.E. in material science from the Japan Advanced Institute of Science and Technology in 1995, and a PhD degree from Mie University in 009. He was with Sendai Polytechnic College from 1995 to 1999 and Kinki Polytechnic College from 1999 to 001. Since 001, he has been the CEO of Aoyama Technology Inc. His major interest lies in RF passive circuit technology. Takashi Takeo received B.E., M.E. and PhD degrees in electrical engineering from Nagoya University in 1976, 1978 and 199, respectively. He joined the Nagoya Municipal Industrial Research Institute in 1978 and in 005, accepted a professorship at Mie University. His chief interests lie in the application of optical and RF technology. He is a member of the Japan Society of Applied Physics, the Laser Society of Japan and the Society of Instrument and Control Engineers. 73