DETERMINATION OF PERMEABILITY FROM IMPEDANCE MEASUREMENT USING VECTOR NETWORK ANALYZER

Transcription

1 Journal of ELECTRICAL ENGINEERING, VOL 63. NO 7s,, 97- DETERMINATION OF PERMEABILITY FROM IMPEDANCE MEAUREMENT UING VECTOR NETWORK ANALYER Rastislav Dosoudil This study treats the optimised one-port (reflection coefficient) and two-port (shunt-through/series-through) measurement s for complex permeaility determination of solid soft magnetic materials using a vector network analyzer (VNA) at frequencies from 9 khz to 6.5 GHz. The principle of measurement s, the relationships of measured phasor voltage ratio ( - parameter) to complex impedance, and permeaility calculation equations are presented. Each gives good measurement sensitivity at the impedance range where the measured ac voltage at the VNA s receiver significantly varies. For permeaility evaluation, the shunt-through provides the est sensitivity and staility and thus is suitale for oth low and high permeaility materials. Keywords: impedance, permeaility, network analyzer, measurement, scattering parameter INTRODUCTION EXPERIMENTAL ET-UP With the trend of wireless communications and digital equipment operating at higher frequencies, the need to evaluate high frequency electronic components (such as RF inductors with cores made of soft ferrites and/or ferrite polymer composites) under higher and wider frequencies is increasingly important not only for research and development engineers of component manufacturers ut also circuit designers of equipment producers. For such electronic components, the frequency dependence of and parts of complex permeaility = j is a significantly important material parameter. At high frequencies, however, the direct measurement of permeaility is difficult. ome reviews on the measurement s for high frequency component/material characterization have een reported [, ]. The permeaility can e determined via impedance analysis using the inductance and/or equivalent circuit model [3] or network analysis using the reflection wave [4], transmission/reflection [5], cavity resonator [6], free space [7], etc. The impedance analysis provides higher measurement accuracy and staility ut requires an expensive impedance analyzer and is suitale only for lower frequency range (up to aout MHz). The work reported here focuses on the network analysis of otaining the permeaility of solid soft magnetic materials (such as ferrites and/or composite materials) over a wide range of frequencies (9 khz 6.5 GHz) y means of a common instrument such as a vector network analyzer (VNA). The descried approach uses the advantages of oth impedance as well as network analysis: ( wide scale of measured impedances (from milliohms to kiloohms), () road frequency range, and (c) higher measurement accuracy (etter than 5 %). Both, the low as well as high permeaility materials can e tested. The relevance of the proposed approach is verified on some soft magnetic materials, namely sintered ferrite and ferrite polymer composite. * Institute of Electrical Engineering, Department of Electromagnetic Theory, lovak University of Technology, Faculty of Electrical Engineering and Information Technology, Ilkovičova 3, 8 9 Bratislava, lovakia, rastislav.dosoudil@stua.sk IN FEI TU For purposes of this study a vector network analyzer (Agilent E57C) making swept high frequency stimulusresponse measurements from 9 khz to 6.5 GHz has een used [8]. The analyzer is equipped with a signal source, signal-separation devices, receivers for signal detection, and display/processing circuitry for reviewing responses, Fig.. Fig.. The view of experimental set-up (E57C analyzer, 6A adapter, and attached 6454A coaxial line holder) and the lock diagram of a vector network analyzer The source is usually a uilt-in phase-locked (synthesized) voltage-controlled oscillator. ignal-separation hardware allows measurements of a portion of the incident signal to provide a reference for ratio measurements and it separates the incident (forward) and reflected (reverse) signals preset at the input of the device under test (DUT). Hardware for this purpose includes power dividers (which are resistive and roadand ut have high insertion loss), directional couplers

2 98 R. Dosoudil: DETERMINATION OF PERMEABILITY FROM IMPEDANCE MEAUREMENT UING VECTOR NETWORK (which have low loss ut are usually limited in andwidth), and directional ridges (which are useful for measuring reflected signals over a road andwidth, ut may also have significant loss). The analyzer relies on a tuned-receiver architecture to provide high signal sensitivity and wide dynamic range ( db or etter), and works with -parameter test set. This test set provides oth forward and reverse measurements of a DUT. The high frequency power is availale from either port or port, and either test port can e connected to the vector network analyzer s receiver inputs. The test set also allows the use of full two-port error correction techniques (such as full two-port caliration procedure) for the highest measurement accuracy. The E57C analyzer is also equipped with an internal computer and Windows operating system, so that all the necessary measurement as well as post-processing routines may e performed without using an external PC. 3 CATTERING PARAMETER ince it is difficult to measure total voltage or current at higher frequencies, -parameters (or scattering parameters ) are generally measured instead [9]. These parameters relate to familiar measurements such as gain, loss, reflection/transmission coefficient, and impedance/admittance. They are relatively simple to measure, and do not require connection of undesirale loads to the DUT (short-circuit and/or open-circuit connections). The numer of - parameters for a given device is equal to the square of the numer of ports. For example, a two-port device has four - parameters. The numering convention for -parameters is that the first numer following the is the port at which energy emerges, and the second numer is the port at which energy enters. o the is a measure of power emerging from port as a result of applying a high frequency stimulus to port. When the numers are the same (e.g. ), a reflection measurement is indicated. l DUT l ) U I I two-port network (DUT) U Fig.. (- Device under test (two-port network) connected to the network analyzer, and, () - two-port network The scattering parameters are defined y the following equations: a a ( a a () where the travelling wave variales, at port and, at port of the two-port network (or device under test, DUT), Fig., are defined in terms of total voltage and current phasors (U, I and U, I ) and reference impedance as follows: U I U I a a (a,) U I U I (c,d) Note that the square of the magnitude of these wave variales has the dimension of power (W): power incident on port, power incident on port (or power reflected from the load), power reflected from port, power reflected from port (or power incident on the load). The -parameters can e measured y emedding the two-port network in a transmission line whose ends are connected to a network analyzer, Fig.a. In practice, the reference impedance is chosen to e = 5. The network analyzer can measure -parameters over a road frequency range and the results can e displayed either on a mith chart ( and/or ) and on a polar diagram ( and/or ) or as a conventional gain versus frequency graph. The two coaxial line segments of lengths l, l are assumed to have characteristic impedance equal to the reference impedance. We may replace the experimental set-up of Fig.a with the electric circuit shown in Fig.3 with the understanding that the generator and segment l have een replaced y their Thévenin s equivalents, and the load impedance has een replaced y its propagated version to distance l. It should e noted that the generator and load impedances, G and L, respectively, are configured y the network analyzer. The connections can also e reversed, with the generator connected to port and the load to port. U g G I I two-port U network U (DUT) Fig. 3. Two-port network connected to generator and load. Equivalent electric circuit to the experimental set-up of Fig.a The actual measurements of the -parameters are made y connecting to a matched load, L =. Then, there will e no reflected waves from the load, =, and the -parameter equations () will give: (3a,) a a a a Reversing the roles of the generator and load, one can measure in the same way the parameters and : (4a,) a a a a Parameter ( ) is equivalent to the input (output) reflection coefficient, while parameter ( ) is equivalent to the L

3 Journal of ELECTRICAL ENGINEERING, VOL 63. NO 7s, 99 forward (reverse) transmission coefficient. Note each scattering parameter is in general complex ij = ij e jij, with ij the ratio of amplitudes and ij the phase difference of travelling waves (, and, ). 4 IMPEDANCE MEAUREMENT WITH VNA Three major techniques used to perform impedance measurements with a network analyzer are ( the reflection coefficient using one-port configuration, () the shunt-through using two-port configuration, and (c) the series-through using two-port configuration, Fig.4, []. ) c) One-port reflection coefficient Two-port shunt-through Two-port series-through Fig. 4. Impedance measurement techniques for VNA: ( - one-port reflection, () - two-port shunt-through and (c) - twoport seriesthrough Each gives good measurement sensitivity at the impedance range where the measured ac voltage at the receiver significantly varies, Fig.5. (-) ensitive range hunt through ( ) hunt-through Reflection Reflection ( ) eries-through eries through ( ) () Fig. 5. Relationship etween impedance and scattering parameters for different measurements techniques The reflection coefficient measures the voltage ratio of the reflected voltage (U r ) and the incident voltage (U i ) from the DUT with impedance, which in turns corresponds to the parameter (equation (3, port is not used): Ur U i Note that U r, U i are phasors. Equation (5) may e inverted to express the impedance in terms of the scattering parameter: (5) (6) The parameter varies greatly with impedance near the reference impedance (5 ). The highest accuracy is otained at equal to, ecause the directional ridge (or coupler) for measuring reflection has a null alance point. However, when the impedance is not in the same vicinity as, the reflection is not suitale due to trace noise. The two-port techniques allow us measure impedance over a road impedance scale using shunt-through and/or series-through configuration. With the two-port technique, we can use either or parameter to perform measurements. However, parameter has a more limited noise floor than, and it is highly susceptile to VWR (voltage standing wave ratio) and other factors that exist etween the holder connector and ground (or sustrate). Because of this, generally parameter is preferred. The shunt-through is suitale for 5 or lower impedances (down to milliohm range) while the series-through is suitale for 5 or higher impedances (up to kiloohm range). port port ) port port = = Fig. 6. The electric circuit for ( - shunt-through and () - series-through connection We now derive the equations for impedance calculation from the measured parameter for oth shunt-through as well as series-through s. Using a shunt impedance and terminating the network in the characteristic impedance (i.e. connecting a matched load at port ), we sets =, Fig.6a. Then the parameter is given y: a a Equation (7) may e inverted to express the impedance in terms of the parameter: imilarly, using a series impedance and terminating the network in the characteristic impedance, we sets =, Fig.6. The scattering parameter is as follows: a a Inverting the equation (9), one can express the impedance in terms of parameter: (7) (8) (9) () The E57C analyzer is equipped with the Impedance parameter display software (which can e downloaded from the Agilent we site, []), Fig.7, that makes it possile to calculate the frequency dependences of impedance parame-

4 Complex permeaility Complex permeaility R. Dosoudil: DETERMINATION OF PERMEABILITY FROM IMPEDANCE MEAUREMENT UING VECTOR NETWORK ters (such as resistance R, reactance X, magnitude, phase,...) from measured scattering parameters and to plot them on the analyzer screen. shunt-through s were used to evaluate the permeaility responses. We oserved the typical resonance type of permeaility dispersion for sintered ferrite and relaxation one for composite. This ehaviour is attriuted to two asic magnetizing mechanisms: domain wall motion and magnetization rotation in domains, [3, 4, ] Reflection coefficient sintered ferrite Ni.5 n.5 Fe O 4 Fig. 7. The view of Impedance parameter display software The complex permeaility of the ring sample can e determined using the following relation []: air j jh f ln r / r o () where and air are the input complex impedances of the 6454A coaxial line holder with and without the ring sample, respectively, h is the height of the sample, f is the frequency, µ o is the permeaility of free space, and r and r are the outer and inner radiuses of the sample. The additional details may e found elsewhere [3, 4]. The impedances and air in equation () can e otained from equations (6), (8) or () according to the actual measurement. After setting several measuring conditions such as power level (from 85 to + dbm), frequency range (from 9 khz to 6.5 GHz), numer of measured points (etween and 6), type of sweep (logarithmic/linear/segment for frequency), numer of traces and channels, the full two-port caliration (with standard short-open-load-through connections) must e performed on the E57C analyzer to achieve the highest measurement accuracy. 4 EXPERIMENT, REULT AND DICUION Figures 8 and 9 show the frequency dependences of () and () parts of complex (relative) permeaility = j for sintered Nin ferrite (with the chemical composition Ni.5 n.5 Fe O 4 and synthesized using conventional ceramic process at C for 6 hours), Fig.8, and for ferrite polymer composite with Nin ferrite as a magnetic filler (with grain size 5 µm) and polyamide (PAD) as a nonmagnetic matrix, Fig.9. The composite sample was prepared y a hot-pressing at a temperature of 35C and a pressure of 5 MPa, and had the total volume concentration of magnetic filler 3 vol%. The prepared samples in the ring form had the outer and inner diameter of 7 and 3. mm, respectively, and the height of.3 mm. Because the permeaility of oth the samples (ferrite and composite) was elow 3, only the one-port reflection coefficient and the two-port ) hunt-through sintered ferrite Ni.5 n.5 Fe O Fig. 8. Complex permeaility versus frequency for sintered Nin ferrite measured y ( - reflection coefficient and () -shuntthrough From figures 8 and 9 it can e clearly seen that the parameter measurement (one-port reflection coefficient ) has a disadvantage in accuracy especially for low impedance measurement ecause the sintered ferrite and composite inserted into the coaxial holder provides very small impedance values, typically 5 m for ferrite (elow MHz) and m for composite (elow MHz). The est results were achieved using the two-port shunt-through, which is specifically targeted at very low impedance measurements down to milliohm range and therefore it is suitale mainly for low permeaility material characterization. It should e noted that the practical impedance measurement ranges for -parameter (one-port reflection and two-port shunt-through) also depend on the test port extension (the coaxial line holder can e attached to port and/or port only via coaxial cale or adapter, Fig.), the test holder characteristics (the lower impedance measurement range of the shunt-through is limited y the short

5 Complex permeaility Complex permeaility Journal of ELECTRICAL ENGINEERING, VOL 63. NO 7s, residual inductance, which is mainly caused y the coupling etween the holder s measurement terminal and analyzer s ports), and the caliration for eliminating the test holder induced errors (instead of full two-port caliration, it is possile to perform the enhanced-response caliration procedure, which is timeless ut it can cause additional induced errors). ) 4 3 Reflection coefficient Ferrite polymer composite Nin - PAD 3 vol% hunt-through Ferrite polymer composite Nin - PAD 3 vol% Fig. 9. Complex permeaility versus frequency for Nin - PAD composite measured y reflection coefficient and ) shunt-through 5 CONCLUION The study was focused on the determination of high frequency permeaility using impedance measurement techniques such as one-port reflection coefficient, two-port shunt-through and two-port seriesthrough y means of a vector network analyzer in the frequency range of 9 khz 6.5 GHz. The measurement principle of the used analyzer is given with emphasis on the extraction of sample holder s impedance from the measured scattering parameters. The shunt-through provided the est sensitivity for low impedance measurement, which in turns is typical for low permeaility materials testing. ome sintered ferrite as well as composite was chosen for verification and proofing of proposed approach. The descried technique provides good measurement accuracy and staility without the importance of an expensive and special instrument. Acknowledgement This work was financially supported y VEGA grants Nr. /63/ and /35/, and y APVV grant Nr. APVV6/. REFERENCE [] BAKER-JARVI, J. JANEIC, M.D. GROVENOR, J.. GEYER, R.G.: Transmission/Reflection and hort-circuit Methods for Measuring Permittivity and Permeaility, NIT Technical Note 355-R, Dec [] AFAR, M. BIRCH, J.B. CLARKE, R.N. CHANTRY, Ed.G.W.: Measurement of the Properties of Materials, Proc. of the IEEE 74, No., (986), [3] DOOUDIL, R. UŠÁK, E. OLAH, V.: Computer Controlled ystem for Complex Permeaility Measurement in the Frequency Range of 5 Hz GHz, Journal of Electrical Engineering 57, No. 8/, (6), 5-9. [4] DOOUDIL, R. OLAH, V.: Measurement of Complex Permeaility in the RF Band, Journal of Electrical Engineering 55, No. /, (4), 97-. l [5] HENHUI, J. DING, D. QUANXING, J.: Measurement of Electromagnetic Properties of Materials using Transmission/Reflection Method in Coaxial Line, CEEM 3, Hangzou, China, (3), [6] COURTNEY, W.E.: Analysis and Evaluation of a Method of Measuring the Complex Permittivity and Permeaility of Microwave Insulators, IEEE Trans. on Microwave Theory and Techniques 8, No. 8, (97), [7] GHODGAONKAR, D.K. VARADAN, V.V. VARADAN, V.K.: Free-space measurement of Complex Permittivity and Complex Permeaility of Magnetic Materials at Microwave Frequencies, IEEE Trans. Instrum. Meas. 39, No., (99), [8] Agilent E57C, Vector Network Analyzer 9 khz 6.5 GHz, Operation manual [9] -parameter Design, Agilent Application Note, No. AN 54 [] Advanced Impedance Measurement Capaility of the RF I-V Method Compared to the Network Analysis Method, Agilent Application Note, No [] Impedance Parameter Display oftware, Agilent Application Note, No [] DOOUDIL, R. UŠÁK, E. OLAH, V.: Automated Measurement of Complex Permeaility and Permittivity at High Frequencies, Journal of Electrical Engineering 6, No. 7/, (), -4. Received 5 August Rastislav Dosoudil (Doc, Ing, PhD) was orn in Bratislava, lovakia, in 97. He graduated from Faculty of Electrical Engineering and Information Technology, lovak University of Technology, in Bratislava, in Material Engineering ranch, 993 (technology of electronic equipments) and received the PhD degree in Theory of Electromagnetism in. At present, he is an Associate Professor (8) at the Institute of Electrical Engineering. He teaches electric circuits, electromagnetics and electronics. His research activities are mainly ferrite-polymer composite materials, complex permittivity/permeaility phenomena, electromagnetic wave asoring properties of composites, ferromagnetic resonance, and magnetic measurements.