756 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 4, AUGUST 2006

A MEMS Reconfigurable DGS Resonatorfor K-Band Applications

Ehab K. I. Hamad, Student Member, IEEE, Amr M. E. Safwat, Member, IEEE, andAbbas S. Omar, Senior Member, IEEE

Abstract—A MEMS reconfigurable defected-ground-structure(DGS) resonator using two-dimensional (2-D) periodic DGS forcoplanar waveguide (CPW) transmission line and RF MEMSseries-resistive switches is proposed. The introduced MEMS re-configurable DGS resonator has approximately a fixed bandwidthof 8.1 GHz over a wideband frequency range (K-band). Theproposed structure can be designed easily for other frequencybands by changing the number of unit-cells of the 2-D PDGS.A cascaded two parallel-resonance circuit model for the MEMSreconfigurable DGS resonator has been introduced as well. Theequivalent circuit parameters extraction methods have also beenderived. Simulations based on the proposed circuit model are in avery good agreement with the electromagnetic (EM) simulations,which suggests that the MEMS reconfigurable DGS resonatoris an inductive controlled reconfigured structure. The structureis designed in CPW environment on a high-resistivity siliconsubstrate. It is therefore suitable for monolithic integration withstandard IC process. [1685]

Index Terms—Circuit parameters extraction, circuit modeling,defected-ground-structure (DGS), microelectromechanical sys-tems (MEMS) resonator, radio frequency microelectromechanicalsystems (RF MEMS) switches, reconfigurable resonator, two-di-mensional (2-D) periodic structures.

I. INTRODUCTION

RESONATORS find widespread use in transceiver archi-tectures, e.g., frequency-controlling elements in reference

oscillators, tunable resonator for VCO’s and building elementsfor filters and diplexers [1]. Based upon their principle ofoperation, resonators can be classified into two types. First,electromagnetic wave resonators, e.g., lumped element LC-typeresonators, transmission line resonators, cavity resonators, anddielectric resonators, and second, electromechanical or acousticwave resonators, e.g., mechanical resonators, bulk acousticwave resonators and surface acoustic wave resonators. MEMStechnology has emerged in each of the above two types [2]and they have shown promising characteristics in achievingimportant filter parameters, such as narrow bandwidth, lowloss, and good stability. In the literature, silicon micromachinedRF MEMS resonators, open-end patch resonator and shortcircuit via resonator were investigated in [3]. A MEMS-based

Manuscript received September 7, 2005; revised November 28, 2005. Thiswork was supported by the Ministry of Education and Cultural Affairs ofSachsen-Anhalt, Germany. Subject Editor E. Obermeier.

E. K. I. Hamad and A. S. Omar are with the Chair of Microwave and Com-munication Engineering, University of Magdeburg, P.O. Box 4120, MagdeburgD-39016, Germany (e-mail: e.hamad@ieee.org; a.omar@ieee.org).

A. M. E. Safwat is with the Electronics and Communication Engineering De-partment, Faculty of Engineering, Ain Shams University, Cairo 11517, Egypt(e-mail: asafwat@ieee.org).

Digital Object Identifier 10.1109/JMEMS.2006.876797

photonic bandgap (PBG) band-stop filter designed using etchedlattice shape of CPW PBG unit cell and fabricated using MEMSsurface micromachining process on a high-resistivity siliconsubstrate was presented in [4].

For many applications, the resonant frequency of the res-onator must have a small degree of tunablity to cover certainfrequency band. Tuning can be obtained electrically or mechani-cally. Micromachined tunable dielectric resonator (DR) was im-plemented in [5]. In this case, tunability was achieved by cou-pling the membrane to the dielectric resonator.

In this paper, the two-dimensional (2-D) PDGS for CPW,which was investigated in [6], has been re-designed on a high-resistivity silicon substrate. The resonant frequency has beentransferred to be in the K-band for transceivers and automotiveapplications. The number of the periodic cells controls the reso-nant frequency as described in [6]. Fixed-fixed beam RF MEMSseries-resistive switches [7] have been constructed on the 2-DPDGS to control the number of the active cells by shorting outthe others as shown in Fig. 1. Therefore, the resonant frequencyis changed according to the number of the un-shorted cells. The2-D PDGS in the presence of the MEMS switches and the rest ofthe CPW compose the introduced MEMS reconfigurable DGSresonator, which through this paper will be called loaded res-onator. While in absence of the MEMS switches it is called un-loaded resonator.

The paper is organized as follows. Section II describes thedesign and the optimization of the 2-D PDGS on a high-resis-tivity silicon substrate to operate at 21.1 GHz. The equivalentcircuit model and how the circuit parameters are extracted aredescribed in the same section as well. The RF MEMS series-re-sistive switch is investigated in Section III. Section IV intro-duces the MEMS reconfigurable DGS resonator and the pro-posed cascaded two-parallel resonance circuit model and themethod of the circuit-parameters extraction. This is followed bythe conclusion.

II. TWO-DIMENSIONAL (2-D) PERIODIC DGS FOR

CPW ON SI-SUBSTRATE

Recently, the 2-D PDGS for CPW line has been proposedin [6]. It has been designed for X-band frequency range andfabricated on a Ro4003c substrate using MIC technology. Itis based on the repetition of a unit-cell (standard dumbbell)in a simplified and systematic way to control the resonanceof the DGS. In this paper, five cells of the 2-D PDGS areconsidered as an example for the analysis and the verifica-tion of the idea. The structure has been re-designed on ahigh-resistivity silicon ( k cm) substrate of 635 mthickness covered by a 1.0- m-SiO buffer layer. The CPW

1057-7157/$20.00 © 2006 IEEE

HAMAD et al.: A MEMS RECONFIGURABLE DGS RESONATOR FOR K-BAND APPLICATIONS 757

Fig. 1. Schematic diagram of the MEMS reconfigurable DGS resonator designed using five unit cells of 2-D PDGS for CPW line and eight fixed-fixed beam RFMEMS series-resistive switches to get 64 resonance states in the K-band frequency domain.

Fig. 2. (a) Schematic diagram of 2-D periodic DGS for CPW line with five periodic unit-cells, (b) Equivalent circuit model, and (c) EM and circuitsimulations S-parameters.

has G/W/G equals to m corresponding to 50-characteristic impedance and 2.5 m thickness of Al met-allization. The defect has been etched in both sides of theground planes of the CPW symmetrically. The dimensions ofthe defected structure, as shown in Fig. 2(a), are m,

m. The designed parameters have been optimizedto achieve a resonance at a selected frequency (here is 21.1GHz) with a rejection more than 34.5 dB at the resonantfrequency and insertion loss of about 0.1 dB in the lower

passband and with less than 2.5 dB in the upper passbandas depicted in Fig. 2(c).

The 2-D PDGS, shown in Fig. 2(a), has been analyzed usingthe full-wave 2.5D planar EM simulator Sonnet version 10.52.The EM simulation provides a frequency response with onecutoff frequency and one-attenuation pole. A single parallelRLC resonance as shown in Fig. 2(b) can model this frequencyresponse accurately. The resistance is always very large andaccounts for the different losses in the structure.

758 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 4, AUGUST 2006

Fig. 3. (a) Schematic diagram of fixed-fixed beam RF MEMS series-resistive switch and (b) RF frequency response of the single-separate switch at the on andOFF states.

To extract the parameters of the equivalent circuit model, theresonant frequency and the 3 dB cutoff frequency are firstdetermined from the EM simulations. The resonant frequency

in terms of the parallel resonant circuit elements is given by

(1)

where and are the inductance and capacitance of the parallelinductor and capacitor, respectively. The 3 dB cutoff frequencyis determined using curve (assuming that both transmissionlines are very short) as follows. The equivalent impedance of theparallel resonance is given by

(2)

and from the circuit theory

(3)

at the 3 dB cutoff frequency point

(4)

Rearranging (4), the capacitance of the equivalent circuit modelis given by

(5)

Substituting back in (1), the inductance value can be deter-mined.

The resistance in the equivalent circuit model is best fittedaround the resonant frequency . In this case, the equivalentimpedance is and the transmission loss is

(6)

To validate the circuit model, the 5-cells 2-D PDGS shownin Fig. 2(a) with the dimensions given above has been simu-lated using an EM simulator. The extracted , , and are 5.22k , 0.546 nH, and 0.104 pF, respectively, where and are14.8 and 21.1 GHz, respectively and . The twosimulation results are in a very good agreement as illustrated inFig. 2(c).

III. RF MEMS SERIES-RESISTIVE SWITCH

Fig. 3(a) shows the schematic diagram of the fixed-fixedbeam, series-configured, and resistive-contact RF-MEMSswitch, which has been investigated in [7]. This switch has beenimplemented in the proposed structure because it operates overa wide frequency band (0–30 GHz). It is based on a fixed-fixedbeam, which makes its fabrication process straightforward. Fur-ther more, it is compatible with the standard MIC technologyand does not require a high dc actuation voltage (Vpi V).These switches are combined with the 2D periodic DGS asshown in Fig. 4, such that when being actuated, some cells willbe shorted out and consequently the properties of the DGS willchange. This will lead to a change in the resonant frequency.

To study the RF performance of the MEMS series-resistiveswitch whose dimensions are adjusted to fit the slots of the2-D PDGS, it has been redesigned in CPW environment, asshown in Fig. 3. The substrate is a high-resistivity silicon (

k .cm) coated by a 1.0- m-SiO layer. The bridge of theMEMS switches is made of Au to improve the mechanical prop-erties. The corresponding length, width, and thickness are 280,80, and 1.0 m, respectively. The initial gap height is 2.5 m.The lower electrode is made of the high-resistivity metal NiCrwith a sheet resistance of 1400 which is coated bya 0.15 m Si N layer to prevent dc short circuit. At the off-

HAMAD et al.: A MEMS RECONFIGURABLE DGS RESONATOR FOR K-BAND APPLICATIONS 759

Fig. 4. Half-symmetrical 2-D view of the MEMS reconfigurable DGS resonator, which is depicted in Fig. 1.

state (no dc bias voltage is applied) the isolation is caused bya gap in the signal line of the CPW under the membrane thathas a width of 40 m. At the on-state (dc bias voltage is ap-plied) a dumbbell of 20 m area and 0.2 m height on thesignal line of the CPW underneath the membrane has been em-ployed to reduce the contact resistance when it is contacting thebridge. The designed MEMS switch has been analyzed usingthe EM simulator (SONNET). The RF frequency responses ofthe single-separated MEMS series-resistive switch in both theON and OFF-states are shown in Fig. 3(b). In the ON-state, theinsertion loss is about 0.1 dB and the return loss is about 30 dBup to 30 GHz. While in the OFF-state, the isolation is more than20 dB up to 10 GHz and more than 12 dB up to 30 GHz.

IV. MEMS RECONFIGURABLE DGS RESONATOR

Fig. 1 shows the schematic diagram of the proposed MEMSreconfigurable DGS resonator. It consists of five cells of the2-D PDGS in CPW environment and eight RF MEMS series-re-sistive switches based on fixed-fixed beam to cover the wholeK-band for automotive applications and transceivers. The re-configured resonator has been designed as follows. First the 2-DPDGS in CPW environment has been designed as described inSection II to operate at a selected frequency (here is 21.1 GHz)using five unit cells arranged as shown in Fig. 2(a). Then eightRF MEMS series-resistive switches that are described in thelast section have been constructed on both ground planes ofthe CPW symmetrically around the slots, which join the cellsin the 2-D PDGS together. To reduce the parasitic capacitanceof the MEMS switches at the up-position (OFF-state of the se-ries switch) and keep the switch isolation quite high, the slotshave been tapered from 200 m down to 90 m as illustratedin Fig. 4. This taper does not affect the 2-D PDGS response it-self and this has been checked before constructing the MEMSswitches. Another advantage of these tapers is the availabilityof free space, which allows the increase of the lower-electrodesarea. Consequently, the reduction of the pull-down voltage ofthe MEMS switches.

The introduced MEMS reconfigurable DGS resonator hasbeen designed and analyzed using the full-wave 2.5D EM

simulator. The RF frequency response of the MEMS recon-figurable DGS resonator in the case of zero applied voltage toall MEMS switches is investigated in Fig. 5. The resonancefrequency is 19.4 GHz with more than 25 dB rejection. Theinsertion loss in the lower passband is less than 0.1 dB, whilethe bandwidth is about 8.1 GHz. The quality factor (determinedfrom the well-known center-frequency/bandwidth definition

) is about 2.4, keeping in mind thatthis value includes the effect of a 500 m length of the CPWtransmission line at both sides and the effects of the RF MEMSswitches as well.

Having eight switches, which can be actuated individually,states can be principally obtained. However, because the struc-ture has a vertical and horizontal symmetries, only statesare available. The highest and the lowest frequency valuesare determined by “no switches are actuated” and “switches

, and are actuated,” respectively. Betweenthese two frequencies 64 states are available, which means afine granularity in discrete frequency steps between the upperand lower limits.

The loaded resonator has been analyzed and simulated usingthe EM simulator at different states of the RF MEMS switches toget the RF frequency response. The lowest resonant frequency(19.4 GHz) has been obtained when no switches are actuated.While the highest resonant frequency (27.1 GHz) has been ob-tained when and are actuated. We shouldmention here that when all switches are actuated, the defectedground structure would be nearly completely destroyed and thetotal structure behaves as a simple coplanar transmission line,i.e., there is no filter resonance in this case.

The following cases describe the performance of the loadedresonator at different conditions of the switches.

Case 1) The MEMS switch —no symmetry—is actuated.In this case the 2-D PDGS operates with four cellsat one side, while the MEMS switch shorts the 5thcell. As a result, the resonant frequency increasesfrom 19.4 GHz up to 20.1 GHz.

Case 2) The two symmetrical switches and are actu-ated. The structure in this case operates with four

760 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 4, AUGUST 2006

Fig. 5. RF frequency response of the MEMS reconfigurable DGS resonator in case of no switches are actuated (gives lowest resonant frequency) and inthe cases 1, 2, 3, 4, 5, and 6, (case 6 gives the highest resonant frequency. (a) Reflection coefficient S and (b) transmission coefficient S . SwitchesS ; S ; S ; S ; S ; S ; S , and S are depicted in Figs. 1 and 4.

Fig. 6. (a) Equivalent circuit model, and (b) Frequency response of the MEMS reconfigurable DGS resonator in case of all MEMS switches are not actuated(loaded resonator).

cells at both sides so that the resonance increases upto 21.1 GHz.

Case 3) Switches and are actuated—no symmetry—tocancel two cells at one side only so that the centerfrequency shifts further up to 21.9 GHz.

Case 4) Switches and as well as their mirrors im-ages are actuated to change the resonance to25.3 GHz.

Case 5) At one side, three switches are actuated (namely,and ) to get the resonance at 22.6 GHz.

Case 6) The symmetrical switches and, respectively, are biased to get the highest

resonant frequency at about 27.1 GHz.The reflection coefficient and the transmission coefficient

in all these cases are illustrated in Fig. 5(a) and (b), respec-tively.

A. Circuit Model and Parameters Extraction

The electromagnetic simulation of the loaded resonatorshows that it has two attenuation poles and one full-transmis-sion frequency within the range of 0–35 GHz. Hence, twocascaded parallel RLC circuits in addition to two transmissionlines at each end, whose lengths equal to half of the physical

length of the total structure (1000 m) will model this structureaccurately. The equivalent circuit model is depicted in Fig. 6(a)and the EM simulations are shown in Fig. 6(b). The first andthe second stop frequencies, and , can be determinedfrom this frequency response. Moreover, the full-transmissionfrequency point and the 3 dB cutoff frequency can bedetermined as well. These frequencies are sufficient to extractall the parameters of the equivalent circuit model as it is shownbelow.

The equivalent impedance of the cascaded parallel resonancecircuits is

(7)

The reflection coefficient is given by

(8)

HAMAD et al.: A MEMS RECONFIGURABLE DGS RESONATOR FOR K-BAND APPLICATIONS 761

Assuming that is reduced to

(9)

The above expression has two poles at

(10)

The transmission coefficient is given by

(11)

It has full transmission at , which is given by

Hence, the full transmission frequency is given by:

(12)

Similarly the 3 dB cutoff frequency at is determined by, which leads to

(13)

From (12) and (13) the capacitances and of the equivalentcircuit model are given by

(14a)

(14b)

The inductances and of the equivalent circuit model canbe directly determined from (10).

The resistances and of the circuit model are best fittedaround the resonant frequencies and , respectively. In thiscase, the impedance around the first resonant frequency isdominated by the first parallel resonance where the equivalentimpedance is and the transmission loss is givenby

(15a)

Fig. 7. Equivalent circuit model capacitance and inductance of the first parallelresonator of Fig. 6(a) as a function of the different cases discussed above in termsof switches states.

The impedance around the second resonant frequency isdominantly by the second parallel resonance where the equiv-alent impedance is and the transmission loss isgiven by

(15b)

To validate the circuit model, the reconfigured resonator issimulated with the dimensions of the 5-cells 2-D PDGS beingthat given in Section II. The dimensions of the RF-MEMSswitches are given in Section III with all MEMS switchesbeing identical. The extracted andare 1.95, 1.02 k , 0.4928, 0.0772 nH, and 0.1366, 0.3307pF, respectively. These values correspond to and

of 19.4, 31.5, 14.05, and 28.5 GHz, respectively, whileand 0.089 22 at and , respectively. The

results of the proposed equivalent-circuit-model simulation arein a very good agreement with the EM simulation results asillustrated in Fig. 6(b).

The introduced MEMS reconfigurable DGS resonator oper-ates as an inductive controlled structure. Fig. 7 shows how theequivalent circuit capacitance and inductance of the first par-allel resonance change when the different switches change theirstates from the ON to the OFF as discussed in the cases mentionedabove. The equivalent capacitance and inductance of the secondparallel resonance are almost constant because they don’t playany role with the first attenuation pole. As shown in Fig. 7, thecapacitance is almost constant while the inductance changes lin-early as a function of the number of the downstate switches or,in the same meaning, as a function of the active unit cells of the2-D PDGS. This agrees well with the investigation presentedin [6] for the 2-D PDGS. The structure is therefore an induc-tive controlled one in terms of the number of the periodic cells.Even with the presence of the MEMS switches the 2-D PDGS isstill an inductive controlled structure because the MEMS seriesswitches control the number of cells in the 2-D PDGS only.

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V. CONCLUSION

In this paper, a MEMS reconfigurable DGS resonator using2-D periodic defected ground structures in CPW environmentand fixed-fixed beam RF MEMS series-resistive switches thatcovers the whole K-band for transceivers and/or automotiveapplications has been presented. The MEMS reconfigurableDGS resonator has been designed on a high-resistivity siliconsubstrate in CPW environment that is suitable for monolithicintegration in the context of a standard planar microwaveprocess. The proposed reconfigured resonator has a bandwidthof 8.1 GHz with more than 20 dB rejection over the wholeK-band frequency range. A cascaded double-parallel-reso-nance circuit model for the reconfigured resonator has beenproposed. Methods to extract the parameters of the equivalentcircuit from the EM simulations for the 2-D PDGS and theMEMS reconfigurable DGS resonator have been derived aswell. The EM and the circuit simulation results are in a verygood agreement, which validates the proposed circuit model.Simulation shows that the introduced resonator is an inductivecontrolled reconfigured structure. The proposed structure isvery flexible to be designed for different frequency bands sincethe resonant frequency can be controlled by either the numberof unit cells of the 2D-PDGS or the unit cell dimensions orboth. The possible combination of the switches provides a finegranularity in discrete steps over a wide frequency range.

ACKNOWLEDGMENT

The authors would like to thank the reviewers for their veryuseful remarks.

REFERENCES

[1] C. T.-C. Nguyen, L. P. B. Katehi, and G. M. Rebeiz, “Micromachineddevices for wireless communications (invited),” Proc. IEEE, vol. 86,no. 8, pp. 1756–1768, Aug. 1998.

[2] H. A. C. Tilmans, W. D. Raedt, and E. Beyne, “MEMS for wirelesscommunications: From RF-MEMS components to RF-MEMS-SiP,” J.Micromech. Microeng., vol. 13, no. 4, pp. S139–S163(1), 2003.

[3] K. M. Strohm, F. J. Schmückle, and B. Schauwecker, “Silicon micro-machined RF MEMS resonators,” in Proc. IEEE MTT-S Int. MicrowaveSymp., Seattle, WA, Jun. 2002, pp. 1209–1212.

[4] X. J. Zhang, A. Q. Liu, M. F. Karim, A. B. Yu, and Z. X. Shen, “MEMS-based photonic bandgap (PBG) band-stop filter,” in Proc. IEEE MTT-SInt. Microwave Symp., TX, Jun. 2004, pp. 1463–1466.

[5] W. Pan, P. Fiorini, O. Di Monaco, K. Baert, B. Nauwelaers, and R.Mertens, “Micromachined tunable dielectric resonators,” in Proc.Workshop Semicond. Sensor and Actuator Technol. (3rd SeSens),Veldhoven, The Netherlands, Nov. 2002, pp. 653–656.

[6] E. K. I. Hamad, A. M. E. Safwat, and A. S. Omar, “2-D periodic de-fected ground structure for coplanar waveguide,” in Proc. German Mi-crow. Conf. “GeMiC 2005”, Ulm, Germany, Apr. 2005, pp. 25–28.

[7] J. B. Muldavin and G. M. Rebeiz, “All-metal high-isolation series andseries/shunt MEMS switches,” IEEE Microw. Wireless Compon. Lett.,vol. 11, pp. 373–375, Sept. 2001.

Ehab K. I. Hamad (S’06) was born in Assiut, Egypt,in 1970. He received the B.Sc. degree in electricalengineering and the M.Sc. degree in electronics andcommunications engineering from Assiut University,Assiut, in 1994 and 1999, respectively. He is cur-rently working toward the Ph.D. degree in microwaveand communications engineering at Otto-von-Guer-icke-University Magdeburg, Magdeburg, Germany.

From 1999 to 2001, he was a teaching/researchassistant in Electrical Engineering Department,Aswan Faculty of Engineering, South Valley Uni-

versity, Aswan, Egypt. His research interest includes RF MEMS analysis,design, modeling, and fabrication with special interest in RF MEMS switchesand filters for RF and microwave applications. Also, he is interested in themicrowave passive planer structures.

Mr. Hamad is a Student Member of the Institute of Electrical and ElectronicsEngineers (IEEE).

Amr M. E. Safwat (S’91–M’01) was born in Cairo,Egypt, in May 1970. He received the B.Sc. and theM.Sc. from Ain Shams University, Cairo, Egypt, in1993 and 1996, respectively, and the Ph.D. degreefrom University of Maryland, College Park, in 2001,all in electrical engineering.

He was a Research and Teaching Assistant at AinShams University from 1993 to 1997. From 1997to 2001, he was a Research Assistant in Laboratoryfor Physical Sciences, University of Maryland. FromAugust 2001 to August 2002, he was with Cascade

Microtech, Inc., where he codeveloped the infinity probes and the on waferdifferential calibration standards. In August 2002, he joined the Electronics andCommunications Engineering Department, Ain Shams University as an Assis-tant Professor. He was a Visiting Professor in the Otto-von-Guericke University,Magdeburg, Germany, in 2004 and in the Institut National Polytechnique deGrenoble (INPG) in 2005, Grenoble, France. His research interests includeon-wafer probing, microwave passive planar structures, microwave integratedcircuits, microwave optoelectronic oscillator, and high-speed photodetectors.

Abbas S. Omar (M’87–SM’89) received the B.Sc.,M.Sc. and Doktor-Ing. degrees in electrical engi-neering in 1978, 1982, and 1986, respectively.

He has been Professor of Electrical Engineeringsince 1990 and Head of the Chair of Microwaveand Communication Engineering at the Universityof Magdeburg, Germany since 1998. He authoredand coauthored more than 220 technical papersextending over a wide spectrum of research areas.His current research fields cover the areas of re-mote sensing and microwave imaging, indoor and

outdoor wireless communication, wideband terrestrial, mobile and satellitecommunication, subsurface tomography, and ground penetrating radar (GPR),ultrawideband antennas, stochastical electromagnetics and their meteorolog-ical, environmental and biomedical applications, field theoretical modeling ofmicrowave systems and components, and microwave measureents.

Dr. Omar is member of the Technical Program Committee of IEEE MTT-SSymposium and member of the editorial board of IEEE TRANSACTIONS ON

MICROWAVE THEORY AND TECHNIQUES, IEEE TRANSACTIONS ON ANTENNAS

AND PROPAGATION, IEEE TRANSACTIONS ON MEDICAL IMAGING, IEEEMICROWAVE AND WIRELESS COMPONENTS LETTERS, Proceedings of the IEE,Electronics Letters, Journal of Electromagnetics, Canadian Journal of Physics,and Radio Science.