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![Electrically tunable split-ring resonators at
microwave frequencies based on
barium-strontium-titanate thick films
M. Gil, C. Damm, A. Giere, M. Sazegar, J. Bonache,
R. Jakoby and F. Martı´n
Split-ring resonators (SRRs) implemented using ferroelectric materials
to modify their resonance frequency by means of a tuning voltage are
presented for the first time. SRRs have been used to load a microstrip
transmission line on a multilayered substrate including a thick film of
barium-strontium-titanate (BST) to obtain a tunable stopband response.
The characteristics of the BST layer allow the application of 140 V as
tuning voltage to obtain frequency tunability values of around 12.5%.
The applied technology is suitable for the fabrication of cost-effective
and reliable planar microwave devices.
Introduction: Split-ring resonators (SRRs) have been used in very
diverse applications, since their appearance in 1999 [1]. Specifically,
they have been widely used, together with other similar resonators, for
the implementation of resonant-type metamaterial transmission lines [2,
3]. This represents an alternative to the CL-loaded approach, formerly
proposed by Caloz et al. [4], and Iyer et al. [5]. Different strategies
have been followed in order to achieve tunability in such resonators at
microwave frequencies, including the use of different kinds of capacitors
[6–9], MEMS [10] or liquid crystals [11]. On the other hand, barium-
strontium-titanate (BST) has been used for the implementation of differ-
ent kinds of ferroelectric varactors [12, 13] as well as in the design of
tunable SRRs [9]. In this case, however, the resonance frequency was
modified by varying the temperature. In the present work, we take advan-
tage of the dependence of the dielectric permittivity of ferroelectric
materials with an external electric field [14] in order to modify the reson-
ance frequency of SRRs by means of an electric voltage (the resonance
frequency of the resonators is modified by tailoring the distributed capaci-
tance between the two rings forming the resonator). The resonators have
been used to load a microstrip transmission line in order to obtain a notch
around the resonance frequency of the SRRs. This strategy allows a cheap
and easy fabrication process for the implementation of artificial tunable
lines based on SRRs, and better reliability than other approaches. In
addition, the measurements show very low insertion losses in the
passband, which are lower than 0.4 dB up to 4 GHz.
Design and fabrication: The resonance frequency of the SRR can be
varied if the capacitance between the two rings forming the resonator
is modified, in a similar way as it is done in BST interdigital varactors
[12]. Thanks to the use of BST and with a proper design of the SRRs,
this capacitance can be tailored and the desired tunability is achievable.
The used BST thick film with a thickness of 3.5 mm is made by screen-
printing an Fe-F co-doped BST paste on an alumina substrate and sinter-
ing at 12008C [15]. Based on this ceramic, the structured metallisation
for the strip of the transmission line and the SRR are realised by a
single lithography step and plating a 2.5 mm-thick Au electrode on a
Cr/Au seed layer, which is afterwards removed by wet etching. A
cross-section scheme of the substrate is shown in Fig. 1a.
Fig. 1 Cross-section scheme of substrate indicating layer thicknesses, and
layout of fabricated microstrip line and SRRs
Dimensions: c ¼ 100 mm, d ¼ 10 mm, f ¼ 590 mm, s ¼ 30 mm, w ¼ 520 mm,
l ¼ 6.1 mm, l1 ¼ 3.1 mm, l2 ¼ 0.8 mm, area a ¼ l1 Â l2 ¼ 2.42 mm2
¼
3.1 mm  0.8 mm ¼ 0.07l  0.02l (l is guided wavelength at resonance of
SRRs)
a Cross-section scheme of substrate
b Layout of fabricated microstrip line and SRRs
The biasing requires the connection of DC feeding lines and pads to
the rings forming the SRR as shown in Fig. 1b, where the relevant
dimensions of the structure are also included. Rogers RO3003 substrate
is used as the carrier substrate for the whole device, including the biasing
network. The carrier substrate is placed on a copper plate, which acts as
microstrip ground and ensures mechanical stability. Owing to the top-
ology of the SRRs, no DC-blocking elements are needed, whereas the
RF signal is blocked by means of 100 KV SMD-resistors. The fabri-
cated device, a microstrip line loaded with a pair of tunable SRRs, is
shown in Fig. 2.
Fig. 2 Photograph of fabricated device
Results: The measured and simulated responses for the tuned (V ¼ 140 V)
and untuned (V ¼ 0 V) states are shown in Fig. 3. Simulations have been
carried out with the commercial software Agilent Momentum, using differ-
ent valuesoftheeffectiverelativepermittivityoftheBSTlayerfor thetuned
(1r,tuned ¼ 255) and untuned (1r,untuned ¼ 340) states, which are typical
values for the considered inter-ring distance (d) and tuning voltages for
such BST thick films. Owing to the limitations of the simulation software,
a homogeneous permittivity must be assumed for the entire BST layeras an
approximation. In general, the permittivity of BST is dependent on the
applied electric field strength, which is itself a function of the structure geo-
metry. Hence, permittivity is actually inhomogeneous. Nevertheless, the
validity of the homogeneity assumption for the simulation of the proposed
structure has been, in general, verified by simulations using a specialised
software for the tuningofBST components[16]. There isa good agreement
between simulation and measurements concerning the tuning range, inser-
tion and return losses, although a small frequency shift can be observed.
Mismatch can be attributed to some discrepancies between the actual geo-
metrical and physical parameters of the structure and those used in the
simulations (dimensions, dielectric permittivity etc.), in addition to
known problems with the appropriate mesh generation for structures with
high dielectric constants.
measurement
tuned
untuned
tuned
simulation
untuned
0
–2
–4
–6
S21
,dB
S11
,dB
1.0 1.5 2.0 2.5 3.0 3.5 4.0
frequency, GHz
0
–10
–20
–30
S11
S21
Fig. 3 Simulated (grey) and measured (black) frequency responses for
fabricated device for tuned and untuned states
The measured resonance frequencies are f0untuned ¼ 2.49 GHz and
f0tuned ¼ 2.80 GHz; that is, the achieved frequency tunability is 12.45%.
The measurement shows very low insertion losses in the passband
(better than 0.4 dB at least up to 4 GHz) and the rejection in the notch is
close to 25 dB. The rejection level can be easily increased by cascading
additional unit cells (n). This has been verified through simulations,
which indicate a rejection level of 215 dB for n ¼ 3, and 230 dB for
n ¼ 6. Work is in progress for experimental demonstration.
Conclusions: Electrically tunable SRRs using a BST thick-film layer
suitable for planar microwave device applications have been developed
for the first time. One fabricated microstrip line loaded with a pair of
tunable SRRs has been characterised and it has been found to exhibit
a notch with 12.5% tunability and very low insertion losses in the
passband. Work is in progress in order to design new tunable structures
based on BST thick-film technology.
ELECTRONICS LETTERS 9th April 2009 Vol. 45 No. 8](https://image.slidesharecdn.com/bonache9-151208150813-lva1-app6892/85/Bonache-9-1-320.jpg)
![Electrically tunable split-ring resonators at
microwave frequencies based on
barium-strontium-titanate thick films
M. Gil, C. Damm, A. Giere, M. Sazegar, J. Bonache,
R. Jakoby and F. Martı´n
Split-ring resonators (SRRs) implemented using ferroelectric materials
to modify their resonance frequency by means of a tuning voltage are
presented for the first time. SRRs have been used to load a microstrip
transmission line on a multilayered substrate including a thick film of
barium-strontium-titanate (BST) to obtain a tunable stopband response.
The characteristics of the BST layer allow the application of 140 V as
tuning voltage to obtain frequency tunability values of around 12.5%.
The applied technology is suitable for the fabrication of cost-effective
and reliable planar microwave devices.
Introduction: Split-ring resonators (SRRs) have been used in very
diverse applications, since their appearance in 1999 [1]. Specifically,
they have been widely used, together with other similar resonators, for
the implementation of resonant-type metamaterial transmission lines [2,
3]. This represents an alternative to the CL-loaded approach, formerly
proposed by Caloz et al. [4], and Iyer et al. [5]. Different strategies
have been followed in order to achieve tunability in such resonators at
microwave frequencies, including the use of different kinds of capacitors
[6–9], MEMS [10] or liquid crystals [11]. On the other hand, barium-
strontium-titanate (BST) has been used for the implementation of differ-
ent kinds of ferroelectric varactors [12, 13] as well as in the design of
tunable SRRs [9]. In this case, however, the resonance frequency was
modified by varying the temperature. In the present work, we take advan-
tage of the dependence of the dielectric permittivity of ferroelectric
materials with an external electric field [14] in order to modify the reson-
ance frequency of SRRs by means of an electric voltage (the resonance
frequency of the resonators is modified by tailoring the distributed capaci-
tance between the two rings forming the resonator). The resonators have
been used to load a microstrip transmission line in order to obtain a notch
around the resonance frequency of the SRRs. This strategy allows a cheap
and easy fabrication process for the implementation of artificial tunable
lines based on SRRs, and better reliability than other approaches. In
addition, the measurements show very low insertion losses in the
passband, which are lower than 0.4 dB up to 4 GHz.
Design and fabrication: The resonance frequency of the SRR can be
varied if the capacitance between the two rings forming the resonator
is modified, in a similar way as it is done in BST interdigital varactors
[12]. Thanks to the use of BST and with a proper design of the SRRs,
this capacitance can be tailored and the desired tunability is achievable.
The used BST thick film with a thickness of 3.5 mm is made by screen-
printing an Fe-F co-doped BST paste on an alumina substrate and sinter-
ing at 12008C [15]. Based on this ceramic, the structured metallisation
for the strip of the transmission line and the SRR are realised by a
single lithography step and plating a 2.5 mm-thick Au electrode on a
Cr/Au seed layer, which is afterwards removed by wet etching. A
cross-section scheme of the substrate is shown in Fig. 1a.
Fig. 1 Cross-section scheme of substrate indicating layer thicknesses, and
layout of fabricated microstrip line and SRRs
Dimensions: c ¼ 100 mm, d ¼ 10 mm, f ¼ 590 mm, s ¼ 30 mm, w ¼ 520 mm,
l ¼ 6.1 mm, l1 ¼ 3.1 mm, l2 ¼ 0.8 mm, area a ¼ l1 Â l2 ¼ 2.42 mm2
¼
3.1 mm  0.8 mm ¼ 0.07l  0.02l (l is guided wavelength at resonance of
SRRs)
a Cross-section scheme of substrate
b Layout of fabricated microstrip line and SRRs
The biasing requires the connection of DC feeding lines and pads to
the rings forming the SRR as shown in Fig. 1b, where the relevant
dimensions of the structure are also included. Rogers RO3003 substrate
is used as the carrier substrate for the whole device, including the biasing
network. The carrier substrate is placed on a copper plate, which acts as
microstrip ground and ensures mechanical stability. Owing to the top-
ology of the SRRs, no DC-blocking elements are needed, whereas the
RF signal is blocked by means of 100 KV SMD-resistors. The fabri-
cated device, a microstrip line loaded with a pair of tunable SRRs, is
shown in Fig. 2.
Fig. 2 Photograph of fabricated device
Results: The measured and simulated responses for the tuned (V ¼ 140 V)
and untuned (V ¼ 0 V) states are shown in Fig. 3. Simulations have been
carried out with the commercial software Agilent Momentum, using differ-
ent valuesoftheeffectiverelativepermittivityoftheBSTlayerfor thetuned
(1r,tuned ¼ 255) and untuned (1r,untuned ¼ 340) states, which are typical
values for the considered inter-ring distance (d) and tuning voltages for
such BST thick films. Owing to the limitations of the simulation software,
a homogeneous permittivity must be assumed for the entire BST layeras an
approximation. In general, the permittivity of BST is dependent on the
applied electric field strength, which is itself a function of the structure geo-
metry. Hence, permittivity is actually inhomogeneous. Nevertheless, the
validity of the homogeneity assumption for the simulation of the proposed
structure has been, in general, verified by simulations using a specialised
software for the tuningofBST components[16]. There isa good agreement
between simulation and measurements concerning the tuning range, inser-
tion and return losses, although a small frequency shift can be observed.
Mismatch can be attributed to some discrepancies between the actual geo-
metrical and physical parameters of the structure and those used in the
simulations (dimensions, dielectric permittivity etc.), in addition to
known problems with the appropriate mesh generation for structures with
high dielectric constants.
measurement
tuned
untuned
tuned
simulation
untuned
0
–2
–4
–6
S21
,dB
S11
,dB
1.0 1.5 2.0 2.5 3.0 3.5 4.0
frequency, GHz
0
–10
–20
–30
S11
S21
Fig. 3 Simulated (grey) and measured (black) frequency responses for
fabricated device for tuned and untuned states
The measured resonance frequencies are f0untuned ¼ 2.49 GHz and
f0tuned ¼ 2.80 GHz; that is, the achieved frequency tunability is 12.45%.
The measurement shows very low insertion losses in the passband
(better than 0.4 dB at least up to 4 GHz) and the rejection in the notch is
close to 25 dB. The rejection level can be easily increased by cascading
additional unit cells (n). This has been verified through simulations,
which indicate a rejection level of 215 dB for n ¼ 3, and 230 dB for
n ¼ 6. Work is in progress for experimental demonstration.
Conclusions: Electrically tunable SRRs using a BST thick-film layer
suitable for planar microwave device applications have been developed
for the first time. One fabricated microstrip line loaded with a pair of
tunable SRRs has been characterised and it has been found to exhibit
a notch with 12.5% tunability and very low insertion losses in the
passband. Work is in progress in order to design new tunable structures
based on BST thick-film technology.
ELECTRONICS LETTERS 9th April 2009 Vol. 45 No. 8](https://image.slidesharecdn.com/bonache9-151208150813-lva1-app6892/75/Bonache-9-1-2048.jpg)
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Bonache 9
- 1. Electrically tunable split-ringresonators at microwave frequencies based on barium-strontium-titanate thick films M. Gil, C. Damm, A. Giere, M. Sazegar, J. Bonache, R. Jakoby and F. Martı´n Split-ring resonators (SRRs) implemented using ferroelectric materials to modify their resonance frequency by means of a tuning voltage are presented for the first time. SRRs have been used to load a microstrip transmission line on a multilayered substrate including a thick film of barium-strontium-titanate (BST) to obtain a tunable stopband response. The characteristics of the BST layer allow the application of 140 V as tuning voltage to obtain frequency tunability values of around 12.5%. The applied technology is suitable for the fabrication of cost-effective and reliable planar microwave devices. Introduction: Split-ring resonators (SRRs) have been used in very diverse applications, since their appearance in 1999 [1]. Specifically, they have been widely used, together with other similar resonators, for the implementation of resonant-type metamaterial transmission lines [2, 3]. This represents an alternative to the CL-loaded approach, formerly proposed by Caloz et al. [4], and Iyer et al. [5]. Different strategies have been followed in order to achieve tunability in such resonators at microwave frequencies, including the use of different kinds of capacitors [6–9], MEMS [10] or liquid crystals [11]. On the other hand, barium- strontium-titanate (BST) has been used for the implementation of differ- ent kinds of ferroelectric varactors [12, 13] as well as in the design of tunable SRRs [9]. In this case, however, the resonance frequency was modified by varying the temperature. In the present work, we take advan- tage of the dependence of the dielectric permittivity of ferroelectric materials with an external electric field [14] in order to modify the reson- ance frequency of SRRs by means of an electric voltage (the resonance frequency of the resonators is modified by tailoring the distributed capaci- tance between the two rings forming the resonator). The resonators have been used to load a microstrip transmission line in order to obtain a notch around the resonance frequency of the SRRs. This strategy allows a cheap and easy fabrication process for the implementation of artificial tunable lines based on SRRs, and better reliability than other approaches. In addition, the measurements show very low insertion losses in the passband, which are lower than 0.4 dB up to 4 GHz. Design and fabrication: The resonance frequency of the SRR can be varied if the capacitance between the two rings forming the resonator is modified, in a similar way as it is done in BST interdigital varactors [12]. Thanks to the use of BST and with a proper design of the SRRs, this capacitance can be tailored and the desired tunability is achievable. The used BST thick film with a thickness of 3.5 mm is made by screen- printing an Fe-F co-doped BST paste on an alumina substrate and sinter- ing at 12008C [15]. Based on this ceramic, the structured metallisation for the strip of the transmission line and the SRR are realised by a single lithography step and plating a 2.5 mm-thick Au electrode on a Cr/Au seed layer, which is afterwards removed by wet etching. A cross-section scheme of the substrate is shown in Fig. 1a. Fig. 1 Cross-section scheme of substrate indicating layer thicknesses, and layout of fabricated microstrip line and SRRs Dimensions: c ¼ 100 mm, d ¼ 10 mm, f ¼ 590 mm, s ¼ 30 mm, w ¼ 520 mm, l ¼ 6.1 mm, l1 ¼ 3.1 mm, l2 ¼ 0.8 mm, area a ¼ l1  l2 ¼ 2.42 mm2 ¼ 3.1 mm  0.8 mm ¼ 0.07l  0.02l (l is guided wavelength at resonance of SRRs) a Cross-section scheme of substrate b Layout of fabricated microstrip line and SRRs The biasing requires the connection of DC feeding lines and pads to the rings forming the SRR as shown in Fig. 1b, where the relevant dimensions of the structure are also included. Rogers RO3003 substrate is used as the carrier substrate for the whole device, including the biasing network. The carrier substrate is placed on a copper plate, which acts as microstrip ground and ensures mechanical stability. Owing to the top- ology of the SRRs, no DC-blocking elements are needed, whereas the RF signal is blocked by means of 100 KV SMD-resistors. The fabri- cated device, a microstrip line loaded with a pair of tunable SRRs, is shown in Fig. 2. Fig. 2 Photograph of fabricated device Results: The measured and simulated responses for the tuned (V ¼ 140 V) and untuned (V ¼ 0 V) states are shown in Fig. 3. Simulations have been carried out with the commercial software Agilent Momentum, using differ- ent valuesoftheeffectiverelativepermittivityoftheBSTlayerfor thetuned (1r,tuned ¼ 255) and untuned (1r,untuned ¼ 340) states, which are typical values for the considered inter-ring distance (d) and tuning voltages for such BST thick films. Owing to the limitations of the simulation software, a homogeneous permittivity must be assumed for the entire BST layeras an approximation. In general, the permittivity of BST is dependent on the applied electric field strength, which is itself a function of the structure geo- metry. Hence, permittivity is actually inhomogeneous. Nevertheless, the validity of the homogeneity assumption for the simulation of the proposed structure has been, in general, verified by simulations using a specialised software for the tuningofBST components[16]. There isa good agreement between simulation and measurements concerning the tuning range, inser- tion and return losses, although a small frequency shift can be observed. Mismatch can be attributed to some discrepancies between the actual geo- metrical and physical parameters of the structure and those used in the simulations (dimensions, dielectric permittivity etc.), in addition to known problems with the appropriate mesh generation for structures with high dielectric constants. measurement tuned untuned tuned simulation untuned 0 –2 –4 –6 S21 ,dB S11 ,dB 1.0 1.5 2.0 2.5 3.0 3.5 4.0 frequency, GHz 0 –10 –20 –30 S11 S21 Fig. 3 Simulated (grey) and measured (black) frequency responses for fabricated device for tuned and untuned states The measured resonance frequencies are f0untuned ¼ 2.49 GHz and f0tuned ¼ 2.80 GHz; that is, the achieved frequency tunability is 12.45%. The measurement shows very low insertion losses in the passband (better than 0.4 dB at least up to 4 GHz) and the rejection in the notch is close to 25 dB. The rejection level can be easily increased by cascading additional unit cells (n). This has been verified through simulations, which indicate a rejection level of 215 dB for n ¼ 3, and 230 dB for n ¼ 6. Work is in progress for experimental demonstration. Conclusions: Electrically tunable SRRs using a BST thick-film layer suitable for planar microwave device applications have been developed for the first time. One fabricated microstrip line loaded with a pair of tunable SRRs has been characterised and it has been found to exhibit a notch with 12.5% tunability and very low insertion losses in the passband. Work is in progress in order to design new tunable structures based on BST thick-film technology. ELECTRONICS LETTERS 9th April 2009 Vol. 45 No. 8
- 2. Acknowledgments: This workhas been supported by MEC (Spain) (TEC2007-68013-C02-02 METAINNOVA and FPU Grant (ref. AP2005-4523) awarded to M. Gil), MCI (Spain) (EMET project ref. CDS2008-00066 within CONSOLIDER INGENIO 2010 Program), CIDEM (Catalan Government) (SGR-2005-00624) and German Research Foundation (GRK 1037). Thanks are also given to J. R. Binder and X. Zhou from FZ Karlsruhe for substrate preparation and production. # The Institution of Engineering and Technology 2009 24 October 2008 doi: 10.1049/el.2009.3055 M. Gil, J. Bonache and F. Martı´n (GEMMA/CIMITEC, Departament d’Enginyeria Electro`nica, Universitat Auto`noma de Barcelona, 08193 Bellaterra, Barcelona, Spain) E-mail: marta.gil.barba@uab.es C. Damm, A. Giere, M. Sazegar and R. Jakoby (MWT, Microwave Engineering, Technische Universita¨t Darmstadt, 64283 Darmstadt, Germany) M. Gil: Also with MWT, Microwave Engineering, Technische Universita¨t Darmstadt, 64283 Darmstadt, Germany References 1 Pendry, J.B., Holden, A.J., Robbins, D.J., and Stewart, W.J.: ‘Magnetism from conductors and enhanced nonlinear phenomena’, IEEE Trans. Microw. Theory Tech., 1999, 47, pp. 2075–2081 2 Martı´n, F., Falcone, F., Bonache, J., Marque´s, R., and Sorolla, M.: ‘Split ring resonator based left handed coplanar waveguide’, Appl. Phys. Lett., 2003, 83, pp. 4652–4654 3 Falcone, F., Lopetegi, T., Laso, M.A.G., Baena, J.D., Bonache, J., Beruete, M., Marque´s, R., Martı´n, F., and Sorolla, M.: ‘Babinet principle applied to the design of metasurfaces and metamaterials’, Phys. Rev. Lett., 2004, 93, p. 197401 4 Caloz, C., and Itoh, T.: ‘Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip LH line,’. IEEE AP-S/URSI Int. Symp. Dig., San Antonio, TX, USA, June 2002, pp. 412–415 5 Iyer, A.K., and Eleftheriades, G.V.: ‘Negative refractive index media supporting 2-D waves,’. IEEE MTT-S Int. Microw. Symp. Dig., Seattle, WA, USA, 2002, pp. 1067–1070 6 Gil, I., Bonache, J., Garcı´a, J., and Martı´n, F.: ‘Tunable metamaterial transmission lines based on varactor loaded split ring resonators’, IEEE Trans. Microw. Theory Tech., 2006, 54, pp. 2665–2674 7 Hand, T.H., and Cummer, S.A.: ‘Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings’, J. Appl. Phys., 2008, 103, p. 066105 8 Velez, A., Bonache, J., and Martı´n, F.: ‘Varactor-loaded complementary split ring resonators (VLCSRR) and their application to tunable metamaterial transmission lines’, IEEE Microw. Wirel. Compon. Lett., 2008, 18, (1), pp. 28–30 9 Ozbay, E., Aydin, K., Butun, S., Kolodziejak, K., and Pawlak, D.: ‘Ferroelectric based tuneable SRR based metamaterial for microwave applications,’. Proc. 37th European Microwave Conf., Munich, Germany, October 2007, pp. 497–499 10 Gil, I., Martı´n, F., Rottenberg, X., and De Raedt, W.: ‘Tunable stop- band filter at Q-band based on RF-MEMS metamaterials’, Electron. Lett., 2007, 43, (21), pp. 1153–1154 11 Zhao, Q., Kang, L., Du, B., Li, B., Zhou, J., Tang, H., Liang, X., and Zhang, B.: ‘Electrically tunable negative permeability metamaterials based on nematic liquid crystals’, Appl. Phys. Lett., 2007, 90, p. 011112 12 Giere, A., Zheng, Y., Gieser, H., Marquardt, K., Wolf, H., Scheele, P., and Jakoby, R.: ‘Coating of planar barium-strontium-titanate thick-film varactors to increase tunability’. Proc. 37th European Microwave Conf., 2007, pp. 114–117 13 Kuylenstierna,D.,Vorobiev,A.,Linner,P.,and Gevorgian, S.:‘Ultrawide- band tunable true-time delay lines using ferroelectric varactors’, IEEE Trans. Microw. Theory Tech., 2007, 53, (6), pp. 2164–2170 14 Tagantsev, A.K., Sherman, V.O., Astafiev, K.F., Venkatesh, J., and Setter, N.: ‘Ferroelectric materials for microwave tunable applications’, J. Electroceram., 2003, 11, pp. 5–66 15 Paul, F., Giere, A., Menesklou, W., Binder, J.R., Scheele, P., Jakoby, R., and Haußelt, J.: ‘Influence of Fe-F-co-doping on the dielectric properties of Ba0.6Sr0.4TiO3 thick-films’,Int. J.Mater. Res., 2008,99, pp.1119–1128 16 Giere, A., Scheele, P., Zheng, Y., and Jakoby, R.: ‘Characterization of the field-dependent permittivity of nonlinear ferroelectric films using tunable coplanar lines’, IEEE Microw. Wirel. Compon. Lett., 2007, 17, pp. 442–444 ELECTRONICS LETTERS 9th April 2009 Vol. 45 No. 8