Ultra High Permittivity Dielectric Helical Resonators Kamal Adamu#1, Chek Pin Yang#2, Paul A Smith#3, WSM Yip#4, Tim W Button*5

#Electrical Engineering Dept, University of Birmingham Pritchatts Road, Edgbaston, Birmingham, UK, B15 2TT

2c.p.yang@bham.ac.uk 3p.smith@bham.ac.uk

*IRC in Metallurgy and Materials, University of Birmingham Pritchatts Road, Edgbaston, Birmingham, UK, B15 2TT

5t.w.button@bham.ac.uk

Abstract— This paper discusses the possibility of constructing a resonant element from ultra high permittivity dielectric material shaped into a helix. The modeling conducted shows that the mode associated with ceramic quarter wave resonators is present within a coiled dielectric helix providing the permittivity is very high. The properties of which are strongly dependent upon the thickness of the coils. Some of the helices studied in this paper are very compact and may possess moderate Q factors, due to the low filling factors.

I. INTRODUCTION

Resonators at microwave frequencies are often employed in communication filters. They can be realized in a variety of ways but for applications at several hundred MHz the use of dielectric resonators is often prohibited by volume constraints. For these applications quarter wave resonators are used, at still lower frequencies metal helical resonators are used.

Previous work [1] has shown that a relatively thick dielectric helix can act as a resonant structure and that the mode was very similar to that found in a Dielectric Combline resonator [2]. However that early work was concerned with ceramics that had a relatively low permittivity, in the region of 40-100. This work is concerned with Dielectric Helical Resonators made from very high permittivity materials such as Barium Strontium Titanate (BST) which can have a permittivity on the order of 500 to 6000 depending upon the exact composition [3].

The principle behind the Dielectric Helical Resonator is similar to that of a Dielectric Combline Resonator, [2], where the inner metal finger is replaced by a high permittivity dielectric rod. It is based upon the concept that a ceramic material, with sufficiently high permittivity, can exclude the electric field from within the rod and hence behave rather like a metal [2]. The key advantage is that conductor losses on the surface of the inner metal finger are eliminated with a corresponding increase in Q.

A conventional metallic helical resonator has an even smaller volume than a combline resonator but its Q is limited to 1000-2000. This paper examines the possibility of using an ultra high permittivity dielectric helix as a resonator. This also serves as a validation for the modeling software for this type of problem. A ceramic helix was made and the method of

fabrication discussed. The frequency and Q of the helix is analyzed and compared to predictions from numerical modeling of the structure.

II. METHOD

A. Numerical Modeling Computer Simulation Technology (CST) Microwave

StudioTM software package was used for numerical modeling within the structures. For the dielectric elements, most were considered to be Barium Strontium Titanate (BST). The permittivity and loss tangent of Polycrystalline BST can vary enormously depending upon the exact composition and dopant used, but in most of this modeling it was assumed to have a complex relative permittivity of �r=1500 and tan�=5x10-3 at 1 GHz. These values were considered reasonable since previous work has shown that an �r of 500-6000 is attainable, [3], and that a loss tangent as low as 10-3 can be achieved even at a high permittivity [4]. The conductive surfaces were all assumed to be copper (resistivity, �=1.7 � 10-8 �m). The modeling assumed a complex relative permittivity for PTFE of �r=2.08 and tan�=2.4 × 10-4 as reported by Krupka et al. [5] at 10GHz. For both BST and PTFE the real part of the permittivity is assumed not to be frequency dispersive. Also for BST the loss tangent is assumed to be proportional to frequency.

In this work all the helices considered had coils wound from material of a circular cross-section. The radius of this cross-section will be referred to as the minor radius, r. The major radius is the mean radius of the coils from the axis of the helix, R. The length along the axis of the helix traversed by one turn denotes the pitch of a helix, p, while the overall height is h.

B. Sample Fabrication and Device Measurement Numerical Modeling

The sample, a ceramic Barium Strontium Titanate (BST) helix, was prepared by extruding dough formed through a viscous processing route [6]. The BST powder was a 99.8% (Ba0.542Sr0.45 TiO3) doped with 0.002%MgO. The powder originally contained ~2.0wt% organic binder that was subsequently burnt out at 500 deg C for 3 hrs. The helix was

978-2-87487-006-4 © 2008 EuMA October 2008, Amsterdam, The Netherlands

Proceedings of the 38th European Microwave Conference

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then sintered on an alumina bar wrapped in Pt foil at 1450 deg C for 2 hrs. The sintered helix is shown in Fig. 1.

Fig. 1 Optical picture of a ceramic helix formed by sintering extruded viscous processed BST powder.

The experimental set-up used to evaluate the ceramic helix is shown in schematic in Fig. 2. The cavity was manufactured from copper and was 70 and 45mm in length and diameter respectively. A PTFE (polytetrafluoroethylene) support centered the helix co-axially within the cylindrical cavity. Therefore the helical resonator considered here was principally a half wavelength resonator. The PTFE support had an outer diameter of approximately 20mm.

Fig. 2 E Field for a BST Dielectric Helix of one turn with the PTFE excluded.

The BST helix was approximately 3.5 turns in size and with a pitch and minor radius of 5mm and 1mm respectively. The Q was measured in transmission using coupling loops fed into the cavity near the centre where the helix was placed.

In order to see the Electric field lines more clearly a single turn BST helix is displayed in Figure 2. In this figure it is clear that the electric field lines are perpendicular to the surface of the dielectric and hence the field pattern is similar to that of a metal helix.

III. RESULTS AND DISCUSSION

A. Measurements upon Rods of BSTIn order to effectively model the 3.5 turn BST helix it was

necessary to have reasonably accurate values for the permittivity and loss tangent of the material. Consequently a rod of BST was produced, from the same batch of powder, to enable the measurement of its permittivity and loss tangent. This rod was then measured using the same technique as that of Geyer et al [4]. At a frequency of 1.538GHz the measured values of permittivity and loss tangent were found to be 1503 �10 and 0.0075�0.001 respectively. Extrapolating to approximately 1GHz the loss tangent would be about 0.005.

B. Modeling and Measurement of a BST HelixIn Table I measured and simulated results are presented for

the fundamental mode in the 3.5 turn BST helix. The permittivity and loss tangent of the BST, at 1.019 GHz, are assumed to be 1500 and (0.005±0.001) respectively.

TABLE I TABLE TO SHOW THE MEASURED & SIMULATED RESULTS OF THE 3.5 TURN

BST HELIX

MEASUREDRESULTS

SIMULATEDRESULTS

ER=1500 TAN�=5X10-3

MODE FREQ (GHZ) Q FREQ

(GHZ) Q

1 1.017 143 1.019 229±46 In Table I the overall Q is calculated from a combination of

dielectric and conductor losses. Qd can be defined as the quality factor due only to the dielectric losses in the ceramic element. Hence it only depends on the electric filling factor, ff, which is the fraction of electric field energy in the ceramic and the dielectric loss tangent, i.e.

�tan.1

ffQd � (1)

The Q due only to conductor losses can be denoted as Qc

and depends upon the Geometric constant for the cavity, G and Rs the surface resistance of the copper walls. Assuming in Table 1, that the permittivity and loss tangent of the BST are 1500 and 0.005 respectively, the error between the simulated and measured resonant frequencies is approximately 0.2%, whereas the error between the measured and simulated Q is nearly 60%. The large error in the Q is surprising given the excellent agreement of the resonant frequency. One reason for this could be the fact that the loss tangent of the BST may not simply scale linearly with frequency. This could result in a significantly higher loss tangent at 1.017GHz giving a lower Qd. In Table I the values of Qd, Qc and ff were 230, 56100 and 0.87 respectively. It should also be noted that in any comparison the geometry of the helix is naturally assumed to

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be perfect. Due to the imperfections of the helix, some discrepancies between modeling and experiment were expected. For all these structures the dominant source of loss was the dielectric loss in the BST. The conductor Q, Qc, was extremely large typically in the range of 105 to 106, suggesting that conductor losses were negligible. Similarly dielectric losses in the PTFE were extremely small, typically over two orders of magnitude smaller than the loss in the BST.

C. Variation of Filling Factor and Resonant Frequency withthe Minor Radius of the Helix

The work presented in this section investigates the effect of changing the minor radius of a single turn helix, i.e. the thickness of the dielectric wire from which the helix is made. The dimensions and material properties used for the modeling are the same as stated in the earlier part of this paper with the exception that the minor radius of the helix is taken as a variable. The permittivity and loss tangent of the helix are taken to be 2000 and 0.001 @1GHz respectively. The height and major radius of the helix are assumed to be 20mm and 9.1mm respectively. The results of the modeling are shown in Figure 3.

Fig. 3 Change in Frequency & Filling factor (ff) with the Minor Radius, r.

Figure 3 suggests that the minor radius of the helix, r, has

quite a strong influence on the properties of the helix. As r increases, both the resonant frequency and the filling factor decrease. Hence the decrease in frequency cannot simply be a result of the greater volume of dielectric material present as the filling factor is decreasing.

Figure 3 also suggests that a filling factor of about 0.3 can be achieved with a radius of 0.6mm. This is interesting since even if the tan� is of the order of 0.001 the dielectric Q, Qd would be approximately 3300. However polycrystalline BST, with a permittivity of 700, has already been produced that has a tan� of 10-3 at 1 GHz [4]. Although this is not a large Q it could potentially be achieved in an extremely compact volume. A single turn DHR appears to posses the potential to achieve the Q of a metal combline resonator, but in a volume

that is at least an order of magnitude smaller. Clearly this depends upon the loss tangent that can be achieved. At present with a loss tangent of 0.008 the maximum Qd that could be achieved is 416.

It is also important to note that although a great deal of effort has gone into the development of BST, almost all of this work has been to try and create tunable materials. In this application the ability to change the permittivity, via the application of a DC voltage is not necessary. Therefore developing lower loss BST, which does not need to be tunable, should be very significantly easier. A single turn Dielectric Helical Resonator appears to posses the potential to achieve the Q of a metal combline resonator, but in a volume that is at least an order of magnitude smaller. Clearly this depends upon the loss tangent that can be achieved.

IV. CONCLUSIONS An ultra high permittivity ceramic helix has been made

using a viscous processing route and the microwave properties measured. The measured results compare well, to those obtained by numerical modeling, for the occurrence of resonant modes. The modeling conducted shows that the mode associated with ceramic quarter wave resonators is present within a coiled helix of very high permittivity. The properties of which are strongly dependent upon the thickness of the coils. Some of the helices studied in this paper could possess moderate quality factors due to the low filling factors associated with the resonant mode. Therefore the potential to create a Dielectric Helical Resonator, with the same Q as a metal combline resonator, but an order of magnitude smaller does appear to exist.

REFERENCES [1] Holmes J E, Yang C P, Smith P A and Button T. W., “Dielectric

Helical Resonators”, IEEE Trans MTT, vol 53, No 1, Jan 2005, pp322-329.

[2] Wang, C., Zaki, K.A., Atia, A.E., Dolan, T, “Dielectric Combline Resonators and Filters”. IEEE Trans. MTT, 1998. Vol 46, Issue 12, Part 2, Dec: p. 2501-2506.

[3] Sengupta, L.C.; Ngo, E.; O'Day, M.E.; Stowell, S.; Lancto, R.; “Fabrication and characterization of barium strontium titanate and non-ferroelectric oxide composites for use in phased array antennas and other electronic devices” Proceedings of the Ninth IEEE InternationalSymposium on Applications of Ferroelectrics, 1994. ISAF 1994., 7-10 Aug. 1994 Page(s):622-625.

[4] Geyer, R.G.; Kabos, P.; Baker-Jarvis, J.; “Dielectric sleeve resonator techniques for microwave complex permittivity evaluation”, IEEETrans on Instrumentation and Measurement, Volume 51, Issue 2, April 2002 Page(s):383 - 392

[5] Krupka J, Derzakowski K., Riddles B., and Baker-Jarvis J., “A dielectric resonator for measurements of complex permittivity of low loss dielectric materials as a function of temperature”. MeasurementScience & Technology, 1998. Volume 9: p. 1751-1756.

[6] Alford, N M, Birchall J D, and Kendal K, “High strength ceramics through colloidal control to remove defects”, Nature, Nov 1987. Vol 330, No 6143, p p. 51-53

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