Bulg. J. Phys. 38 (2011) 191–198

Measurement of Dielectric SubstrateParameters Using Split-Post DielectricResonator Assisted by 3D Simulators

B.N. Hadjistamov, P.I. DankovFaculty of Physics, University of Sofia, Sofia 1164, Bulgaria

Received 6 January 2011

Abstract. In this paper the split-post dielectric resonator is investigated as ameasurement tool for dielectric substrate parameters characterization by usinga suitable 3D model, assisted by modern 3D electro-magnetic simulators. Thedielectric parameters of a known substrate are measured by a set of different di-electric resonators in order to find the most appropriate measurement conditionsand dielectric resonator shapes. Results are analyzed and presented in tabularform.

PACS codes: 77.22.d

1 Dielectric Substrates and Measurement of Their Parameters

The measurement of dielectric substrate parameters is one of the most importantthings connected with modern electronics, computer and communication hard-ware [1]. The main reason is the manner of design of the electronic devices,based on electromagnetic or schematic simulators, where precise knowledge ofthe substrate dielectric constant (εr) and loss tangent (tan δε) is very important.Modern high-integrated active or passive devices, such as microwave integratedcircuits, systems on chips, antenna-array panels, chip carriers, etc. are multi-layered composite structures, and a possible inaccuracy in the dielectric param-eters of the used materials could deteriorate the numerical simulations.

Usually the catalogue data given by substrate producers is obtained by the IPCTM-6502.5.5.5 stripline test method and is for a limited number of frequen-cies (commonly 1 MHz or 10 GHz), which can be quite insufficient. Fur-thermore, this method gives information only for the normal to the surface di-electric parameters – ε′⊥, tan δε⊥ , while substrate materials are usually com-posite materials and may be anisotropic (Figure 1). In our previous work wehave established that most of the commercial reinforced laminates (with lay-ers of woven glass, ceramic powders, organic filling, etc.) have a noticeable

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Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric...

',tan

'||,tan ||

OyOz

Ox

'00

0'0

00'

' ||

||

r

Figure 1. Anisotropy of the dielectric parameters.

dielectric anisotropy (e.g. up to 15–25% for dielectric constant anisotropyΔAε = 2|ε′‖ − ε′⊥|/(ε′‖ + ε′⊥) and up to 50–80% for dielectric loss tangentanisotropy ΔAtan δε = 2| tan δε‖ − tan δε⊥ |/(tan δε‖ + tan δε⊥). The char-acterization of anisotropic materials generally requires two techniques, one forthe component of permittivity perpendicular to the plane of the sample and onefor the in-plane permittivity. The two-resonators method [2,3], based on twocylindrical resonators with different modes TE011 and TM010 is suitable fordetermination of substrate anisotropy at a set of fixed frequencies (Figure 2a). Apossibility of tuning the resonance frequency by moving the inner cylinder andworking at lower frequencies is achieved by the tunable coaxial and re-entrantresonators [4,5] (Figure 2b).

In this paper we investigate a new pair of measurement tools based on dielectriccylindrical, ring or prismatic resonators inserted into metal cavities – the split-post dielectric resonator – SPDR (Figures 2c,3). The parameters determinationis assisted by commercial 3D electro-magnetic simulators creating a suitable 3Dmodel, which ensures high accuracy and computational efficiency. We investi-gate numerically a number of configurations with different dielectric resonators– DR, in different frequency ranges in order to obtain the best measurement con-ditions and DR shapes. Finally, we present measurement data for the dielectric

a) b)

c)

Legend:

Resonancecavity

M etalpost

E-fieldorientation

DielectricResonator

Substrate

Figure 2. Pairs of measurement cylindrical cavities for determination of dielectric param-eters anisotropy: a) cylinder resonators, b) coaxial cylinder and re-entrant resonators, c)split-post dielectric resonators.

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B.N. Hadjistamov, P.I. Dankov

Figure 3. Split-post dielectric resonator with a set of dielectric resonators.

parameters of a known substrate, analyze and compare these results with thosefrom the pure split-cylinder resonator. We use DR based on high-quality sap-phire and alumina with very high Q factors.

2 3D Model of the Split-Post Dielectric Resonator

Analytical solutions of the split-post dielectric resonator, due to the complexityof the structure are difficult and give only approximate results. Instead, by usingmodern 3D electro-magnetic simulators we create and simulate a 3D model ofthe structure (Figure 4). There are three basic principles in the creation of themodel, which ensure fast and accurate simulations. First, we draw a stylizedmodel of the resonator as a pure cylinder, where the influence of the couplingloops, screws, diameter eccentricity and etc. is taken into account in equivalentdiameter and surface conductivity of the model. This considerably facilitates the

23

14

1

Legend:1–finiteconductivity;2–E-fieldsymmetry(E fieldperpendiculartotheboundarysurface);3–H-fieldsymmetry(E fieldparalleltotheboundarysurface);4–perfectH-walls;

Figure 4. Equivalent 3D models of the considered cavities and their main boundary con-ditions.

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Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric...

drawing procedure and the simulation of the structure. Second, we define thecylindrical surfaces with an optimal number of line segments – N = 144. Smallvalues of N do not fit well, while big values considerably increase the computa-tional time. In fact, a simple rule is that the width of the linear segment shouldbe smaller than λg/16 (λg – the wave length in the structure). Finally, takingadvantage of the symmetry of the electromagnetic field of the modes of interest,we split the resonators and simulate just one quarter of them. This approachrequires suitable symmetrical boundary conditions to be chosen for the split-resonator surfaces illustrated in Figure 4. The utilization of these split-cylinder3D equivalents instead of the whole resonator cavities is a key assumption forthe applicability of the 3D models and it solves several important problems: 1)it considerably decreases the computational time (up to several hundred times);2) allows to increase the computational accuracy and 3) suppresses a possiblevirtual excitation of non-physical modes, which occur during simulations of thewhole resonator near to the mode of interest.

3 Measurement Procedure and Error Analysis

We use two cylindrical resonators, one split TE011 mode, for measurement ofε′‖, tan δε‖ and one TM010 mode for ε ′

⊥, tan δε⊥ , a piece of foam and a spacer,a set of dielectric resonators with different shapes, dimensions and materials(Figure 5, dimensions given in Table 1). For the analysis we use a sample –Ro4003, substrate produced by the Rogers Corporation.

The measurement procedure is as follows: first we measure the resonance fre-quency and quality factor of the empty resonators, from which we determinethe equivalent diameters and wall conductivity of the 3D models by assuringa coincidence of the measured resonance parameters and the simulated ones.Doing this at the beginning of every measurement procedure makes it indepen-

Figure 5. Picture of the used dielectric resonators.

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dent of daily variations of temperature and other immeasurable factors like wallroughness and diameter eccentricity. The accuracy in determining the equivalentdiameters is quite high – in terms of micrometers. Next we put the supportingfoam in the TE011 mode resonator and the spacer in the TM010 mode resonator,and again by achieving a coincidence of the measured and the simulated reso-nance parameters determine the dielectric constant and loss tangent of the foamand the spacer. Then the same is done with the dielectric resonators. Althoughthe method can be used for measurement of ε ′, tan δε of the dielectric resonatorsthemselves, we must note that in these parameters we put the uncertainties oftheir shape manufacturing, roughness, and dimensions measurement. Thus, wehave a well calibrated 3D model which is used for determination of the substrateparameters. The main error comes from the measurement of the height of thesample.

4 Analysis of the Results

We have done series of measurements of one and the same substrate with a set ofdifferent dielectric resonators (Table 1). The aim is to see which shapes, mate-rials and dimensions are the most appropriate for dielectric substrate parametersdetermination. The analysis of the results is made in the following aspects:

4.1 Low vs.High Dielectric Resonators

As our investigations show high dielectric resonators pull the E-field away fromthe sample (Figure 6). The substrate is in an inactive zone and the sensitivityof measuring its parameters is weak. This leads to uncertainties in the measure-ments (Table 1, No 2, 13). We recommend dielectric resonators with heights upto 2/3 of the height of the resonator.

Figure 6. Low vs. high dielectric resonators. High DR pull the E-field away from thesample.

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Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric...

Table 1. Experimental data for the dielectric and resonance parameters of SPDR witha set of different dielectric resonators (sample – Ro4003, h = 0.5 mm; PR – prismaticresonator, RR – ring resonator, CR – cylindrical resonator)

TE011 m oderesonator TM 010 moderesonator

(Deq= 30.013;H = 30.16; eq= 5.7M S/m) (Deq= 30.045;H = 12.12; eq= 11.05M S/m)

DR(dimensions,mm)

f,GHz/Q(DR)

tan(DR)

f,GHz/Q(sample)

tan(sample)

f,GHz/Q(DR)

tan(DR)

f,GHz/Q(sample)

tan(sample)

0 Emptyresonator 13.1574/8171

1/0 12.5028/1680

3.700/0.00334

7.6382/3820

1/0 7.5208/3407

3.391/0.00185

1 foam /spacer 13.0953/7383

1.0176/0.0000232

- - 7.6348/3815

1.021/0.0 - -

2 AluminaPR1(19.1x18.4x12)

5.1800/6234

9.8515/0.0000725

5.1405/5467

3.548/0.00342

Nodata

3 AluminaPR2(19.8x19.6x6)

5.8039/8638

9.883/0.0000523

5.7565/6223

3.710/0.00219

5.2302/3482

9.0895/0.000028

4.9165/2144

3.26/0.00210

4 AluminaPR3(19.3x11.9x6)

6.8144/14498

9.885/0.0000331

6.7467/6775

3.602/0.00303

5.5567/3670

8.660/0.0000285

5.2809/2467

3.08/0.00187

5 AluminaPR4(19x6.8x6)

8.9997/7342

9.724/0.000134

8.8300/2311

3.520/0.00545

5.9774/3805

8.322/0.0000323

5.7103/2599

3.378/0.00213

6 AluminaDR5(12.5x11.1x6)

7.7052/18514

9.704/0.0000318

7.6233/6890

3.6705/0.00312

5.8379/3831

8.289/0.0000331

5.5749/2641

3.314/0.00210

7 AluminaPR6(12.6x7x6)

9.3160/12137

9.708/0.0000695

9.1585/3673

3.740/0.0039

6.1552/3899

8.103/0.0000342

5.8900/2673

3.389/0.00226

8 SapphirePR1(17.7x12.5x6.6)

6.5510/16655

10.1118/0.0000293

6.4935/7848

3.74/0.00302

5.3658/3800

8.425/<0.0000001

5.0942/2516

3.165/0.00198

9 SapphirePR2(10.3x8.0x5.3)

9.1840/20750

10.2915/0.0000302

9.0520/5675

3.665/0.00303

6.4057/3935

7.820/0.000005

6.1505/2814

3.395/0.00208

10 QuartzPR(12.8x12.3x9.3)

9.4450/9700

4.462/0.0000685

9.2885/3850

3.697/0.00362

5.3520/3766

4.177/0.0000211

5.1396/2793

3.375/0.00210

11 AluminaRR1(20.5x10.3x3.3)

7.6620/2508

9.166/0.000402

7.53181/1894

3.740/0.0029

6.7618/3231

8.200/0.000351

6.5374/2446

3.312/0.00214

12 AluminaRR2(20.5x10.3x5.2)

6.7925/2245

9.052/0.000426

6.72970/1829

3.710/0.0027

6.1476/2947

7.750/0.000335

5.8911/2175

3.322/0.00219

13 AluminaRR3(20.5x10.3x8.5)

6.0502/1437

9.064/0.000665

6.0067/1283

3.620/0.0060

5.0661/2491

8.190/0.00035

4.7980/1818

3.443/0.00210

14 AluminaCR1(9.5x8.95)

8.9719/1897

9.154/0.000605

8.8808/1809

3.78/0.0016

5.3813/2566

8.640/0.000505

5.1000/1847

3.302/0.00193

15 AluminaCR2(8.8x8.5)

9.64105/3572

8.8912/0.000311

9.5189/2752

3.865/0.00285

5.6864/3698

8.178/0.0001195

5.4147/2552

3.312/0.00197

16 CR red(8x10.1)

9.58349/1453

10.182/0.000847

9.4838/1300

3.730/0.00327

5.2390/2125

9.58/0.00065

4.9482/1507

3.19/0.00215

4.2 Dielectric Resonators with Prismatic Forms

We have investigated dielectric resonators made from one and the same material– Alumina, but with different prismatic forms (Table 1, No 2–7). The resultsshow that in the case of TE011 mode resonator, where the E-field is concentratedmostly in the dielectric resonator, DRs with big difference in their horizontaldimensions are not appropriate (Table 1, No 5). The SPDR in this case haslower quality factor and the mode is not well defined (Figure 7a).

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a) b)

Figure 7. Dielectric resonators with different prismatic forms. The electro-magneticmode is not well expressed in SPDR with DR with big difference in their horizontaldimensions – a).

4.3 Symmetrical Dielectric Resonators

Cylindrical and ring dielectric resonators, made of Alumina with different di-mensions are investigated (Table 1, No 11–15). Small cylindrical resonatorsconcentrate the E-field in a small part of the substrate (Figure 8a). Better resultsare obtained by ring DR, where the field is stronger and more widely distributed(Figure 8b).

a) b)

Figure 8. E-field distribution in SPDR with: a) cylindrical DR, b) ring DR.

4.4 Dielectric Resonators with Different Dielectric Constants

As can be seen (Table 1, No 17, 18), dielectric resonators with dielectric con-stants, which differ much from that of the sample, lead to a lack of sensitivityto the presence of the substrate (very small change in the resonance frequency)and are not appropriate for parameters measurements. We recommend DR withdielectric constants close to that of the substrate or up to 3,4 times bigger.

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Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric...

5 Conclusions

The pair of TE011 mode and TM010 mode split-post dielectric resonators offera good possibility for measurement of dielectric parameters anisotropy. Themethod has the following advantages:

— Higher quality factors, compared to those of the pure split cylindrical res-onators. This leads to better sensitivity in the dielectric loss tangent deter-mination.

— Possibility of tuning the resonance frequency by using a set of appropriatedielectric resonators.

Appropriate are DR with heights up to 2/3 of that of the cylindrical resonatorand dielectric constants close to that of the sample or up to 3–4 times bigger.Good measurement conditions are achieved by using ring dielectric resonators.

References

[1] J. Baker-Jarvis, B. Ridldle, M.D. Janezic, “Dielectric and Magnetic Properties ofPrinted Wiring Boards and Other Substrate Materials”, National Institute of Stan-dards and Technology, Technical Note 1512, Boulder, CO, USA.

[2] P.I. Dankov (2006) IEEE Trans. Microwave Theory and Technique 54 1534-1544.[3] P.I. Dankov, V.P. Levcheva, V.N. Peshlov (2005) Utilization of 3D Simulators for

Characterization of Dielectric Properties of Anisotropic Materials, 35th EuropeanMicrowave Conference EuMW’2005, Paris, France, Oct.2005, p.515.

[4] B. Hadjistamov, V. Levcheva, P.I. Dankov (2007) In: “Meetings in Physics at Uni-versity of Sofia” 7, edited by A. Proykova, Heron Press, Sofia, p. 55.

[5] P.I. Dankov, B. Hadjistamov (2007) Characterization of Microwave Substrates withSplit-Cylinder and Split-Coaxial-Cylinder Resonators, 37th European MicrowaveConference, Munich, Germany, Oct.2007, p. 933.

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