Chapter 2 Page 34

CHAPTER -2

Characterization of Dielectric

Materials using Coupled Ring

Resonators

2.1 Introduction

Material characterization is an important field in microwave engineering and is

used in the system design from high speed circuits to satellite and telemetry

applications. [1]

Every material has a unique set of electrical characteristics that are dependent

on its dielectric properties. A measurement of these properties provides valuable

information to scientists, to properly incorporate the material into its intended

application, such as for more materials designs or to monitor a manufacturing

process for improved quality control. Several measurement techniques for

dielectric characterization have been reported in literature [1-4] and can be

classified as transmission-reflection and resonance techniques. The resonance

techniques do not have the sweep frequency capability, unlike resonance

techniques; the transmission techniques usually have the sweep frequency

ability for the measured frequency range. The transmission and/or reflection

signals are always tested to calculate the dielectric properties of the material.

However, resonance techniques are more accurate than transmission techniques,

Chapter 2 Page 35

especially in calculating small loss tangent or loss factors, therefore resonance

techniques are widely used.

2.2 Literature Review

Several techniques were developed to characterize the dielectric properties of

materials. These days’ researchers are working on the characterization of

dielectric materials using different resonance and transmission/reflection

techniques like coaxial line technique, CPW waveguide, Cavity perturbation,

parallel plate capacitor, microstrip line and ring resonator techniques.

M.S. Kheir, H.F Hammad, and A.S Omar designed a ring resonator with a

rectangular waveguide cavity for estimating the dielectric constant of liquids. By

measuring the resonance frequency of the hybrid resonator they calculated the

dielectric constant [1]. Somporn Seewathanapon and his group developed a

folded ring resonator sensor for dielectric constant measurement. The material

was placed in a very compact area, and the response was measured in the

frequency range of 500MHz to 3 GHz [6].

H. Fang et. al. calculated the dielectric constant using ring resonator and they

combined it with the Ansoft HFSS electromagnetic simulation software, to

measure the dielectric constant on the multiple frequency points [10]. A new

technique to characterize the homogeneous dielectric materials using rectangular

shaped perturb cavity was proposed by A.Kumar, S.Sharma and G.Singh. In this

method the samples were placed in the cylindrical form at the center of the

Chapter 2 Page 36

cavity. The real and imaginary parts of material’s permittivity were calculated

using the shift in the resonance frequency [11].

Luiene S. Denenicis et al. also proposed a coplanar waveguide linear resonator

technique for the characterization of dielectric properties of thin films at room

temperature. They deposited thin films of unknown dielectric constant on the

resonator using photolithography and measured the response of ‘s’ parameters

[12]. For the characterization of dielectric constant, in which a microstrip line

coupled with the fork shaped feed element, to improve the coupling efficiency

were proposed by A.H. Muqaibel and his group members [13].

C.Y. Tan et.al. developed a dual resonator, for permittivity characterization. The

microstrip dual resonator consists of two half wavelength resonators, and the

gap between these two resonators was covered with the ferroelectric thin films.

The dielectric constant was calculated by measuring the resonance frequency

and the quality factor. In this method there was some inaccuracy in the

measurements due the air gap between the resonator and the ferroelectric film

[14].

Sompain Seewathanopon also developed a microstrip ring resonator for

dielectric constant measurement [15]. Victor F.M.B Melo has also proposed a

new configuration for the ring resonator to determine dielectric permittivity of

printed circuit board with high accuracy operating at higher frequency [16]. Jyh

Seen too, presented a review on transmission/reflection and resonance technique

for the characterization of dielectric constant.

Chapter 2 Page 37

In the resonance technique materials are characterized using dielectric and

cavity perturbation techniques. Also in the transmission/reflection technique

different types of resonators are used to characterize the materials. Resonance

techniques cannot be used to determine dielectric constant over a frequency

range whereas in the reflection techniques it is possible [17].

Serhan Yamaeli, Coner Ozdemir, Ali akdagii had presented a method to

determine the dielectric constant of microwave PCB substrate. In this a bandpass

microstrip filter, designed on PCB substrate, was used [18]. P. A. Bernard et al.

have calculated the permittivity of dielectric materials using a microstrip ring

resonator. In this method material was placed in the form of a slab on the

resonator and by the variation of line capacitance of multilayer microstrip

transmission line, the permittivity of material substrate was computed [19]. A

model for calculating the dielectric constant was also developed by Sofin and

Aiyer [20]. In this a resonator was designed at 10 GHz; it is a very useful

technique for the grain moisture sensing. Andrew R. Fulford et.al. designed a

pair of microstrip Tee resonator, with different impedance resonating element,

which were used to extract conductor-sheet resistance and dielectric properties

[21]. To measure the moisture and dielectric constant of soil, microstrip ring

resonator had also been developed by Komal Sarabandi and Eric S.Li. Here they

placed the resonator between the soil content and then determine the value of

real and imaginary part of the permittivity by measuring the s parameter and the

quality factor [22].

Chapter 2 Page 38

Sushanta Sen, et.al. presented a cavity perturbation technique for microwave

characterization of dielectric constant with the modified cylindrical cavity,

which was suitable for low dielectric materials only [23]. Elenea Semouhkina

and researchers applied a FDTD method to simulate the s parameters of ring

resonator and calculate the dielectric constant of alumina and rutile substrate

[24].

This chapter deals with the dielectric constant measurements and theoretical

analysis of spirulina and ferrite, which are in, liquid and powder phase

respectively, using CRR and SRR resonators.

2.3 Design of Ring Resonator

Closed ring resonators (CRRs) and split ring resonators (SRRs) are designed on

a PCB substrate having dielectric constant (εr) 5.5. Ring resonators are coupled

through a gap to the microstrip line, satisfying the resonance condition:

(2.1)

Where, R is the mean radius of the ring and n is the harmonic order of

resonance. The dimension of ring resonator is calculated using well known

expression given in Literature [3].

In order to calculate the radius of the ring, guided wavelength is computed using

the following relation

(2.2)

Chapter 2 Page 39

Where, is guided wavelength, c is the speed of light, f is desired frequency

and is the effective dielectric constant which is given by

(2.3)

Where, is relative dielectric constant, w is width of the ring and d is the

substrate thickness.

For a given characteristic impedance and dielectric constant , w/d ratio

can be found by using

(2.4)

(2.5)

Where,

(2.6)

(2.7)

Feedline length and coupling gap are computed using the following relations:

Feed line length =

(2.8)

And, Coupling gap

(

(2.9)

Calculated mean radius of ring is 15.85 mm, feedline length is 24.9 mm, width

of the feedline is 1.77 mm, and coupling gap is 0.4108 mm as shown in Table

2.1. Inner and outer radius of the ring is calculated by subtraction and addition

of the half of width of microstrip to the mean radius respectively.

Chapter 2 Page 40

Inner radius

(2.10)

Outer radius

(2.11)

Table 2.1 Dimension of the CRR and SRR

Feed line length 24.9 mm

Width of the feed line

1.77 mm

Coupling Gap 0.4108 mm

Total length of the substrate 84.16 mm

Total width of the substrate 41.08 mm

Radius of first ring

Inner radius

Outer radius

14.97 mm

16.74 mm

Radius of second ring

Inner radius

Outer radius

7.041mm

8.811 mm

Radius of third ring

Inner radius

Outer radius

3.075 mm

4.845 mm

Chapter 2 Page 41

Coupling between the feed line and the ring is taken into consideration because

its capacitive effect can change the resonance frequency significantly [8]. The

coupling gap between the feed lines represents network capacitance C and a

shunt circuit consisting of inductance (Lr) and capacitance (Cr) represents the

ring. In the split ring resonators, one more network capacitance C is added in the

shunt circuit of the ring. Fig: 2.1(a) & 2.1(b) shows the closed coupled and split

ring resonators.

(a) (b)

Figure 2.1(a) and (b): Split and closed coupled ring resonators of the wavelength λ, λ/2 and λ/4

with the coupling gap 0.41 mm

2.4 Experimental and Theoretical Analysis

Two materials, Spirulina Platensis-Gietler in semisolid phase and Ferrite in

powder phase are subjected to microwave characterization for calculation of

dielectric constants and loss tangent in the L-band. The study of response of the

CRR and SRR without the Spirulina Platensis-Gietler and Ferrite are followed

by the frequency response of the CRR and SRR with Spirulina Platensis-Gietler

and Ferrite have been studied. 1mm thin layer of sample is loaded onto the

resonators and characterization of the sample is done using shift in resonance.

Chapter 2 Page 42

In the first step, complex permittivity and loss tangent of the substrate are

calculated. Loaded quality factor QL is computed using the following relation:

(2.12)

Where f0 is the resonance frequency, Δf is the 3dB bandwidth. Unloaded quality

factor is estimated using:

(2.13)

Where QU is the unloaded quality factor which depends on total insertion loss

(IL) of the system. Total loss of the resonator is inverse of loaded quality factor,

which is the sum of losses due to the dielectric component, conducting

component and the losses of the resonator without any external load. QD which

is the direct measure of the loss tangent of the materials loaded to the resonator

is calculated using following expression:

(2.14)

In the present study conductor, loss is neglected due to very high conductivity of

the copper deposited on the substrate.

The loss tangent tanδ(substrate) is calculated using the following relation

(2.15)

where ρe is the energy filling factor which is the ratio of average energy stored

in the specimen to the average energy stored in resonant structure. The

Chapter 2 Page 43

following relation relates loss tangent in equation (2.15) to the real and

imaginary part of permittivity:

(2.16)

Is the dielectric constant of the substrate of CRR and SRR.

The inaccuracy of the dielectric constant of the substrate does not affect the

measurement because the effect of the substrate’s dielectric constant gets

cancelled as shown by the equation (2.17):

(2.17)

Using eq. (2.5), eq. (2.7) can be re-written as:

(2.18)

where ρ is energy filling factor of sample and & are energy filling factors

of substrate with sample and only substrate respectively. Values of the filling

factor are chosen empirically on the basis of transmission loss and values of

quality factor on loading the resonator with sample.

2.5 Results and Discussions

Figure: 2.2 show the simulated results for Spirulina Platensis-Gietler (in

semisolid Phase) and Ferrite (in powder phase) using CST microwave studio

software for coupled 1, 2 and 3 CRR at 1.5GHz. Resonance frequency response

Chapter 2 Page 44

of 1CRR of length λ, 2CRR of length λ and λ/2 and 3CRR of length λ, λ/2 and

λ/4 with and without Spirulina Platensis-Gietler (in semisolid phase) and Ferrite

(in powder phase), is shown in figure 2.3, are measured by the vector network

analyzer (ZVA 50 Rohde & Schwartz). Figure 2.4 show simulated results in

which the shift in frequency response of 1SRR of length λ, 2SRR of length λ

and λ/2 and 3SRR of length λ, λ/2 and λ/4 with and without Spirulina Platensis-

Gietler in semisolid phase respectively. Figure 2.5 shows experimental results of

the shift in frequency of 1SRR of length λ, 2SRR of length λ and λ/2 and 3SRR

of length λ, λ/2 and λ/4 with and without Spirulina Platensis-Gietler (in

semisolid phase) and ferrite (in powder phase) respectively.

Figure 2.2: Simulated results with CRRs, ____CRR without any load, _ _ _ _ CRR loaded with

Ferrite, CRR loaded with Spirulina.

Chapter 2 Page 45

Figure 2.3: Experimental results with CRRs, ______CRR without any load _ _ _ _ CRR loaded

with Ferrite and - - - - - CRR loaded with Spirulina.

Figure 2.4: Simulated results with SRRs, _____SRR without any load, _ _ _SRR loaded

with Ferrite and ……… SRR loaded with Spirulina.

Figure 2.5: Experimental results with SRRs, ____ SRR without any load, _ _ _ _ SRR loaded

with Ferrite and - - - - - SRR loaded with Spirulina.

Chapter 2 Page 46

Extracted values of effective dielectric constant for Spirulina Platensis-Gietler

and Ferrite, from simulation and experiment are given in table 2.2. The

predicted results for CRR are within ± 5% accuracy and the SRR accuracy

factor is around ±10%. The results clearly show that, the closed ring resonators

have better accuracy as compared to the split ring resonators.

Table 2.2 Experimental and simulation results of dielectric constant of

spirulina platensis-Gietler and Ferrite calculated using different types of

resonators

Type of ring

resonator

Dielectric Constant of

spirulina platensis-

Gietler

('ε )

Dielectric constant of

Ferrite

('ε )

Simulated

Results

Experimental

Results

Simulated

Results

Experimental

Results

CRR of length 1.9 1.92 15.1 14.6

CRR of length

and

1.93 1.84 14.76 14.05

CRR of length ,

and

2 1.788 14.39 14.17

SRR of length 1.74 1.75 13.8 13.68

SRR of length

and

1.76 1.76 13.6 14.01

SRR of length ,

and

2.04 1.76 14.32 13.78

Chapter 2 Page 47

Higher sensitivity of CRR can also be explained by lumped element circuits of

the ring. In the circuit, C1 and L1 represent the capacitance and inductance

between the two rings. The quality factor of the parallel RLC circuit is

calculated using the following equation:

(2.19)

where C is the total capacitance and, L is the total inductance and Q is quality

factor of the parallel RLC circuit.

In the ring resonators, L1 and C1 are the mutual inductance and capacitance

between the rings respectively and Lr, Lr1, Lr2 are the inductance of the rings of

length λ, and , by using these capacitance and inductance, CT, LT RT,

and Q the total capacitance, total inductance, total resistance of the ring and

quality factor of the ring can be calculated as shown in figure 2.6.

Chapter 2 Page 48

(i)

(ii)

(iii)

Figure: 2.6 a (i), (ii) and (iii) Structures and the equivalent lumped circuits of the 1CRR, 2CRR,

3CRR respectively.

Chapter 2 Page 49

(i)

(ii)

(iii)

Figure: 2.6 b (i), (ii) and (iii) Structur and the equivalent lumped circuits of the 1SRR, 2SRR,

3SRR respectively.

Chapter 2 Page 50

The preceding equations and the equivalent circuit diagrams elucidate the reason

for higher sensitivity of CRR as compared to SRR. The effective capacitive

reactance of the rings increases due to additional gap capacitance resulting in

higher losses and poor sensitivity.

This could be the reason for lowest sensitivity in 3-SRR. Further, from the

theoretical model it is clear that due to the presence of split, inductance

decreases in SRR as compared to CRR, therefore the Q of the circuit also

decreases as shown in table 2.3. Thus the capacitance gap plays an important

role in deciding the sensitivity.

Reported dielectric constant of Lithium Zinc Titanium (LiZnTi) Ferrite and

Spirulina Platensis-Gietler is 15 and 1.9 respectively [6], [7]. Experimentally

measured dielectric constant of Ferrite and Spirulina Platensis-Gietler is 14.17 –

13.68 and 1.76-1.92 with accuracy of ± 5% using closed ring resonator.

Dielectric constant values using SRR are in the range of 15.1-13.6 for ferrite and

1.74-2.04 for Spirulina Platensis-Gietler respectively, with ± 10% accuracy as

shown in table 2.2 and 2.3.

Value of ρ1 for Spirulina Platensis-Gietler was 0.014, for Ferrite was 0.1 and

value of ρ2 for substrate were 0.04, lower value of filling factor in case of

Spirulina Platensis-Gietler is also confirmed with decrease in Q values and in

case of ferrite filling factor is greater than the value of filling factor of substrate

due to which quality factor increases. Quality factor value, which is a direct

measure of energy stored in dielectric materials, is tabulated in table 2.4.

Chapter 2 Page 51

Chapter 2 Page 52

Table 2.4 Quality factor of unloaded and loaded CRRs and SRRs

Comparison of Q values as observed the in present work with the perturbation

technique as reported by other groups [9] [10], is given in table 2.5.

Table 2.5 comparison of the achieved accuracy in the present method with

the cavity perturbation methods

Type of ring

resonator

Quality Factor

Unloaded With

Spirulina

With

Ferrite

CRR of length 379 370 471

CRR of length

and

377 397 479

CRR of length ,

and

377 356 485

SRR of length 408 398 423

SRR of length

and

403 399 316

SRR of length ,

and

405 398 418

Method Accuracy

Closed Ring Resonator 5%

Split Ring resonator 10%

Cavity Perturbation [9] 6%

Cavity Perturbation [10] 4-7%

Chapter 2 Page 53

2.6 Conclusion

The technique elaborated in this chapter presents, the comparative study of

dielectric characterization of closed and split ring resonator. Two different kinds

of samples via ferromagnetic sample in powder form and bio sample in semi

liquid form were taken. The analysis shows that measured values of dielectric

parameters using CRR were more accurate than SRR. Experimental results were

validated by simulations of the experimental design on the CST Microwave

Studio. The method proposed herein can be used for the dielectric

characterization of liquids and solids in powder phase.

Chapter 2 Page 54

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