J. Electromagnetic Analysis & Applications, 2010, 2, 664-671
doi:10.4236/jemaa.2010.212087 Published Online December 2010 (http://www.SciRP.org/journal/jemaa)
Copyright © 2010 SciRes. JEMAA
Study of Dielectric Constant of (1-x) Zn.xMg.TiO3
(ZMT) Ceramic Material at Microwave
Frequencies as a Function of Composition x and
Processing Temperature
Ravi Kumar Gangwar1, Surya Pal Singh1, Meenakshi Choudhary2, Nitish Kumar Singh2*, Devendra
Kumar2, Om Parkash2
1Department of Electronics Engineering Institute of Technology, Banaras Hindu University, Varanasi, India; 2Department of Ceramic
Engineering, Institute of Technology, Banaras Hindu University, Varanasi, India; *Affiliated address: Department of Physics, Udai
Pratap Autonomous College,Varanasi, India.
Email:ravi.gangwar.ece07@itbhu.ac.in
Received October 9th, 2010; revised November 22nd, 2010; accepted November 29th, 2010.
ABSTRACT
In this paper measurement of real part of permittivity a nd loss tangent of (1-x) Zn.xMg.TiO3 (ZMT) material in powder
form in S-band of microwave frequencies is presented and the associated accuracy estimated. This approach is based
on the measurement of transmitted power from the cavity at and off resonance. Details of the design and fabrication of
the rectangular cavity and the input and output coupling are given. The variation of dielectric properties of (1-x)
Zn.xMg.TiO3 (ZMT) with x-value and calcination temperature (for x = 0.1) is presented. The effect of doping of V2O5 is
also studied. The results of present work may provide useful design guidelines for development of microwave compo-
nents including dielectric resonator antennas.
Keywords: Cavity Perturbation Method, Permittivity, Loss Tangent And Ceramic Material
1. Introduction
The measurement of electromagnetic properties of mate-
rials at microwave frequencies is considered important
since it provides the relaxation time, dipole moment in
liquids, characteristics of materials for device applica-
tions, microwave conductivity, effective mass in semi-
conductors etc. [1].
The microwave measurement techniques for electro-
magnetic characterization of materials generally are di-
vided into two groups: Non-resonant methods and reso-
nant methods. Non-resonant methods mainly involve
reflection or transmission methods. The reflection meth-
ods include open-circuit and short-circuit line methods.
The transmission/reflection methods have many varieties,
including free-space, coaxial line, waveguide, and planar
structures such as microstrip and stripline. These meth-
ods have achieved success in permittivity and permeabil-
ity measurements of high- and medium-loss materials.
However, non-resonant methods usually require large
size samples and have strict requirements on sample
preparation, and their measurement accuracy is not very
high, especially for low-loss materials. Resonant meth-
ods including resonant perturbation methods can provide
higher accuracy as compared with non-resonant ones for
these low loss materials [2]. The resonance techniques
can be further divided into two categories: The first one
is a resonance technique, basically supported by the di-
electric sample itself. The sample acts as a dielectric
resonator. Metal shields with different geometries are
always introduced to prevent radiation loss. This type is
called dielectric resonance technique. The second one is
perturbation technique, where the resonance is supported
by the metal walls of the cavity. The presence of small
size sample in the cavity causes only a “perturbation” on
the field distributions in the metal cavity [3]. In resonator
methods, the sample under measurement is excited as a
resonator in the measurement circuit, and its electro-
magnetic properties are deduced from its resonant prop-
erties. In resonant perturbation methods, the sample un-
der measurement is introduced into a resonator (meas-
Study of Dielectric Constant of (1-x) Zn.xMg.TiO(ZMT) Ceramic Material at Microwave 665
3
Frequencies as a Function of Composition x and Processing Temperature
urement fixture) thus altering the electromagnetic bounda-
ries of the resonator and the electromagnetic properties
of the sample are deduced from the change in the reso-
nant properties of the resonator. Due to its high accuracy
and flexibility in sample preparation, resonant. perturba-
tion method is widely used for low-loss samples, samples
in powder form, small size samples and samples of ir-
regular shapes. Resonant perturbation methods mainly
include wall replacement methods and cavity perturba-
tion methods. In wall replacement methods, part of the
resonator wall is replaced by sample surfaces. Wall-re-
placement methods are often used in the study of the
electro-dynamic properties of conductors after the dis-
covery of high Tc superconductors. Many methods have
been developed based on wall-replacement method to
measure the surface resistance of superconducting thin
films. The cavity perturbation method is based on the
change in the resonant frequency and quality factor of the
cavity due to the insertion of a sample inside the cavity at
the position of maximum electric field or maximum
magnetic field depending on the nature of the parameter
to be studied. In this method, the sample under study is
introduced into a resonant cavity, and its complex per-
mittivity or complex permeability is determined from the
change of resonant frequency and quality factor of the
cavity due to the introduction of the sample. Cavity per-
turbation methods are popular in the study of the elec-
tromagnetic properties of dielectrics, semiconductors,
magnetic materials and composite materials [4].
Ceramic materials are widely used in the design and
development of microwave circuits. Further, low loss
ceramic materials find applications in the development of
stable microwave sources and dielectric resonator antennas.
In this paper cavity perturbation technique, which is
highly accurate and advantageous in the determination of
small loss tangents is used to measure the dielectric con-
stant and the loss tangent of ZMT material in powder
form in S-band of microwave frequencies. The accuracy
of the present technique is determined through measure-
ment on Teflon and comparison of results with that
available in the literature [5]. The variations in dielectric
properties of the ZMT material with the x-value, the cal-
cination temperature and the V2O5 doping for x = 0.1 are
also studied experimentally.
2. Theory
The cavity perturbation technique for measurements of
dielectric constant of material has been analyzed in the
literature [4,6-10]. A brief description of the analysis is
given in the following:
Consider two almost identical cavities which are dis-
tinguished by subscripts 1 and 2. Cavity 1 is empty and
cavity 2 contains very small size dielectric material. Both
cavity walls are assumed to be lossless. Maxwell’s equa-
tions for these cavities can be written as
j
j
jj
EjH

  (1)
j
j
jj
H
jE

  1, 2j
By taking suitable dot products with the four equations
given in Equation (1), subtracting and integrating over
the cavity volume (remembering that cavity walls are
perfectly conducting), one obtains

12 12
20 20
21
2
2
01
.
2
S
C
VV
V
s
H
HdV EEdV
dV
E
 


 

(2)
where 1
and 2
are respectively the complex reso-
nant angular frequencies before and after the introduction
of the sample; 0
and 2
are respectively the permit-
tivities of free-space and the sample; 0
and 2
are
respectively the magnetic permeabilities of free-space
and the sample; C is the region enclosed by the cavity,
and is the volume of the sample.
V
S
Equation (2) is the basic cavity perturbation formula.
Derivation of the formula has been done under the as-
sumptions that the cavity walls are perfectly conducting
and the perturbation is small [4,10].
V
In the present work, non-magnetic ceramic material is
considered and therefore Equation (2) reduces to

12
2
21
2
21
1
2
s
C
V
r
V
EEdV
EdV


(3)
The relationship of complex angular frequency to real
frequency and Q factor is given by
212 1
22 2
11
2
rr
rL
ffj
fQQ




1L
(4)
where 1r and 2r are respectively the resonant fre-
quencies of the cavity before and after the introduction of
sample; and 1
f f
L
Q and 2
L
Q are the corresponding loaded
quality factors.
From Equations (3) and (4), we get

12
12
22
221 1
.
11
21
S
C
V
rr r
rLL
V
EEdV
ff j
fQQ dV
E
 

 
 


(5)
Copyright © 2010 SciRes. JEMAA
Study of Dielectric Constant of (1-x) Zn.xMg.TiO(ZMT) Ceramic Material at Microwave
666 3
Frequencies as a Function of Composition x and Processing Temperature
3. Dielectric Constant and Loss Factor
The length of very small diameter (as compared to cavity
size and the wavelength) cylindrical plastic tube which
can hold the sample is slightly greater than the narrow
dimension ‘b’ of the cavity so that it can occupy the en-
tire narrow dimension of the cavity and can be taken out
from or inserted into the TE101 mode cavity through a
small hole cut in the broad wall centre where electric
field is maximum.
From Equation (5) the expressions for real and imagi-
nary parts of the dielectric constant can be written as

12
21
2
cr r
rr cs
Vf f
VV


  (6)
2
21
11
4
c
rr sL L
V
VQ Q


 
 

(7)
The Loss factor
tan
can be written as
tan r
r

(8)
4. Design and Fabrication
4.1. Preparation of Sample
In the present study the sample is prepared by the con-
ventional solid state ceramic route. Stoichiometric
amount of MgCO3 [99.5%, Thomas Baker, India], ZnO
[99.5%, S. D. Fine. Chem. India] and TiO2 [98%, S. D.
Fine. Chem. India] are weighed accurately to make the
total amount equal to 15 grams. Weighed powders are
mixed thoroughly using acetone in a mortar with pestle
for about 2 hour. After that powders were ball milled for
4 hours using acetone as mixing medium. The mixture is
then dried and placed for calcination in platinum cruci-
bles at 1200˚C for 12 hours. The calcined powders were
ground and mixed with 2% polyvinyl alcohol as binder.
It was then pressed using a hydraulic press at optimized
load (= 60 kN) to get the pellets. The pellets of all the
compositions (x = 0.1, 0.2, 0.3, 0.4 and 0.5) were sin-
tered at 1300˚C for 24 hours at a heating and cooling rate
of 4˚C /min. on a platinum foil. The pellets of all the
compositions were crushed in a mortar with the help of
pestle to obtain powdered sample for measurement pur-
pose.
Other samples of composition (x = 0.1) were also pre-
pared but the calcination temperatures are different for
different samples. The calcination temperatures used are
900, 950 and 1000˚C, and total heating time for each
sample was chosen to be 9 hours. The doping of V2O5
was done in one of the samples for which calcination
temperature is 1000˚C.
4.2. Design and Fabrication of Cavity
Rectangular TE101 mode transmission cavity for reso-
nance at 2.62 GHz was designed [11] and fabricated us-
ing a standard S-band waveguide (WR-284) (Figure 1).
The length of the cavity is 9.14 cm (=2
g
at 2.62 GHz).
Two copper plates were used as shorting plates to form
the cavity from the standard waveguide. For coupling
power into the cavity, a hole of diameter D = b/2.2,
where b is the height of waveguide [11], was made at the
centre of each of the shorting plates. The diameter of each
coupling hole comes out to be 1.54 cm for the designed
cavity. To insert the powdered sample material into the
cavity, a circular slot of diameter 2.5 mm was cut at the
centre of one of the broad walls of the cavity. The inner
and outer diameters of the polythene capillary tube used
for filling the powdered sample are chosen to be 1.3 and
2.3 mm respectively and its length is equal to 3.6 cm.
5. Experiments, Results and Discussion
The arrangement for measuring the dielectric properties
of (1-x)Zn.xMg.TiO3 ceramic material consists of
Agilent Technologies make analog microwave source
(Model no. E8257D, 250 kHz-20 GHz), SICO make
waveguide/coaxial transition, variable attenuator, fabri-
cated cavity and HP power sensor (Model no. 436A) and
meter forming a test bench as shown in Figure 2. The
standard procedure given in the reference [10] was fol-
lowed to measure power fed to and transmitted from the
cavity with and without the sample as a function of fre-
quency deviation from resonance. Resonant frequency
corresponds to maximum transmitted power in each
case.Measurement of dielectric properties of (1-x)
Zn.xMg. TiO3 ceramic material was carried out for dif-
ferent x-values and different calcination temperatures for
x = 0.1. A number of measurements were performed to
determine the resonance frequency and 3-dB frequencies
f1’ and ‘f2’ both for cavity with the capillary tube and
cavity with tube containing the powdered sample mate-
rial. The average values of measured and computed pa-
rameters of the cavity with the capillary tube but without
the sample are shown in Table 1. The average values of
the parameters of the cavity with the capillary tube con-
taining the sample for different x-values and calcination
temperatures are shown respectively in Tables 2 and 3.
The loaded quality factor for the cavity with and without
the sample material is computed using the formula

21
r
Lf
Qff
, where is the resonant frequency
r
f
of TE101 mode cavity .The values of r
, r
and tan δ
of the sample material are evaluated using Equations (6-8)
Copyright © 2010 SciRes. JEMAA
Study of Dielectric Constant of (1-x) Zn.xMg.TiO3 (ZMT) Ceramic Material at Microwave
Frequencies as a Function of Composition x and Processing Temperature
Copyright © 2010 SciRes. JEMAA
667
and the results are shown in Tables 2 and 3 respectively
for different x-values and calcination temperature.
The variations in the values of r
and
tan with
x-value are shown in Figures 3 and 4 respectively.
The variations in the values of r
and
tan with
calcination temperature for x = 0.1 are shown in Figures
5 and 6 respectively.
From Figure 3 and Table 2 it can be seen that
r
value first decreases with increase in x-value and
reaches 5.768 at x = 0.3 and then increases for x > 0.3.
The loss tangent first increases and reaches 0.004 at x =
0.2, it then decreases and reaches 0.001 at x = 0.3, and
again increases for values of x above 0.3, as shown in
Figure 4 and Table 2. These variations in the dielectric
properties may be attributed to the presence of multiple
phases in the material and the variation in the amount of
phases determined by the area under peaks with change
in x-value as shown in Figure 7. The possible 2
values
(Bragg angle) where reflections occur are determined by
unit cell dimensions. However, the intensities of the re-
flections are determined by the distribution of the elec-
trons in the unit cell. The highest electron density is
found around atoms. Therefore, the intensities depend on
what kind of atoms we have and where in the unit cell
they are located. Planes going through areas with high
electron density will reflect strongly, planes with low
electron density will give weak intensities. From Figures
5 and 6 and Tab le 3, it is observed that the material r
value increases and tan δ decreases with increase in cal-
cination temperature of the material, though the rates of
increase are different. This variation in the dielectric
properties with calcinations temperature may be attrib-
uted to the presence of single phase in the material. The
dielectric constant and loss tangent of V2O5 doped and
1000˚C calcined sample were 4.04 and 0.002698. Di-
electric constant is higher and loss tangent is lower in
comparison with undoped and 1000˚C calcined sample.
The change inr
and tan δ of ZMT with the addition of
V2O5 is due to increase in densification rate of ZMT. The
measured dielectric constant values are lower than those
reported in reference [5]. This is due to lower value of
percentage density of sample material. The sample mate-
rial used for measurement in [5] was in highly dense pel-
let form, while in the present study we measured dielec-
tric constant of sample material in powder form. The
reported percentage density of solid sample material
studied in reference [5] is more than 95%.
To test the accuracy of the cavity perturbation tech-
nique measurement on a sample of Teflon-AF of known
dielectric constant () [12] was repeated three
times. The measured and computed parameters are pre-
sented in Tables 3 and 4. The average values of
1.93
r
r
and tan
are found to be 1.795 and 0.0094.
6. Conclusions
The microwave dielectric properties of Zinc Magnesium
Titanate (1-x) Zn.xMg.TiO3 (x = 0.1, 0.2, 0.3, 0.4, 0.5) in
(a)
(b)
Figure 1. Rectangular S-band cavity (a) Design layout (b)
Fabricated cavity.
Figure 2. Experimental setup for dielectric constant meas-
urement.
Table 1. Resonant frequency and quality factor of cavity with only the capillary tube.
Average Centre or
Resonance Fre-
quency (fr) (GHz)
Average Lower 3 dB Fre-
quency (f1)
(GHz)
Average Upper 3 dB Fre-
quency (f2)
(GHz)
Average Band-
width
(f2-f1)
(GHz)
Average Quality Factor

1
21
r
Lf
Q
f
f
2.62138 2.62100 2.62174 0.00074 3542.40
Study of Dielectric Constant of (1-x) Zn.xMg.TiO(ZMT) Ceramic Material at Microwave
668 3
Frequencies as a Function of Composition x and Processing Temperature
Table 2. Dielectric constant of ((1-x) Zn.xMg.TiO3) for different values of x.
X value
Average Centre
or Resonant
Frequency (fr)
(GHz)
Average
Lower 3dB
Frequency
(f1)
(GHz)
Average
Upper 3 dB
Frequency
(f2)
(GHz)
Average Quality Fac-
tor

2
21
L
r
f
Q
f
f
r
r
 tan r
r

0.1
0.2
0.3
0.4
0.5
2.61462
2.61494
2.61548
2.61504
2.61456
2.61422
2.61454
2.61546
2.61468
2.61418
2.61500
2.61534
2.61620
2.61542
2.61494
3352.07
3268.67
3534.91
3533.83
3404.21
6.4648
6.2055
5.768
6.1244
6.5134
0.0169
0.0249
0.00063
0.00072
0.0121
0.0026
0.0040
0.0001
0.00011
0.00185
Table 3. Dielectric constant of ((1-x) Zn.xMg.TiO3) where x = 0.1, for different values of calcination temperatures.
Sample
Calcination
Temperature
( 0C)
Centre or
Resonant
Frequency (fr)
(GHz)
Lower
3dB Fre-
quency (f1)
(GHz)
Upper 3 dB
Frequency
(f2)
(GHz)
Quality Factor

2
21
L
r
f
Q
f
f
r
r
 tan r
r

ZMT
ZMT
ZMT
ZMT
+V2O5
900
950
1000
1000
2.61728
2.61736
2.61752
2.61472
2.61688
2.61696
2.61712
2.61434
2.61770
2.61778
2.61790
2.61514
3191.80
3191.90
3355.79
3268.40
2.94
3.03
3.67
4.04
0.0174
0.0173
0.0111
0.01188
0.005914
0.00507
0.003026
0.002698
Table 4. Resonance frequenc y and quality factor of cavity without standard sample.
Average Centre or
Resonance Fre-
quency (fr) (GHz)
Average Lower 3 dB Fre-
quency ( f1)
(GHz)
Average Upper 3 dB Fre-
quency (f2)
(GHz)
Average Bandwidth
(f2-f1)
(GHz)
Average Quality Factor

1
21
r
Lf
Q
f
f
2.62794 2.62754 2.62834 0.00080 3284.925
Table 5. Dielectric constant of standard material (Teflon-AF).
Standard
Material
Centre or
Resonant
Frequency
(fr)
(GHz)
Lower
3 dB Fre-
quency (f1)
(GHz)
Upper
3 dB Fre-
quency (f2)
(GHz)
Quality Factor

2
21
L
r
f
Q
f
f
r
r
tan r
r

Average
Value
r
and
tan
Teflon-AF
(diameter = 2.5 mm
and length = 37.25
mm)
2.62386
2.62388
2.62382
2.62340
2.62340
2.62344
2.62438
2.62436
2.62432
2677.408
2733.208
2677.367
1.794
1.790
1.801
0.0176
0.0156
0.0176
0.0098
0.0087
0.0097
1.795
and
0.0094
powder form have been investigated. The cavity pertur-
bation technique has been used for the evaluation of di-
electric properties of the material in S-band of micro-
wave frequencies. In this technique, a cavity has been
designed with very small slot at the centre of the broad
wall of rectangular waveguide in order to insert the sam-
ple material. A cylindrical capillary is designed for
holding of the sample. According to Wang [5] dielectric
Copyright © 2010 SciRes. JEMAA
Study of Dielectric Constant of (1-x) Zn.xMg.TiO(ZMT) Ceramic Material at Microwave 669
3
Frequencies as a Function of Composition x and Processing Temperature
5.2
5.4
5.6
5.8
6
6.2
6.4
6.6
0.1 0.2 0.3 0.4 0.5
x-value
Dielectric Constant
Figure 3. The experimentally observed variation of dielectric constant with x-value.
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045
0.1 0.2 0.3 0.4 0.5
x-value
Loss Tangent
Figure 4. The experimentally observed variation of loss tangent with x-value
Copyright © 2010 SciRes. JEMAA
Study of Dielectric Constant of (1-x) Zn.xMg.TiO3 (ZMT) Ceramic Material at Microwave
Frequencies as a Function of Composition x and Processing Temperature
Copyright © 2010 SciRes. JEMAA
670
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
900950 1000
Calcination Temperature
Dielectric Constant
Figure 5. The experimentally observed variation of dielectric constant with calcination temperature for composition x = 0.1.
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
900950 1000
Calcination Tempera ture
Loss Tange nt
Figure 6. The experimentally observed variation of loss tangent with calcination temperature for composition x = 0.1.
Study of Dielectric Constant of (1-x) Zn.xMg.TiO(ZMT) Ceramic Material at Microwave 671
3
Frequencies as a Function of Composition x and Processing Temperature
20 25 30 35 40 45 50 55 60 65 70
$
$
$
##
#
$
#
#
##
#
#
#
#
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
**
*
*
*#
*
(a)
(b)
(c)
(d)
(e)
Intensity (arb. units)
2 (degree)
Figure 7. X-ray diffraction patterns of (1-x)Zn.xMg.TiO3
with (a) x = 0.1, (b) x = 0.2, (c) x = 0.3, (d) x = 0.4 and (e) x =
0.5 ( where * (Mg, Zn)TiO3, # (Mg, Zn)Ti2O5 and $ TiO2).
constant decreases with increase in x-value. In the pre-
sent study the dielectric constant value decreased for
x–values from x = 0.1 to 0.3 and then increased for x >
0.3. This is because of the presence of different phases in
the composite material and the variation in the amount of
phases with change in x-values as shown in the XRD
patterns of the material. The dielectric constant has in-
creased and loss tangent reduced with increase in calci-
nation temperature. This may be attributed to the pres-
ence of single phase in the material. The r
value in-
creased and tan δ reduced with the addition of V2O5 in
ZMT material. This is because of improvement in the
rate of densification of ZMT material. The measured
dielectric constant values are lower than those reported
in reference [5]. This is due to lower value of percentage
density of sample material. The reported percentage den-
sity of sample materials studied in reference [5] is more
than 95%. Sample material used for measurement in ref-
erence [5] is in highly dense pellet form while in the
present study we measured the permittivity of sample
material in powder form.
It is concluded that the results represented here may
provide important inputs for the design of devices at mi-
crowave frequencies.
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