Characterization of MgTiO3-CaTiO3-layered microwave dielectric resonators with TE01δ mode

Article abstract of DOI:10.1111/j.1551-2916.2005.00746.x

MgTiO₃ and CaTiO₃ ceramics were stacked in different schemes as the key components of the microwave dielectric resonators, and the microwave dielectric characteristics were evaluated with TE_01δ resonant mode. With increasi

Full text of DOI:10.1111/j.1551-2916.2005.00746.x

J. Am. Ceram. Soc., 89 [2] 557–561 (2006)
DOI: 10.1111/j.1551-2916.2005.00746.x
r 2005 The American Ceramic Society
ournal
J
Characterization of MgTiO3–CaTiO3-Layered Microwave Dielectric
Resonators with TE01d Mode
Lei Li, Xiang Ming Chen*,w and Xie Cheng Fan
Department of Materials Science & Engineering, Zhejiang University, Hangzhou 310027, China
MgTiO3 and CaTiO3 ceramics were stacked in different
schemes as the key components of the microwave dielectric res-
onators, and the microwave dielectric characteristics were eval-
uated with TE01d resonant mode. With increasing thickness
fraction of CaTiO3, the resonant frequency and Q ꢀ f value de-
creased, while the effective dielectric constant and temperature
coefficient of resonant frequency increased. The microwave di-
electric characteristics were also affected by the stacking
scheme. These effects were analyzed by the finite-element meth-
od, and the predicted characteristics agreed well with the ex-
perimental results. It was indicated that the temperature-stable
resonators with high-Q ꢀ f values could be attained by changing
the thickness fractions of CaTiO3, and the corresponding mi-
crowave dielectric characteristics could also be predicted by the
finite-element method.
microwave dielectric characteristics vary much from each other14
so that the effects of the thickness ratio and stacking scheme are
easily observed. (The measured properties in the present exper-
iments are: er 5 17.17, Q ꢀ f 5 92000 GHz, tf 5 ꢁ50.0 ppm/1C
for MgTiO3 and er 5 174.3, Q ꢀ f 5 11260 GHz, tf 5 804.1
ppm/1C for CaTiO3). The effects of the thickness fraction of
CaTiO3 and the stacking scheme on the microwave dielectric
characteristics for the layered resonators with TE01d mode are
investigated and discussed in the present work. Moreover, the
finite-element method is used for evaluating the layered dielec-
tric resonators, and the predicted characteristics are compared
with the experimental results.
II. Experimental Procedure
MgTiO3 and CaTiO3 powders were synthesized by a solid-state
reaction process. MgO (97%), CaCO3 (99%) and TiO2 (99.5%)
raw powders with proper ratios were mixed by ball milling in
distilled water with zirconia media for 24 h and then calcined at
11001C in air for 3 h to synthesize MgTiO3 and CaTiO3, respec-
tively. MgTiO3 and CaTiO3 powders with organic binder of PVA
water solution were pressed into cylindrical compacts and sinte-
red at 13501C in air for 3 h. XRD analysis was conducted to
determine the phase constitutions of the as-prepared MgTiO3 and
CaTiO3 ceramics. The as-sintered pellets with the same diameter
of 10.60 mm were thinned to different thicknesses as desired, and
polished well with paralleling and smooth surfaces. The pellets
were stacked together carefully with different stacking schemes
and thickness ratios, then they were placed in the shielded cavity
with axial symmetry and could work as dielectric resonators. The
total thickness for all these stacks was 5.0070.01 mm. As shown
in Fig. 1, bi-layer and tri-layer resonators were investigated with
four MgTiO3–CaTiO3 stacking schemes in the present experi-
ment, and they were indicated by MgTiO3/CaTiO3, CaTiO3/
MgTiO3, MgTiO3/CaTiO3/MgTiO3, and CaTiO3/MgTiO3/
CaTiO3, respectively. The thickness of each layer and the thick-
ness fractions of CaTiO3 for these stacks are shown in Table I.
The resonant frequency and temperature coefficient of reso-
nant frequency with TE01d mode between 201 and 801C were
determined by network analyzer (8720 ES, Agilent Technologies
Inc., Palo Alto, CA) using the reflection-type cavity method, and
the cross-section of the resonator is shown in Fig. 2(a). The un-
loaded Q ꢀ f value of the stack is calculated by fitting the meas-
ured complex reflection coefficients at different frequencies near
the resonant frequency to a circle using a personal computer,15
and then removing the effect of the loss of the cavity wall.16
Assuming a homogeneous dielectric with the same diameter and
thickness as the stack, if they give the same resonant frequency
under the present conditions, the dielectric constant of the ho-
mogeneous dielectric is defined as the effective dielectric constant
(er,eff) of the stack. er,eff can be calculated with high accuracy
using the finite-element method from the resonant frequency and
dimensions of the stack.17
I. Introduction
IELECTRIC ceramics have been widely used for microwave
D
applications as the key components of the dielectric reso-
nators in the microwave circuits.1 To attain miniaturized, high-
Q and temperature-stable resonators, the microwave dielectric
ceramics should have high dielectric constant (er), high-Q ꢀ f
value, and near-zero temperature coefficient of resonant fre-
quency (tf ).1,2 Many ceramics have high-dielectric constants and
high-Q ꢀ f values, although their temperature coefficients of res-
onant frequency are large and need to be tuned. Conventional
tuning methods focus on mixing two materials with opposite
temperature coefficients to form a solid solution.3–6 However,
not all ceramics can be tuned by this method as the possible in-
compatibility of ionic radius, ionic charge, or crystal structure
will bring undesired secondary phases and damage the Q ꢀ f
value much.
Modifying the resonator structure is another way to improve
the temperature stability of the dielectric resonator.7–9 Layered
dielectric resonator is just such a new method by stacking two
dielectric ceramics with opposite temperature coefficients of res-
onant frequency, and the near-zero temperature coefficient
could be obtained without damaging the high-Q ꢀ f value
much.9–13 This method makes it possible to use ceramics with
large temperature coefficients in temperature-stable resonators.
Although much work on layered dielectric resonator has been
done, many problems have not been understood deeply yet, such
as the effects of the thickness ratio and stacking scheme. Accu-
rate prediction of the microwave dielectric characteristics is also
an important issue for the layered resonators.
In the present work, MgTiO3 and CaTiO3 ceramics are
selected as the components of the layered resonators, as their
P. K. Davies—contributing editor
Manuscript No. 20349. Received March 25, 2005; approved August 28, 2005.
The present work was partially supported by the National Science Foundation under
grant numbers 50332030 and 50025205, and the Chinese National Key Project for Funda-
mental Researches under grant No. 2002 CB613302.
III. Finite-Element Analysis
*Member, American Ceramic Society.
The axis symmetry exists for TE01d mode and the electric field
has only a rotational component Ey that is also axis symmetri-
wAuthor to whom correspondence should be addressed. e-mail: xmchen@cmsce.
zju.edu.cn
557

558
Journal of the American Ceramic Society—Li et al.
Vol. 89, No. 2
(a)
(b)
(d)
CaTiO
MgTiO
3
3
MgTiO
CaTiO
3
3
(c)
MgTiO
CaTiO
3
3
3
CaTiO
MgTiO
MgTiO
3
CaTiO
3
3
Fig. 1. Stacking schemes for the MgTiO3–CaTiO3 stacks, (a) MgTiO3/
CaTiO3, (b) CaTiO3/MgTiO3, (c) MgTiO3/CaTiO3/MgTiO3, and
(d) CaTiO3/ MgTiO3/CaTiO3.
cal, so the two-dimension finite-element method can be used to
analyze the layered dielectric resonators, and only half of the
cross-section needs to be analyzed. The half section for finite-
element analysis is shown in Fig. 2(b), where the triangular first-
order element is employed. Many resonant frequencies corre-
sponding to TE0n(p1d) modes can be attained after resolving
special linear equations, and the lowest is the resonant frequency
of the layered resonator with TE01d mode. Also, the relative
electric field intensity of each node can be given. The detailed
analyzing process has been reported in the previous work.18,19
From the electric field distribution, the electric filling factor of
each component, Pe,i, can be calculated by
R
ꢃ
~ ~
1=2 er;iE ꢂ E dV
V
ꢀ
R
ꢁ
Pe;i
¼
P
P
ꢃ
~ ~
1=2 er;iE ꢂ E dV
i
V
R
S er;iEy2 ꢂ rdS
ꢂR
ꢃ
¼
(1)
S er;iEy2 ꢂ rdS
i
For the layered resonators with TE01d mode, Alford et al.10,11
have shown that the temperature coefficient of resonant fre-
quency obeys
X
tf ¼ A þ
ðtf ;iPe;iÞ
(2)
i
Fig. 2. (a) Structure of the resonator, (b) half of the cross-section of the
resonator for finite-element analysis, where the fractional number n/m
denotes that the length is n millimeter and divided into m segments
averagely.
where tf,i is the temperature coefficient of resonant frequency for
each component with the electric energy filling factor of unity
and A is the effect of the cavity on tf because of the thermal ex-
pansion coefficient of the cavity wall (17 ppm/1C for Cu). A can
be calculated by Kajfez’s incremental frequency rule16, and it is
usually minus several tenths ppm/1C for the present resonators.
For the MgTiO3–CaTiO3 stack and individual MgTiO3 and
CaTiO3 ceramics,
so we can attain
!
ꢁ1
X
X
Pe;i
Q ꢀ f ¼
ꢂ
Pe;i
(5)
ðQ ꢀ f Þi
i
i
f0
f0
tan d ¼
; ðtan dÞi ¼
(3)
Q ꢀ f
ðQ ꢀ f Þi
IV. Results and Discussion
Figure 3 shows XRD patterns of the as-prepared ceramics. Pure
CaTiO3 is attained in the present work, while a small amount of
MgTi2O5 secondary phase is found in the MgTiO3 ceramics.
According to the previous reports on MgTiO3-based ceramics,
the MgTi2O5 secondary phase is difficult to eliminate completely
and
ꢂ
ꢃ
ðtan dÞiPe;i
P
P
i
tan d ¼
(4)
i Pe;i
Table I. Experimental Parameters for the MgTiO3–CaTiO3 Stacks
Stacking scheme
Thickness of each layer (mm)
MgTiO3/CaTiO3
CaTiO3/MgTiO3
3.75/1.25
1.25/3.75
3.33/1.67
1.67/3.33
2.50/2.50
2.50/2.50
1.67/3.33
3.33/1.67
1.25/3.75
3.75/1.25
MgTiO3/CaTiO3/MgTiO3
CaTiO3/MgTiO3/CaTiO3
Thickness fraction of CaTiO3
1.88/1.25/1.88
0.62/3.75/0.62
0.25
1.67/1.67/1.67
0.83/3.33/0.83
0.33
1.25/2.50/1.25
1.25/2.50/1.25
0.50
0.83/3.33/0.83
1.67/1.67/1.67
0.67
0.62/3.75/0.62
1.88/1.25/1.88
0.75

February 2006
MgTiO3–CaTiO3 Layered Microwave Dielectric Resonators
559
180
(a)
ꢀ : MgTiO3
ꢁ: MgTi2O5
160
140
120
100
80
(b)
ꢀ: CaTiO3
60
MgTiO /CaTiO
CaTiO /MgTiO
MgTiO /CaTiO /MgTiO
CaTiO /MgTiO /CaTiO
40
20
0.0
0.2
0.4
0.6
0.8
1.0
20
30
40
50
60
70
Thickness fraction of CaTiO3
2θ (°)
Fig. 5. Effective dielectric constant as function of thickness fraction of
CaTiO3 (lines, predicted; dots, experimental).
Fig. 3. XRD patterns of the as-prepared MgTiO3 and CaTiO3 ceram-
ics: (a) MgTiO3; (b) CaTiO3.
higher dielectric constant and temperature coefficient of reso-
nant frequency than MgTiO3, so the resonant frequency de-
creases with increasing thickness fraction of CaTiO3, while the
effective dielectric constant and temperature coefficient of reso-
nant frequency increase for the same stacking scheme.
and it will damage the Q ꢀ f value.20,21 But it does not matter
much as the main aim of the present work is to discuss the
mechanisms of the layered resonator. Surely, it is necessary to
improve the preparing conditions to enhance the Q ꢀ f value for
further research on resonators with high-Q ꢀ f value and tem-
perature stability.
Figures 4–6 show the experimental and predicted resonant
frequency, effective dielectric constant and temperature coeffi-
cient of resonant frequency for the MgTiO3–CaTiO3 layered
resonators with TE01d mode as a function of the thickness frac-
tion of CaTiO3. The dots and lines correspond to the experi-
mental and predicted values, respectively. To judge the accuracy
of the finite-element method, the relative error is given as the
difference between the predicted and experimental result divided
by the experimental result. The relative errors for the resonant
frequency, effective dielectric constant, and temperature coeffi-
cient of resonant frequency are within ꢁ0.54% to ꢁ0.01%,
0.02%–1.10%, and ꢁ0.76% to 0.68%, respectively. It is con-
cluded that the finite-element method can give accurate predic-
tions for the resonant frequency, effective dielectric constant and
temperature coefficient of resonant frequency.
The stacking scheme also affects the microwave dielectric
characteristics as well as the thickness fraction of CaTiO3. The
curves of resonant frequency, effective dielectric constant, and
temperature coefficient of resonant frequency as functions of the
thickness fraction of CaTiO3 for CaTiO3/MgTiO3 are very near
to those for MgTiO3/CaTiO3, but they do not coincide. The
differences are because of the unsymmetrical structure of the
present cavity along the z direction (see Fig. 2(a)). The unsym-
metrical structure leads to the difference of the electric field dis-
tribution between the CaTiO3/MgTiO3 and MgTiO3/CaTiO3
stacking schemes. Also, the dielectric constants of the air and
supporter are much smaller than those of MgTiO3 and CaTiO3,
so the effect of the unsymmetrical structure is slight. For exam-
ple, the experimental resonant frequency of the CaTiO3/MgTiO3
resonator is 6–25 MHz larger than that for MgTiO3/CaTiO3
with the same thickness fraction of CaTiO3. The difference is
slight, but larger than the experimental error. To further under-
stand the differences, the contours of the relative electric field
intensity near the stacks for the MgTiO3/CaTiO3 and CaTiO3/
MgTiO3 resonators with the same thickness fraction of CaTiO3
of 0.5 are given in Figs. 7(a) and (b). The electric field distribu-
tions in MgTiO3 and CaTiO3 layers for bi-layer CaTiO3/
MgTiO3 and MgTiO3/CaTiO3 resonators are actually a little
different.
The thickness fraction of CaTiO3 has a significant effect on
the microwave properties for the layered resonators. This is be-
cause increasing the thickness fraction of CaTiO3 means that
CaTiO3 contributes more and MgTiO3 contributes less to the
final microwave dielectric characteristics for the layered resona-
tors with the same stacking scheme. Also, CaTiO3 has a much
7
800
600
MgTiO3/CaTiO3
CaTiO3/MgTiO3
MgTiO3/CaTiO3/MgTiO3
CaTiO3/MgTiO3/CaTiO3
6
5
4
3
2
400
MgTiO /CaTiO
CaTiO /MgTiO
MgTiO /CaTiO /MgTiO
CaTiO /MgTiO /CaTiO
200
0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Thickness fraction of CaTiO
Thickness fraction of CaTiO3
3
Fig. 6. Temperature coefficient of resonant frequency as a function of
thickness fraction of CaTiO3 (lines, predicted; dots, experimental).
Fig. 4. Resonant frequency as a function of thickness fraction of
CaTiO3 (lines, predicted; dots, experimental).

560
Journal of the American Ceramic Society—Li et al.
Vol. 89, No. 2
Fig. 7. Contours of the electric field intensity for the layered MgTiO3–CaTiO3 resonators with the same thickness fraction of CaTiO3 of 0.5 with TE01d
mode, simulated by the finite-element method: (a) MgTiO3/CaTiO3; (b) CaTiO3/MgTiO3; (c) MgTiO3/CaTiO3/MgTiO3; and (d) CaTiO3/MgTiO3/
CaTiO3.
Among the tri-layer resonators, the curves for the resonators
with a stacking scheme of CaTiO3/MgTiO3/CaTiO3 deviate
much more from the bi-layer resonators than those for
MgTiO3/CaTiO3/MgTiO3. A simple explanation is given from
the structure similarity of the resonators as the microwave di-
electric characteristics are determined by the components of the
resonators and the schemes of the components. The air and
the supporter (Teflon) have low dielectric constants of 1 and
2.1, respectively, and are designated as ‘‘L’’. Also, MgTiO3
(with middle er of 17.17) and CaTiO3 (with high er of 174.3)
are designated as ‘‘M’’ and ‘‘H,’’ respectively. Thus, accord-
ing to the sequences of the dielectrics from the bottom to
the top, the resonators with different schemes can be denoted
as the following:
both cases. The predicted Q ꢀ f values are given in Fig. 8(a), as
the lines indicate. The relative error between the predicted and
measured Q ꢀ f value (((Q ꢀ f )preꢁ(Q ꢀ f )meas)/(Q ꢀ f )meas) is
from ꢁ1.4% to 4.7%, depending on the stacking scheme and
thickness fraction of CaTiO3. Although the prediction is not
very accurate, the predicted trends are consistent with the ex-
perimental results. The errors may be attributed to many un-
certainties of the Q ꢀ f measurement, such as difference between
the samples,12 limited accuracy of the network analyzer,22 im-
perfect data fitting to an ideal circle,22 effect of the coupling co-
efficient23 and so on. For each stacking scheme, a sharp rise of
Q ꢀ f value is observed when the thickness fraction of CaTiO3
decreases to a certain value (see Fig. 8(b)).
The layered resonators with zero temperature coefficient of
resonant frequency can be attained since MgTiO3 and CaTiO3
have reverse temperature coefficients of resonant frequency.
The finite-element method gives the predicted thickness
fractions of CaTiO3 and corresponding microwave dielectric
characteristics for the temperature-stable-layered dielectric res-
onators, as shown in Table II, and high-Q ꢀ f values can be at-
tained. For different stacking schemes, the zero temperature
coefficient of resonant frequency is attended at different thick-
ness fractions of CaTiO3, where the dielectric constant and Q ꢀ f
value are almost the same for all these situations. This is because
the effects of CaTiO3 on the temperature coefficient of resonant
frequency are dependent on the stacking schemes. Although the
predicted microwave dielectric properties of the temperature-
stable-layered resonators are not better than those of the
(Mg,Ca)TiO3-based resonators (er 5 20–22, Q ꢀ f 5 56 000–
92000 GHz and tfꢄ0 ppm/1C21–26), they are expected to be
much improved through optimizing the preparing conditions to
improve the corresponding properties, especially the Q ꢀ f val-
ues of MgTiO3 and CaTiO3.
MgTiO3/CaTiO3: L–M–H–L,
CaTiO3/MgTiO3: L–H–M–L,
MgTiO3/CaTiO3/MgTiO3: L–M–H–M–L, and
CaTiO3/MgTiO3/CaTiO3: L–H–M–H–L.
It is obvious that the resonator with a stacking scheme of
MgTiO3/CaTiO3/MgTiO3 has a more similar structure to the
bi-layer resonators than to that for CaTiO3/MgTiO3/CaTiO3.
Also, the contours of the relative electric field intensity give the
same results (see Fig. 7).
The measured Q ꢀ f value of the MgTiO3–CaTiO3 stack as
a function of the thickness fraction of CaTiO3 is shown in
Fig. 8(a), as the dots indicate. For the same stacking scheme, the
Q ꢀ f value decreases with increasing the thickness fraction of
CaTiO3. The stacking scheme also has an effect on the Q ꢀ f
value. For the same thickness fraction of CaTiO3, the highest
Q ꢀ f value is obtained for the stacking scheme of CaTiO3/
MgTiO3/CaTiO3. It is followed by MgTiO3/CaTiO3/MgTiO3,
and the bi-layer MgTiO3/CaTiO3 and CaTiO3/MgTiO3 resona-
tors indicate the lowest Q ꢀ f values which are near the same for

February 2006
MgTiO3–CaTiO3 Layered Microwave Dielectric Resonators
561
microwave dielectric characteristics, and it is a useful tool for
analyzing the layered dielectric resonators and designing tem-
perature-stable-layered dielectric resonators. Temperature-sta-
ble dielectric resonators with high-Q ꢀ f values are expected to
be attained through this new method, and the details should be
investigated further in the future work.
(a)
14000
13500
13000
12500
12000
11500
MgTiO /CaTiO
CaTiO /MgTiO
MgTiO /CaTiO /MgTiO
CaTiO /MgTiO /CaTiO
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Thickness
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CaTiO3
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(GHz)
er,eff
(GHz) tf (ppm/1C)
MgTiO3/CaTiO3 0.0085 6.9135 18.03 66,850
CaTiO3/MgTiO3 0.0090 6.9149 18.02 66,870
MgTiO3/CaTiO3/ 0.0047 6.8978 18.12 66,880
MgTiO3
CaTiO3/MgTiO3/ 0.0103 6.9019 18.10 66,860
CaTiO3
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V. Conclusion
The microwave dielectric characteristics for the layered
MgTiO3–CaTiO3 resonators with TE01d mode are discussed in
detail. The stacking scheme has a significant effect on the electric
field distribution as well as the thickness fraction of CaTiO3. The
finite-element method can give accurate predictions for the
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&