H. Hsu, M. Hill, R. Ziolkowski and J. Papapolymerou, A Duroid-based planar EBG cavity resonator filter with improved quality factor, IEEE Antennas and Wireless Propagation Letters, Vol. 1, Issue 2, pp. 67

H. Hsu, M. Hill, R. Ziolkowski and J. Papapolymerou, A Duroid-based planar EBG cavity resonator filter with improved quality factor, IEEE Antennas and Wireless Propagation Letters, Vol. 1, Issue 2, pp. 67
A Duroid-Based Planar EBG Cavity Resonator
Filter With Improved Quality Factor
Hsiuan-ju Hsu, Michael J. Hill, Richard W. Ziolkowski, and John Papapolymerou
Abstract—A highDuroid-based planar electromagnetic
bandgap (EBG) cavity resonator/filter has been designed, fabricated, and tested. It was implemented in Rogers Duroid 5880
with standard board fabrication techniques. This filter provides a
measured of 844 and a 0.91% bandwidth passband response at
10.63 GHz with a corresponding insertion loss of 2.76 dB.
Index Terms—Cavity resonators, cavity resonator filters, electromagnetic bandgap structure, filters, high-Q resonator.
EVERAL papers dealing with the design and realization
of electromagnetic bandgap (EBG) cavity resonator filters
have appeared recently [1]–[5]. There are at least two main advantages of using this EBG implementation instead of a fully
conducting side wall (FCSW) structure. One is that the requisite
EBG structures can be fabricated on soft or organic substrates
by using inexpensive standard printed circuit board (PCB) processing techniques. As a result, an EBG-based cavity resonator
filter can be incorporated in commercial products readily. The
second advantage is that the dimensions of the cavities can be
reconfigured as in [2] by switching on and off the metallic posts
electrically or mechanically to achieve a different resonant frequency and, hence, realize a reconfigurable high- cavity resonator filter. This paper presents an EBG cavity resonator with
the highest ever-reported unloaded quality factor, .
All simulations of the performance of the EBG cavity resonator filter were performed with ANSOFT’s high-frequency
simulation software (HFSS) tools. To determine the reflection
performance of the walls of the EBG cavity, a parallel-plate
waveguide configuration with the EBG lattice centered in the
middle of the guide was designed to allow variations in the
spacing between the posts of the EBG lattice. To find the filter’s
bandwidth, insertion loss, and the unloaded quality factor
the EBG cavity resonator filter was designed using two models.
One was a strongly coupled EBG cavity resonator that was used
to determine the bandwidth and insertion loss. The second was
a weakly coupled EBG cavity resonator used to determine
Manuscript received June 24, 2002.
H. Hsu and R. W. Ziolkowski are with the Department of Electrical and
Computer Engineering, University of Arizona, Tucson, AZ 85721-0104 USA
(e-mail: [email protected]; [email protected]).
M. J. Hill is with Intel, Chandler, AZ 85226 USA (e-mail: [email protected]).
J. Papapolymerou is with the School of Electrical and Computer Engineering,
Georgia Institute of Technology, Atlanta, GA 30332-0250 USA (e-mail: [email protected]).
Digital Object Identifier 10.1109/LAWP.2002.802548
Fig. 1. EBG cavity resonator filter; top and side views.
The high- Duroid-based planar EBG cavity resonator filter
is shown in Fig. 1. In order to make a stop-band in the EBG
structure at the desired cavity resonant frequencies, the spacing
and size of the cylindrical metallic posts were properly designed
to achieve low electromagnetic (EM) field leakage. As shown
in [1]–[4], the gap between the metallic posts in the EBG walls
needs to be shorter than 0.5 at the highest frequency of interest. A square EBG lattice was found to be the most effective. The number of rows of posts used must produce a high-reflection cavity wall to minimize leakage and, hence, produce a
high-quality factor .
According to simulations and experiments, two rows of posts
for each cavity are sufficient [1]–[4]. The dimensions of the
completed EBG cavity resonator filter design shown in Fig. 1
are given in Table I. The HFSS simulation results of the performance of the walls of the EBG cavity for normally incident
waves are provided in Fig. 2. Based on the design frequency of
1181 mils,
796 mils), the distance be10 GHz (
tween the centers of the posts of the two element deep square
, 186 mils 0.235
, and 93 mils
lattice: 372 mils 0.47
, were examined. Typical EBG reflection behavior
is apparent. The reflection coefficient at 10 GHz in these cases
1536-1225/02$17.00 © 2002 IEEE
The resonant frequency of the TE
mode can be found as
are, respectively, the effective length and width
where and
is the relative perof the cavity, is the speed of light, and
mittivity. Note that the higher order parallel-plate modes of the
structure perpendicular to the boards occur far above the operating frequency range of the fabricated cavity; hence, they do
not contribute to the performance of the cavity. The unloaded
of the cavity can be expressed as [7]
is the quality factor with respect to the dielectric
is the quality factor related to lossy conducting
losses and
can be determined, rewalls. The quality factors
spectively, from the following relations [7]:
is the effective height of the
where is the wavenumber,
is the effective surcavity, is the intrinsic impedance, and
face resistance of the cavity walls.
Given the geometry specified by Table I, the theoretical value
was calculated to be 830 with the loss tangent equal to
0.0009. Note that the largest variations in this value are dependent on the actual values of the material parameters. For instance, according to the data sheet from Rogers, Inc., the loss
tangent of this Duroid material is typically equal to 0.0009 at
10 GHz with a 2.22% error tolerance. Thus, the loss tangent
could vary in the range from 0.00088 to 0.00092, with corre. In particular,
sponding variations in the predicted
844 when the loss tangent equals 0.00088.
Fig. 2. Reflection coefficient of the walls of the EBG cavity resonator filter
as a function of the frequency for different values of the distance between the
centers of the posts in the two-element-deep square EBG lattice.
was 0.7614, 0.9976, and 0.9997, respectively. The smaller lattice spacing of the fabricated EBG cavity, 74.4 mils, was selected to ensure extremely good reflectivity even for the oblique
incidence of the cavity modes.
The EBG cavity resonator filter requires two boards. The
low-loss dielectric Duroid substrate, Rogers 5880 (
thickness 31 mils), was selected for use in the fabrication of
the top board. The low-loss dielectric Duroid substrate, Rogers
2.2, thickness 125 mils) was used for constructing
5880 (
the bottom board. The thicker board for the cavity section was
selected based upon the predictions in [2] that thicker dielectric
substrates would lead to a higher value for the cavity. The
from the edge
coupling slots were located approximately
of the cavities to maximize the coupling, where is the cavity
length [6]. They are “dog bone” shaped to improve the coupling.
To provide an electric short circuit at the center of the coupling
slot, a shorting via was used.
Standard PCB techniques were applied to fabricate the blind
and buried vias required by our design. The vias were first constructed by drilling holes in the substrates. Copper was then
plated on the surface of the holes and their edges. Next, the
circuit pattern was wet etched. The bonding surface was then
coated with solder and the boards were thermally fused together,
leaving a highly conductive and oxidation-free bond.
Both the weakly coupled and the strongly coupled models of
the EBG cavity resonator filter were fabricated and mounted on
a SMA-launch microstrip fixture and were measured with an
HP8510 network analyzer. The low-coupling model represents
the case where a very small amount of energy is inserted into the
resonator in order to accurately estimate or measure its quality
factor. The influence of the external circuitry that can affect the
measurements is thus minimized. On the other hand, in the
high-coupling case the resonator is strongly coupled to the ex-
Fig. 3. Simulated and measured insertion loss of the cavity resonator with
weakly coupled slots.
was extracted
The value of the unloaded quality factor
and the
from the measured external quality factor
loaded quality factor
[6] with the following equations:
The measured value of
was 842 (
13.686 MHz and
22.7615 dB). This result is very close to the predicted
theoretical value, 844, associated with the low value of the loss
tangent for Duroid 5880. The measured operating frequency
10.628 GHz was 0.066% different from the predicetd value
10.635 GHz. The measured insertion loss 2.76 dB was larger
than the simulated value 1.20 dB; but, correspondingly, the
measured bandwidth 0.91% or 97 MHz was (50 MHz) smaller
than the predicted value 1.38% or 147 MHz. The difference between them is most likely due to fabrication issues (especially
the bonding of the two substrates), but is well within reasonable
tolerances. We should note that the fabrication issues have a
more pronounced effect on the resonator with the strongly
coupled slots than the weakly coupled one.
Fig. 4. Simulated and measured insertion loss of the cavity resonator with
strongly coupled slots.
ternal circuitry for minimization of the insertion loss. Operation
of the resonator more as a filter is achieved in this case. It is important to note that most practical filter implementations would
utilize several of these high- EBG resonators to achieve a desired frequency response as was accomplished in [4].
The -parameter data was collected in both cases. The results
are shown in Figs. 3 and 4. The fixture losses were de-embedded
from these measurements since they would not be present in an
value is limited
integrated design. The minimum measured
by the noise floor of the network analyzer. A comparison of the
simulated and measured results for the EBG cavity resonator
filter is shown in Table II. Quite favorable agreement between
these results was obtained.
A high- Duroid-based planar EBG cavity resonator filter
demonstrating an unloaded of 844 was designed, simulated,
fabricated, and tested. When configured as a simple, single pole
filter, this device resonated at 10.63 GHz with a 0.91% bandwidth and with an insertion loss equal to 2.76 dB. The improvement in the unloaded value of the quality factor from previous cases reported in [1]–[4] and for a related structure in [5]
resulted, as predicted in [2], from the increase in the height of
the EBG cavity. To the best of the authors’ knowledge, this is
the highest ever reported for such a kind of PCB based cavity
resonator. Generally, the measured results agree well with the
theoretical and simulated results. This particular resonator can
be used for the development of very narrowband, low-loss filters for wireless communication systems. As in [4], a more desirable frequency response and an improved insertion loss can
be achieved by using this novel high- resonator in a multipole
filter design. Typically, the design equations used in a multipole
filter design assume resonators with infinite s. Therefore, the
use of these enhanced high- resonators may allow the realized
filter response to match more closely the anticipated result. In
particular, the high- EBG cavity resonator can be used immediately to improve further the three-pole filter design given in
[4]. The assembly and bonding of these resonators will play a
primary role in ensuring a superior performance in any specific
The authors would like to thank D. Brownstein, President of
U.S. Microwave, Tucson, AZ, for his efforts to bring the fabrication of the circuit introduced here to a successful conclusion.
[1] M. J. Hill, R. W. Ziolkowski, and J. Papapolymerou, “Simulated and
measured results from a Duroid-based planar MBG cavity resonator
filter,” IEEE Microwave Guided Wave Lett., vol. 10, pp. 528–530, Dec.
, “A high- reconfigurable planar EBG cavity resonator,” IEEE
Microwave Wireless Components Lett., vol. 11, pp. 255–257, June 2001.
[3] M. J. Hill, J. Papapolymerou, and R. W. Ziolkowski, “High- micromachined resonant cavities in a K-band diplexer configuration,” Proc.
Inst. Elect. Eng. Microwaves, Antennas, Propagat., vol. 148, no. 5, pp.
307–312, Oct. 2001.
[4] H.-J. Hsu, M. J. Hill, J. Papapolymerou, and R. W. Ziolkowski, “A
planar X-band Electromagnetic Band-Gap (EBG) 3-pole filter,” IEEE
Microwave Wireless Components Lett., to be published.
[5] W. J. Chappell, M. P. Little, and L. P. B. Katehi, “High isolation, planar
filters using EBG substrates,” IEEE Microwave Wireless Components
Lett., vol. 11, pp. 246–248, June 2001.
[6] J. Papapolymerou, J. Cheng, J. East, and L. Katehi, “A micromachined
high- X-band resonator,” IEEE Microwave Guided Wave Lett., vol. 7,
pp. 168–170, June 1997.
[7] D. M. Pozar, Microwave Engineering, 2nd ed. New York: Wiley, 1998.
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