# Investigation on Harmonic Tuning for Active Ku-Band Rectangular Dielectric Resonator Antennas

Authors: Anda Guraliuc; Giuliano Manara; Paolo Nepa; Giuseppe Pelosi; Stefano Selleri
Journal: International Journal of Antennas and Propagation
 (2008)

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## Abstract

A slot-coupled rectangular dielectric resonator antenna (DRA) operating in the 14–14.5 GHz frequency band is investigated as a possible radiating element for an active integrated antenna of a transmitting phased array. The effectiveness of the resonator shape factor on achieving harmonic tuning is addressed. Simulation results show that the DRA shape factor can be used to provide a fine tuning of the DRA input impedance both at the fundamental frequency and its first harmonics, so synthesizing the proper load for the optimization of the microwave amplifier power-added efficiency (PAE).


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## Body

## 1. Introduction

During the latest years, an increasing research interest has
been devoted to dielectric resonator antennas (DRAs) [1–3] in the
microwave and millimeter frequency ranges, since they show several attractive
features over conventional antennas, such as small size, high radiation
efficiency, light weight, intrinsic simple structure, high power-handling
capability, extreme flexibility in terms of resonator shapes and feeding
techniques. Moreover, different radiation patterns can be achieved with the
same resonator by exciting different radiating modes, and for a given resonant
frequency, they can realize miniaturized antennas if a dielectric resonator
with high permittivity is used. Also, when compared with microstrip or slot
antennas exhibiting a comparable layout complexity, the DRA has a relatively
larger impedance bandwidth and does not suffer of conductor and surface wave
losses. DRA development is also strictly related to the recent technological
advances on low-loss dielectric materials exhibiting a wide range of dielectric
permittivity (up to εr=100). As far as phased arrays are concerned, the
compactness of DRAs (obtained by high-permittivity dielectric resonators) allows
smaller interelement separation compared with many other antenna types, and it
results in reduced scan losses.Although DRAs have been deeply investigated, previous
studies have been mainly focused on radiated field characteristics, radiation
efficiency, and impedance bandwidth widening. Conversely, reduced attention has
been devoted to the investigation of DRA arrays [4–7] and harmonic
tuning of active DRAs [8]. On the other hand, the tuning of the antenna input
impedance at the fundamental frequency as well as at the first harmonics is
strongly recommended in transmitting active integrated antennas (AIAs) [9, 10], where high
power added efficiency (PAE) values are required. Moreover, the harmonics
generated by the power amplifier will be radiated by the antenna if the latter
does not exhibit a sufficiently high reflection coefficient at those
frequencies. As a consequence, harmonic radiation causes system efficiency
reduction and electromagnetic interference with other radio systems. Therefore,
an efficient design of an AIA that does not consider an impedance matching
network between the antenna and the active device must require the tuning of
the antenna input impedance at the first and second harmonic, and, possibly, at
the third harmonic too, even if latter requirement is less restrictive since
third harmonics power levels are anyway quite low. Several configurations have
been devised for harmonic tuning of microstrip antennas, which are based on the
use of holes, pins, or slots, as well as on the shaping of the radiating patch
[11, 12].In this paper, harmonic tuning of a rectangular DRA for
an active-phased array antenna working in the 14–14.5 GHz frequency band (VSWR<−10 dB) is addressed. It is shown that the input impedance control at the harmonic
frequencies can be effectively carried out through a modification of the rectangular
resonator shape factor. A DRA-phased array represents an effective alternative
to printed technology in Ku-band satellite broadband communication systems,
mainly due to their compactness, high efficiency, compatibility with microwave
integrated circuits, and low scan losses. A slot coupling feeding technique has
been chosen, since it is the most suitable for large DRA arrays, where a relatively
simple circuit integration is required, as compared with other feeding mechanisms.
Moreover, since a ground plane isolates the feeding structure from the
radiator, the radiation characteristics are mainly those of the dielectric
resonator and surface waves are not excited.The paper is organized as follow. In Section1, a brief overview on
rectangular DRAs is reported to summarize their main features. Then in Section 2 it is shown that a fine tuning of the input impedance of a slot-coupled rectangular
DRA at the first harmonics can be easily obtained by changing the resonator length-to-width
and length-to-height ratios. Indeed, it is possible to vary the above ratios of
the DRA to obtain a wide variability range for the input impedance at the
second harmonic, without seriously affecting the input impedance and radiation
patterns at the center frequency (14.25 GHz). Simulation results have been
obtained by using the Ansoft HFSS software package, which has been demonstrated
being an accurate tool for the analysis of rectangular slot-coupled DRAs.


## 2. A Brief Overview on Rectangular Dielectric Resonator Antennas

The basic configuration of a rectangulara×d×b/2 DRA over a finite conducting ground plane is
shown in Figure 1. Theoretical and experimental investigations on various
shapes of DRAs have been reported in the open literature [1–3], showing that
the rectangular DRA has some advantages over the cylindrical and hemispherical
DRAs [13]. Indeed, by properly choosing the dielectric resonator sizes, mode
degeneracy can be avoided and cross-polarization can be taken under control. Moreover,
compared to the above DRA shapes, rectangular DRAs are easier to fabricate.Figure 1
Geometry of the slot-coupled rectangular DRA,
comprehensive of finite ground plane and feeding microstrip.The DRA impedance bandwidth can be increased (lower radiationQ factor) by using low-permittivity dielectric resonators or by resorting to
parasitic elements, at the cost of increasing the DRA size and fabrication
complexity, respectively [1–3]. Several nonhomogeneous DRA configurations
have also been proposed such as stacked, notched, or multisegment
configurations [1–3] as well as
rectangular resonators with a metal coating [14]. In addition, for a given
resonant frequency, in a rectangular DRA the two aspect ratios
(length-to-height and length-to-width) can be chosen independently, and then used
to achieve impedance bandwidth widening [15].Different feeding mechanisms have been theoretically and
experimentally investigated [1], as, for example, a coaxial probe, a microstrip
feedline, a coplanar waveguide, a rectangular waveguide, which make the DRAs
amenable to integration with different existing electronic technologies. Recently,
a differential feed has also been proposed [16], to avoid using a balun when
connecting the antenna to a differential circuit for the common mode rejection.
As far as circular polarization (CP) DRAs are concerned, single-point feed
systems have been suggested, such as quasisquared and crossed DRAs, which
exhibit a CP bandwidth up to 7% [2].Finally, although most of the work has been done for single
element optimization, the advantages of using linear or planar DRA arrays to
implement phased arrays with beam steering capabilities have also been
investigated. In planar arrays, the compactness of DRAs using high-permittivity
dielectric resonators allows for a small separation between the array elements,
which is often required in electronically beam steering antenna or when a proper
excitation tapering must be implemented. In [17], it has been shown that when
used as an active antenna, a rectangular DRA shows superior tolerance levels
with respect to fabrication and larger impedance bandwidth, as compared to an
active microstrip patch antenna. However, in [17] impedance matching networks comprising
an open-circuit stub have been used, and the harmonic tuning issue is not faced
with. In [8], harmonic tuning of a rectangular DRA has been achieved by adding
a pair of parasitic slots adjacent to the coupling slot located between the
microstrip line and the dielectric resonator.


## 3. Shape-Factor-Based Harmonic Tuning

The effectiveness of the shape factor on achieving the
harmonic tuning of a rectangular DRA is shown in this section, where the design
of a slot-coupled rectangular DRA suitable for a Ku-band phased array is used
as a test case. The rectangulara×d×b/2 DRA fed through a rectangular slot coupled
with a microstrip line is shown in Figure 1. The resonator relative
permittivity has been set to εr=20.
The DRA is placed above a ground plane, and is centered with respect to the l×w nonresonant rectangular slot. The antenna is
fed through a microstrip line (25Ω characteristic impedance, as requested
by the chosen PA layout for maximum PAE) of width ws=1.6mm, which is printed on the bottom of a grounded
substrate (thickness and relative permittivity equal to h=0.5mm and εr=10.2, resp.) whose sizes are L=17mm, W=14mm. The antenna has to operate in the TE111z mode at a frequency f0=14.25GHz, with a VSWR <−10dB in a 500 MHz frequency band (3.5% percentage bandwidth).As far as the fundamental “magnetic dipole” mode of a
rectangular DRA is concerned, efficient analytical formulas have been derived
to estimate the resonator dimensions for a given resonant frequency [13],  which
exhibit a percentage error less than a few percent. Specifically, for a given (a,b) pair, it is possible to
analytically estimate the value of d corresponding
to a resonant frequency close to f0=14.25GHz. A sample of numerical results is shown in Figure 2(a), where the
length-to-width ratio a/d versus the length-to-height ratio a/b is shown for two different values of the DRA length: a=3.85mm and a=4.25mm. Tables 1 and 2 show the numerical values of these setups. By means of HFSS simulations,
it has been verified that all the geometrical configurations shown in Figure 2 provide
the correct resonant frequency, when the DRA is fed through a slot with l=2.2mm and w=0.3mm. A fine tuning of the length of the open-circuit
stub at the end of the feeding line, ls,
was adopted to optimize the return loss performance at f0=14.25GHz (see Figure 2(b)).Table 1
First set of DRA dimensions(a,b,d) considered for a rectangular DRA
operating in the fundamental TE111z mode at f0=14.25GHz.
IDa [mm]b [mm]d [mm]I.13.855.022.06I.25.621.85I.36.201.70I.46.801.60I.57.421.56Table 2
Second set of DRA dimensions(a,b,d) considered for a rectangular DRA
operating in the fundamental TE111z mode at f0=14.25GHz.
IDa [mm]b [mm]d [mm]II.14.254.681.90II.25.881.54II.36.481.44II.47.081.37II.57.681.32Length-to-width ratio (a) and open-circuit stub
length (b) versus length-to-height ratio for a rectangular DRA operating in the
fundamentalTE111z mode at f0=14.25GHz.
(a)(b)The values of the input impedance at the fundamental
frequency,f0=14.25GHz,
are shown in Figure 3 for all the aspect ratios analyzed in Figure 2. As
apparent, a pretty good impedance matching at 25Ω has been achieved for
all the configurations listed in Tables 1 and 2. The input impedance values obtained
at 2f0=28.5GHz and 3f0=42.75GHz are also shown in Figures 4(a) and 4(b),
respectively. As apparent, by varying the DRA-shape factor, a wide range of
imaginary part values can be provided, leading to either inductive or
capacitive input reactance. In Figure 5, the input impedance values are plotted
on a Smith Chart over a 200 MHz frequency range around f0 and 2f0,
for the a=3.85mm (case I). For frequencies around f0, the curves are clustered around the Smith Chart origin, so demonstrating that a
quite good impedance matching condition is always met independently of the
specific DRA configuration chosen between those in Table 1. For frequencies
around 2f0,
the return loss is always greater than −4 dB (except for case I.1). It is also
apparent that by changing the DRA configuration (between the different aspect
ratios in Figure 2) it is possible to control the phase of the return loss,
namely, the reactive component of the DRA input impedance. The latter is an
important feature in an AIA design since the antenna must not only reject higher
harmonics, but also exhibit a proper reflection coefficient phase to optimize
the PAE. Similar considerations apply to the results in Figure 6, where the
input impedance values over a 200 MHz frequency range around f0 and 2f0 are plotted on a Smith Chart for the a=4.25mm (case II). In this case, it is apparent how a
couple of DRA configurations (cases II.1 and II.2) do not guarantee a return
loss higher than −2 dB at the second harmonic 2f0.Figure 3
Real and imaginary values of the DRA input
impedance at the fundamental frequency versus length-to-height ratio, for two
values of the resonator length:a=3.85mm and a=4.25mm.Real and imaginary values of the DRA input
impedance at the second and third harmonic frequencies versus length-to-height
ratio, for two values of the resonator length: (a)a=3.85mm and (b) a=4.25mm.
(a)(b)Figure 5
Input impedance over a 200 MHz frequency band
aroundf0 and 2f0 for the DRA with a=3.85mm (the geometrical configurations I.1 to I.5 are those
listed in Table 1).Figure 6
Input impedance over a 500 MHz frequency band aroundf0 and 2f0 for the DRA with a=4.25mm (the geometrical configurations II.1 to II.5 are those
listed in Table 2).Figure 7
Percentage bandwidth (VSWR<−10dB) versus the length-to-height
ratio (the other geometrical parameters are those shown in Figure 2).In Figure6, the percentage impedance bandwidth (VSWR <−10 dB)
for the configurations in Figure 2 is shown, to demonstrate that beside
controlling the input impedance at the frequencies 2f0 and 3f0,
we can also met the bandwidth specifications (percentage bandwidth greater than
3.5%). It is worth noting that the percentage bandwidth decreases at the
increasing of the length-to-height ratio, as already found in [15] where the
degree of freedom represented by the DRA-shape factor was adopted to enlarge
the antenna impedance bandwidth.Finally, Figure8 shows the radiation
patterns in the principal planes (both copolar and cross-polar components), for
the DRA geometrical configurations, when a=4.25mm and for two different values of the
length-to-height ratio: the II.1 configuration, which has a/b=(a/b)max=0.91,
and the II.5 configuration, which has a/b=(a/b)min=0.55.
It is apparent that the radiation patterns do not vary significantly with
respect to the length-to-height ratio a/b, as expected, since the same mode is
excited (it is worth noting that the slot-fed DRA radiates as a short magnetic
dipole parallel to the slot itself, in its lowest order mode). The cross-polar
components are mainly due to the field scattered at the borders of the finite
ground plane. A small asymmetry in the E-plane is due to the presence of the
microstrip line feeding the slot and to radiating surface waves excited at the
open circuit stub. The larger cross-polar level is around 15 dB and 20 dB in
the E-plane and H-plane, respectively, and it is associated with configuration
II.1 exhibiting the maximum value of the length-to-height ratio, that is, a/b=(a/b)max=0.91.
This result is in agreement with [6], where it is stated that higher
cross-polar levels are obtained with lower values of the length-to-width ratio, a/d (from Tables 1 and 2 it results that a/d=3.21 if a/b=(a/b)min=0.55,
while a/d=2.23 if a/b=(a/b)max=0.91).Radiation patterns for a DRA witha=4.25mm, and a/b=min(a/b)=0.55 or a/b=max(a/b)=0.91: (a) xy plane (E-plane); (b) yz plane (H-plane).
(a)(b)


## 4. Conclusions

It has been shown
that the aspect ratios of a Ku-band slot-coupled rectangular DRA can be used to
control the antenna input impedance at the fundamental and first harmonic frequencies,
without any significant change in antenna radiation patterns. Besides, the
three dimensions of the dielectric resonator, only a fine tuning of the stub
length is needed to optimize the return loss at the fundamental frequency,
while the slot geometrical parameters can remain unchanged. Work is in progress
to estimate the effect of a poor mechanical contact between the DRA and the
ground plane (air gap), which can significantly modify the DRA input impedance
especially at the higher harmonics as well as the effect of misaglinments in
centering the DRA over the slot.



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*Source: 437538-2008-05-21.xml*