# Cylindrical Dielectric Resonator Antennas with  Harmonic Control as an Active Antenna Radiator

Authors: L. Lucci; G. Manara; P. Nepa; G. Pelosi; S. Selleri
Journal: International Journal of Antennas and Propagation
 (2009)

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## Abstract

A cylindrical dielectric resonator antenna
is proposed as a radiator for an active integrated antenna.
Harmonic tuning, which is the key step in designing active antenna
radiators, is achieved via a combination of shape factor control
over the resonator and insertion of reactive elements in the feed
system. Numerical simulations are carried out in a finite elements
framework and a layout for the complete antenna is proposed,
aimed at compactness for subsequent utilization of the radiator
as an element in an active array for satellite communications.


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## Body

## 1. Introduction

Active
integrated antennas (AIAs) are  microwave systems which integrate on a single
substrate several functions, at least one of which is that of a radiating
element and another is that of an active device, be it a power amplifier for a
transmitting AIA, or a low noise amplifier for a receiving AIA.Albeit more complex functions can be embedded in the
AIA, as frequency conversions with its own local oscillator, phase locking and
many more, the key feature of an AIA is the tight integration between the
active device and the radiating element.Conventional antenna system design leads to radiators
whose input impedance is matched to50Ω via some appropriate matching network, and to
amplifier which are themselves matched to the same 50Ω via some appropriate matching network. The two
devices are then connected via a 50Ω transmission line. The two matching network
can be fairly complex, especially the one which must be designed for a power
amplifier (PA). In this case the matching network needs not only to match the
output of the PA to 50Ω at the working frequency, but must also
provide an appropriate load for the higher harmonics. The essence of AIAs is to
eliminate both matching networks and the interconnecting line, by designing the
radiating element so that it provides the correct load to the PA at the
fundamental frequency and higher harmonics. In transmission mode, in
particular, the antenna should provide a given, generally complex, load for the
power amplifier at the system working frequency in order to optimize the system
performance, while for the first two higher harmonics, the impedance must be
typically purely imaginary, be it capacitive or inductive.By attaining this the overall system is simplified and
reduced in size, by removing two matching networks, the losses in the lines are
of course reduced, hence higher efficiencies, and lower power consumptions,
attained. These characteristics make AIAs very attractive in wireless
communications. The possibility of integrating also some sort of phase control
in the AIA, for example, with a voltage controlled oscillator (VCO) leads to
very attractive possibilities in the field of smart antennas and electronically
steering phased arrays for vehicle-to-satellite broadband communications
[1, 2].As stated before AIAs are devices in which the
radiating element and the active circuit, the amplifier, are treated as a
single entity. The radiating element, which will be the focus of this paper, is
to be seen as a filter, output matching circuit, and harmonic tuner in addition
to its characteristics of load and radiating element. The core issue is that
radiating elements are either broad band or resonating structures. Broadband
antennas are usually large and unsuitable for commercial telecommunications
usage, since standards give fairly narrow bands. Resonating antennas are much
more compact but, being resonant, have the strong tendency to behave in a very
similar way at the working frequency and at its harmonics, at least for what
concerns the input impedance. This implies that higher harmonics have an input
impedance which is essentially real. To allow for a resonant radiator to be
embedded in an AIA some modifications are necessary to attain its harmonic
tuning, that is, the  separate design of the input impedance at the fundamental
frequency and at at least the first two higher harmonics.In literature there are several works presenting
different patch and slot antenna configurations for harmonic tuning, most of
them relies on the suppression of higher resonances. Rectangular patches can be
loaded with shortening posts [3]
or with notches [4] or
by feeding them with photonic band-gap structures [5], while circular ones can
have a slice chopped of as in [6]. Slot antennas can be loaded with reactive components
shortening higher frequencies, as in [7, 8], leading to excellent harmonic suppression, but slot
antennas tend to have poor radiating characteristics.In this paper a harmonic tuning technique for a
dielectric resonator antenna (DRA) working in Ku band at
14.25 GHz is
described. DRAs are a class of antennas which has interesting characteristics
for usage as an AIA radiator. They exhibit low losses and, if fed via ground
plane slot coupling, allow for a decoupling between the DRA, which lies on one
side of the ground plane, and the substrate with its circuits and active
elements, which lies on the other side of the ground plane. The absence of a
substrate on the radiating side has additional benefits in array
configurations, eliminating the possible interantenna coupling due to surface
wave excitation.In literature several kinds and shapes of DRAs have
been considered, rectangular (RDRA), cylindrical (CDRA), hemispherical (HDRA)
and all of these received much attention for what concerns antenna efficiency,
compactness [9–11],
and bandwidth. Nevertheless, there have been very few studies regarding the
behavior of DRAs at higher harmonics for their usage as AIAs. More recent
papers are focused on RDRA harmonic tuning [12, 13] while few preliminary results on CDRA harmonic tuning
were presented in [14, 15].Here a study of a slot-coupled cylindrical DRA
configuration is presented, analyzing its harmonic response first at a shape
factor level, then by introducing reactive elements in the coupling slot, and
lastly by introducing additional slots. A complete design ready to be
integrated with a PA is then presented.The paper is organized as follows. In Section2 the
slot-coupled CDRA is described, with particular attention to higher-order
resonant modes, to devise a possible optimal shape factor.
Section 3 will
present two modified configurations for the optimization of the resonator
antenna electromagnetic performance at fundamental frequency and higher
harmonics. Section 4 will present the final design suitable for the
integration with a power amplifier and Section 5 will draw some conclusions.


## 2. Shape Factor Tuning

A first investigation is done by analyzing the modes
which are theoretically present on a cylindrical resonator of radiusa and height 2d made by a dielectric characterized by a
permittivity ε and a permeability μ.
The resonant frequencies are [16](1)fnmp=12πaμε[Xnp∣Xnp′]2+(πa2d(2m+1))2, where n=1,2,3,…,  m=1,2,3,…, and p=0,1,2,… are three integer numbers, and [Xnp∣Xnp′] are either the pth zeros of the Bessel function of the first kind
and order n or the zeros of the derivative of the Bessel
function of the first kind and order n,
respectively.If the zeros of the   Bessel function are used the
frequencies of theTEnmp modes are obtained. If the zeros of the
derivative are used then the TMnmp modes are obtained. It is easy to obtain that
the fundamental mode in a cylindrical resonator is the TM110,
which is relevant to X11′=1.841.It is then quite easy to invert (1) so as to obtain
the value of a as a function of d which leads to a desired fundamental mode
frequency f0:(2)a=X11′2dπ4(f0/c)2(2d)2−1 being c=1/εμ the speed of light in the dielectric.By choosing an appropriate range for2d and by computing the relevant values of a via (2) a set of resonators whose fundamental
mode frequency is 14.25 GHz is obtained. By applying on this set (1)
the frequencies of all the other modes can be computed as a function of 2d.
Figure 1 shows such a diagram, presenting the values of 2d on the y axis and the frequencies on the x axis. TE modes are represented with solid lines, while TM modes represented with dashed lines. It is apparent how
the fundamental frequency, being a vertical line, does not vary with 2d.
In this preliminary analysis a relatively low permittivity resonator (ε=9.8) is used.Figure 1
Curves of the resonant frequencies of the modes of the
CDRA under analysis, as a function of resonator height having let radius to
vary so that the first resonance remains fixed at14.25 GHz. TE modes: solid lines; TM modes: dashed
line.While the fundamental mode is of course fixed at the
desired value independently of2d,
nearly all other modes are 2d dependent. The first step will then be that of
choosing 2d so that no modes are present at the harmonics
of the fundamental frequencies 2f0 and 3f0,
represented with pale blue stripes in the figure.While this is possible for2f0 by choosing a relatively low thickness
resonator, for what concerns 3f0, there is a TE mode which is independent of 2d and exactly at 3f0.
This implies that the second harmonic will be more critical and that it will be
impossible to handle it by resorting only to the resonator shape factor.Figure2 shows a practical CDRA setup. The resonator,
whose height is halved to d, is placed on a ground plane and slot-coupled
to a feeding microstrip. The dimensions of the setup are given in Table 1, the
substrate has ε=10.2, and the whole set up has been analyzed with
the finite elements method (FEM) in an enclosing box featuring perfectly
matched layer (PML) radiation boundary conditions.Table 1
CDRA setup dimensions [millimeters].
WLtwslswl16160.63542.880.74.7Geometry of the CDRA under
exam, top view (right) and 3D view (left).
(a)(b)If a parametric analysis  is performed over an
appropriate range ford and  over the whole f=10–45 GHz frequency range, with the values of a computed by (2),  the return loss at the
microstrip port can be represented as a surface graph function of d and f.
Figure 3  shows such a surface as a contour plot. Only the lines where |S11| is equal to −10 and −20 dB are reported for
the sake of clearness.Figure 3
Contour plot of the magnitude of theS11 parameter at the microstrip port of the
antenna.It is evident from Figure3 how the fundamental mode is
well matched for any d value, even if the full wave analysis of the
DRA over a finite ground leads to a slight dependence of the matching frequency
with d (i.e., the zone of matching is not a
vertical line). Then there are zones, at higher frequencies, where the antenna
is more or less matched, and these zones assume a form which is quite similar
to the lines in the dispersion graph in Figure 1. Lines are less numerous than in
Figure 1 due to the fact that  the coupling slot, due to its symmetries, does not
excite  all the possible modes and that matching has its own band, so
neighboring lines easily merge in a single matched area. Around 2f0 the reflection coefficient amplitude is high
for low d and gets lower as d increases, confirming that, a low d value is desirable. In the end, as expected,
the reflection coefficient at 3f0 is generally quite low. As a first conclusion
a d=1 mm will be the first choice, and, for this
value of the resonator height, in Figure 4 the return loss as a function of the
frequency is reported from 10 GHz to 45 GHz, to show the antenna behavior at
fundamental frequency and at first and second harmonics.Figure 4
Return loss numerically computed for the CDRA setup of
Figure2. Good matching at the fundamental frequency is evident, while mismatch
at first and second higher-order harmonics is insufficient.


## 3. Slot Harmonic Suppression

Working only on
the shape factor does not lead to a complete control over the reflection
coefficient at higher harmonics. The3f0 one in particular being extremely critical as
the previous section showed.As an upgrade to the previously shown configuration a
parasitic element has been inserted in the coupling slot, in a fashion similar
to [7, 8]. It is worth noticing how
the “T” shape metalization inserted has to be designed differently since the
slot itself is not resonant in our case. In Figure 5 the geometry of the proposed
structure is reported. Dimensions are w=0.6 mm, wt=0.26 mm, l=6.3 mm, lt=5.48 mm, r=0.34 mm, and s=1.1 mm.Figure 5
Geometry of the modified slot coupling. Inside the
slot a parasitic reactive dipole provides higher harmonic rejection.In Figure6 the return loss as a function of
the frequency is reported from 10 GHz to 45 GHz, to show the antenna behavior at
fundamental frequency and at first and second harmonics. For this structure the
antenna input impedance is about Z11=45+j5Ω at f0 and Z11=85+j28Ω at 2f0.Figure 6
Return loss of the modified structure exhibiting the
in-slot parasitic element as sketched in Figure5.A real full control of the second harmonic using the
parasitic element is not possible, due to both  the reduced size of the slot and
a further phenomenon which will be described in detail in the following
section. Hence, to further improve the antenna performances at the second
harmonic, two parallel additional slots have been added to the previous
configuration as shown in
Figure7, where w=0.6 mm, wt=0.26 mm, wa=0.4 mm, l=6.3 mm, lt=5.48 mm, la=2.0 mm, r=0.34 mm, d1=2.8 mm, s=1.1 mm, and d2=1.4 mm.Figure 7
Geometry of the modified slot coupling
with two additional parallel slots.In Figure8 the return loss as a function of the
frequency is reported from 10 GHz to 45 GHz, to show that the antenna behavior at
the second harmonics has been improved. In particular for this modified
structure the antenna input impedance is about Z11=50+j5Ω at f0, Z11=10+j17Ω at 2f0 and Z11=35+j25Ω at 3f0.
The reason why the insertion of additional slots might help in rejecting higher-order harmonics lies in the fact that they perturb these more, due to their
reduced wavelength. A deeper insight can be found in [12].Figure 8
Return loss of the modified structure with two
additional parallel slots as sketched in Figure7.


## 4. Final Layout

In this section
a complete design ready to be integrated with a PA is presented. The design
comprises not only the pad where the PA output is to be placed but also the
line for the DC feed of the PA front-end. This latter has been designed so as
to help in rejecting the second harmonic, while an additional stub shortening
the third harmonic is also present. As shown in Figure9, where the geometry of
the final layout is reported, the parasitic element in the slot presented in
the previous section has been retained, while the two additional slots have not,
since their influence is relatively small and they can be replaced by the
aforementioned stub. The geometric parameters defining the dimensions of the
structure are as follows: l=6.224 mm, w=611 μm, lt=5 mm, wt=220 μm, s=1.107 mm, a=1.39 mm, h=1.21 mm, ll1=6.124 mm, ll2=8.876 mm, ls1=2.243 mm, ls2=1.754 mm, ls3=283 μm, wl1=521 μm, wl2=400 μm, ws=380 μm, and λ0=21.053 mm  being λ0 the wavelength along the microstrip at fundamental frequency f0.Geometry of the final layout: top view (a) and side view (b). The green rectangular area represents the DC feed, whereas the red rectangular pad represents the area where the PA output is to be soldered.
(a)(b)To show the active antenna electromagnetic
performances in Figure10 the input impedance is reported as a function of
frequency, zooming around the fundamental frequency and the first two
harmonics.  Table 2 summarizes the input impedance simulation results at the
above mentioned frequency together with the desired values as given by the
PA designers [17].Table 2
Final layout input
impedance.
Frequency [GHz]Z11[Ω]RequestedZ11[Ω]f017.7 +j17.715 +j182f021.5 +j94.71j1003f053.81 +j28.61j17Final layout: input impedance at central frequency (a), at first harmonic (b), and at second harmonic (c).
(a)(b)(c)In Figure11 the electric field maps on the y=0 plane at fundamental frequency and at the
first and second harmonics are represented. It is evident that the fundamental
frequency radiates, while the second harmonic does not. This is due to the DC
feed line for the power amplifier, which is loaded by the DC source which in turn
is essentially a short circuit at radio frequency. The feed is λ0/4 wavelength away from the PA output at f0,
hence the short circuit reverts to an open one and no energy is present on the
stub at f0 (see Figure 11(b)). On the other hand, at the
first harmonic, 2f0,
the same stub is λ/2 long and hence the PA output is almost
shortened. This explains the strong standing wave which can be seen in Figure 11(c). The issue still lies in the third  harmonic because, even  if the
additional stub ls2 should shorten it, the slab is not thin with
respect to λ at 3f0 hence surface waves can arise quite easily.
Indeed the presence of a surface wave originating at the matching stub
immediately below the coupling slot is very evident in Figure 11(d). Radiation from both the CDRA and the open-ended feeding line stub accounts for
the much higher real part of the third-order input
impedance.Final layout:
(from top to bottom) observation plane geometry, electric field maps ony=0 plane at 14.25 GHZ, 28.5 GHz, and 42.75 GHz.
(a)(b)(c)(d)


## 5. Conclusions

In this paper, a harmonic tuning technique for a
dielectric resonator antenna working in Ku band at 14.25 GHz has been
described. As a first study a slot-coupled cylindrical DRA configuration has
been considered, studying its harmonic response at a shape factor level, with
particular attention to higher-order resonant modes, to devise a possible
optimal shape factor.As a second step of the study the basic resonator
antenna layout has been modified by introducing a parasitic reactive element in
the coupling slot to improve antenna performances at first and second
harmonics. This configuration allows us to obtain a significant improvement of
the antenna performances at first harmonic but a real full control of the
second harmonic is not yet possible, both mainly due  to the reduced size of the
slot. Yet this issue is of minor importance due to the fact that the power
generated by the PA at the second harmonic is a few percent of the total one.At last, a complete design suitable for the
integration with a PA has been presented, where the feeding line has been
optimized as well to achieve full impedance matching at fundamental frequency
and higher harmonics.



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*Source: 519850-2009-04-23.xml*