END OF STUDIES PROJECT
Presented to
UNIVERSIDAD DE LOS ANDES AND TELECOM BRETAGNE
FACULTY OF ENGINEERING
DEPARTMENT OF ELECTRONICS AND ELECTRICAL
ENGINEERING
To obtain the title
ELECTRONIC ENGINEER
By
Andrés Mauricio Cárdenas Hernández
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wave applications
Presented on
12 July 2013
Composition of jury
- Assessors: Christian PERSON, Télécom Bretagne
Camilla KÄRNFELT, Télécom Bretagne
- Co-Assessor. Nestor PEÑA, Universidad de los Andes
- Jury: Christian PERSON, Télécom Bretagne
Camilla KÄRNFELT, Télécom Bretagne Jean Philippe COUPEZ, Télécom Bretagne
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Table of Content
1 INTRODUCTION ... 3
2 OBJECTIVES ... 3
3 STATE OF THE ART ... 4
4 BACKGROUND THEORY ... 9
4.1 Microstrip Line ... 9
4.2 Slot Antenna ... 11
4.3 The Rectangular Waveguide ... 12
4.4 The Substrate Integrated Waveguide (SIW) ... 14
4.4.1 General Structure of a Substrate Integrated Waveguide ... 15
4.4.2 Basic design equations of a Substrate Integrated Waveguide ... 16
4.5 Dielectric Resonator Antenna (DRA) ... 18
4.6 Cylindrical Resonator Antenna (CRA) ... 18
4.7 Cylindrical Dielectric Resonator Antenna Modes ... 19
4.7.1 Mode Nomenclature of Cylindrical Dielectric Resonators ... 20
5 RESONANT MODES VALIDATION THROUGH EIGENMODE SIMULATIONS (HFSS™) ... 22
5.1 Modes in Isolated Cylindrical Resonator ... 22
6 THE HEM11δ MODE ... 27
7 DRA EXCITATION METHODS (FOCUSED ON HEM11δ MODE) ... 28
7.1 Slot Fed Excitation ... 28
7.2 Microstrip Line-‐Slot Fed Excitation ... 28
7.3 SIW Fed Excitation ... 29
8 RECTANGULAR WAVEGUIDE AND SIW VALIDATION ... 30
9 DRA VALIDATION AT 60GHz ... 34
9.1 Model Design ... 34
9.2 Simulation Results – Infinite Ground Plane ... 36
9.3 Simulation Results – Finite Ground Plane ... 38
9.4 Simulation Results – Adding the substrate/ Infinite Ground Plane ... 39
9.5 Simulation Results – Adding the substrate/ finite Ground Plane ... 42
9.6 Comparing the results to the thesis ... 44
10 MICROSTRIP LINE – SLOT COUPLING VALIDATION ... 46
10.1 Wave Port and Lumped Port Excitation ... 47
10.1.1 Wave Port Validation ... 47
10.1.1.1 Transmission line validation ... 47
10.1.1.2 Stub and Slot Validation ... 49
10.1.1.3 Simulations with DRA – Wave Port Validation ... 53
10.1.2 Lumped Port Validation ... 55
10.1.2.1 Transmission line validation ... 56
10.1.2.2 Simulations with DRA – Lumped Port Validation ... 57
11 SIW-‐FED DRA ... 59
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11.2 Slotted SIW-‐fed DRA model in HFSS™ ... 60
11.3 Side SIW-‐fed DRA ... 63
11.3.1 Adding a transition to the side SIW-‐fed DRA ... 66
12 CONCLUSIONS ... 68
13 ACKNOWLEDGEMENT ... 69
14 REFERENCES ... 69
15 ANNEX INTRODUCTION ... 74
16 ISOLATED DRA ... 74
16.1 Creating the geometry ... 74
16.2 Setting up the problem ... 76
16.2.1 Materials ... 76
16.2.2 Boundary Conditions ... 77
16.2.3 Excitation ... 78
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1
INTRODUCTION
This work is the continuation of a thesis made in 2012 [1] which presents a new dielectric resonator antenna solution at 60 GHz for a front-end integration using the technology of SoC (System on Chip) to integrate a power amplifier (PA). This solution can reach a high gain of 5 dBi and a bandwidth of 5 GHz in the 60 GHz band.
The applications of this work are mostly WLAN (Wireless Local Area Networks) communication system i.e. kiosk downloading, interface with data media center, wireless HD TV, etc. As already mentioned, the operating frequency of 60 GHz, allows the use of a large bandwidth of 7 GHz, which is an unlicensed band
A new solution for these applications is developed by proposing an SIW (Substrate Integrated Waveguide) as a DRA (Dielectric Resonator Antenna) excitation structure that can be manufactured in the LTCC (Low Temperature Co-fired Ceramic) technology. The SIW structure provides higher quality factor than microstrip line structure but lower quality factor than a conventional rectangular waveguide; this mixed with a DRA that usually has a lower quality factor, leads to a high efficiency antenna where almost all the power carried from the SIW is successfully transmitted by the antenna. In addition, the fact that the SIW is filled with high permittivity substrate makes the solution more compact than could be achieved with a conventional rectangular waveguide excitation.
This work presents design equations for already available dielectric resonator antenna solutions where a possible bandwidth in the range of 6 GHz to 7 GHz around 60 GHz is achieved. It also includes a side SIW-DRA fed solution that can be integrated using LTCC technology. In order to achieve these goals, the commercial electromagnetic software HFSS™ has been used to the analysis of the different structures.
2
OBJECTIVES
The main objectives of this project are concentrated on understanding how DRA and their different resonant modes work in a cylindrical dielectric cavity. This project will also validate the resonant modes in the cylindrical dielectric resonator. Further more, it is important to understand and learn how to use the formulas discussed while allow us to differentiate an isolated DRA from a DRA with a ground plane or with specific boundary conditions. Mapping of electric and magnetic fields in the DRA have been studied to find which resonant mode will lead us to better antenna efficiency. There are many studies regarding the DRA and its different feeds, in this work we have been aiming at understanding the different methods presented in previous publications in order to repeat what it has been done with a good methodology.
A final objective has been to validate and characterize different DRA solutions like a slot-fed or microstrip line-slot-fed DRA which will lead us to an SIW-slot-fed DRA antenna filter characterization with all the background as mentioned before.
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3
STATE OF THE
ART
The state of the art for a 60 GHz front-end integration using SoC technology is presented next.
The final design is shown in Figure 1 and It shows the final integration of an alumina based substrate and DRA (Dielectric Resonator Antenna), assembled under the slot of a silicon chip which is mounted on a PCB (Printed Circuit Board). The solder balls seen in the Figure 1 have the purpose of carrying the DC (Direct Current) biasing and the RF (Radio Frequency) signals to a power amplifier.
Figure 1 Lateral view of DRA integration [1]
When simulated under the 3D electromagnetic software HFSS™, a 4.8 GHz bandwidth with a 6.5 dBi gain were obtained at 60 GHz as is shown in Figure 2.
a) b)
Figure 2 Simulated results at 60 GHz of the packaged DRA: a) reflection coefficient b) radiation pattern [1]
A non-resonant slot fed by a CPW (Coplanar Waveguide) as is seen on Figure 3 excites the DRA. The DRA structure is processed on alumina substrate (er=9.9). The slot is placed in order to have a direct contact with the DRA, thus guaranteeing proper excitation.
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The dimensions and configuration used to simulate the model shown in Figure 3 are L=1.1mm W=0.04mm, a=DRA radius, h=DRA height. This configuration facilitates the measurements by probe.
The DRA mode that is excited is the HEM11, which is coupled by the slot configuration in order to obtain the best coupling between the slot and the DRA by placing the slot just in the center of the Dielectric Resonator (DR). Figure 4 shows the H field distribution for the HEM11 mode in a cylindrical dielectric resonator.
Figure 4 Top view of the H field distribution for the HEM11 mode in a cylindrical dielectric resonator. [1]
There is also a parametrical analysis developed by Juan Pablo Guzman [2] that validates the use of a finite ground plane and an infinite ground plane with and without substrate when a slot-fed DRA is simulated.
Figure 5 DRA on an infinite ground plane
In that work, the DRA as shown in Figure 5 has a radius of 0.74 mm and height of 0.508 mm in order to have a resonant frequency of 60 GHz.
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Figure 6 a) Slot placement; b) Lumped port excitation
The length of the slot is optimized by HFSS™ and the results are shown in Figure 7.
Figure 7 Parametric analysis of the slot length.
Note that the slot length changes the adaptation of the antenna; in this case a slot with length equal to 0.9 mm results in the best reflection coefficient.
Later on, after simulating the same structure with a finite and infinite ground plane, he arrives at a gain pattern comparison shown in Figure 8.
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Figure 8 Gain pattern comparison and ground plane length variation
It can be noted that the finer gain pattern is obtained when the ground plane is infinite, while it has a lot of variations and a particular back lobe at -180º when the ground plane is finite.
The main idea of this project is to replicate the results of the dielectric resonator while different types of feeds excite it. The HEM11 mode has to be excited looking for a good adaptation with a large bandwidth and gain; when this part is finished, we will concentrate in a type of feed called Substrate Integrated Waveguide (SIW) and maintain the same levels of gain, adaptation and bandwidth for the DRA also in the band of 60 GHz.
Some studies have been made regarding DRAs fed by SIW using an aperture coupling [3]-[4]. By SIW excitation, return loss and parasitic radiation of the feeding structure can be avoided because the SIW is covered by metal and the feeding modes are limited inside the substrate. It’s easy to build because it uses metallic vias that can be fabricated on a PCB [3].
Another advantage of the SIW-fed DRA is that the SIW has a higher Q-factor than a conventional waveguide and the DRA has low losses in the millimeter-wave range frequency, so if we put them together, the efficiency will be higher because the majority of the energy will be successfully transmitted to the DRA without high losses. [3]
In Figure 9 is shown a proposed SIW fed DRA where the DRA has a cylindrical shape and the mode excited is the HEM11 or TM11.
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a) b)
Figure 9 Configuration of the proposed SIW fed DRA: a) 3D view; b) Top view [3]
As is seen in Figure 9a, the propagating mode in the SIW is the TE10, which is the mode that is going to be used in this work to excite the HEM11 mode in the DRA.
The SIW structure has a width of 10.1 mm, the metallic vias have diameters of 0.4 mm and the space between each via is 0.8 mm. The DRA structure placed above the SIW has a diameter of 3.29 mm and a height of 2.44 mm that leads an operating frequency of 18 GHz [3]. Finally the width and length of the slot are 1.03 mm and 3.2 mm respectively.
The results of the simulation are plotted in Figure 10.
a) b)
Figure 10 a) Return loss for the proposed SIW-fed DRA; b) radiation pattern for the proposed SIW-fed DRA
From Figure 10, it can be inferred that the antenna has a bandwidth with better than -10 dB return loss from 17.9 GHz to 18.2 GHz. Also, the gain has a maximum of 6 dBi.
The previous values are more or less what is wanted in this work when the DRA is excited by an SIW, the difference is that the DRA is going to be excited by the side and not by a slot at the bottom.
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4
BACKGROUND THEORY
Before starting with the methodology and results, it is very important to know the main bases and theory on which are founded the results obtained later.
4.1 Microstrip Line
The microstrip line is a type of electric transmission line that can be fabricated using a PCB. This line is mostly used for microwave transmission.
It consists in a metal strip with a certain thickness, width and length; the strip is deposited on a dielectric substrate with a certain height, which is supported by a ground plane. The permittivity of the microstrip takes not only into account the permittivity of the substrate but also the permittivity of the medium which is outside the microstrip, this permittivity is called effective dielectric constant (𝜀!"") and it’s going to be calculated later. Is shown below an example of a typical microstrip line.
Figure 11 Single Microstrip Line1
The electrical parameters of the standard microstrip line are the impedance (Z0),
wavelength 𝜆! and attenuation (𝛼), which are calculated from the equations [13] shown
below:
𝑍! =
60 𝜀!""
ln 8ℎ
𝑊 +
𝑊
4ℎ 𝑓𝑜𝑟 𝑊/ℎ ≤1
120𝜋
𝜀!"" 𝑊ℎ +1.393+0.667ln 𝑊ℎ +1.444 𝑓𝑜𝑟 𝑊/ℎ ≥1 1
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𝜆! = 𝜆!
𝜀!"" 2
𝛼! =𝑘!𝜀! 𝜀!"" −1 𝑡𝑎𝑛𝛿
2 𝜀!"" 𝜀!−1 𝑁𝑝/𝑚 3
𝑎! = 𝑅!
𝑍!𝑊 𝑁𝑝/𝑚 (4)
Where 𝑍! is the characteristic impedance of the transmission line, 𝜆! is the free space wavelength; 𝑡𝑎𝑛𝛿 is the loss tangent of the dielectric, 𝛼! is the attenuation due to dielectric loss, the 𝛼! is the attenuation due to conductor loss with 𝑅! = 𝜔𝜇!/2𝜎 with
𝜔,𝜇!and 𝜎 as the angular frequency, free space permeability and conductivity respectively.
The previous formulas are the result of rigorous curve-fit approximations that don’t take into account some aspects of the microstrip line as the parasitic effects, frequency dependency effects or higher order modes. [13]
The effective dielectric constant ε!"" has to be calculated. From Pozar [13], the effective dielectric constant for a standard microstrip line is:
𝜀!"" =𝜀!+1
2 +
𝜀!−1 2 1+
12ℎ 𝑊
!!!
(5)
Where W is the width of the microstrip line, h is the height of the substrate, ε! is the substrate permittivity and 𝜀!"" is the effective permittivity.
The electromagnetic (EM) fields that propagates in the microstrip, not only propagates inside the substrate but also outside the microstrip. Therefore the propagating mode is not entirely a TEM mode, in consequent, the mode is called quasi-TEM.
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Figure 12 Electromagnetic fields in the microstrip2
4.2 Slot Antenna
These antennas are used normally in frequencies between 300 MHz and 24 GHz and they have typically an omnidirectional radiation. These antennas typically are apertures on a ground plane and from which they radiate in a very similar way as a dipole would radiate.
The antenna considered in this study consists in a slot placed on a ground plane and its radiation pattern is the equivalent to a magnetic dipole, the first resonant frequency happens when the length of the dipole is 𝜆!/2 where 𝜆!is the guided wavelength in the slot.
Figure 13 Slot on a ground plane
To excite this type of antenna, a voltage source is needed. This source is applied across the short end of the slot antenna; also it induces an E-field distribution as seen in Figure 14 that also shows the Babinet’s Principle which explains that the radiation pattern of a slot on an infinite ground plane is the same as a dipole radiating in the free space [23].
2Development of a microsystem based on a microfluidic network to tune and reconfigure RF circuits, S Pinon et al 2012 J. Micromech. Microeng.
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Figure 14 E-Field distribution within the slot and radiattion pattern of a magnetic [12]
4.3 The Rectangular Waveguide
This type of waveguide has been studied over the years because is one of the simplest ways to transport microwave signals. This type of waveguide allows the propagation of TE and TM modes but no TEM because only one conductor is present; these are the main modes to excite many different structures like DRA’s for example.
The standard rectangular waveguide that is going to be analyzed in the present document is shown below:
Figure 15 Rectangular waveguide3
- TE modes:
In order to calculate the cutoff frequency of the transverse electric mode, it’s necessary to understand the geometry of the rectangular waveguide.
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It is assumed that the guide shown above is filled with a material with permittivity ε and
permeability µ. The convention is that the longest side of the waveguide is placed along
the x-axis, in consequence, a>b.
The transversal electric modes are characterized because the z component (the component in the direction of propagation) of the E-field is zero. With this assumption, and after solving the field’s main equations clearly explained in Pozar’s book [13], the cutoff frequency for a TEmn mode is:
Cutoff Frequency:
𝑓!!" = 1
2𝜋 𝜇𝜀 𝑚𝜋 𝑎 ! + 𝑛𝜋 𝑏 !
(6)
The integers m and n can take values of 0,1,2,3… except for m=n=0 because there is no mode TE00.
The mode with the lowest cutoff frequency is called the dominant mode. In this case the dominant mode occurs for the TE10(𝑚= 1,𝑛 =0) mode:
𝑓!!" = 1
2𝑎 𝜇𝜀 (7)
With an operating frequency 𝑓, the modes with 𝑓 >𝑓! will propagate; otherwise they’ll decay away from the excitation source.
Other basics of the rectangular waveguide are the guided wavelength [13]:
𝜆! =
2𝜋 𝛽 >
2𝜋
𝑘 =𝜆 8
So the guided wavelength is greater than 𝜆.
- TM Modes:
These modes are characterized by having the z component of the magnetic field equal to zero. After making the same analysis but having this assumption, the cutoff frequency for
TMmn modes is:
Cutoff Frequency:
𝑓!!" = 1
2𝜋 𝜇𝜀
𝑚𝜋 𝑎 ! + 𝑛𝜋 𝑏 !
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The integers m and n can only take values of 1,2,3… the modes TM00, TM10, TM01 can’t
be feasible because the lowest order mode to propagate is the TM11.
Which is the same equation as the TEmn cutoff frequency equation. In summary, the equations of cutoff frequency and guided wavelength are the same as for the TEmn
modes.
From the book of Pozar [13] are taken the field lines of the lower propagating modes inside the rectangular waveguide.
Figure 16 Field lines for some of the lower order modes of a rectangular waveguide [13]
4.4 The Substrate Integrated Waveguide (SIW)
Early in the 90’s, there was a boom in the waveguide research, the technology known as Substrate Integrated Waveguide (SIW) was developed; as its name indicates, it consists in integrating a waveguide inside a dielectric substrate, in other words, a waveguide using the microstrip technology. This technology can integrate the advantages of a conventional rectangular waveguide minimizing the principal disadvantages of it. It is known that in the conventional rectangular waveguide, the waves are locked inside the metallic surface of the waveguide when they reach the walls, in consequence, the radiation losses are low. The disadvantages of a conventional waveguide as compared to the SIW, reside in its structure, because it requires a huge quantity of metal to build it, and that makes the costs higher. [3]-[4]-[5]
To well design an SIW, there are a few precautions to take into account because there are some vias that try to make the analogy of metallic walls and the idea is to design those vias in order to have the minimum of losses when the wave propagates.
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4.4.1 General Structure of a Substrate Integrated Waveguide
This Substrate Integrated Waveguide technology, use similar components of the microstrip technology like:
• Dielectric Substrate • Ground Plane • Conductor Line
• Metal Vias
Figure 17 Geometry of a substrate integrated waveguide 4
Generally, the SIW characteristics are similar to the conventional rectangular waveguide; the modes practically coincide with the propagating modes inside the SIW with the exception that the TM modes cannot exist in the SIW due to the space between the vias. On the other side, the TE10 known as the dominant mode in the rectangular waveguide is
similar in the SIW with the difference of having vertical current density on the sidewalls. For the mode TE10 the thickness of the substrate doesn’t affect the cutoff frequency if the
thickness h is lower than W. therefore the thickness can have any value (lower than W) and will only affect the dielectric loss.
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4.4.2 Basic design equations of a Substrate Integrated Waveguide
To analyze the equations of an SIW it’s important to know the difference between the common structure between a conventional air filled rectangular waveguide, a dielectric filled waveguide and a substrate integrated waveguide:
Figure 18 (a) Air Filled Waveguide, (b) Dielectric Filled Waveguide, (c) Substrate Integrated Waveguide.5
As the name indicates, the difference between the two first models is the permittivity of the material which is used to fill the waveguide, and the difference between the two last models is the use of metal vias as walls in the substrate integrated waveguide.
The SIW can be analyzed as a Dielectric Filled Waveguide (DFW), which the only difference is that it doesn’t have the metal vias as waveguide walls. Hence, the cutoff frequency is calculated using the following equations:
The cutoff frequency for an air filled waveguide is:
f! = c
2π mπ a ! + nπ b !
(6)
For the mode TE10, the formula becomes:
f! = c
2a (9)
Taking into account the substrate inside the waveguide in a DFW, the dimension ‘a’ changes and becomes:
a!"# = a
ε! (10)
With the ‘a’ dimension calculated and using the following SIW topology, the design equations of a SIW are shown below.
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Figure 19 Topology of an SIW guide with its physical dimensions [6]
There are some basics measures to consider the SIW design like [6]:
• The thickness ‘h’. For a good-guided transmission, we are looking for a thickness in the limit of the dominant propagating mode in order to avoid a huge dielectric loss.
• The distance between the metal vias ‘b’. This distance is important to assure that
these vias behave like metallic walls along the SIW as a conventional rectangular waveguide. If the distance is big, there will be greater losses and the waveguide operation will be undesired.
• The vias diameter ‘D’. In order to minimize losses, the most important relation is
D/b, so to reduce losses it’s necessary to reduce diameter.
• The guide width ‘W’. This measure corresponds to the distance between the two
metal vias centers.
• The effective guide width ‘Weff’ is the distance between the vias’ closest edges.
This distance varies according to the cutoff frequency chose for the waveguide.
There are some considerations or design rules in order to have the maximum efficiency and to have almost the same behavior as the conventional rectangular waveguide [6].
1. The distance ‘b’ must be reduced. To maintain that distance little enough, the rule is:
b≤ 2D (11)
As it is observed, the distance is in function of its diameter (D) so the diameter has to be reduced (the factor that has to be reduced is in fact D/b) in order to minimize losses.
2. According to the last rule, there has to be a consideration respecting the wavelength in order to achieve a reduced diameter.
D<λ!
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Where
λ! =
2π
ε! 2πf !
c! − πa
! (13)
These previous considerations only work as parameters to assure that the losses remain at reduced levels, but there could be some designs that don’t take into account these rules and despite that, have reduced losses levels.
4.5 Dielectric Resonator Antenna (DRA)
A Dielectric Resonator Antenna (DRA) is a resonant structure composed by a dielectric resonator and an excitation element. The dielectric resonator presents many advantages for high frequency applications when is used as a filter or as an antenna, for example its high permittivity material, its small size, its low cost fabrication and its good temperature stability. On the other hand, the main disadvantage of the dielectric resonator is the proximity of resonant frequencies of many modes and the difficulty to excite one in particular. The excitation of each mode depends on the excitation element used to feed the dielectric resonator.
Before, the dielectric resonators have been used as cavity filters, resonators, etc. profiting from its resonant capacity with a high-Q factor, but it has been shown later that these structures can also behave like antennas when they have a low-Q factor, and that’s why in this work the Dielectric Resonator is used as an antenna application due to it wideband and high gain capacity.
The equations of DRA design taking into account the Q-factor and the bandwidth are shown below in order to explain a little more about the behavior of the antenna design.[7]
Estimation of the fractional bandwidth of an antenna:
𝐵𝑊= Δ𝑓
𝑓! =
𝑠−1
𝑠𝑄 14
Δ𝑓 is the absolute bandwidth, 𝑓! is the resonant frequency and 𝑠 is the VSWR relation. The dielectric resonators can have as many shapes as one want to improve its gain efficiency or wideband, but it depends on the final application. For this study the main interest is the analysis of the cylindrical resonator antenna (CRA) because of its simplicity and easy integration.[8]
4.6 Cylindrical Resonator Antenna (CRA)
The non cylindrical DRA’s that are currently in use for the microwave band doesn’t have the possibility to scale up in frequency, near the millimeter wave region or the extremely
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high frequency region (30 - 300 GHz). For those applications, the structure that has the possibility of radiating efficiently in this frequency band is the cylindrical resonator cavity. The present work on CRA defines the resonant frequency taking into account the boundaries that can simulate the real behavior of this antenna in the medium. The theory presented utilizes as background the magnetic wall boundary condition.
The resonant frequency of a CRA also depends on the shape and dimensions of the dielectric resonant cavity. Only one shape is going to be considered in this study, the cylindrical dielectric resonator, which resonant frequency is given by[9]:
𝑓!"# = 𝑐
2𝜋𝑎 𝜀!
𝑋!"! 𝑋!"!" +
𝜋𝑎
2𝑑 2𝑚+1 !
(15)
Where n, p and m represent the mode index that is going to be explained in detail later.
The previous formula considers the cylindrical resonant cavity shown below:
Figure 20 Cylindrical resonator antenna configuration
The terms 𝑋!"! ,𝑋!"!" refers to the zeros of the Bessel function of the first kind:
𝐽! 𝑋!" =0 16 𝐽!"! 𝑋
!"! =0 (17)
The dominant mode of the equation (15) is the one that has the lowest resonant frequency. This happens when 𝑚= 0,𝑛 =1,𝜌= 1:𝑋!!! =1.841 [9].
Later in this chapter it will be explained why that mode is the most important for this study.
4.7 Cylindrical Dielectric Resonator Antenna Modes
To simplify the understanding of resonant modes inside a cylindrical resonant cavity, we have to take into account that each resonant frequency has a unique internal
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electromagnetic mode that generates a characteristic radiation pattern that in this case can be assimilated to the same radiation mechanism of an ordinary electric or magnetic dipole.
In the next diagram is shown that for the main resonant modes, each one has a comparable radiation pattern to an electric dipole source or a magnetic dipole source.
Figure 21 Classification of the main modes inside a CRA
4.7.1 Mode Nomenclature of Cylindrical Dielectric Resonators
The modes excited within a cylindrical DRA are classified in: TE, TM and HEM. [10]
The modes are established according to its electromagnetic field distribution and their index as it is shown below.
Cylindrical Dielectric Resonator Antenna
TE01
RadiaYon PaZern: MagneYc
Dipole
Axisymmetric
HEM11
RadiaYon PaZern: MagneYc
Dipole
Azimuthally dependent
HEM12
RadiaYon PaZern: Electric
Dipole
Azimuthally dependent
TM01
RadiaYon PaZern: Electric
Dipole
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Figure 22 Mode Nomenclature in a Cylindrical Resonator Antenna
Each index represents the number of half or full period electromagnetic variations along its respective direction (maximum-minimum field cycles). The index 𝑚 implies the number of full period field variations along the azimuthal direction with 𝑚= 1,2,3…
.The index 𝑛 denotes a variation of the half wave field along the radial direction with
𝑛 =1,2,3… . And the index 𝑝+𝛿 denotes the half wave variations along the vertical direction, with 𝑝= 0,1,2,3…
The index 𝛿 denotes that the half wave field is bigger than the length of the resonator, so the index is comprised between 0 and 1. That is because the boundary conditions are not perfect at the interface between the air and the dielectric.
For example, the mode 𝑇𝐸!"" means that there is no variation along the azimuthal direction but there is indeed a variation along the radial and the vertical direction as indicates the index 𝑛 =1 and 𝑝+𝛿=1. The field distribution is shown below in Figure 4.
The simplest way to identify the modes is to know that the modes 𝑇𝐸!!",𝑇𝑀!!" are
axisymmetric on the equatorial plane (no changes in the azimuthal direction because
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Figure 23 Field Distribution Mode TE011 [8]
Having said what is a Dielectric Resonator Antenna and which type of cavity or structure is going to be used in this work, is necessary to verify this theory background presented before. To do this, we make use of 3D electromagnetic simulation software called HFSS™, which is the one we will use throughout this work.
5
RESONANT MODES VALIDATION THROUGH EIGENMODE SIMULATIONS
(HFSS™)
5.1 Modes in Isolated Cylindrical Resonator
In this validation stage, an isolated cylindrical dielectric resonator is simulated in order to find the same results as in theory.
The dimensions of the simulated CRA are:
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The resonator is called isolated because no object interacts with it. According to [8] and [11] the CRA needs to be in an enclosed magnetic wall boundary in order to satisfy the following equations for the resonant frequency and Q-factor calculation in an isolated cylindrical dielectric resonator. These equations are also extracted from [11].
𝑓! !! !"! =
𝑐 2.327
2𝜋𝑎 𝜀!+1 1.0+0.2123
𝑎
ℎ −0.00898 𝑎 ℎ
!
18
𝑄!!!"! =0.078192𝜀!.!" 1+17.31 ℎ
𝑎 −21.57 ℎ 𝑎
!
+10.86 ℎ
𝑎
!
−1.98 ℎ
𝑎 !
(19)
𝑓! !"#!! =
𝑐 6.324
2𝜋𝑎 𝜀!+2 0.27+0.36
𝑎
2ℎ +0.02 𝑎
2ℎ
!
20
𝑄!"#!! = 0.01007𝜀!!.! 𝑎
ℎ 1+100𝑒
!!.!" !"!!!"! !! !
(21)
𝑓! !!!"! =
𝑐 3.83!+ 𝜋𝑎
2ℎ !
2𝜋𝑎 𝜀!+2 22
𝑄!"!"! =0.008721𝜀!!.!!!"#$𝑒!,!"#$%$&!! 1− 0.3−0.2𝑎
ℎ
38−𝜀!
28 × 9.498186𝑎
ℎ+2058.33 𝑎 ℎ
!.!"""#$
𝑒!!.!""## !! (23)
Where c is the speed of light in the vacuum, 𝜀! is the relative permittivity, 𝑎 is the
cylinder radius and ℎ is the cylinder height.
These equations are used instead of (14) because these ones are easier to calculate even if they are also good approximations of the resonant frequency inside the isolated cylindrical dielectric resonator.
To know which one of these modes are the first one to be excited inside the resonant cavity, a chart is made where the x-axis is the ratio 𝑎/ℎ and the y-axis is the resonant frequency, that information let us to know the desired information in function of the their dimensions.
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Figure 25 First Mode Excited in the Resonant Cavity
In the Figure 25 is shown the propagation order of the different modes inside the cylindrical cavity. It’s easy to observe the resonant modes when are plotted against the ratio 𝑎/ℎ because this ratio takes into account the radius and the height of the resonator and in this case, when the ratio takes the value of 𝑎/ℎ= 2.283, the first mode excited in the analyzed cavity is the mode 𝑇𝐸!"!.
Now what is left to do is to analyze through HFSS™ the first mode excited in the cavity and compare the theory with the simulation. Also it’s possible to verify the order of the resonant modes given in the table below:
Frequency (GHz) for a/h=2.283
Mode 𝑻𝑬𝟎𝟏𝜹 Mode 𝑯𝑬𝑴𝟏𝟏𝜹 Mode 𝑻𝑴𝟎𝟏𝜹
4.87 6.43 7.54
Table 1 Resonant modes order
The program HFSS™ is going to be used for the simulation, especially the solution type
Eigenmode, which helps to find the principals resonant modes, the resonance frequency and the Q factor for each mode without any type of excitation or feed.
The results of the simulation are shown below in Table 3 that compares the results with a study of the modes in an isolated CRA [15]. These images show the electromagnetic fields viewed from the top and the side of the cylindrical resonator antenna, in order to validate the resonant modes, the fields simulated must be the same as in the validation shown below. 0.00.E+00 2.00.E+09 4.00.E+09 6.00.E+09 8.00.E+09 1.00.E+10 1.20.E+10 1.40.E+10
0.0 1.0 2.0 3.0 4.0 5.0 6.0
F re q u en cy (H z) a/h ratio
Resonant Modes
Mode TE01d Mode TM01d Mode HEM11d a/h= 2.283Integrated antenna packaged in SIW-‐LTCC
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Mode and Frequency
(GHz)
E-Field H-Field
𝑻𝑬𝟎𝟏𝜹
4.24 GHz
𝑻𝑬𝟎𝟏𝜹
Validation
𝑯𝑬𝑴𝟏𝟏𝜹
6.29GHz
𝑯𝑬𝑴𝟏𝟏𝜹
Validation
𝑯𝑬𝑴𝟏𝟏𝜹
Sides 6.29GHz
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Table 2 Resonant Modes Validation
Frequency (GHz) for a/h=2.283
Resonant Modes Theory (GHz) HFSS™ Eigenmode Difference
𝑯𝑬𝑴𝟏𝟏𝜹 Sides Validation
𝑯𝑬𝑴𝟏𝟐𝜹
6.48GHz
𝑯𝑬𝑴𝟏𝟐𝜹
Validation
𝑻𝑴𝟎𝟏𝜹
7.62GHz
𝑻𝑴𝟎𝟏𝜹
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(GHz) (GHz)
Mode 𝑻𝑬𝟎𝟏𝜹 4.87 4.24 0.63
Mode 𝑯𝑬𝑴𝟏𝟏𝜹 6.43 6.29 0.14
Mode 𝑻𝑴𝟎𝟏𝜹 7.54 7.62 0.08
Table 3 Comparison of theoretically calculated resonant modes to simulation results
The results shown in Table 2 and Table 3 infer that, the solver Eigenmode is reliable because the results taken from the theory can be reproduced through the solver, obviously some slights shifts in frequency caused by the simulator calculations and the approximations used to calculate the frequency for each resonant modes. Despite this fact, they keep the same excitation order.
Now that we have validated the Eigenmode solver, we want to know how is the Q-factor behavior with this type of structure when the ratio is 2.283.
In the next table is shown the Q-factor for each mode plotted, a lower Q-factor implies a highly radiating structure.
Q factor for a/h=2.283
Mode 𝑻𝑬𝟎𝟏𝜹 Mode 𝑯𝑬𝑴𝟏𝟏𝜹 Mode 𝑻𝑴𝟎𝟏𝜹
45.58 43.04 77.88
Table 4 Q-factor Comparisons
The Q-factor calculated for the three modes plotted is shown in Table 4. Note that the lowest Q-factor is obtained for the modes 𝐻𝐸𝑀!!! and 𝑇𝐸!"𝜹, which means that those modes will radiate more energy than the others, which in turn it means that they are a good choice for an antenna application.
Hence, the main modes in the resonant cavity are validated, so the next step is exciting the DRA with the best excitation method.
6
THE HEM
11δMODE
In the previous section, the importance of the 𝐻𝐸𝑀!!! mode shown, in order to explain
better the choice of the HEM mode, some reasons are prepared to understand the importance of that mode.
One of the main features of the resonance modes is the quality factor or factor Q, this factor is mathematically the ratio between the energy stored and the energy lost (including loss by radiation) in a certain structure, so if a radiation is desired (as it is for an antenna application), a low Q-factor is required; the lower the Q factor is, the better it will be for an antenna application. In addition, a larger bandwidth is needed because of the main DRA applications in the 60 GHz band, so the lowest Q factor will be chosen due to the bandwidth formula that is inversely proportional to the Q factor.
Finally, another interesting feature of the mode is that, as is seen in the previous section, is the first mode to be excited when the ratio between the radius and the heigh of the
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dielectric resonator is greater than one (𝑎/ℎ> 1). This means that the dimensions chosen to excite a given frequency are the smallest possible compared to the DRA higher resonance modes. In consequence, if a higher mode is needed, a bigger DR size will be required (valid for 𝑎/ℎ>1).
7
DRA EXCITATION METHODS (FOCUSED ON
𝐇
𝐄𝐌
𝟏𝟏𝛅MODE
)
To successfully excite the wanted mode an efficient way is needed. Below are explained the most convenient ways to excite the 𝐻𝐸𝑀!!! mode.
7.1 Slot Fed Excitation
To well excite the desired mode, the electric fields of the feeding component should follow the same trajectory of the resonant electric fields.
Figure 26 Slot excitation
In Figure 26, the slot has to excite the H field in the direction along the slot length while the electric field has to follow the direction of the arrow that goes in the transversal direction of the slot. The slot has to be placed at the bottom of the DR.
The slot must be placed in the center to have a maximum coupling.
7.2 Microstrip Line-Slot Fed Excitation
This type of excitation regards the slot fed by a microstrip line. The microstrip line has to excite the slot in the right way to avoid the slot behaving like an antenna; this is because the microstrip line and the slot are used as a coupling element between the feed and the DRA. The coupling between the two components is mainly magnetic where the magnetic field has to be maximum at the center of the slot. Below is shown the design used to excite the DRA.
fsdasdadada
H PLANE
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Figure 27 DRA model with transmission line and slot coupling
With the right length of the line and the slot, the right mode of the DRA is going to be excited.
7.3 SIW Fed Excitation
There are two ways of exciting a DRA by an SIW, the first one is placing a slot on the SIW and then the DR over the slot so the DR is going to be excited by the slot as seen before in the slot-fed excitation (See Figure 28). The slot will be excited by an SIW with a resonance mode TE10.
Figure 28 slot-SIW-Fed excitation
Another way of exciting the DRA is placing the SIW by the side so that the TE10 mode with the Electric and Magnetic Fields, will excite the DRA as is depicted in Figure 29. The main problem will be the distance from between the SIW and the DRA in order to excite the correct mode.
SIW DRA
TE10 HEM11
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Figure 29 Side SIW-fed DRA
8
RECTANGULAR WAVEGUIDE AND SIW VALIDATION
Before exciting the DRA with an SIW, it’s important to know how the simulator works with a simple waveguide and then replicate the results with a SIW.
In this case the main idea is to validate the three first resonant modes in a rectangular waveguide: TE10, TE20 and TE01.
Figure 30 shows the dimensions and the design. Perfect E is used as boundary condition on the walls, the interior is vacuum and the wave port is located on the front of the waveguide. The dimensions are taken from an HFSS tutorial [17]
Figure 30 Waveguide design and dimensions
According to HFSS™ and equation (6), the cutoff frequency of each mode is:
TE mode Cutoff Frequency (GHz) HFSS™
Cutoff Frequency (GHz)
TE10 6.561 6.5
TE20 13.123 13.1
TE01 13.562 13.5
Table 5 Comparison between theoretical and HFSS™ cutoff frequency
SIW
DRA TE10
HEM11
MODE TE10 HEM
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To verify this, the phase constant is plotted, so when the line crosses by zero a mark is placed to show the cutoff frequency. The phase constant came from the imaginary term of the propagation constant:
The phase constant plot is showed below:
Figure 31 Phase constant plot (three waveguide modes)
The E-field lines are showed next as a validation point of each mode.
TE Mode E-Field Line (Wave Port View)
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TE
10 (front)TE
20 (front)TE01 (front)
Table 6 E-Field (3 propagation modes) from the wave port view
Finally, it is possible to follow the same validation order to simulate an SIW that achieves the same results as the waveguide showed before.
From the design equations for a SIW, to have the same behavior as the conventional rectangular waveguide, the dimensions have to be:
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Where 𝐷 is the Vias diameter, 𝑏𝑝 is the distance between each via measured from center to center, and 𝐸! is the substrate permittivity. The dimension 𝑎 goes from the center of
one via to the center of the other.
Figure 33 First three modes excited in the SIW
The three excited modes are the same as seen before and the wave port is at the same face as in the waveguide validation.
To verify the cutoff frequency of each mode, again, the phase constant is plotted:
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The cutoff frequency of the first mode is the same, so the validation is complete but it’s important to show that the cutoff frequency of the third mode is not the same as in the rectangular waveguide validation, that is because the dimension of 𝑏 is different and it doesn’t maintain the same relation with 𝑎 as in the rectangular waveguide, so, according to the equation (6), the mode TE01 depends only on the dimension 𝑏.
From now on, the main idea is to validate what has been done regarding the DRA excitation and then observe how other feedings can excite the DRA including an SIW.
9
DRA VALIDATION AT 60GHz
Continuing the work of a thesis made this year [2], the main idea is to develop and validate a DRA at 60 GHz. To successfully accomplish this objective, the design equations are validated using lumped port excitation and a design model contains a CRA over a substrate and a ground plane. The boundary conditions and rules of simulation were also validated next.
9.1 Model Design
The final model designed to make the DRA resonate at 60 GHz is indicated below.
Figure 35 Model design of the DRA at 60 GHz
The model shown above has the following dimensions (which are calculated from equations (15), (18))
Model Part Model Design Dimensions (mm)
a 0.74
h 0.508
W 0.3
L 5
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Also, the permittivity of the substrate used in the simulations was 𝜀! =9.9 and the
outside was filled with air.
When the model is designed in HFSS™, we have taken into account the characteristics of a DRA presented early in the section 3 like the boundary conditions to simulate a DRA in the free space like the air box, the ground plane and the boundary conditions on the DRA’s surface.
In order to excite the DRA, a lumped port will be placed in the middle of the non-resonant slot (see Annex section 1).
Figure 36 HFSS™ model design according to DRA design equations.
The boundary conditions used in the model are electric walls due to the ground plane below the DRA and magnetic walls on the exterior of the DRA to let it radiate as an antenna when it is excited. [9]
Figure 37 DRA boundary conditions
After setting the boundary conditions, the DRA placed on the ground plane without substrate is then simulated in HFSS™ (Figure 36) in order to observe its behavior alone.
A lumped port is placed in the middle of the slot to excite the DRA.
Before the final model design is simulated, is important to take a step back and simulate just the DRA and an isolated ground plane to notice all the changes that the model is going to have and how these changes affect the final results.
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9.2 Simulation Results – Infinite Ground Plane
In this case, the ground plane is simulated with an infinite ground plane that uses the PERFECT E boundary condition available in HFSS™.
Figure 38 Reflection coefficient of an infinite ground plane/ Lumped Port Fed DRA
This reflection coefficient shows that the antenna is well adapted at 61.8 GHz, which is near 60 GHz and the -10dB bandwidth is close to 6 GHz.
Figure 39 Gain infinite ground plane/ Lumped Port Fed DRA
In Figure 39, the red line shows the radiation pattern on the H plane while the brown line shows the radiation pattern on the E plane. Note that the position of the slot will control
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the H plane, in this case the H plane will be linearly distributed along the slot length. This color configuration will be the same for every gain plot in this section.
The gain shows how directive the antenna is in one direction, and the gain from above, shows that the DRA have a high gain along the z direction of the antenna (4.3 dBi), while is less directive in the back, which is good for the purpose of the DRA antenna.
It is important now to observe the EM fields to verify the excitation mode.
EM
FIELDS TOP VIEW SIDE VIEW
𝑯𝑬𝑴𝟏𝟏𝜹 E-FIELD
𝑯𝑬𝑴𝟏𝟏𝜹
H-FIELD
Table 8 EM Fields of a DRA fed by a lumped port on a ground plane
The EM fields from the table are excited from the lumped port placed at the middle of the slot, those fields means that the HEM11 mode is well excited whit this type of feed, so what is left is to validate what happens if the ground plane is made of PEC material (which means that the ground plane is finite) because in this case the infinite ground plane covered by an useful tool of HFSS™ called PERFECT E BOUNDARY.
Also it’s important to note that the gain is 2 dBi less than the DRA with a finite ground plane. The fact of having a finite ground plane implies that the waves are going to be reflected when they reach the end of the ground plane; in consequence, the gain is going to be increased. [14]
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9.3 Simulation Results – Finite Ground Plane
The DRA is going to be simulated taking into account a finite ground plane, because instead of using a PERFECT E boundary, is used the PEC material which changes a little bit the radiation response.
Figure 40 Reflection coefficient of a DRA on a ground plane
This reflection coefficient shows that the antenna is well adapted at 61.4 GHz, which is near 60 GHz.
Compared to the S11 with the infinite ground plane, the resonant frequency when the slot has a length equal to 0.9 mm, is almost the same, which means that the length of the ground plane doesn’t affect the resonant frequency of the antenna at all; also, the bandwidth covers the frequencies from 58 GHz to 64 GHz so it indicates that the propagation mode will be excited in that range of frequencies.
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Figure 41 Gain of DRA on a ground plane made of PEC- lumped port fed @60GHz
On the other hand, the gain has changed and the radiation pattern is less fine than that one of the infinite ground plane, which indicates that the length of the ground plane does affect the radiation pattern of the antenna, and that makes sense because the radiation tends to cover all the antenna from the top to the bottom, however if there is a ground plane larger-enough, the radiation will not pass from the top to the bottom of the antenna and in consequence, the radiation pattern improve as compared to the previous one.
Also it’s important to note that the gain is 2 dBi higher than the DRA with an infinite ground plane. The fact of having a finite ground plane implies that the waves are going to be reflected when they reach the end of the ground plane; in consequence, the gain is going to be increased [14].
The gain and the reflection coefficient of this type of feeding are similar to the measured parameters studied in the bibliographical study, which indicates that this is the right path.
Now, the next step is to add the substrate to observe the difference.
9.4 Simulation Results – Adding the substrate/ Infinite Ground
Plane
The next step in the Lumped Port fed DRA validation is adding the substrate below the infinite ground plane, to compare the results from those who don’t have a substrate as a base. The structure can be handled if we add a sufficiently thick enough substrate.
As seen in the section 10.1, the height of the substrate is going to be fixed at 0.3 mm, and the results are shown below:
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Figure 42 Reflection coefficient of DRA with radius = 0.74 mm and height = 0.508 mm
Note that the resonant frequency has changed from 61 GHz to 70 GHz when the slot length is 0.9mm, on the other hand, a better result has appeared when the slot length is 0.7 mm, nevertheless the substrate added a reactive component to the circuit and to correct that shift in frequency, the dimensions of the DRA must be changed.
Figure 43 Reflection coefficient of DRA with radius = 0.9 mm and height = 0.508 mm
Compared to the previous S11 parameter, the resonant frequency in Figure 43 has been shifted with a slight change in the DRA radius. This shift has moved the peak where the slot length is 0.9 mm to a frequency close to 60 GHz, which is one of the priorities of this work. Below are shown the other parameters in order to validate the substrate addition.
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Figure 44Gain of DRA with radius = 0.9mm @60 GHz
The gain hasn’t changed a lot from the previous one, which means that the substrate addition with an infinite ground plane above the DRA doesn’t change the radiation pattern or the gain value at all.
EM
FIELDS TOP VIEW SIDE VIEW
𝑯𝑬𝑴𝟏𝟏𝜹
E-FIELD
𝑯𝑬𝑴𝟏𝟏𝜹 H-FIELD
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The mode excitation is the same as it has been seen in the previous section.
9.5 Simulation Results – Adding the substrate/ finite Ground
Plane
Having validated the excitation inserting a substrate with an infinite ground plane, a comparison inserting a finite ground plane instead is needed.
The methodology is the same as seen in the previous subsections and the results are shown below.
Leaving a radius of 0.74 mm, the reflection coefficient is shown in Figure 45.
Figure 45Reflection coefficient of DRA over a finite ground plane and substrate with radius = 0.74 mm
The reflection coefficient shown in Figure 45 doesn’t have a strong variation compared to the S11 showed in Figure 42 because the resonance frequency is located in almost the same place. However as seen before in Figure 42 a shift in frequency is observed so the solution is to make the radius bigger in order to have a better adaptation at 60 GHz.
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Figure 46Reflection coefficient of DRA over a finite ground plane and substrate with radius = 0.9 mm
Is observed that for the first slot length chosen (Lslot=0.9mm), the resonance frequency is at 61 GHz, that indicates a good shift in frequency, that leads to a conclusion that the substrate does shift the resonance frequency, but the fact of having an infinite or finite ground plane doesn’t.
Figure 47Gain pattern of DRA over a finite ground plane and substrate with radius = 0.9 mm and Lslot=0.9mm
Regarding the gain pattern, is noticed that the field watched on the E plane (brown line) has a higher back radiation than the one observed in Figure 44 with the infinite ground, that could be explained because of the reflection on the ground plane on the low part of the antenna which mounts the gain a little bit.
The EM fields are always important to watch to know if the correct mode is excited, so in Table 10 the EM fields are shown.
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EM
FIELDS TOP VIEW SIDE VIEW
𝑯𝑬𝑴𝟏𝟏𝜹
E-FIELD
𝑯𝑬𝑴𝟏𝟏𝜹 H-FIELD
Table 10EM Fields for a Lumped Port Fed-DRA on a finite ground plane with substrate.
As always, the HEM11 mode is successfully excited. The next step is to validate these results comparing them with a previous work.
9.6 Comparing the results to the thesis
The results obtained for the infinite and finite ground with and without substrate, are then compared with those obtained by Juan Pablo Guzman in his thesis [2].
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WORK REFLECTION COEFFICIENT FOR A SLOT LENGTH PARAMETRIC ANALYSIS
THIS WORK
THESIS
Table 11 Slot length parametric analysis comparison
In this comparison, the length that fits best is that with L=0.9 mm which is the same in both cases, so the path taken for the rest of the simulations is good.
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WORK GAIN PATTERN FOR A SLOT LENGTH PARAMETRIC ANALYSIS
THIS WORK
A) B)
THESIS
Table 12 Gain pattern comparison A) DRA on infinite ground plane; B) DRA on finite ground plane; a) Radiation pattern on E plane for DRA; b) Radiation pattern on H plane for DRA
In Table 12 is possible to make important comparisons, the first one is that regarding the E plane of Figure ‘a’ in Table 12, it’s possible to note similarities between the infinite ground plane plot (black line of the thesis) and the plot in figure A (brown line of this work) where the scale of both figures and the shape of each are similar, so the conditions taken to plot this results are good.
Another comparison can be made regarding the figure B in Table 12 which is the finite ground plane simulation, if that plot is compared with the one shown in figure ‘a’ (blue line) and figure ‘b’ (blue line also), the plot is almost the same, and it makes sense because the condition is having a size equal to 5 mm for the ground plane which is the same size taken to simulate in HFSS™ in this work.
In conclusion, the plots of the infinite and finite ground plane are very accurate regarding the work that has been done before so it leads us to continue the simulation with another excitation methods.
10
MICROSTRIP LINE – SLOT COUPLING VALIDATION
To validate the DRA coupled with a microstrip line-slot transition HFSS™ is used. The solutions obtained from the software are divided into two types to well validate the model.