O RGANIZATION

This thesis will begin with the introduction of the leaky wave antenna and some relating theories and techniques in order to facilitate the later analysis. The following chapters will focus on the proposed antenna design.

Chapter 1 gives the brief introduction and the motivation of this paper.

Fundamental theories and properties of the micro-strip leaky wave antennas will be summarized in chapter 2. And then, chapter 3 will be demonstrated the design and the operating process of the dual-band circularly polarized slotted monopole antenna. And finally, the future works will be made in the chapter 4.

C ^HAPTER 2

U SING SPLIT RING RESONATORS TO SUPPRESS THE SIDE LOBE AND MINIATURIZE THE LENGTH OF A TAPERED LEAKY WAVE ANTENNA

In this chapter, we will first give a simple introduction on the characteristic of the leaky wave antenna. Second, we will discuss the basic theories and the radiation characteristics of the micro-strip leaky wave antenna. Furthermore, we will also mention the theories of the tapering method and the split ring resonators. Finally, we will give a competition between the different positions of the split ring resonators.

By adding split ring resonators on the tapered antenna or on the ground, the current distribution of this antenna can be improved. Besides, the split ring resonators can trap the reflection current which generates the reflection wave. Because of the reducing reflection wave, the side-lobe can also be reduced. This technique not only suppresses the side-lobe but miniaturizes the length of the antenna. According to the measured results of the split ring resonators on the antenna, the impedance bandwidth achieves about 600MHz for 6-dB return loss, which covers the range from 3.4GHz to 4.9GHz, and the scanning angle of the measured main beam is about 31˚, which covers the range from 14˚ to 45˚. In the other case of the split ring resonators on the ground, the measured results show the impedance bandwidth covers from 4.4GHz to 5.0GHz, whose impedance bandwidth achieves about 600MHz for 6-dB return loss.

2.1 Basic theories

2.1.1 Theories of leaky wave antenna

The first prototype of micro-strip leaky wave antenna is presented by Menzel[1] in 1979, which used an asymmetric feed line to excite the first higher order mode.

Because the leaky wave antenna is operated in the first higher order mode, and the width of the leaky wave antenna, the thickness of the substrate, and the dielectric constant determines the radiation bandwidth.

Leaky wave antenna uses an asymmetric feed line to excite the first higher order mode (𝑇𝐸₀₁, 𝑙𝑒𝑎𝑘𝑦 𝑚𝑜𝑑𝑒). Generally speaking, the radiation mode of antenna is the dominant mode, which is a slow wave relative to radiating in free space. Comparing to the dominant mode, the first higher mode is a fast wave and excites the characteristics of narrow beam-width and frequency scanning. Figure 2-1 shows the electric and magnetic fields of the first higher order mode, which the electric field is an odd symmetric about the axial centerline and excites a traveling wave.

The theories and the phenomenon of leaky wave antenna had been clearly

The variation of the normalized phase constant and attenuation constant are plotted in Figure 2-2.

According to Figure 2-2, we divide the first higher order mode into four regions:

But when the operating frequency gets larger enough to build up the mode, since the mode is now dominated by fast wave and the wave leads to leak and radiate from the edge of the micro-strip line. When we increase the frequency continuously, the wave may eventually become a slow wave and then there is no space wave radiation[4]. The frequency range we can use for leaky wave antennas falls in the space wave leakage region, which we can simply determine the range between the lower edge (𝑓_𝐿) and the upper edge (𝑓_𝐻):

𝛼_𝑦(𝑓_𝐿) = 𝛽_𝑦(𝑓_𝐿) (2.2) 𝛽_𝑦(𝑓_𝐻) = 𝑘₀ (2.3) This “lossy transmission line” can be regarded as an antenna which can radiate toward a specific direction, and the direction is dependent on the specific phase constant of the different frequency of the lossy transmission line. Moreover, in Figure 2-3, the elevation angle 𝜃_𝑀 between the main-beam direction and end-fire direction (the Z-axis direction) can be estimated approximately as following equation:

𝜃_𝑀 ≅ sin⁻¹(𝛽_𝑦⁄ ) (2.4) 𝑘₀

𝛼_𝑦

𝑘₀ ≅ 0.183 × 𝜃_{𝐻𝑃𝐵𝑊} × cos(𝜃_𝑀) (2.5) Where 𝛽_𝑦⁄𝑘₀, 𝛼_𝑦⁄ are the normalized phase constant and attenuation constant. 𝑘₀

Figure 2-1. The electric field distribution of the first higher order mode of the micro-strip line.[5]

Figure 2-2. Normalized complex propagation constant for the first higher order mode in the micro-strip line with split ring resonators at the antenna.

Figure 2-3. The coordinate system of a leaky wave antenna.

2.1.2 Theories of tapering method

In order to improve the radiation bandwidth, some researches choose the method of tapering. A tapered leaky wave antenna operates by using sections with different width to excite different operating frequency bands, so the tapered leaky wave antenna can achieve broad impedance bandwidth[6, 7]. Although we can increase the impedance bandwidth by tapering the micro-strip line, the problem with tapered leaky wave antenna is that there is a spurious side-lobe generated by the reflection wave.

The theory of tapered leaky wave antenna is that the wider width of leaky wave antenna radiates in the lower frequency region and the narrow width acts in the reactive region and not radiates power. Similarly, the narrower width radiates in the higher frequency region and the wider width operates in the bound mode region. The width of the tapered leaky wave antenna can be determined by the start and the end frequency. The equations of the radiation region and cutoff frequency (𝑓_𝑐) of each caused by the original tapered leaky wave antenna (TYPE 1), the following structures (TYPE 2 and TYPE 3) are fabricated to solve and improve the bandwidth.

Figure 2-4. Three structures of tapered leaky wave antenna [7, 8].

2.1.2 Theories of split ring resonators

Because of the significant growing of the communication technology and wireless communication market, consumers’ requirements about the circuits have been trending to be smaller, more reliable and more power efficient[9]. To integrate the whole transceivers on a single chip is the trend for future wireless systems. First of all, we should consider the largest components of the integrated circuit, and it is an important target for wireless communication systems to achieve the miniaturization of antennas[10] .

In recent years, split ring resonators (SRRs) shown in Figure 2-5 (a), proposed by Pendry[10-12], have played a main role of the miniaturization and compatibility in the planar circuits. Because of the characteristics of the negative permeability and permittivity, split ring resonators have attracted a great interest in the circuit and antenna design. Besides, we need to have periodic structures which will not only be easy to fabricate but also will not increase the dimensions of the devices[10].

Split ring resonators are one of the electromagnetic metamaterials (MTMs) which are broadly called left-handed(LH) structures[12]. LH materials are characterized by antiparallel phase and group velocities, or negative relative permittivity and permeability(𝜀_𝑟 , 𝜇_𝑟 < 0).

where 𝐹 = 𝜋(𝑎 𝑝⁄ )² (a : the inner radius of the smaller ring), 𝜔_0𝑚 = 𝑐√_{𝜋 ln(2𝜔𝑎}^3𝑝 _{3⁄ )𝛿} ( ω : width of the rings, δ : radial spacing between the rings), and ζ = 2𝑝𝑅′ 𝑎𝜇⁄ ₀ (𝑅^′: the metal resistance per unit length). Equation (2.8) reveals that a frequency range can exist:

𝜇_𝑟 < 0, for 𝜔_0𝑚 < 𝜔 < ^𝜔0𝑚

√1−𝐹= 𝜔_𝑝𝑚 , (2.9) where the 𝜔_𝑝𝑚 is called the magnetic plasma frequency. The equivalent circuit of a SRR is shown in Figure 2-6. In the single SRR, the circuit model is the RLC resonator with resonant frequency 𝜔₀ = 1 √𝐿𝐶⁄ .

Figure 2-5. (a) SRR produced by Pendry and (b) CSRR.[10]

Figure 2-6. Equivalent circuit model of SRRs.[12]

(a) Single SRR configuration. (b) Double SRR configuration.

2.2 Design of the proposed leaky wave antenna with different position of split ring resonators

2.2.1 The influence of the split ring resonators

From [12, 13], we can know that the split ring resonators generate an important phenomenon called stop-band which can forbid the wave to pass through. In order to finding the difference between the transmission line with and without the split ring resonators, the following simulation shown in Figure 2-7 can tell us the influence of the split ring resonators.

In this section, we focus on the influence of the split ring resonators. First of all, comparing the simulation between the transmission line and the transmission line with split ring resonators, and we can easily find out that the electric field and magnetic field are trapped by the split ring resonators which are shown in Figure 2-7.

In other words, the split ring resonators will reduce the reflection wave of the open end side of the leaky wave antenna when the split ring resonators are operating at the stop-band. According to this phenomenon, we can choose the split ring resonators not only to suppress the reflection wave but also to reduce the size of leaky wave antenna.

From Figure 2-8, we can know that the resonant frequency of the transmission line starts to resonate from 4GHz to 9.5GHz.

From these simulations, we can know that we must choose the right position of the split ring resonators. Our purpose is to reduce the side-lobe, so we have to put the split ring resonators at the end of the antenna.

Figure 2-7. The electric and magnetic field intensity in the transmission line and the transmission line with the SRRs.

Figure 2-8. The s-parameters of the transmission line with SRRs at the ground plane.

2.2.2 First structure - split ring resonator at the end of the antenna

Figure 2-10 shows the proposed configuration of the leaky wave antenna. This antenna is fabricated on FR4 substrate with a dielectric constant (𝜀_𝑟) of 4.4, loss tangent (tan 𝛿) of 0.024, and thickness of 0.8mm. The total length (𝐿_𝑡) of the tapered short leaky wave antenna is chosen to be 82mm (about 1.18𝜆₀ at 4.3GHz). The radius of each ring and the other antenna parameter are listed in Table 2-1.

In this section, the design procedures of this antenna, including the etched split ring resonators on the antenna for suppressing the reflection wave, are presented sequentially.

Figure 2-9. The first structure of the leaky wave antenna.

Figure 2-10. Configuration of the proposed leaky wave antenna.

T

ABLE

2-1. D

IMENSIONS OF

T

HE

F

IRST

L

EAKY

-W

AVE

A

NTENNA

S

TRUCTURE

.

Name of parameters Dimension (mm)

𝐿

_𝑡

82

𝑟

_𝑏1

2

𝑟

_𝑐1

3

𝑟

_{𝑔𝑎𝑝1}

1

2.2.3 Second structure - split ring resonator at the end of the ground

Figure 2-12 shows the proposed configuration of the leaky wave antenna. This antenna is also fabricated on FR4 substrate with thickness of 0.8mm. The total length (𝐿_𝑡) of the tapered short leaky wave antenna is chosen to be 82mm (about 1.18𝜆₀ at 4.3GHz). The radius of each ring and the other antenna parameter are the same as the first structure.

In this section, the design procedures of this antenna, including the etched split ring resonators on the ground for suppressing the reflection wave, are presented sequentially.

Figure 2-11. The second structure of the leaky wave antenna.

Figure 2-12. Configuration of the proposed leaky wave antenna.

T

ABLE

2-2. D

IMENSIONS OF

T

HE

S

ECOND

L

EAKY

-W

AVE

A

NTENNA

S

TRUCTURE

.

Name of parameters Dimension (mm)

𝐿

_𝑡

82

𝑟

_𝑏2

2

𝑟

_𝑐2

3

𝑟

_{𝑔𝑎𝑝2}

1

2.3 Simulation and measurement

2.3.1 Simulations between the prototype and the tapered LWA

In this section, we take the first step to check the difference between the prototype and the tapered leaky wave antenna. In order to figure out the influence of the tapering method using on the leaky wave antenna, we use the simulation tools(HFSS) to check the differences. First, we make the length (Lt) of the prototype LWA which is shown in Figure 2-13 to be 82mm which is about 1.18𝜆₀ at 4.3GHz. And for the second step, we use the HFSS to make sure that the tapering method also suppresses the side-lobe of the LWA.

From Figure 2-14 to Figure 2-17 show the comparison of the radiation patterns between the prototype and the tapered leaky wave antenna. We can notice that the orientation of the main beam seems tilt toward broad side, because the proposed tapering reduces the width and make the phase constant be reduced in the same frequency point. From Eq(2.4), we can expect that tapering method can lead the beam to toward the broadside. It can be seen that the side lobes are suppressed due to the tapering method in the scanning range (from 4.3GHz to 4.9GHz). Moreover, we can know that the side-lobe is suppressed efficiently by more than 20dB in the 4.3GHz and 4.5GHz which are shown in Figure 2-14 and Figure 2-15. And for 4.7GHz and 4.9GHz, the side lobe levels are approximately suppressed by 9dB and 5dB, respectively.

Figure 2-13. The two structures: (a) prototype, (b) tapered LWA.

Figure 2-14. Simulated radiation pattern of the prototype and tapered LWA at 4.3GHz

Figure 2-15. Simulated radiation pattern of the prototype and tapered LWA at 4.5GHz

Figure 2-16. Simulated radiation pattern of the prototype and tapered LWA at 4.7GHz

Figure 2-17. Simulated radiation pattern of the prototype and tapered LWA at 4.9GHz

2.3.2 Simulation and measurement of the first structure

In this section, we take the first step to verify that whether the split ring resonators work or not. From the simulation shown in Figure 2-18, we can know that the reflecting wave from the open end can be gathered by the split ring resonators, so it won’t be radiated to the air. Due to the results from these simulations, we can verify that the position of the split ring resonators should be put at the open end which generating reflecting waves.

The simulated normalized phase constant and attenuation constant are shown in Figure 2-19, and the usable range is approximately from 4.3GHz to 4.9GHz. From Figure 2-20, we can see the simulated and measured return loss of the first structure of leaky wave antenna. The measured impedance bandwidth of the first leaky wave antenna for 6-dB return loss is approximately from 4.3GHz to 4.9GHz, and it has good agreement between the simulation and the measurement. And then, from Figure 2-21 to Figure 2-25, they show the simulated and measured normalized radiation patterns in the Y-Z plane, and finally illustrate the measured radiation pattern at each operating frequency: 4.3GHz, 4.5GHz, 4.7GHz, and 4.9GHz. And from the radiation patterns, we can find that the scanning degree is nearly from 10˚ to 45˚ of the first structure of the leaky wave antenna. The simulated and measured maximum gain and radiation angle are also shown in Figure 2-26 and Figure 2-27, respectively.

Figure 2-18. The different operating frequency of the first structure.

LWA operates at : (a) 4.3GHz ,(b) 4.5GHz, (c) 4.7GHz, (d) 4.9GHz.

Figure 2-19. Normalized complex propagation constant for the first higher order mode in the micro-strip line with split ring resonators at the antenna.

Figure 2-20. The measured and simulated return loss of the first structure.

Figure 2-21. Simulated and measured normalized radiation pattern at 4.3GHz.

Figure 2-22. Simulated and measured normalized radiation pattern at 4.5GHz.

Figure 2-23. Simulated and measured normalized radiation pattern at 4.7GHz.

Figure 2-24. Simulated and measured normalized radiation pattern at 4.9GHz.

Figure 2-25. Measured normalized radiation patterns of the first LWA structure.

Figure 2-26. Simulated and measured radiation angle of main beam of the first LWA.

Figure 2-27. Simulated and measured radiation gain of main beam of the first LWA.

2.3.2 Simulation and measurement of the second structure

In this part, we focus on the same structure but put the split ring resonators at the ground plane. In the second structure, the first verification is to check the simulation results whether the structure works or not. From Figure 2-28, we know that the reflecting wave is also trapped by the split ring resonators.

The simulated normalized phase constant and attenuation constant are shown in Figure 2-29, and the usable range is approximately from 4.3GHz to 4.9GHz. From Figure 2-30, we will see the simulated and measured return loss of the second structure of leaky wave antenna. The measured impedance bandwidth of the second leaky wave antenna for 6-dB return loss is approximately from 4.3GHz to 4.9GHz, and it has good agreement between the simulation and the measurement. And then, from Figure 2-31 to Figure 2-35, they show the simulated and measured normalized radiation patterns in the Y-Z plane, and finally illustrate the measured radiation pattern at each operation frequency: 4.3GHz, 4.5GHz, 4.7GHz, and 4.9GHz. And from the radiation patterns, we can find that the scanning degree is nearly from 10˚ to 45˚ of the second structure of the leaky wave antenna. The simulated and measured maximum gain and radiation angle are also shown in Figure 2-36 and Figure 2-37, respectively.

Figure 2-28. The different operating frequency of the second structure.

LWA operates at : (a) 4.3GHz ,(b) 4.5GHz, (c) 4.7GHz, (d) 4.9GHz.

Figure 2-29. Normalized complex propagation constant for the first higher order mode in the micro-strip line with split ring resonators at the ground plane.

Figure 2-30. The measured and simulated return loss of the second structure.

Figure 2-31. Simulated and measured normalized radiation pattern at 4.3GHz.

Figure 2-32. Simulated and measured normalized radiation pattern at 4.5GHz.

Figure 2-33. Simulated and measured normalized radiation pattern at 4.7GHz.

Figure 2-34. Simulated and measured normalized radiation pattern. at 4.9GHz

Figure 2-35. Measured normalized radiation patterns of the second LWA structure.

Figure 2-36. Simulated and measured radiation angle of main beam of second LWA.

Figure 2-37. Simulated and measured radiation gain of main beam of second LWA.

2.4 Conclusions

In this chapter, a method of using split ring resonators is proposed to suppress the reflection wave from the open-end side. By using the split ring resonators, they can trap the reflection wave which generates the side lobe of the radiation of the antenna.

According to these two structures, the measured results show the scanning range both cover 37˚ for these structures. From Figure 2-20 and Figure 2-30, the measured 6-dB impedance bandwidth achieves from 4.3GHz to 4.9GHz which is about 13% with respect to the center frequency at 4.6GHz. The scanning capabilities of these antennas are from 10˚ to 45˚. The leaky-wave antenna whose length is only about 82mm (1.18𝜆₀ at 4.3GHz) not only successfully reduces the length but also suppresses the side lobe. Furthermore, this method does not use any parasitic elements or circuits, thus we can avoid increase the antenna size and cost. The competitions of the two structures are shown in Table 2-3.

T

ABLE

2-3. T

HE COMPARISONS OF THE TWO STRUCTURES

.

First Structure Second Structure

C ^HAPTER 3

A ^DUAL - BAND CIRCULARLY

POLARIZED SLOTTED MONOPOLE ANTENNA

Nowadays, antenna with circular polarization plays an important role in communication systems[15], because they allow for more flexibility in orientation angle between transmitter and receiver antennas, high penetration, and stability.[16]

Therefore, circular polarization antennas can provide much better connectivity with fixed and mobile communication systems.[17]

In order to have a circular polarized radiation, the orthogonal field components should have the equal magnitude and a phase difference of 90˚. It is not easy to satisfy the conditions of generating a circular polarization. In recently, slots are widely used in micro-strip antenna designs. The geometry structures of the slots are corresponding to the radiation patterns and usually leading to get narrow impedance bandwidth and axial ratio.[18-20]

It is known that the spiral structure can achieve circular polarization characteristics.

In this chapter, we demonstrate a circular polarization design by etching slots at a spiral structure to achieve the dual-band circular polarization. The proposed antenna shown in this chapter is a single layer of a micro-strip antenna. The top layer is composed of a 50Ω micro-strip transmission line and a spiral-shaped conductor. A dual-band slotted monopole antenna has been proposed, which operates on the following bands: 2.45GHz and 5.2GHz, and the axial ratio demonstrate the equal magnitude of the field components at these bands.

3.1 Basic theories of monopole antenna and polarization

3.1.1 Theories of monopole antennas

Monopole antenna is widely used in the communication systems, because it is easily fabricated, and low cost. In the operating theory, monopole antenna is one half of a dipole antenna, and it is always mounted on an infinite ground plane. Therefore, we can regard a monopole antenna as a dipole antenna with the principles of image theory. In the following, we will discuss the operating theory of the dipole antenna in this section[21].

Dipole antenna is formed by two symmetrically metal elements, the total length of the dipole antenna is equal to half wavelength, and it is fed by a two-wire transmission line to construct a half-wave dipole antenna. In Figure 3-1, we can see

Dipole antenna is formed by two symmetrically metal elements, the total length of the dipole antenna is equal to half wavelength, and it is fed by a two-wire transmission line to construct a half-wave dipole antenna. In Figure 3-1, we can see

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