Chapter 1 Introduction
1.2 Organization
The dissertation is organized as follows. Chapter 1 gives an introduction of this paper.
Chapter 2 is devoted to the general descriptions of the fundamental theories of the microstrip leaky wave antenna, contained the emergence of microstrip leaky wave antenna, propagate phenomenon, radiation characteristic, the design of “full-width” and “half-width” microstrip leaky wave antenna. In chapter 3, a design of the half-width microstrip leaky wave antenna with suppressed back lobes has been presented, which is considered the direction of the reflected wave in the microstrip line. In chapter 4, we demonstrated a Yagi-Uda-like elements fabricating on microstrip leaky wave antenna. Based on the characteristics of Yagi-Uda antenna, we supported a suppressed back lobe and increased scanning region microstrip leaky wave antenna. A conclusion is attached in each design of Chapter 3 and Chapter 4.
3
Chapter 2
Theory of microstrip leaky wave antenna
In this chapter, we will demonstrate the leaky phenomenon on the microstrip line, the radiation characteristics of the microstrip leaky wave antenna and design consideration. Based on the feathers of the microstrip leaky wave antenna, it is an effective technique for providing the direction steering of the transmit/receive modules. And the frequency beam-scanning microstrip line leaky wave antenna has become more popular for extensive research.
2.1 Emergence of microstrip leaky wave antenna
The microstrip leaky-wave antenna (MLWA) was first constructed by Menzel in 1979, which was based on exciting the first higher order mode (TE01, leaky mode) of the microstrip line to obtain a radiation characteristics. A simple traveling wave antenna as the microstrip line leaky wave antenna was investigated in [1]. The leaky phenomenon was detected subsequently by Oliner and Lee [2]; the traveling wave in a microstrip leaky wave antenna would leak power to air due to a small attenuation constant. Comparing to resonator antenna operated in fundamental mode, the microstrip leaky antenna has a larger bandwidth due to the traveling wave in the microstrip line. This leaky mode antenna also possess the advantages of having a low profile, less weight, simple construction, being simple to fabricate and ease of matching. In addition, narrow beam width and frequency scanning characteristics are the extraordinary properties of the microstrip leaky wave antenna’s physical behavior. Recently, this microstrip leaky wave antenna has attracted a lot of interests to investigate.
A major problem of microstrip leaky wave antenna is the long length of the structure.
The MLWA proposed by Menzel was mentioned in [3] that the length of the antenna requires
4
about five wavelengths to radiate out power efficiently. A short length of the microstrip line would accompany with a large back lobe in radiation pattern. Recent research found that the back lobes could be suppressed by array topology [4] or a taper-loaded antenna end [5]. The array topology in [4] could suppress to 10.5 dB with the length of about 2λ0. The taper-loaded LWA end in [5] suppressed the back lobe 15 dB with the length of about 3λ0. Also, in [6], adding parasitic elements beside the MLWA can suppress the back lobe about 12 dB at 6.9 GHz while the length was about 2λ0. The back lobes were suppressed 10 dB at 10 GHz and 8 dB at 10.5 GHz by the radiating circuits in [7] and [8] respectively while the length was 2λ0. However, these designs mentioned above required a large length (at least 2λ0) or a complicated structure.
Here, we proposed two designs with short lengths to suppress back lobes of both full-width and half-width microstrip leaky wave antennas. Only about 1λ0 of the antenna length is demonstrated. The following chapters will report our recent effort in suppressing back lobe.
5
2.2 Propagation phenomenon on microstrip leaky wave antenna
In the microstrip line, there exist several modes while electromagnetic waves travel in the microstrip line. Usually, the uniform microstrip line is operated in the fundamental mode to transmit power; a slow wave relative to traveling in free space is traveling in a uniform microstrip line. As a result, the fundamental mode would not radiate power to air and cannot use to perform radiation characteristics in the microstrip line. To perform a microstrip leaky wave antenna, we employ a higher order mode in an appropriate region of operation frequency [9]. Among the higher modes, the first higher order mode (TE01, leaky mode) is the most practical mode to excite. Compared to the fundamental mode, the first higher order mode has a nonzero cutoff frequency dependent on the width of the microstrip line; different widths have different cutoff frequencies and operated regions. The leaky phenomenon of the microstrip line was detected by Oliner and Lee [2], a small attenuation constant cause power leakage. The leaky wave can occur in two forms: a surface wave and a space wave. A top view of the strip and the dielectric region around it is shown in Figure 2.1. There is a leakage from the strip in the form of a surface wave on the dielectric layer outside of the strip region.
The surface wave number ks has two components: kz in z direction and kx in x direction. The real part of the wave number kz must be equal to β, the phase constant of the leaky mode.
Since all field constituents are part of the same leaky modal field. Therefore, we may express the kz condition to (2.1), we can find that, for leakage to occur
6
ks
β< (2.3)
This is the shadow region shown in the Figure 2.2 which show β/k0 versus frequency in GHz. k0 is presented for the wave number in free space. The upper boundary of that region is the dispersion curve for the surface wave of wave number ks. This ks can be supported by the dielectric layer on a ground plane if it has no top cover. As β is decreased below ks (and therefore the frequency), power starts to leak away in the form of a surface wave. If β is further decreased, then the leakage will take place in another form of space wave in addition to the surface wave.
Fig. 2.1 Top view of the strip of microstrip line and dielectric region around it. ks is the wave number of the surface wave that propagates away at some angle during the leakage process.
7
Fig. 2.2 Dispersion curves for the lowest mode and the first two higher modes in microstrip line with a top cover. The normalized phase constant β/k0 is plotted against frequency. The solid lines represent real wavenumbers, whereas the dashed lines correspond to the real parts of the leaky mode (complex) solutions in the “radiation region.”
8
2.3 Discussions on leaky mode
Microstrip (transmission) line is usually operated in the fundamental mode which is purely bound mode [10]. The electric and magnetic fields of such a bound mode are shown in Figure 2.3 (a); it is an even symmetry about the axial centerline. To realize a radiating traveling wave structure, higher order modes must be excited. The first higher order mode is one such radiating mode. The electric and magnetic fields of this mode are shown in Figure 2.3 (b), and exhibit odd symmetry about the axial centerline of the antenna. From the electric field polarization on the top of the strip, it is obvious that the radiation will occur above the strip for this first higher order mode. The power leakage results in the space wave radiation, as in microstrip leaky wave antennas, the structure can be used to be a practical antenna.
(a)
(b)
Fig. 2.3 Field diagram for the (a) fundamental and (b) first higher order mode (E-field = solid, H-field = dashed).
9
2.4 Dispersion characteristic of a microstrip leaky wave antenna
In section 2.2, we have shown that the z component kz of the surface wave number can be expressed in the form of β – jα, where β is phase constant and α is attenuation constant. It is the complex propagation constant of the leaky mode in the microstrip line. We employed the rigorous (Wiener-Hopf) solution mentioning by [3] to obtain the normalized complex propagation constant. Figure 2.4 shows the variation of the normalized phase constant (β/k0) and normalize attenuation constant (α/k0), where k0 is the wave number in free space. These two constants are functions of frequency. In [11], Lin et al divide the first higher mode of microstrip line into the following four regions:
1) β > ks, α = 0, bound mode region;
2) ks > β > k0, small α, surface wave leakage region;
3) k0 > β, small α, surface wave and space wave leakage region;
4) k0 > β, largeα, cutoff region.
For the condition of β < k0, the traveling wave is in the first higher order mode. The power traveling in the microstrip line will leak into space and exist in the form of space wave in addition to the surface wave. The lowest order TM01 surface wave with zero cutoff frequency is often weakly excited [12]. Therefore, the space wave is dominant in the case of the microstrip leaky mode antenna.
10
ε
rN o rm a li z e d p ro p a g a ti o n c o n st a n t
Frequency (GHz)
h W
4 4.2 4.4 4.6 4.8
0 0.2 0.4 0.6 0.8
1 α /k
0β /k
0Fig. 2.4 Normalized complex propagation constant β/k0-jα/k0 of the first higher order mode in the microstrip line (W = 15.0 mm, h = 1.6 mm εr = 4.4).
11
2.5 Frequency scanning capability of microstrip leaky wave antenna
One important feature of the microstrip leaky wave antenna is that the frequency scanning capability. The main beam direction of radiation pattern can be operated by changing frequency. This angle can be characterized by an approximation equation,
1
sin ( /k0)
θ= − β (2.4)
The equation reveals that the angle of the main beam is a function of frequency. Thus the scanning capability is worked by controlling frequency.
: Microstrip Leaky Wave Antenna X
Z ( , , ) r θ φ Y
θ φ
Fig. 2.5 Coordinates of the microstrip leaky wave antenna.
Several significant steps in design of the microstrip leaky wave antenna depends on the plot of β and α versus frequency and eqn. (2.4). The procedures are summarized below and are only valid in leakage condition (see eqn. (2.3)) [13].
12
1) At the onset of the space wave (β = k0, corresponding to f ~ GHz in Figure 2.4), the main beam direction is theoretically parallel to the end-fire direction and the beam moves to the broadside direction as the frequency decreases.
2) As the frequency decreases, due to a small α, a large amount of power is reflected from the open structure end of the microstrip line, in turn producing a large back lobe at the same angle opposite to the broadside direction. A longer length of the antenna can reduce the back radiation.
3) In the radiation region, corresponding to reasonable α value (roughly contained between 4.2 GHz and 5.0 GHz in Figure 2.4), a continuous leaky wave occurs along the microstrip line. As a result, a large radiation space wave and a small amount of reflected wave are obtained. The beamwidth of the leaky wave is very narrow.
4) As the frequency continues to decreases, the attenuation constant of the guided mode strongly increases. The small attenuation constant here dose not promise a strong radiation. The phenomenon then indicates that the first higher mode is reactive below cutoff and the mode can only propagate small real power in the guided direction.
13
2.6 Design of microstrip leaky wave antenna
According to the theory of section 2.2, we can determine the complex propagation constant as plotted in Figure 2.4 by changing the width of the microstrip leaky wave antenna.
The leaky mode region is began from β/k0 = α/k0 and ended at β/k0 > 1. Here, the width of MLWA is designed to be 15mm. Consequently, the leaky mode region is between about 4.2GHz to 5.0 GHz. This leaky region is calculated based on the assumption that the infinite length of the microstrip line.
In practical, the antenna length is always not infinite. A conventional MLWA with finite length usually has an open structure end. A finite length of microstrip line would cause large reflection wave due to the mismatch of the open structure end. The reflection wave also leaks power to air and produces a large back lobe. The MLWA proposed by Menzel was mentioned in [3] that the short length (2.23λ0) of the microstrip line radiated only about 65% of the power. The remainder power would be reflected from the open structure end, and produces a large back lobe. To radiate 90% of the power, the length would be increasing to 4.85λ0. Usually, the length of the MLWA requires about five wavelengths to suppress back lobes and radiate out power efficiently.
A rule that considers the remnant guided wave power is applies to design the length of the microstrip leaky wave antenna. The remnant guided wave power (e-2αL) must be less than 5% when the length L of the antenna is chosen. That is,
2 L 0.05
e− α < (2.5)
A rigorous (Wiener-Hopf) solution [12] is employed to find the normalized complex propagation constant β/k0 - jα/k0 of the first higher mode, where β/k0 is the normalized phase constant and α/k0 is the normalize attenuation constant. As the normalized phase constant β/k0 is less than 1, the leakage occurs in the form of space wave.
14
2.7 Half-width microstrip leaky wave antenna
Menzel’s original microstrip leaky wave antenna shown in Figure 2.6 was using slots cut from the antenna along the centerline to suppress the fundamental mode. This “full-width”
design requires great effort to develop the appropriate slot structure and feed to reduce the fundamental mode as much as possible.
Microstrip line structure typically operates in the fundamental mode which does not radiate (discussed in section 2.3). However, the first higher order mode can radiate when the fundamental mode is blocked and thus, the microstrip line can be used as a leaky traveling wave antenna. This is due to the phase reversal in the fields at the center of the structure (see Figure 2.3 (b)) allowing the fields to decouple into the substrate and free space region [14].
This phase reversal at the center of the structure is that the basis for the “half-width”
microstrip leaky wave antenna. The use of a shorting wall to reduce the size of the microstrip
“patch” antenna is well known [15]. Such a method of using a shorting wall on the microstrip leaky wave antenna has been investigated to reduce size in [16]. Figure 2.7 (a) shows the enhancement design proposed in [16] based on Menzel’s antenna that incorporates a metal bifurcation down the centerline to block the fundamental mode. Symmetry along this metal wall prompts the application of image theory. One entire side of the antenna is now an image of the other side, making it redundant and not needed. The resulting modified antenna in Figure 2.7 (b) is the half-width microstrip leaky wave antenna.
Advantages of such the half-width antenna compared to the Menzel’s antenna are:
a. No need to suppress the fundamental mode;
b. No slot cross-polarized radiation that reduces radiation efficiency;
c. Purer guided mode compared to the Menzel configuration, which improves radiation efficiency; and
d. Potentially less interaction in an array environment.
15
W
εr
Fig. 2.6 Menzel’s original antenna with slots cut from the antenna along the centerline to suppress the fundamental mode.
W
εr
W/2
εr
(a) (b)
Fig. 2.7 (a) Enhancement design proposed in [16] based on Menzel’s antenna that incorporates a metal bifurcation down the centerline to block the fundamental mode.
(b) Half-width microstrip leaky wave antenna.
16
Chapter 3
A Novel Short Half-Width Microstrip Leaky-Wave Antenna with Suppressed Back Lobes
A novel short half-width microstrip leaky wave antenna (MLWA) with suppressed back lobes is introduced. It contains an oblique shape termination and a linked square metal with a grounded via hole. The oblique termination changes the direction of the reflected wave at the end, and a linked square metal with a grounded via hole guides the remainder power of the reflected wave to the ground plane without radiating to air. We will display the simulation and experimental results of this design.
3.1 Design of short half-width microstrip leaky-wave antenna with suppressed back lobes
Based on the half-width MLWA, the configuration of the proposed short length half-width MLWA is shown in Figure 3.1 (a). It contains an oblique shape termination and a linked square metal with a grounded via hole. The proposed MLWA has the length of L = 55 mm (about only 1λ0) and the width of W = 7.5 mm. The whole configuration is fabricated on a substrate of thickness h = 1.6 mm and dielectric constant εr = 4.4. The shorting wall of the half-width MLWA is realized by a row of grounded via holes. The details of the oblique shape termination and the linked square metal are shown in a magnified picture of Figure 3.1 (b).
By using the oblique shape termination, the direction of the surface current could be changed. Such that the reflected wave at the end would not travel straightly along the longitude edge of the proposed MLWA. The current distribution of the original half-width MLWA and the proposed MLWA with the oblique shape termination are shown in Figure 3.2
17
(a) and (b), respectively. It’s obvious that the current distribution has been changed at the oblique termination of the proposed MLWA. As a result, the traveling direction of reflected wave has been changed.
A square metal with a grounded via hole is linked beside the proposed MLWA, it is used to guide the remainder power to the ground plane. When the remainder power reflected at the oblique shape termination, the reflected wave would be guided to the ground thru the linked metal without leaking the power. One slot at the oblique termination is added to ensure that the remainder power is guided to the ground plane.
By these manners, the reflected wave at the end would not travel straightly and could be guided to the ground plane without leaking to air. The back lobe of the proposed short length half-width MLWA could be suppressed successfully.
18
L
W Shorting wall
Grounded via hole Top view
Side view ε
r(a)
9.014 mm 3 mm
3 mm
5 .7 5 mm
0.5 mm
2 mm
Groun ded via hole
(b)
Fig. 3.1 (a) Configuration of the proposed MLWA with an oblique shape termination and a linked square metal.
(b) Magnified picture of the dash line area of (a) with details.
19
(a)
(b)
Fig. 3.2 Current distribution of (a) the original half-width MLWA and (b) the proposed MLWA.
20
3.2 Simulated and experimental results of short half-width microstrip leaky-wave antenna with suppressed back lobes
The simulated radiation patterns of the proposed half-width MLWA at 4.6 and 4.7 GHz are shown in Figure 3.3 (a) and (b), they are compared with the original half-width MLWA.
The original half-width MLWA has the same shorting wall and length as the proposed LWA.
The simulated results illustrate that the back lobes have been suppressed successfully; the back lobes of the proposed LWA have been suppressed by about 9.1 and 6.1 dB at 4.6 and 4.7 GHz respectively compared to the original half-width MLWA. Below 4.6 GHz, the back lobes have also been improved significantly. The measured radiation patterns at 4.6 GHz and 4.7 GHz are shown in Figure 3.4 (a) and (b), respectively. The gain difference between the main beam and back lobe are 13.1 dB at 4.6 and 7.2 dB at 4.7 GHz. The back lobes of the proposed half-width MLWA are suppressed indeed in experimental results.
It is noticeable to speak of the scanning angle of the main beams about the proposed MLWA and original half-width MLWA. In simulated radiation patterns, the main beams of the proposed MLWA are slightly slanted to broadside direction compared to the original one. It is mainly due to the oblique shape termination. The oblique termination destroys the current distribution of the leaky mode of the proposed MLWA (see Figure 3.2 (b)). Therefore the scanning region of the proposed MLWA is smaller than the original one but not by much. In the simulated results, the scanning angle of main beam of the original half-width MLWA is 34° while the proposed MLWA is 30° at 4.7 GHz. There is about 4° difference between the proposed MLWA and original half-width MLWA.
Although in Figure 3.4, the main beams of the experimental results are slanted to end-fire direction unexpectedly. An error degree in the spinning mechanism of the measurement may take the blame for this issue. However, the scanning region of the main beams could sweep from 13° to 35° between 4.2GHz and 4.7 GHz in experimental results.
21
Fig. 3.3 Simulated H-plane radiation pattern of the original half-width MLWA and the proposed MLWA at (a) 4.6GHz and (b) 4.7 GHz
22
Fig. 3.4 Measured H-plane radiation pattern of the original half-width MLWA and the proposed MLWA compared to simulated results at (a) 4.6GHz and (b) 4.7 GHz