Summary - Cylindrical Microstrip Leaky-wave Antennas

CHAPTER 2 Cylindrical Microstrip Leaky-wave Antennas

2.4 Summary

This Chapter proposes a cylindrical microstrip antenna structure with a full-wave analysis and its implementation. We investigate how the angular widths and the substrate thicknesses affect the propagation constants and radiation patterns of this cylindrical structure. Measured scattering parameters and radiation patterns of these realized antennas circuits are presented. Finally, we conclude that cylindrical leaky-wave antennas have the high-gain and wideband features, similar to those of the planar leaky-wave antennas.

Chapter 3 Leaky Modes on Cylindrical Substrates

In this Chapter, the first higher order leaky modes on the other two types of cylindrical structures are demonstrated: slotted coaxial lines and cylindrical coplanar waveguides. They have different field symmetries which are represented with virtual PMC or PEC about the center. With the same method used in Chapter 2, spectral domain approach, propagation characteristics of the first higher order leaky modes on both structures are investigated. From the measurement results of two design examples, these two types of antennas can also be high-gain and wideband. Briefly, we have shown that such two structures can support space-wave leaky modes.

3.1 Leaky Modes of Slotted Coaxial Lines

3.1.1 Spectral Domain Analysis of Slotted Coaxial Lines

This section discusses the propagation characteristics of slotted coaxial lines. Fig.

3.1(a) shows the cross section of slotted coaxial lines. The slot with width w is on top of the substrate. The inner ground conductor and the outer conductor shell are located at circumferences of radii a and b, respectively. The permeabilities of all materials are µ₀. The thickness of the outer shell and the ground conductor are assumed to be zero.

In the analysis of the first high order leaky mode of slotted coaxial lines, we place a PMC boundary at the bottom (φ=π ) in Fig. 3.1(b) to represent the appropriate field symmetry about the center.

The z-direction fields represented as inverse Fourier series are the same as in (2.1)-(2.4). Similarly, the time-harmonic expression e^{j t}^ω and z-dependence e⁻^{jk z}^z are assumed. The longitudinal (z-direction) electric field on the slot is

φwφ_w

φ φ =⁰

φL = −π φ_R =π

(a) (b)

Fig. 3.1 (a) The cross-sectional view of the slotted coaxial line. (b) The PMC boundary representation the slotted coaxial line.

even-symmetric about φ = , whereas the transverse electric field (0 φ-direction ) is odd-symmetric about φ = . For slotted coaxial lines, the longitudinal electric field 0 distributions are like the transverse current distributions of cylindrical microstrip lines, and the transverse electric field distributions are like the longitudinal current distributions of cylindrical microstrip lines. If the electric fields of the first higher leaky mode in slotted coaxial lines are equivalent to magnetic currents (M_z =E_φ×ρ, M_φ =E_z×ρ), these magnetic currents will be similar to electric currents of the first higher leaky mode in cylindrical microstrip lines.

We solve the coefficients by applying boundary conditions. Therefore we obtain substrate thickness h, are investigated. The dielectric constant of the substrate εr is 2.2.

In Fig. 3.2, the radius b is 100 mm, the thickness h is 10 mm, and the widths w are 10, 15 and 20 mm. As the slot width w increases, the curve of the propagation constant moves to a lower frequency region. Fig. 3.3 shows how the radius b affects the curves.

The slot width w is 10 mm, the thickness h is 10 mm, and the outer radii b are 20, 40, and 80mm.The larger radius also changes the propagation constant to a lower frequency band.

Fig. 3.4 plots the curves for three different substrate thicknesses h, which are 6, 8, and 10mm. The slot width w is 10 mm and the outer radius b is 50 mm. The lower

Frequency (GHz)

2 4 6 8 10 12

β /k

, α /k

0.0 0.5 1.0 1.5 2.0 2.5

β/k₀, w=10mm α/k₀, w=10mm β/k₀, w=15mm α/k₀, w=15mm β/k₀, w=20mm α/k₀, w=20mm

Fig. 3.2 The normalized propagation constants of different slot widths ( b = 100 mm, h = 10 mm, εr = 2.2, and w = 10, 15 and 20 mm).

bounds

(

^α⁼^β

)

of the radiation regions

(

α≤β≤k0

)

occur at 9.675, 8.750, and 6.125GHz, corresponding to h = 6, 8, and 10 mm. It is notably that these frequencies are approximately proportional to the reciprocal of substrate thicknesses. We conclude that the outer radius and slot widths do not affect propagation constants very much, whereas the substrate thickness may dominate the operating frequency.

Frequency (GHz)

Fig. 3.3 The normalized propagation constants of different slot widths ( b = 100 mm, h = 10 mm, εr = 2.2, and w = 10, 15 and 20 mm).

Fig. 3.4 The normalized propagation constants of different substrate thicknesses ( b = 50 mm, h = 6, 8, and 10 mm, εr = 2.2, and w = 10 mm).

Fig. 3.5 The proposed conductor-backed slotline leaky-wave antenna.

3.1.3 Design Example: A Conductor-backed Slotline Leaky-Wave Antenna

From the numerical results in Section 3.1.2, the radius of the coaxial line is too large (6 mm or more) in fabrication for operating frequencies less than 14 GHz.

Therefore we design a planar type of slotted coaxial lines, which are equivalent to the conductor-backed slotlines to demonstrate that such a leaky mode can propagate in this structure. Fig. 3.5 illustrates the proposed conductor-backed slotline leaky-wave antenna, with a simple microstrip line and a gap resonator feeding. The substrate is chosen as air to reduce the electrical length of the substrate thickness, and the operating frequency is lowered. The substrate thickness h is 10 mm, the slot width w₁ is 10 mm, the width of two side top conductors w2 is 20mm, and the length of top conductors is 150 mm.

Fig. 3.6 The normalized phase constants and attenuation constants.

Fig. 3.6 displays the normalized phase constants and attenuation constants. The radiation region starts at 12 GHz. As shown Fig. 3.7, the bandwidth of this antenna is about 2.95 GHz, which begins from 15.95 to 18.90 GHz. At 13, 14, 15 GHz, the antenna gains plotted in Fig. 3.8 are 9.75, 12.16, 14.01 dBi, respectively. At 16, 17, 18 GHz, the antenna gains plotted in Fig. 3.9 are 15.02, 14.95, 16.52 dBi, respectively.

This conductor-backed slotline leaky-wave antenna has the similar frequency-scanning property as a microstrip leaky-wave antenna does.

Fig. 3.7 The return loss of the conductor-backed slotline antenna.

Fig. 3.8 The copolarization radiation patterns at 13, 14 15 GHz in the xz-plane.

Fig. 3.9 The copolarization radiation patterns at 16, 17, 18 GHz in the xz-plane.

φwφ_w φ

φ =0

φL = −π

φR =π φs φ_s

(a) (b)

Fig. 3.10 (a) The cross-sectional view of the CPW on the cylindrical substrate.

(b) The PEC boundary representation.

3.2 Leaky Modes of

Coplanar Waveguides on Cylindrical Substrates

3.2.1 Spectral Domain Analysis of Coplanar Waveguides on Cylindrical Substrates

The proposed leaky CPW on cylindrical substrate is plotted in Fig. 3.10(a).

Region I and III are both free space. Region II is the cylindrical substrate with a permittivity of ε2=εrεo and a thickness of h. The center strip (with the width w) and the slots (with the widths s) are on the top of the substrate. The center strip, slots, and ground conductor are all located at circumferences of radius b. As the same symmetry shown in Chapter 1, a PEC boundary is placed at the top and the bottom (φ =0, π ) in Fig. 3.10(b). The longitudinal currents (z-direction) on the center strip and the ground conductor are odd-symmetric about φ =0, π . The transverse currents (φ-direction) are even-symmetric about φ =0, π. This CPW leaky mode is similar to the coupled slotline mode [34]-[35], and the main difference is that the currents of CPW leaky mode are attenuating.

The three sets of longitudinal (z-direction) fields

(

Ezi^,Hzi

)

are represented as inverse basis functions. The remaining procedures are identical to those in Section 3.1 except the different Green’s functions, which are obtained after applying boundary conditions.

3.2.2 Numerical Results

Three parameters, outer radius b, center strip width w, and slot widths s have been changed to check how they influence the propagation constants of the first higher order leaky mode. The two unchanged parameters: dielectric constant of the substrate εr is 2.2, and the thickness of the substrate h is 0.508 mm. Fig. 3.11, 3.12, and 3.13 plotted the calculated normalized attenuation constants and phase constants( /α k₀^,β/ )k₀ . In Fig. 3.11, the outer radii b are 10, 12, and 14mm, the center strip width w is 10 mm, and the slot width is 5mm. When the outer radius b increases, the curve of the propagation constants moves to a lower frequency region.

Fig. 3.12 shows the effect of the center strip width w. The slot width s is 5mm, while the center strip widths w are 10, 8, and 6mm. Narrower w causes the propagation constants shift to a higher frequency band.

Fig. 3.13 plots the curves for three different slot widths s, which are 10, 5, and 1 mm. The center stripe width w is 10 mm and the outer radius b is 20 mm. It is

Frequency (GHz)

6 8 10 12 14 16

-α/k 0 , β/k 0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

1.4 ^β/k0, b=10mm

−α/k₀, b=10mm β/k₀, b=12mm

−α/k₀, b=12mm β/k₀, b=14mm

−α/k₀, b=14mm

Fig. 3.11 The normalized propagation constants of different outer radii ( b = 10, 12 and 14 mm, h =0.508 mm, εr = 2.2, s = 5 mm, and w = 10 mm).

interesting that Fig. 3.13 is very analogous to Fig. 3.12. This implies that both of center strip width and slot width may have the equivalent effect for leaky modes of CPW on cylindrical substrates. The normalized phase constants β/k₀ in all figures are less than

unity, and this implies that this structure has a wide radiation region (α β≤ ≤k₀).

Frequency (GHz)

Fig. 3.12 The normalized propagation constants of different center strip widths ( b = 20 mm, h =0.508 mm, εr = 2.2, s = 5 mm, and w = 10, 8, and 6

Fig. 3.13 The normalized propagation constants of different slot widths ( b = 20 mm, h =0.508 mm, εr = 2.2, s = 10, 5, and 1 mm, and w = 10 mm).

Fig. 3.14 The proposed cylindrical coplanar waveguide leaky-wave antenna.

3.2.3 Design Example: A Cylindrical Coplanar Waveguide Leaky-Wave Antenna In this section, we design a cylindrical coplanar waveguide leaky-wave antenna.

The dielectric constant of the substrate ε_ris 2.2, and the thickness h is 0.508mm. The outer radius b is 80 mm, the center strip width w is 10 mm, and the slot width is 5mm.

Due to the odd-symmetry of longitudinal currents, two sets of inverted balanced lines [23] are fed into the CPW, as shown in Fig. 3.14. The length of the CPW antenna is 150 mm.

Fig. 3.15 plots the normalized propagation constants. Its radiation region starts at 9.5 GHz and extend to 16.0 GHz. The measured return loss is shown in Fig. 3.16. At 6, 7, and 8 GHz, the measured antenna gains are 6.8, 9.2, and 7.3 dBi, respectively. In addition, the measured antenna gains are 9.1, 9.4, and 8.5 dBi at 9, 10, and 11 GHz, respectively. In Fig. 3.17 and 3.18, the antenna mainbeams are fixed at the endfire direction. Both of CPW leaky-wave antennas and single-conductor leaky-wave antennas [23] have fixed mainbeams because their similar structures and current symmetries.

6 8 10 12 14 16

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Frequency (GHz)

Fig. 3.15 The normalized phase constants and attenuation constants.

Fig. 3.16 The measured return loss of the proposed cylindrical coplanar waveguide leaky-wave antenna.

-15 -10 -5 0 5 10

Fig. 3.18 The measured copolarization radiation patterns at 9, 10, and 11 GHz in the xz-plane.

Fig. 3.17 The measured copolarization radiation patterns at 6, 7, and 8 GHz in the xz-plane.

(a) (b)

Fig. 4.1 (a) The single-conductor strip line with the virtual PEC.

(b) The slotline with the virtual PMC.

Chapter 4 Broadband Leaky-Wave Antennas

This chapter mainly discusses planar broadband leaky-wave antennas. The slotline antenna is a complementary structure of the single-conductor strip antenna, whereas the inverted-T antenna is derived from the single-conductor strip antenna. All of these three types of structures can be very wideband antennas, due to their surface-wave-like leaky modes. A wideband slotline leaky-wave antenna with a microstrip-to-CPW feeding structure and an inverted-T leaky-wave antenna with simple ground plate are presented.

4.1 Slotline Leaky-Wave Antennas

The cross-sectional views of single-conductor strip leaky-wave antennas [23] and slotline leaky-wave antennas [36] and are plotted in Fig. 4.1. It is obvious that they are complementary structures. The center PEC and PMC represent odd-symmetry and even-symmetry for longitudinal currents, respectively. In this section, we focus on the slotline leaky mode and its corresponding feeding structure.

Frequency (GHz)

Fig. 4.2 The normalized phase constants and attenuation constants of slotlines and TM1 surface wave mode of grounded dielectric slab (w=0 case).

By using the spectral domain approach, we calculate the normalized phase constants and attenuation constants of the first higher leaky-mode of slotlines.

Moreover, slotlines belong to the structure plotted in Fig. 3(f) in Oliner's paper [37], which indicates the existence of leaky modes. The propagation constants of TM1

surface wave of grounded dielectric slabs [33] are also computed. When we compare these two different propagation constants in Fig. 4.2, it can be found that as the slot width decreases, the propagation constants of slotlines are approaching those of grounded dielectric slabs. Therefore, the first higher order leaky mode of slotlines may be treated as a guided surface wave propagating along the longitudinal direction of the slot. Since single-conductor strips are complementary structures of slotlines, the surface wave mode and the first higher leaky mode should have the similar relationship in single-conductor strips.

(a) (b)

Fig. 4.3 The proposed slotline leaky-wave antenna. (a) The top view . (b) The bottom view.

Since the radiation region of the slotline leaky mode is very wide, a broadband feeding circuit should be utilized to provide the required bandwidth. The broadband microstrip-to-CPW transition [24] is adopted to excite the first higher leaky mode of slotlines. Besiders, a section of tapered line is also combined with the microstrip-to-CPW transition.

Frequency (GHz)

5 10 15 20 25 30

Return Loss (dB)

-25 -20 -15 -10 -5 0

Fig. 4.4 The measured return loss of the slotline leaky-wave antenna.

The proposed slotline leaky-wave antenna shown in Fig. 4.3 has the following structural parameters: slot width is 10 mm, antenna length is 90 mm, the dielectric constant is 2.2, and the substrate thickness is 0.508 mm. Fig. 4.4 plots the measured return loss, and this antenna has a bandwidth about 14.7 GHz, starting from 11.8 to 26.5 GHz. The measured copolarization radiation patterns at 14 and 16 GHz are illustrated in Fig. 4.5, with antenna gains 8.9 and 10.1 dBi, respectively. In Fig. 4.6, the measured radiation patterns at 18 and 20 GHz are, with antenna gains 11.5 and 12.3 dBi, respectively. In Fig. 4.7, antenna gains at 22 and 24 GHz are 13.3 and 12.3 dBi.

The two mainbeams of upper and lower half-space are closer to each other as the frequency increases.

-15 -10 -5 0 5 10 15

Fig. 4.5 The measured copolariztion radiation patterns at 14 and 16 GHz.

-15 -10 -5 0 5 10 15

Fig. 4.6 The measured copolariztion radiation patterns at 18 and 20 GHz.

-15 -10 -5 0 5 10 15

Fig. 4.7 The measured copolariztion radiation patterns at 22 and 24 GHz.

4.2 Broadband Inverted-T Leaky-Wave Antenna

For the first higher order leaky mode in single-conductor strip leaky-wave antenna plotted in Fig 4.8(a), an infinite virtual PEC boundary is assumed at the center of the strip, in which the longitudinal currents are odd-symmetric and transverse currents are even-symmetric with respect to the center. From the image theory, the inverted-T leaky-wave antenna with infinite PEC boundary in Fig. 4.8(b) will have the same radiation characteristics for the y > 0 plane with that of the single-conductor strip leaky-wave antenna shown in Fig. 4.8 (a).

(a) (b)

Fig. 4.8 (a) The single-conductor strip leaky-wave antenna.

(b) The inverted-T leaky-wave antenna.

Since the inverted-T and the single-conductor strip leaky-wave antenna are equivalent in the half space, we first calculate the normalized propagation constants of the single-conductor strip leaky-wave antenna with the spectral domain approach.

Shown in Fig. 4.9 are the normalized phase constants and attenuation constants for the single-conductor strip leaky-wave antenna with the following structural parameters:

antenna width w_s=14 mm, the dielectric constant of the substrate ε_r=2.2 and the substrate thickness h=0.508 mm. The radiation region is from 6.6 GHz to 18.0 GHz, with the normalized phase constant remains almost a constant, which implies that the mainbeam will be fixed around the endfire direction.

To excite the first higher order leaky mode of single-conductor strip antenna in Fig. 4.8(a), a broadband feeding structure consists of two out-of-phase balanced microstrip lines that utilizes a broadband phase inverter [23]. However, only a finite conductor plate is needed for the inverted-T leaky-wave antenna, and the difficulty in design of the broadband phase inverter is removed.

We implement an inverted-T antenna shown in Fig. 4.10 with the antenna width w_a=7 mm, the antenna length L_a=100 mm, a substrate of dielectric constant ε_r=2.2 and the substrate thickness h = 0.508 mm. The half-width strip is mounted vertically over the conductor plate. A signal line is fed at the edge opposite to the plate, and the conductor plate is the ground. The measured return loss is plotted in Fig. 4.11. The bandwidth extends from 10.9 to 18.0 GHz, for a bandwidth ratio about 1.65:1.

Themeasured co-polarization radiation patterns in the xz-plane at 13, 14, and 15 GHz are shown in Fig. 4.12, with the measured gains 7.44, 9.48, and 10.58dBi, respectively. The mainbeam directions at these three frequencies are all around 66°

from the broadside direction. Fig. 4.13 plots the measured co-polarization radiation patterns in the xz-plane at 16, 17, and 18GHz, while the measured gains are 10.94,

11.71, and 10.94 dBi, respectively. The mainbeam directions at these three frequencies are close to 68° from the broadside direction.

The patterns of this antenna vary slightly from 13 to 18 GHz, and the shapes of the mainbeams are almost the same. For a single-conductor strip leaky-wave antenna, its mainbeam always keeps at the endfire direction. But the mainbeam of an inverted-T leaky-wave antenna is tilted from the endfire direction since the ground plate is not infinite.

Frequency (GHz)

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0.00

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

β/k₀ α/k0

Fig. 4.9 The computed normalized phase constants and attenuation constants

Frequency (GHz)

2 4 6 8 10 12 14 16 18

Return Loss (dB)

-25 -20 -15 -10 -5 0

Fig. 4.11 The measured return loss.

Fig. 4.10 The proposed inverted-T leaky-wave antenna.

-15 Fig. 4.12 Measured co-polarization radiation patterns at 13, 14 and 15 GHz in the

xz-plane. Fig. 4.13 Measured co-polarization radiation patterns at 16, 17 and 18 GHz in the

xz-plane.

Chapter 5 Conclusion and Future Work

This thesis studies the propagation characteristics of leaky modes on cylindrical substrates and broadband planar leaky-wave antennas. Two kinds of leaky-mode symmetries represented with PEC and PMC on both structures are analyzed by the full-wave method.

Three cylindrical types of transmission lines: microstrip lines, slotted coaxial lines, and coplanar waveguides are investigated. The effects on propagation constants under different structural parameters are presented. All of these leaky modes on cylindrical substrates have wide radiation regions. Feeding structures used in planar leaky-wave antennas, such as aperture-coupling and inverted balanced microstrip lines, are applied to excite the first higher leaky mode on cylindrical leaky-wave antennas successfully.

A broadband feeding structure, microstrip-to-CPW transition, is utilized for slotline leaky-wave antennas. From the measured radiation patterns, slotline leaky-wave antennas can have high gains in a wide bandwidth. Besides, a novel inverted-T leaky-wave antenna, which is modified from a single-conductor strip leaky-wave antenna, is developed and implemented. The feeding circuits are simplified by replacing the phase inverter by a finite ground plate.

However, there are still many issues that need to be further investigated in this thesis. These topics are listed in the following:

1. The creeping waves, the second or higher leaky modes on cylindrical substrates . 2. Mode-coupling between transmission lines on cylindrical substrates.

3. Implementation of slotted leaky-wave antenna on standard coaxial lines like

4. Better impedance matching circuits for planar and cylindrical CPW leaky-wave antennas.

5. More relationships between surface waves and leaky modes on slotlines and single-conductor strip lines.

6. Design of feeding structure of slotline leaky-wave antennas to obtain a leaky mode purity and reduce the sidelobes.

Appendix

The Green’s functions used in cylindrical microstrip lines are listed as following:

( )

The Green’s functions used in slotted coaxial lines are listed as following:

References

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IEEE Trans. Antennas and Propagat., vol 44, no. 8, pp. 1078-1085, Aug. 1996.

[2] Y.-D. Lin, J.-W. Sheen and C.-K. C. Tzuang, “Analysis and design of feeding structures for microstrip leaky wave antenna,” IEEE Trans. Microwave Theory and Tech., vol. 44, no. 9, pp. 1540-1547, Sep. 1996.

[3] T.-L. Chen and Y.-D. Lin, “Aperture-coupled microstrip line leaky wave antenna with broadside mainbeam,” Electronics Letters, vol. 34, issue 14,pp. 1366 – 1367, July 1998.

[4] Y.-D. Lin and J.-W. Sheen, “Mode distinction and radiation efficiency analysis of planar leaky-wave line source,” IEEE Trans. Microwave Theory and Tech., vol.

45, no. 10, pp. 1672-1680, Oct. 1997.

[5] T.-L. Chen, Aperture-Coupling Excitation and Mode-coupling Phenomena of Microstrip Leaky Modes, Ph.D. dissertation, National Chiao Tung University,

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[6] W. Hong, T.-L. Chen, C.-Y. Chang, J.-W. Sheen, and Y.-D. Lin, “Broadband tapered microstrip leaky-wave antenna,” IEEE Trans. Antennas and Propagat., vol.

51, no. 8, pp. 1922–1928, Aug. 2003.

[7] I. Jayakumar, R. Garg, B. Sarap, and B. Lal, “A conformal cylindrical microstrip array for producing omnidirectional radiation pattern,” IEEE Trans.

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