The Radiation Far Field of the Antenna

A

fter the propagation constant (kz = βz-jαz) is determined by solving the dispersion root with the transverse resonance equation, we are now in a position to realize the radiation

characteristics of this leaky-wave antenna. First, we roughly estimate the angle of radiation main beam. It can be approximated and re-state equation (5) here:

ko

θ ≈sin⁻¹ β (34)

In addition to the radiation angle of the main beam, we can also calculate the radiation pattern by the equivalent sources in front of the shorted circuit of slot. From the equivalence principle, the equivalent electric- and magnetic- currents J_s and M_s over the slot can be expressed as equations (30) and (31), where is the unit vector in the direction normal to the surface of the slot,

nˆ

E and H are the electric and magnetic field on the slot. Assuming the presence of a baffle, which is an infinitely extended PEC plane, the equivalent electric current in front of this PEC plate will not radiate at all. As a result, the radiation pattern is only from the equivalent magnetic current, and is proportional the integration that is given as follows:

z wd z r M

r

r r jk

s L

o ′ ′

− ′

− ′

≈

∫

^exp(− ^{) ( )}

ϕ (35)

, r is the observation position vector, and r′ is the source position vector which is located at the z axis. And w is the width of the antenna slit, and L is the antenna slit length. We assume the field strength is uniform along the width direction of the slit. Since the magnitude of the magnetic current is proportional to exp(-jβ_zz)exp(-α_zz), it can be characterized as a traveling wave antenna. The parameter αL plays an important role in determining the amount of power leakage from this waveguide.

Figure 1. The leaky wave above a partially open waveguide.

k _z =β _z -jα _z

θ=sin ^-1 (β _z /k ₀ ) x=z cot θ

input power

θ x

z

Leaky Waves

Figure 2. A beam steering leaky-wave antenna for the airborne radar of B-29 bomber implemented in WWII by perturbation to the waveguide sidewall.

Moving waveguide side wall to change the propagation constant of TE₁₀ mode.

a

b

Antenna Slit

Slitted Rectangular Waveguide

x=0.5a-h t a b

s L

0.5a h

y

0.5t

x

Fig. 2(c) Structural parameters of the leaky wave waveguide antenna.

Figure 3(a). Structural parameters and the coordinate systems of the leaky waveguide antenna.

Figure 3(b) A slitted waveguide with bottom plate removed.

Figure 3(c) A slitted waveguide with bottom

plate removed, then adding the flanges at input

and terminated port.

Figure 3(d) A slitted waveguide with input and output ports.

Figure 3(e) A slitted terminated waveguide and

the placed dielectric slab on top of the metal block.

Figure 3(f) A beam steering slitted waveguide

leaky-wave antenna

Figure 3: (g) Front view of the leaky wave antenna (h) Equivalent transmission line network of the leaky wave antenna

k _x

^{( l)}

Z

^{( l)}

k _x ^{( d)} Z ^{( d)}

k _x

^{( r)}

Z

^{( r)}

^{G B}

t

x axis y axis

a

s b

h a/ 2

Figure 4 (a) Original electromagnetic fields with sources enclosed by a closed surface S.

Figure 4(b) Equivalent sources on S to produce equivalent electromagnetic fiels.

S

S

Null fields inside

E H

n

E H J M

E H

n

H n

J _s = ×

n

E

M _s = ×

CHAPTER3. FABRICATION, MEASUREMENT SETUP, AND COMPARISON BETWEEN EXPERIMENTAL AND THEORETICAL RESULTS

3.1 Fabrication of this Antenna and the Measurement Setup

T

he proposed beam steering leaky wave antenna consists of a slitted waveguide, a moveable dielectric slab, a feed flange and a termination flange has been already shown in figure 3(a).

The slitted waveguide is a Ku-band rectangular waveguide with two slits on the narrow walls of the rectangular waveguide. The slit used for the leakage of electromagnetic energy is located at the center of the narrow sidewall, at x = 0, with 1.5mm in width, and 125mm in length. Contrary to the slit for radiating the electromagnetic energy, a slit is cut in the opposite narrow sidewall of the antenna slit for moving a dielectric slab. To reduce the extra power leakage from this slit, the slit width is cut as narrow as possible. This slit is 125mm in length and 0.1mm in thickness (y=0 to 0.1 mm). A dielectric slab linearly tapered (triangular tapering with 2cm height) at both ends is mounted longitudinally on top of a thin (0.1mm thickness) rectangular (125mm length, 50mm width) plastic sheet. This sheet affects negligibly the electromagnetic field inside the waveguide. Moving this plastic sheet outside the waveguide moves the dielectric slab inside the waveguide also. This mechanism makes it possible to change the propagation constant of the dominated mode in the waveguide.

Thus, the radiation angle of antenna main beam can be steered to a desired direction.

Another version of mechanical setup to move the dielectric slab conveniently is to put the dielectric slab on a stationary metal block, then move the slitted waveguide (with the bottom wide plate removed also) on top of this metal block. This version of fabrication process is further demonstrated by the photographs shown from figure 3(b) to figure 3 (f). Figure 3(b) shows the slitted waveguide with its bottom plate removed, and figure 3(c) shows the flanges to add the above slitted waveguide. Figure 3(d) is already with the input port and the output port, where figure 3(e) is with an additional dielectric slab on top of the sliding metal block.

Figure 3(f) is the overall beam steering antenna with the sliding metal blocks attached.

3.2 Measurement Setup

As for the experimental setup, there is a PC-based controller with a built-in data acquisition board, a vector network analyzer (VNA), a two-stage cascaded Ku-band amplifier, an

anechoic chamber equipped with a turntable and a receiving horn antenna. Test frequency is selected at 15 GHz, though this antenna can be scaled to any desired operation frequencies with a careful re-design.

In conducting experiment, the PC-based controller drives the turntable, initializes VNA, and records the measured data. Amplifiers after VNA port1 amplify the received signal to compensate system loss due to system loss, including cable and path losses. The amplified output is coupled to the antenna mounted on the turntable in the chamber. Step-motor of the turntable is with an angle resolution of 0.9 degrees. Angular error due to alignment should be controlled much smaller than 0.9 degrees. At the time the antenna is radiating and rotating on the turntable, the receiving horn antenna in the chamber delivers the received RF signal to port 2 of the VNA, where the received signal strength is measured. The acquisition board collects the data of received power versus the angular position of the turntable. A post data processor in the controller is used to plot the antenna pattern.

Far field radiation pattern should be measured in the quiet zone of the chamber with a distance greater than that of Fresnel zone (2D²/λ), where D is the maximum length of the antenna under test. That corresponds to 156cm in the test requirement for the desired test antenna. However, at the time we tested the antenna pattern, we were constrained to do measurement in a chamber with limited Fresnel zone distance of 140cm. The antenna patterns of various perturbation conditions (a combination of variant dielectric constant, dielectric slab width, and position) are measured to verify the beam steering capability of the designed antenna in this thesis.

We have also developed a chamber calibration procedure by applying the Friis’s transmission formula and the Purcell’s method for antenna gain measurement. Before conducting the antenna gain test, we are thus able to know the quietness of our chamber first. The above calibration procedure for quality control of antenna gain measurement has been shown in [40].

3.3 Comparison between experimental and theoretical results

T

o demonstrate the beam-steering capability of the leaky-wave antenna, three examples described previously were employed to verify this mechanism. The structural parameters of

the antenna have been described above in the second section. The electrical length of the antenna slit is 6.25 λ, where λ is the operation wavelength. To reduce the reflection from the output port, the antenna was terminated with a matched load. This could further reduce the backward wave radiation.

After solving the propagation constants to the dispersion relation in equation (24), we obtained the distribution of propagation constant (k_z = β_z-jα_z) versus shift distance (h) of the dielectric slab. These plots were shown in figure 5-7 for case1, case2, and case3, respectively. And we summarized the results of all the three cases in figure 8. As shown in the inset in these figures, the shift distance of the moveable dielectric slab is defined as the distance from the center of the waveguide to the center of the dielectric slab. To avoid directly perturb the antenna slit, the dielectric slab was placed at the position from the central waveguide to its side wall opposite to the radiation slit, i.e. from x = -0.5a to x =-a+ 0.5t.

Since the electric field distribution of TE₁₀ mode within the waveguide is non-uniform, the maximum field strength is around the waveguide central part and the minimum field is at the edge. If the dielectric slab was placed around the center of the waveguide (x=-0.5a), it will strongly perturb the field distribution; and result in heavily perturbing its propagation constant (compared with the case without dielectric slab). Conversely, if the dielectric slab is positioned at the edge of the waveguide, it will (x=-a+0.5t) affect the field distribution lightly. Consequently, the normalized phase constant is close to that of the homogeneous waveguide (0.6972k_o).

In figure 5 to figure 8, the variation of normalized attenuation constant (αλ) versus the shift distance (h) for each of the previous three samples was shown, where the wavelength λ and waveguide width a are 20 mm and 15.68 mm, respectively. Since the attenuation constant determines the power leakage rate of the leaky-wave antenna, it facilitates us to estimate the radiation efficiency of this antenna. The variation of the attenuation constant will reflect in the level of power leakage. The numerical results showed that the maximum variation of attenuation constant was less than 14% for the second sample case.

Another factor affecting the radiation power is the impedance match at the antenna input port.

We have measured the return loss S11 at antenna input port for each case with various shift distances. The results showed that S₁₁ was decreased as the shift distance was increased.

Lower return loss occurs when the dielectric slab is located near the waveguide sidewall, where the electric field is comparatively weak. On the other hand, significant influence on

the return loss was observed as the dielectric slab was moved to the center of the waveguide, since the field strength is relatively strong and being perturbed by the dielectric slab in this region. In this experiment, the measured S11 at 15GHz was less than -12dB as the shift distance took the values from 0mm to 7mm.

The power leakage could be estimated using 1-e^-2αL, where α is the leaky constant and L is the antenna slit length. Note that, the leaky constant α depends on the slit width S of the antenna. By solving the dispersion relation in equation (24), we could obtain the phase and attenuation constant for a given slit width S. In figure 9, we calculated the function of antenna slit length (normalized to free-space wavelength) against power leakage (1-e^-2αL) for the three cases with slit widths S=1mm, 1.5mm and 2mm. Note that, the dielectric slab was placed at the position with h=4mm, where the attenuation constant was of minimum value.

This enables us to determine the minimum antenna length to meet a required power leakage specification. This analytical result showed that the wider the slit width the more the radiated power, which confirms the physical intuition. This figure provided us a criterion to determine the antenna slit length for a given percentage of radiation power.

To show the beam steering capability of the proposed antenna, far-field radiation pattern of the antenna at different shift distances of the dielectric slab was studied. The first dielectric slab used was the case1 dielectric sample described in the second section. The radiation patterns were measured with 1mm increment in shift distance. Results were taken, at eight shift distance values: 0mm to 7mm, as shown in figure 10 to figure 17.

The overall results in this case, both the MLTM and the experimental main beam radiation angles as functions of shift distance of the dielectric slab were summarized in figure 18.

Both the angular excursion developed in this case is 9.9^o according to the results.

Then, we moved to measure the far-field antenna radiation pattern at different shift distances for case 2 dielectric slab. The radiation patterns were measured with 1mm increment in shift distance, either. Results were taken, at eight shift distance values: from 0mm to 7mm, as shown in figure 19 to figure 26. We observed that the radiation angle can be continuously steered up to 23.4 degrees as the shift distance varies from 0mm to 7mm. The summarized results, both the Theoretical (MLTM) and the experimental main beam radiation angles as functions of shift distance of the dielectric slab, were collected in figure 27.

Figure 28 showed the antenna radiation patterns obtained by using the modal transmission line method (MTLM) and the experiment. Case2 dielectric slab was used, the relative dielectric constant and thickness (mm) of the dielectric slab are 2.55 and 1.62 respectively, and the shift distances h are 0, 4 and 7mm.

The last set of far-field radiation patterns of the antenna at different shift distances were studied using the case 3 dielectric slab. The radiation patterns were measured with the same 1mm increment in shift distance as the above measurements. Results were taken, at eight shift distance values: 0mm to 7mm, as shown in figure 29 to figure 36. In case3, the theoretical (MLTM) and the experimental main beam radiation angles as functions of shift distance of the dielectric slab, were summarized in figure 37. Theoretical angular scan as shift distance varied from 0mm to 7mm was 8.1^o, and the experimental one was 10.3^o.

For all the theoretical and experimental main beam radiation angles of the above three cases of dielectric slabs, we have summarized the results in figure 38. Note that the main beam radiation angles while shift distances are at h=7mm were close to 45^o (~sin^-10.6972), because the normalized phase constant is close to that (0.6972 ) of the homogeneous waveguide without the dielectric slab’s perturbation. Those measured radiation patterns shown in the above figures agree fairly well with those obtained by the theoretical (modal transmission line) method developed in this paper. In this radiation pattern measurement, the sweep angles φ were 0

ko

o to 360^o in an increment of 0.9^o, where the angle φ was counted from z-axis, as was depicted in the inset of each figure showed the radiation angle pattern. The antenna back-lobe level was 15dB below the main-lobe, so we neglect the back-lobe and only display the radiation pattern between 0^o to 90^o. In addition, the antenna side lobes of the radiation patterns were significant both in the measured and the theoretical results, since the antenna slit was simply rectangular without tapering. Observable difference between these side-lobe results was probably due to the imperfect environment of our anechoic chamber. However, the trend of the measured side-lobe agreed with the theoretical one. Besides, due to the limited far-field distance (1.4 meters) of the anechoic chamber, the antenna slit length operating in the frequency in this experiment was constrained. In all the above antenna pattern measurement, numerous results have been taken, all the measured radiation patterns agreed fairly well with the theoretical results.

Figure 38 showed the variation of theoretical and experimental radiation main-beam angle versus the shift distance of the three samples of dielectric slab given in the previous section.

The theoretical radiation angle was obtained by substituting the β /k_o in figure 8 into equation (34). In figure 38, it was observed that the second case has the maximum deviation in the phase constant. It caused the beam-steering angle to be up to 23.4^o. In the calculation of the theoretical phase constant, it was based on the assumption that uniform slit and dielectric slab are infinitely extended. In fact, the length of the slit and dielectric slab are finite. The discontinuities at both ends of the slit introduced some parasitic effects, such as the excitation of slot mode or cross-polarization. These effects were neglected in our theoretical analysis. Besides, precise alignment of the dielectric slab in its longitudinal direction must be carefully performed to approach the ideal case. These uncertainties may explain the differences between the theoretical and the experimental results in figure 9.

In addition to the experimental verification of an antenna design, we employed a three-dimensional electromagnetic simulation package based on Finite Integration Technique (FIT), to simulate such a leaky wave antenna. In figure39, antenna radiation pattern obtained by modal transmission line method, experimental test and Finite Integration Technique (FIT of CST Microwave Studio), using dielectric slab of case 2, and the shift distance of the dielectric slab are 0 and 7mm, respectively. We observed that when shift distance is 7mm, the angle difference of radiation main beam between the theoretical method in this paper and that of CST is 1.2^o, where it is 3.7^o for 0mm shift distance. Since the equivalent source on the aperture was assumed to be uniform along the width direction in our theoretical calculation, its radiation pattern may have difference compared with the FIT method. However, from the two numerical results, we found that there was only a slight difference between those two results, which proves that the assumption of uniform electric-field distribution is reasonable. Thus both these two numerical methods can be used to approve the antenna design before its fabrication. Note that, in this case, the computation resources needed in our method is considerably less than that of the FIT method.

Figure 40 depicted the variation of antenna efficiency and antenna gain against the shift distance (h) of the case 2 dielectric slab. The antenna efficiency was obtained by evaluating1−S₁₁² − S₂₁² , because that such a leaky-wave antenna could be regarded as a two-port device. Notably, the dielectric slab employed in this numerical simulation was assumed to be loss free. Therefore, the power loss for this two-port device was totally attributed to the radiation loss.

Besides, comparing figure 40 with figure 6, we found that they share the similar tendency of

variation. The smallest normalized attenuation constant occurred around h=4mm, which corresponds to the lowest antenna efficiency shown in figure 40. It was evidently to know that the larger the attenuation constant, the larger amount of power leakage from the waveguide. In addition to the antenna efficiency, we also calculated the antenna gain for the same antenna in figure 40. The variation of antenna gain against shift distance (h) was plotted in this figure. Observe that the antenna gain maintained a value between 12.5 dBi and 15 dBi for changing the position of the dielectric slab. This means that the antenna gain is not so sensitive to the variation of the position of dielectric slab. It also proved the reliability of the beam-steering mechanism developed in this research.

0 1 2 3 4 5 6 7 8

Shif t Distance h (mm)

0.7 0.8 0.9 1 1.1

β/ k 0

0.04 0.08 0.12 0.16 0.2

αλ

Figure 5. Normalized phase constants and attenuation constants as a function of shift distance using case 1 dielectric slab inside the leaky waveguide.

s

h a/2

0 1 2 3 4 5 6 7 8

Shif t Distance h (mm)

0.7 0.8 0.9 1 1.1

β/ k 0

0.04 0.08 0.12 0.16 0.2

αλ

Figure 6. Normalized phase constants and attenuation constants as a function of shift distance for case 2 dielectric slab inside the leaky waveguide.

s

h a/2

0 1 2 3 4 5 6 7 8

Shif t Distance h (mm)

0.7 0.8 0.9 1 1.1

β/ k 0

0.04 0.08 0.12 0.16 0.2

α λ

Figure 7. Normalized phase constants and attenuation constants as a function of shift distance for case 3 dielectric slab inside the leaky waveguide.

s

h a/2

0 1 2 3 4 5 6 7 8

Shif t Distance h (mm)

0.7 0.8 0.9 1 1.1

β/ k 0

0.04 0.08 0.12 0.16 0.2

αλ

case1 case2 case3

Figure 8. Normalized phase constants and attenuation constants as a function of shift distance for case 1, case 2 and case 3 dielectric slab inside the leaky waveguide.

s

h _a/

2

0 10 20 30 40 50 60 70 80 90 1

Percentage of power radiated

00 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

L /λ 0

h=4 mm

slit width=1 mm slit width=1.5 mm slit width=2 mm

Figure 9. Relationships of normalized slit lengths as a function of percentage of radiation power, the slit widths are 1, 1.5, and 2mm. The dielectric slab is case 2 and being placed at t h=4 mm.

h=4mm a/2

S

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Relati ve Receive d Powe r (d B )

_h

shift=0mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure10. Theoretical(MTLM) and experimental radiation

patterns of case 1 dielectric slab with relative dielectric

constant and thickness are 2.55 and 0.81mm respectively,

while shift distance h=0mm.

0 10 20 30 40 50 60 70 80

Radiation Angle φ (Degree)

⁹⁰

-30 -20 -10 0

Relati v e Rec e ived Power ( d B)

^h=1mmTheoretical

Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure11. Theoretical(MTLM) and experimental radiation

patterns of case 1 dielectric slab with relative dielectric

constant and thickness are 2.55 and 0.81mm respectively,

while shift distance h=1mm.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

R e la ti ve Re ce iv ed P o we r (d B)

^h=2mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

Figure12. Theoretical(MTLM) and experimental radiation patterns of case 1 dielectric slab with relative dielectric constant and thickness are 2.55 and 0.81mm respectively, when shift distance h=2mm.

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Rel a tive Received Powe r (d B )

h=3mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure13. Theoretical(MTLM) and experimental radiation

patterns of case 1 dielectric slab with relative dielectric

constant and thickness are 2.55 and 0.81mm respectively,

while shift distance h=3mm.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Relat ive Received Powe r (d B)

^h=4mmTheoretical

Experimental

0 10 20 30 40 50 60 70 80 90

Figure14. Theoretical(MTLM) and experimental radiation patterns of case 1 dielectric slab with relative dielectric constant and thickness are 2.55 and 0.81mm respectively, while shift distance h=4mm.

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Rel a tive R e ce ive d P owe r (dB )

^h=5mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure15. Theoretical(MTLM) and experimental radiation

patterns of case 1 dielectric slab with relative dielectric

constant and thickness are 2.55 and 0.81mm respectively,

while shift distance h=5mm.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Rela tive Received Powe r (d B)

^h=6mmTheoretical

Experimental

0 10 20 30 40 50 60 70 80 90

Figure16. Theoretical(MTLM) and experimental radiation patterns of case 1 dielectric slab with relative dielectric constant and thickness are 2.55 and 0.81mm respectively, while shift distance h=6mm.

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Rel a tive Received Power (d B)

^h=7mmTheoretical

Experimental

0 10 20 30 40 50 60 70 80 90

Figure17. Theoretical(MTLM) and experimental radiation patterns of case 1 dielectric slab with relative dielectric constant and thickness are 2.55 and 0.81mm respectively, while shift distance h=7mm.

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

0 1 2 3 4 5 6 7

Shift Distance h (mm)

20 25 30 35 40 45 50

Radiation A ngle (deg ree)

case1, MTLM

case1, experimental

Figure 18. Radiation angles of the leaky-wave antenna as the functions of the shift distances using case 1 dielectric slab.

Antenna radiation angles are obtained by modal transmission

line method and experimental tests.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

R e la tive Rece iv ed Power (d B)

^h=0mmTheoretical

Experimental

0 10 20 30 40 50 60 70 80 90

Figure19. Theoretical(MTLM) and experimental antenna radiation patterns using case 2 dielectric slab with relative

dielectric constant and thickness 2.55 and 1.62mm respectively , while shift distance h=0mm.

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Relative Received Power (d B)

^h=1mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

Figure20. Theoretical(MTLM) and experimental antenna radiation patterns using case 2 dielectric slab with relative

dielectric constant and thickness 2.55 and 1.62mm respectively , while shift distance h=1mm.

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Rel a tive R ece ived Pow e r (dB )

^h=2mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure 21. Theoretical(MTLM) and experimental antenna radiation patterns using case 2 dielectric slab with relative

dielectric constant and thickness 2.55 and 1.62mm respectively

, while shift distance h=2mm.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Relative Received Power (d B)

^h=3mmTheoretical

Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure 22. Theoretical(MTLM) and experimental antenna radiation patterns using case 2 dielectric slab with relative

dielectric constant and thickness 2.55 and 1.62mm respectively

, while shift distance h=3mm.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Relative Received Power (d B)

^h=4mmTheoretical

Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure 23. Theoretical(MTLM) and experimental antenna radiation patterns using case 2 dielectric slab with relative

dielectric constant and thickness 2.55 and 1.62mm respectively

, while shift distance h=4mm.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Relat ive Re ceived Pow e r (dB )

h=5mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure 24. Theoretical(MTLM) and experimental antenna radiation patterns using case 2 dielectric slab with relative

dielectric constant and thickness 2.55 and 1.62mm respectively

, while shift distance h=5mm.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Relat ive Re ceived Pow e r (dB )

h=5mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure 25. Theoretical(MTLM) and experimental antenna radiation patterns using case 2 dielectric slab with relative

dielectric constant and thickness 2.55 and 1.62mm respectively

, while shift distance h=5mm.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Relative Received Power (dB)

h=7mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure 26. Theoretical(MTLM) and experimental antenna radiation patterns using case 2 dielectric slab with relative

dielectric constant and thickness 2.55 and 1.62mm respectively

, while shift distance h=7mm.

0 1 2 3 4 5 6 7

Shift Distance h (mm)

20 25 30 35 40 45 50

R a dia tion A n gle (deg re e)

case2, Theoretical

case2, Experimental

Figure 27. Radiation angles of the leaky-wave antenna as the functions of the shift distances using the case 2 dielectric slab.

Antenna radiation angles were obtained by theoretical modal

transmission line method and experimental tests.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (degree)

-30 -20 -10 0

Relative R e ceived Power ( dB )

MTLM, h=0mm

Experimental, h= 0 mm MTLM, h=4mm Experimental, h=4mm MTLM, h=7mm Experimental, h=7mm

0 10 20 30 40 50 60 70 80 90

Figure 28. Antenna radiation patterns obtained by using the modal transmission line method (MTLM) and the experiment. Case 2 dielectric slab was used, the relative dielectric constant and

thickness (mm) of the dielectric slab are 2.55 and 1.62 respectively, and the shift distances h are 0, 4 and 7mm.

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

0 10 20 30 40 50 60 70 80 9

Radiation Angle φ (Degree)

⁰

-30 -20 -10 0

Rel a tive Re ce ive d Pow e r (dB)

h=0mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 9

Figure29. Theoretical (MTLM) and experimental radiation patterns using case 3 dielectric slab with relative dielectric constant and thickness 3.84 and 0.38mm respectively, while shift distance h=0mm.

0

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

R e la ti v e R e c e iv ed Powe r (d B)

^h=1mmTheoretical

Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

z-direction Antenna Slit

x-direction

Figure 30. Theoretical (MTLM) and experimental

radiation patterns using case 3 dielectric slab with

relative dielectric constant and thickness 3.84 and

0.38mm respectively, while shift distance h=1mm.

0 10 20 30 40 50 60 70 80 90

Radiation Angle φ (Degree)

-30 -20 -10 0

Rel a ti ve R ece ive d Powe r (dB)

^h=2mm

Theoretical Experimental

0 10 20 30 40 50 60 70 80 90

φ θ

Pin

φ=90ο−θ

Antenna Main Beam

Antenna Main Beam

在文檔中 波束可掃描之波導漏波天線設計－理論分析與天線製作量測 (頁 25-93)