For many communication systems, it is preferable to operate in the circular polarization mode, where the trajectory of the tip of the E vector rotates about the propagation axis as a function of time. Such operation is the case for satellite and ground station antennas, since circular polarization (CP) operation removes the need to continuously align the two apertures, which would otherwise be required to maximize the
receive power. In addition, CP signals are not subject to the Faraday rotation effect [50], which causes the linear-field vectors to rotate as a consequence of interaction with static magnetic fields along the propagation path. Therefore, again, the polarization match between the antennas can be maintained without the use of complex tracking systems. A perfectly circularly polarized wave is generated by an antenna that simultaneously excites two orthogonal vectors of equal amplitude and in phase quadrature. Formal definitions for this mode of propagation are given in the IEEE Standard Test Procedures for Antennas [51], where the sense of polarization is given by the direction of the rotation of the vector describing a circle for an observer looking in the direction of propagation as shown in Figure 3-2-7.
Figure 3-2-7 Polarization ellipse
IF the complex voltage terms in the horizontal and vertical planes (or any two orthogonal cuts)EHandE are of equal amplitude and in phase quadrature, these terms V may be combined to express either the RHCP or LHCP wave components [52] as follows:
) quantities that are measured at each angleθ in the far field of the antenna, which source
horn orientated at anglesφ =0oandφ =90o as presented in Figure 3-2-8.
Figure 3-2-8 Antenna measurement setup for measuring polarization pattern
Besides, inserting above equations into estimating the two hands of polarization:
In each hand of polarization, the power can be expressed by
)
From our measurement of antenna polarization patterns, the definition of axial ratio can be modified from ( ) 20log( )
We will use the preceding formulas to predicate and simulate the polarization pattern as shown in Figure 3-2-9, and thus the simulated data will be also in comparison with the measuring results. This is the first time to present the polarization patterns by simulations.
Figure 3-2-9 Measurement of the polarization pattern
From above figure, we can observe that a practical antenna normally generates a desired reference polarization in addition to an undesirable cross-polar component, which is polarized in opposite hand. The reference and cross-polar spatial patterns can also be retrieved from an AR plot, which is generated using a linearly polarized spinning source antenna. This information requires the source horn to be continuously rotated about its axis (φ) while moving the antenna under test in azimuthal (θ ). The ripples in the polarization pattern are a consequence of the beam ellipticity, which occurs when a finite cross-polar component exists. Thus, the depth of the nulls defines the AR.
Chapter 3 Electric current excited CP slot antenna
In this research, we proposed several different circularly polarized slot antennas.
They are mainly divided into two different mechanisms which are electric current excitation and magnetic current excitation. In this chapter, only the CP slot antennas by electric current excitation are discussed, and the antennas by magnetic current excitation are presented in the next chapter.
3.1 Type 1
3.1.1 Antenna Configurations
The geometry of the proposed CPW-fed circularly polarized slot antenna is depicted in Figure 3-3-1. The substrate used an inexpensive FR4 dielectric substrate with a thickness of 1.6 mm, a relative permittivity of 4.4, and a loss tangent of 0.0245. In this suggested antenna, the lengths of L1, L2, L3, Lf are fixed to be 49 mm, 29 mm, 17 mm, 11mm respectively, and the widths of W1, W2, W3, W5, W6 are fixed to be 49 mm, 23 mm, 17 mm, 15 mm, 10 mm respectively. A 50 ohm CPW transmission line, having a protruded single strip of width Wf = 6.3 mm and a gap of distance g1 = 0.5 mm between the signal strip and the ground plane, is used to feed the proposed antenna. By adjusting the length of the protruded strip LC, the impedance matching of the slot antenna can be easily controlled, and its width of the protruded strip is fixed to be 1 mm. Besides, for the proposed antenna, an outer rectangular ring is printed on the center of the slot antenna, and it has a gap (g2) to excite circularly polarized radiation. If the gap is located at the lower-left corner of the rectangular ring, the slot antenna excites a left hand circular polarization (LHCP). However, if the gap is located at the lower-right corner, the slot antenna generates a right hand circular polarization (RHCP). From the empirical
experiences, the circumference of the midline of the outer rectangular ring is about 1.03λ (λ is the wavelength of operational frequency) for the sake of achieving the desirable operational frequency as the width of the outer rectangular ring is chosen to be 1mm. In order to improve the 3dB AR bandwidth and the impedance bandwidth, an inner rectangular ring has been implemented. The space between inner ring and outer ring is 1 mm, and the width of both rings is 1 mm.
3.1.2 Summary
The length of the protruded signal strip (LC) in the proposed antenna is varied and the influence on the impedance matching is investigated. Figure 3-3-2 shows the return loss against frequency for the proposed antenna with different signal strip length of LC = 9, 8, 7, 6, 5 mm when g2 =1.35 mm and L4 = W4 = 10 mm. It is apparent that as the length of LC decreases, the fundamental resonant frequency increases, and the return loss decreases and then increases. The minimum value of return loss occurs as LC = 7 mm. It presents a fundamental resonant frequency of 2.44GHz with a return loss of -40.93 dB, and has the impedance bandwidth of 880 MHz or 36.07% which is from 2.19 GHz to 3.07 GHz. Besides, from the analysis of AR against frequency with the variation of LC, the fundamental resonant frequency consisting with the frequency of minimum AR value only occurs in the condition of LC = 7mm. The return loss against frequency and AR against frequency for the proposed antenna with different ground size (W4, L4) as LC = 7 mm and g2 = 1.35 mm are demonstrated in Figure 3-3-3(a), Figure 3-3-3(b) respectively.
It is evident that the ground size has less influence on the fundamental resonant frequency, but has larger effect on the value of return loss. Besides, the ground size also affects the AR profile, and it is obvious that as W4 = L4 = 12, 11, 10 mm, the minimum AR value for the proposed antenna occurs at the frequency of 2.44 GHz. However, as W4 = L4 = 9, 8 mm, the minimum AR value occurs at 2.34 GHz and 2.24 GHz respectively, but they
does not meet the fundamental resonant frequency. In comparison with these different ground sizes, the proposed antenna with the length of L4 = W4 = 10 mm has the widest 3dB AR bandwidth of 420 MHz or 17.21% which is from 2.23 GHz to 2.65 GHz, the minimum AR value of 0.54 dB, and the fundamental resonant frequency of 2.44GHz.
Figure 3-3-4(a) and Figure 3-3-4(b) present respectively the return loss against frequency and the AR against frequency with different gap (g2) located at the lower- left corner of the outer rectangular ring as the length of L4 = W4 =10 mm and LC =7 mm. It is apparent that as the space of g2 decreases, both the fundamental resonant frequency and the return loss value decrease. As the space of g2 = 1.35 mm, the proposed antenna has the maximum 3dB AR bandwidth of 420 MHz or 17.21% which is from 2.23 GHz to 2.65 GHz within the impedance bandwidth (-10 dB return loss), and its minimum value of axial ratio is about 0.54dB at the frequency of 2.44GHz.
From above discussions, the best condition for the proposed antenna is the length of LC = 7mm, L4 = W4 =10 mm, and g2 = 1.35 mm. Figure 3-3-5 shows the axial ratio against elevation angle (θ) for the proposed antenna with different azimuthal angles of φ
= 0, 45, 90, 135 degrees. From Fig. 3.1.5, all of the 3 dB AR bandwidth for the proposed antenna at the four azimuthal angles is at least covered the range of θ from -30 to 30 degrees, and all of the AR values at the elevation angle of zero degree are below 1dB. It is obvious that the proposed antenna demonstrates very well performance of AR space distribution.
The radiation patterns against elevation angle and against azimuthal angle are shown in Figure 3-3-6 (a) and (b) respectively. From these figures, the proposed antenna presents good LHCP radiation, and shows omni-directional radiation pattern for all of the azimuthal angles. These good radiation characteristics are very attractive to modern wireless communication applications.
Figure 3-3-1 Geometry of the proposed CPW-fed circularly polarized slot antenna
1.0 1.5 2.0 2.5 3.0 3.5 4.0
-45 -40 -35 -30 -25 -20 -15 -10 -5 0
S11 (dB)
Frequency (GHz)
lc (mm) 9 8 7 6 5
Figure 3-3-2 Return loss against frequency for the proposed antenna with different signal strip length (L ) as the length of L = W = 10mm and g =1.35 mm
1.0 1.5 2.0 2.5 3.0 3.5 4.0
Figure 3-3-3 (a) Return loss against frequency and (b) axial ratio against frequency for the proposed antenna with different ground size (L4 = W4) as the length of LC = 10 mm, and g2 =1.35 mm.
1.0 1.5 2.0 2.5 3.0 3.5 4.0
Figure 3-3-4(a) Return loss against frequency and (b) axial ratio against frequency for the proposed antenna with different gap space (g2) as the length of LC = 10 mm, and L4 = W4
=10 mm.
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180
Figure 3-3-5 Axial ratio against elevation angle (θ) at the resonant frequency of 2.44 GHz for the proposed antenna with the different azimuthal angle as the length of LC = 10 mm, L4 = W4 =10 mm, g2 =1.35 mm.
-60
Figure 3-3-6 Radiation patterns on the (a) elevation plane and (b) azimuthal plane at the resonant frequency of 2.44 GHz for the proposed antenna as the length of LC = 10 mm, L4
= W4 =10 mm, g2 =1.35 mm.
3.2 Type 2
3.2.1 Antenna Configurations
The geometry of the proposed antenna is shown in Figure 3-3-7. The proposed slot antenna is realized on an inexpensive FR4 dielectric material with a thickness (h) of 1.6 mm, a relative permittivity (εr) of 4.4, and a loss tangent of 0.0245. The square slot of a side length of L2 was printed on a grounded substrate. A 50 Ohm CPW transmission line with a protruded signal strip is used to feed the proposed antenna. The 50 Ohm CPW feed has a signal strip of width Wf = 6.3 mm and a gap of distance g2 = 0.5 mm between the signal strip and the ground plane. The signal strip of the CPW is narrowed to have a width of Wp, and protrudes a length of Lc to connect with a square ring located at the center of the square slot. In this proposed geometry, CP radiation can be excited by using a gap (g1) at the lower left or lower right corner of the square ring. If the gap is located at the lower-left corner of the square ring, the slot antenna excites a left hand circular polarization (LHCP). Conversely, if the gap is located at the lower-right corner, the slot antenna generates a right hand circular polarization (RHCP). The most impotent design procedure to carry out the proposed CP slot antenna is to make a decision on the square-ring circumference, because the operational frequency mainly depends on the circumference of the square ring. In order to excite CP radiation, the square-ring circumference is designed to equal one effective wavelength on the substrate at the desirable operational frequency. However, in this condition, good CP radiation and good impedance matching of the proposed antenna cannot be achieved at the same time, though we maybe sacrifice AR performance to attain better impedance matching.
Therefore, many optimum simulations in this paper are conducted to obtain both of good CP radiation (the minimum AR value less than 1.5 dB) and good impedance matching (return loss less than -30 dB).
From many simulated results, better CP radiation and wider 3dB AR bandwidth can be obtained at the frequency of 2.45 GHz in this study as the square-ring circumference is about 1.15 λeff (λeff is the effective wavelength of the operational frequency within the coplanar waveguide structure) on the FR4 substrate used here. In addition to the square-ring circumference, the impedance of the proposed slot antenna can be matched at the desirable frequency by adjusting the length of the protruded strip Lc. If the square-ring circumference does not appropriately choose, the impedance matching only using the protruded strip is hard to match well.
3.2.2 Results and Discussions
The goal of this study was to develop a new CP square-slot antenna including a square ring with a gap on a grounded FR4 substrate of thickness1.6mm, relatively permittivity 4.4, dielectric loss tangent 0.0245, and grounded plane size 51 x 42 mm2. The geometrical parameters of the proposed slot antenna are designed at the operational frequency of 2.45 GHz.
In order to easily evaluate the circumference of the square ring related to the desirable operational frequency, several simulations on three different substrates which have the relative permittivity and thickness of (4.4 and 1.6 mm), (4.4 and 20 mm), and (9 and 1.6 mm) have been done by IE3D simulator, and the geometrical parameters of these slot antennas are listed and marked as Case1, Case 2 and Case 3 in Table 3.1. To simplify the comparisons between these cases, all of the simulations with respect to return loss and CP axial ratio are optimum to have the minimum values at the operational frequency of 2.45 GHz, and, in the proposed antenna geometry, the dimensions of W2, g1 and the width of the square ring are fixed to be 7 mm, 1.3 mm and 1 mm, respectively. The optimum goals in these simulations are the 3-dB AR value less than 1.5 dB at the angle of (0, 0) and the return loss less than -30 dB at the frequency of 2.45GHz. These three fixed
values obtained by many simulations can achieve good performances of return loss and axial ratio on the substrate used in Case 1. In Table I, these effective wavelengths (λeff) on different substrates at the frequency of 2.45 GHz are calculated by the software of LineGauge included in IE3D simulator. It can be seen that the circumferences of these square rings are about 1.15 λeff, 1.12 λeff, and 1.12 λeff for these three different substrates, respectively. The simulated results of return loss and axial ratio against frequency for these different substrates are shown in Figure 3-3-8 (a) and (b), respectively. Besides, if we introduce 1.12 λeff to the square-ring circumference in Case 1, we can also obtain good CP radiation and 3-dB AR bandwidth. However, the proposed antenna with the use of 1.15 λeff can obtain better antenna performances than that of using 1.12 λeff.
Besides, the geometrical parameters obtained from the optimum simulations on the substrate of FR4 at two different operational frequencies of 4 and 1.8 GHz are also listed and marked as Case 4 and Case5, respectively, in Table 3.2.1. It should be noted that the ratio of the square-ring circumference to the effective wavelength is also about 1.12 λeff at each case. The simulated results of axial ratio against frequency are shown in Figure 3-3-8(c). The AR values at their desirable frequencies have the minimum values (less than 1.5 dB) within their simulated ranges.
From above discussions, if the desirable frequency and the substrate parameters are known, we can use simulator to calculate the effective wavelength. Then, the square-ring circumference is equal to the effective wavelength multiplied by 1.12. Hence, the most important parameter affecting the response of the proposed antenna is decided. The further simulations need to be conducted to achieve the desirable response of the proposed antenna on different substrates or at different frequencies. It is worth noticing that the square-slot width and grounded plane width at the frequency of 1.965 GHz are about 36 mm and 50 mm based on our antenna designs and smaller than that presented in Ref. [53].
The influences of the protruded strip length (Lc) and the grounded plane width (W1) have also been simulated and discussed in the following. Figure 3-3-9(a) and Figure 3-3-9(b) show the simulated results of return loss and ratio axial against frequency with the different protruded signal strip lengths (Lc), respectively. With the increase of the protruded strip length (Lc), the frequency with the minimum return loss slightly increases when the length of Lc is in the ranges of 5 - 7 mm and 8 - 9 mm. However, there are large variations in frequency within the range of 7 mm to 8 mm. The 3-dB AR bandwidth and the frequency with the minimum AR value only slightly change with the variation of the length of Lc. Thus, the protruded strip length mainly affects the behavior of return loss, but slightly influences the axial-ratio response.
The axial ratio could also be affected by the substrate width. The grounded plane effect has been simulated with variation of grounded plane widths. The return loss and axial ratio against frequency with different grounded plane widths (W1) are demonstrated in Figure 3-3-10 (a) and (b), respectively. From simulated results, it can be seen that the grounded plane width has major influence on axial ratio response and has less effect on return loss. The frequency with the minimum return loss slightly increases as the decrease of the grounded plane width (W1) except for W1 = 38 mm. Besides, the impedance bandwidths with different grounded plane widths are almost the same. From Figure 3-3-10(b), it can be noted that the grounded plane effect has large influence on axial ratio response. With the increase of grounded plane width, the frequency with the minimum AR value increases. Both AR bandwidths of the proposed antenna with W1 of 40 and 42 are widest in the simulated results, but the antenna with W1 of 42 has better AR response than that with W1 of 40. Furthermore, from other simulations which did not show here, if the range of the gap width (g1) is between 1.1 mm and 1.5 mm, it does not nearly affects both of the impedance matching and CP radiation.
In order to present the antenna geometrical parameters with the best antenna
performances at the operational frequency of 2.45 GHz, many simulated results and optimum procedures have been done. Figure 3-3-11(a) and Figure 3-3-11(b) show the measured and simulated results of return loss and axial ratio against frequency, respectively, for the proposed antenna with the protruded strip length of Lc = 7 mm, the gap (g1) of 1.3 mm, the length of L3 = 24 mm, and the grounded plane width (W1) of 42 mm. The fundamental resonant frequency is about 2.45 GHz and 2.5 GHz for the simulated and measured results, respectively. The difference between the simulation and measurement results from the fabrication inaccuracy and measured error. From the measured curve in Figure 3-3-11(a), the proposed antenna has a fundamental resonant frequency of 2.5 GHz with the minimum return loss of -39.9 dB, and the impedance bandwidth of 460 MHz (or 18.4%) including the frequency from 2.28 GHz to 2.74 GHz.
In addition, Fig. 3.2.5(b) presents the measured bandwidth of 3-dB axial-ratio (AR) of 360 MHz or (14.4%) including the frequency from 2.28 GHz to 2.64 GHz, and the bandwidth of 1dB axial-ratio is about 100 MHz and the frequency from 2.42 GHz to 2.52 GHz. The minimum AR value occurs at the frequency of 2.5 GHz and is about 0.8 dB.
The circularly polarized radiation patterns against elevation angle with different azimuthal angles of phi = 0 and 90 degrees at the frequency of 2.45 GHz are simulated and demonstrated in Figure 3-3-12. As can been seen from Figure 3-3-12, the proposed antenna with a gap (g1) located at the lower left corner of a square ring demonstrates good LHCP radiations on both the azimuthal directions for the upper half free space. As we known, the slot antenna is a bi-directional radiator. Therefore, if we look at this antenna from the upper half free space, we can observe LHCP radiation. While we look at it from the lower half space, RHCP radiation can be observed. Figure 3-3-13 demonstrates this phenomenon.
Though this type of CP radiation pattern presented in Figure 3-3-13 can show the properties of circular polarization, it cannot be seen at a glance the space distribution of
the 3dB axial ratio. Hence, the measurement of polarization patterns in this study employs the rotating source method [54]. The measured results of polarization patterns at
the 3dB axial ratio. Hence, the measurement of polarization patterns in this study employs the rotating source method [54]. The measured results of polarization patterns at