4.1 Motivation
In the previous chapter, we have designed a TEM horn antenna that has ultra-wideband characteristic. In this chapter, we want to develop design criterion for fabricating TEM horn antennas meeting the specification. Because the computation by FEM method should be performed within a finite volume, air box and perfect matching layer boundary condition are required to truncate the infinite volume into a finite one. The distance between boundaries of the air box and antenna should be at least quarter wavelength corresponding to the operational frequency. However, since the ratio of maximum to minimum frequency is usually large for ultra-wideband antennas, the dimension of air box set for the lowest frequency will be too large compared with its highest frequency. Then the computation time will be excessively long for full band simulation. Although we can divide the entire frequency band into several sub-bands and utilize the bisection characteristic for the symmetrical feature of this antenna to reduce the computation time as being done in the previous chapter, it is not efficient for characterizing the radiation characteristic of this antenna by full-wave simulation, since there are too many structural parameters should be changed to see this influence. Thus, in this chapter, we will concentrate ourselves on the studies of radiation beam pattern based on the empirical model of the aperture field and invoking the equivalence principle. Since the
empirical formula does not contain the effect of several parameters, such as the transition length, flare angle and etc. on the aperture field distribution, this may be the main problem resulting the errors between the measured and calculation results for a few extreme cases, which will be become clear later on.
4.2 Design considerations
Since full- wave simulation is no longer utilized to predict the behavior of antennas, we should make certain that the antenna could maintain its radiation for a ultra-wideband. At the feed point, we use the same feeding structure shown in chapter 3 to guarantee the matching at the input end. On the other hand, since we can regard the cross section of the aperture as a parallel plate waveguide, then the characteristic impedance for parallel waveguide can be written as follows.
wη
Z = d (4. 30)
where d and W are the separation distance between two metal plates and the width of metal plate, respectively.
Since the wave impedanceη of air is roughly equal to377Ω , the d
W ratio is set to be unity that the aperture of an antenna is matched to free space. Therefore, with the given distance between two plates at the feed point, the separation at the aperture can be determined from the desired antenna length and flare angle. The corresponding plate widths are then equal to their separation. In the next step, we study the effect of the antenna length and flare angle on the antenna performance. The Matlab program based on the equivalence principle
described in chapter 2 will also be developed to obtain the design reference before implementing the antenna.
4.3 Effect of antenna length on the radiation characteristics
The first three cases demonstrate the variation of H-plane radiation pattern and operational bandwidth for various antenna lengths and constant flare angle. In general, we observed that the measured H-plane pattern agrees with computation by equivalence principle under the condition of smaller flare angles. Therefore, firstly we fixed the flare angleα to
and varied the antenna length from 50mm to 100mm with 25mm increment. The measured return loss for these three antennas is shown in Fig. 4.1. Evidently, the antennas fabricated based on the design procedure described in the previous section exhibit ultra-wideband characteristic. For example, the antenna with 50mm length has the widest bandwidth more than 18GHz, while the one with 100mm length can extend to the lower frequency.
30°
The comparison of measured and calculated H-plane patterns at 7GHz for these three cases are shown from Fig. 4.2 to 4.4. In these figures, one could observe that the 3dB beamwidth decreases as the increase in the antenna length. Besides, the back lobes for the three cases are -7dB, -13dB and -18dB, respectively. The back lobe level is considerable for small size antennas. This is because, for a given flare angle, the impedance mismatch is obvious for the case of small antenna length, thus, the incident power will directly reflected and produce a strong radiation in the backward direction. On the contrary, the antenna for 100mm long has lower back lobe, below -15dB. In a word, though the short antenna has the wide bandwidth, the long antenna has small back lobe level. These figures also verified again that the measured radiation patterns are in considerable agreement with those calculated
according to equivalence principle. Although the approximation method is hard to predict the side lobe level, however, the side low levels for all cases in our experiments are lower than -15 dB. Thus, it affects the radiation characteristic inconsiderably. Therefore, the program developed in this thesis is able to predict radiation pattern prior to fabricate the antenna, therefore, it further reduces the time consuming for cut-and-try.
4.4 Effect of flare angle on the radiation characteristics
In chapter 3, we have designed a TEM horn antenna with flare angle and 50mm length. As mentioned in that section, the measured return loss consisted very well with computation based on Ansoft HFSS simulation tool. However, the approximated radiation patterns using equivalence principle coincide with measured ones only within a small range of elevation angle (
75°
≤20
θ ). The disagreement becomes apparent especially for the high frequency range of operation. However, for all the three examples with a flare angle in the preceding section, the equivalence principle could well predict the radiation pattern in both amplitude and shape as shown in Fig.3.2 ~ Fig.3.4. From these figures we may conjecture that the factor determining the accuracy of approximation is the flare angle.
Therefore, it is needed to explore the accuracy of this approximation for engineering design in practice.
30°
On the other hand, it is also necessary to examine the variation of radiation characteristics for various flare angles while the antenna length is fixed. In this section, several experiments were carried out to demonstrate how the radiation behavior varies with different flare angles. Since the antenna with a 100mm in length in the preceding section exhibits low back lobe, the antenna length was fixed at 100mm and the flare angle was
increased progressively from30°to60°with15°increment to measure its radiation pattern.
The measured H-plane pattern at 7 GHz for three different flare angles are respectively shown in Fig.4.4, 4.5, and 4.6. It could be seen that calculated radiation patterns agree with that by measurement for the two cases ofα=30°and45°. For all frequency within the bandwidth, we will obtain the same good agreement. But for the case with a flare angle of , the measured pattern is much wider than the computed one. The inconsistence between measurement and calculation will become obvious for higher frequency range, as shown in Fig.3.7. The reason for this deviation could be inferred as follows. In chapter 2 we assumed the field distribution on the aperture to according to equation (2.19)-(2.20) and zero outside the aperture. Based on the experiment studies, we observed that the empirical formula is valid for the flare angle small than . As the flare angle increases, the separation changes accordingly. Under this condition, the approximated aperture field distribution is no longer valid. Moreover, the edge diffraction effect might be obvious in the situation such that the assumption of zero fields outside aperture remains to be modified. This diffraction has significant effect on its radiation as shown in Fig. 4.6.
60°
45°
In generally speaking, the H-plane 3dB beamwidth decreases as the flare angle increases.
We have plotted the half-power beamwidth as a function of flare angle at 7GHz, as shown in Fig.4.7. Similar figures can also be obtained for arbitrary antenna lengths and frequencies. An improvement of this figure can be made by representing the antenna length in its electrical length and then we can obtain this new figure as shown in Fig. 4.8. However, for a given length, the antenna exhibits a monotonic decrease in 3dB beamwidth up to a certain flare angle. Beyond that point an increase in beamwidth is observed. It can be accounted for the broadening in the main beam as shown in Fig. 4.6.
0 2 4 6 8 10 12 14 16 18 Frequency(GHz)
-45 -40 -35 -30 -25 -20 -15 -10 -5 0
S11(dB)
L=50mm L=75mm L=100mm