附錄三
Hsing-Feng Chen
Department of Electrical Engineering, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan
Ken-Huang Lin
Department of Electrical Engineering, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan
Abstract
The antenna factor (AF) values are typically determined based on the assumption that the antenna is in free space.
In practice, the NSA and EMC measurements are often conducted in the presence of a perfectly conducting ground plane. The AF of bilog antenna used for measurement might be seriously affected by a ground plane. In addition, the variation of the active phase center of log periodic element can also induce variations in AF. In this paper, software codes based on method of moments are used to study the AF of a bilog antenna over a ground plane at different heights for both horizontal and vertical
polarizations. Meanwhile, the numerical analyses of the mutual coupling between antenna and its image, and the variation of the active phase center are also carried out.
Keywords
Antenna factor, bilog antenna, ground effect, mutual coupling, phase center, standard site method.
INTRODUCTION
Bilog antennas are widely used in radiated emission and normalized site attenuation (NSA) measurements for their broad frequency coverage from 30 MHz to 3 GHz. In general, an accurate antenna factor (AF) is highly desirable to obtain correct results in NSA or EMC measurements.
However, conventional measurements have used the same value of the AF provided by manufacturer for each
frequency regardless of the antenna height and polarization.
The AF values are typically determined based on the assumption that the antenna is in free space. In practice, the NSA and EMC measurements are often conducted in the presence of a perfectly conducting ground plane [1-3].
The AF of antenna used for measurement might be seriously affected by a ground plane especially in the frequency range below 300 MHz. It can therefore give rise to considerable errors and poor reproducibility in measurement results. The effects of ground plane on the AF for some broadband antennas, e.g. biconical and log periodic dipole array (LPDA) antennas have been investigated [4,5].
In this paper, we study the influence of the ground plane on the AF of a bilog antenna to gain some insight into the behavior of it. We categorize the ground plane influence into two types. First, the ground plane will affect the electromagnetic field by altering the magnitude and distribution of the incident field for a receiving antenna.
In such a case, the actual AF can deviate from the free
space one. Second, the mutual coupling between antenna and its image beneath the ground plane can result in the variation of antenna impedance when the antenna orientation is changed. These two types of effects can give rise to different AF values when the receiving antenna is scanned from 1 m to 4 m in height, or polarized
horizontally or vertically with respect to the ground plane [4].
In addition to the ground plane effects, the variation of the active phase center of log periodic element can also induce variations in AF. The fact that the active phase center changes with frequency leads to a shift in separation distance between the radiation and reception points.
Under this case, calculation of the AF in a fixed separation distance will introduce some amount of error [5].
To evaluate and minimize measurement uncertainties, these effects on the AF of bilog antennas should be thoroughly understood. In this paper, software codes based on method of moments are used to study the AF of a bilog antenna over a ground plane at different heights for both horizontal and vertical polarizations. Meanwhile, the numerical analyses of the mutual coupling between antenna and its image, and the variation of the active phase center are also carried out.
NUMERICAL MODEL OF A BILOG ANTENNA The bilog antenna used in this paper is Chase Bilog CBL6111B, which is approximately 79 cm long and 135 cm wide, with 17 pairs of dipole elements and a bow-tie part. The specified frequency range is from 30 MHz to 1 GHz. The numerical model of a bilog antenna used in the simulation is shown in Figure 1. This model is composed of 365 segments, and elements of antenna are connected each other by transmission lines. The scale factor τ and the spacing factor σ of LPDA elements are 0.865 and 0.06. The longest element length of LPDA is 75 cm. The bow-tie element has the flare angle 53°, the height of triangle 67.8 cm and the height of feed point 7.8 cm.
To validate the numerical model, the simulated values of AF are compared with the measured values provided by the manufacturer. The numerical models simulate the AF values of bilog antenna in two ways. One is the standard
site method (SSM) [2] and the other is the free space model.
In SSM model, the transmit antenna and receive antenna are identical pairs located above an infinite perfect electrically conducting (PEC) ground plane. The receive antenna is scanned from 1 to 4 m in height with a step size of 5 cm. The can be obtained from the standard site attenuation using the following expression:
SSM(dB) E field (dB⋅μV/m) at the receive antenna position during height scanning for a half-wave dipole (gain = 1.64) with 1 pW of radiated power. is the site attenuation.
max
ED
(dB) A
In free space model, the numerical simulation is done by placing a short dipole antenna a distance of 100 m away from the receive bilog antenna. To make an uniform field at the receiving antenna position, the transmit short dipole is chosen to be 4 cm long from tip to tip. The free space feed point of the receive antenna.
Ein
V
These simulated results of AF shown in Figure 2 and 3 are compared with the AF values provided by the manufacturer which were also measured by standard site method. There are differences between the simulated values of AFfree and those of AFSSM. The values of AFfree are obviously
Figure 2. Simulated horizontal AF using the standard site method
Figure 1. Numerical model of bilog
Figure 3. Simulated vertical AF using the standard site method
smaller than those of AFSSM above the frequency of 120 MHz. It is speculated that the differences could be mainly due to the non-dipole-like radiation pattern of the bilog antenna and some other possible effects of geometry specific. These effects are worthy of further investigation in a future study. Another difference exists between simulated AFSSM and the one provided by the manufacturer at the frequency range above 300 MHz may be due to the fact that the practical measured results include the effect of the balun, whereas the simulated ones do not. The rising trends of the AFSSM curves coincide with the measured one even though their difference is 4 dB. For the case of 3m separation distance, the range of AF curve’s change is larger than the one of 10m case. This is due to the effect of mutual coupling between the transmitting and receiving antennas. To identify the effects of the ground plane, AFfree
is used as the reference values. For analyzing the effect of active phase center variation, the AF error correction values with phase center correction are calculated. In fact, the AFSSM of d=10m which is less sensitive to the PC position’s variation can be use as the reference AF.
GROUND EFFECT ON ANTENNA FACTOR
The numerical experiment for ground effect is conducted in two conditions: (1) Calculating the uniformities of the incident field at different separation distance with a ground plane, and comparing the AF variation with the field uniformities to verify the correlation between them. (2) Calculating the input impedances of receive antenna at different height above a ground plane, and evaluating the relationship between mutual coupling and AF variation. As mentioned earlier, these two cases use the AFfree as their reference AF.
Figure 4. Field uniformity at d=3,4,5,10,50,and 100m distance along a 1.35m line at the boresight of a vertical point dipole placed 2m height above a PEC ground plane.
Figure 5. AF variation versus distance when the receiving vertical bilog antenna is placed at d=3,4,5,10,50, and 100m away from two point dipoles that emulating a vertical point dipole above a PEC ground plane.
Non-uniform Incident Field
To evaluate the field uniformity of incident E field, a dipole with a total length 4 cm is used as a transmitting antenna.
The point dipole, polarized vertically, is placed 2 m height above a PEC ground plane. The E field is calculated at some finite distance along an imaginary line of 135 cm (the physical size of a vertical bilog antenna) at the boresight of the point dipole. Figure 4 shows the field uniformity along
this line, where Emax/Emin is used to represent the field uniformity. To show the non-uniform field effect on the AF, a bilog antenna is placed where the field uniformity is tested. For preventing the calculated AF values from including any coupling effect between the bilog antenna and its image, the PEC ground plane is removed and another one transmitting point dipole is used as the image of the original one beneath the ground plane.
The AF variations shown in Figure 5 are obtained by subtracting AFfree from the AF values calculated under the condition of non-uniform field. The AF variation correlates to the field uniformity. However, their relation is not absolute proportional. During the frequency range above 120 MHz, the AF variation at a distance of 3 m is larger than that of 10 m, but the values of Emax/Emin (range of non-uniform field) for 3 m case is smaller. The AF variation at a distance of 3 m is smaller than that for the 5 m case at the frequency below 120 MHz, which is consistent with the results of [4]. For a horizontal polarization case, the AF variation is much smaller than the vertical case. In the standard site method, the way that a receiving antenna is scanned from 1 to 4 m can reduce the effect of non-uniform field.
Mutual Coupling with Ground Plane
The input impedance of a receiving antenna would vary with height when the antenna is placed above a PEC ground plane. For ANSI C63.5 standard site method, it requires that the receiving antenna is scanned in height (from 1 to 4 m) to get the maximum reception. It causes the AF measurement to be taken at different heights at different frequencies. In other words, the input impedance of the receiving antenna changes with the frequency during measurement. To evaluate the effect of mutual coupling with ground plane, a numerical simulation for the input impedance of a receiving bilog antenna at different heights above a PEC ground plane is carried out. Meanwhile, the AF values of the antenna under the same condition are also calculated. We place a point dipole excitation
at a height of 2 m and a distance of 100 m away from the receiving bilog antenna. The large separation distance of 100 m is to make sure that the incident field on the receiving antenna is a plane wave, that is, to remove the effect of non-uniform field.
Figure 6 shows the variation of input impedance for a horizontal bilog antenna. The AF variation refers to the free space AFfree is shown in Figure 7. For the case of height 1 m, the variation of AF is about ±2 dB. In comparing the two results, the trends of both variations are similar.
Furthermore, the number of oscillations and their frequency dependence also correspond to each other. The AF variation is obviously large at the frequency below 200 MHz which is the active range of bow-tie antenna. By contrast, the effect of mutual coupling with ground plane is smaller for higher frequency period. This is also consistent
with earlier results with biconical and LPDA antennas [4,5].
Similar analysis is also done for a vertically polarized bilog antenna. The AF variation is much smaller than the horizontal case.
Figure 6. Input impedance variation (%) of a horizontal biolg antenna at different heights above a PEC ground.
Figure 7. AF variation versus height for a horizontal bilog placed above a PEC ground plane.
PHASE CENTER CORRECTION
A bilog antenna consists of a LPDA and a bow-tie antenna.
In general, a measurement center of the bilog, almost located at the center position of antenna boom, is marked by the manufacturer to conveniently determine the separation distance between the transmitting and the receiving antennas. However, the active elements of this antenna move when the frequency sweep, which causes the phase center (PC) to change with frequency. PC of antenna is defined as the location from which radiation is considered to emanate. Under the condition of PC variation with frequency, to measure the AF of bilog at a fix separation distance in SSM must introduce some amount error. On the other hand, if the location of PC is exactly known or predicted, the correct distance can be used to gain a correct AF.
Figure 8. Phase center of the bilog antenna In this paper, the PC of bilog antenna is calculated by the method called a variation of the “center of minimum phase variation” [5]. According to the formula it provides, we obtain the PC of bilog antenna shown in Figure 8. The curve of PC position shows an unexpected trend at the frequency period after 600 MHz. By checking the current distribution along the boom of antenna, we find that the bilog antenna has more than one active region during the frequency period from 600MHz to 1 GHz. Once the PC positions are known, the exact distance between transmit and receive antennas can be determined. We apply the PC correction for calculating AF in SSM, and the results are shown in Figure 9 and 11. The AF error correction values are also calculated, shown in Figure 10 and 12. Most of the AF error correction values for horizontal and vertical polarization are within ± 2 dB, except the horizontal case at d = 3 m, h1 = 1 m. In comparing Figure 1, 2, 9 and 10, the horizontal AF values with PC correction are obviously coincide with each other in the frequency range below 300 MHz. However, there still exist unexpected results at higher frequency for both polarizations. The possible error due to the effects such as radiation pattern error, near field coupling and cross-polarization are not considered in this paper. It requires a further investigation in the future study.
CONCLUSION
Software codes based on a method of moments are used to numerically determine the antenna factor of a bilog antenna.
To evaluate the effect of ground plane on AF, numerical analyses for the variations of AF due to non-uniform incident field and mutual coupling with ground plane are implemented. These results indicate that the variations of AF correlate closely with the ground plane. To analyze the influence of PC’s change with frequency, the phase center of bilog antenna is calculated and the AF errors of PC correction are also obtained. These results of analysis can be involved to gain a more correct measurement when a bilog antenna is used for EMI and NSA measurement.
Figure 9. Simulated horizontal AF with phase center correction
Figure 10. Horizontal AF error of phase center correction
Figure 11. Simulated vertical AF with phase center
correction
Figure 12. Vertical AF error of phase center correction
REFERENCES
[1] ANSI C63.5-1988 American National Standard for electromagnetic compatible-radiated emission measurements in electromagnetic interference (EMI) control-calibration of antennas (9 kHz to 40 GHz), American National Standards Institute, New York, 1988.
[2] A. A. Smith Jr., “Standard-site method for determining antenna factors,” IEEE Transactions on Electromagnetic Compatibility, vol. 24, no. 3, August 1982, pp. 316-322.
[3] A. A. Smith Jr., R. F. German, and J. B. Pate,
“Calculation of site attenuation from antenna factors,”
IEEE Transactions on Electromagnetic Compatibility, vol. 24, no. 3, August 1982, pp. 301-316.
[4] Z. Chen and M. D. Foegelle, “A numerical investigation of ground plane effects on biconical antenna factor,” in Proceedings of the 1998 IEEE International Symposium on EMC, pp. 802-806.
[5] Z. Chen, M. D. Foegelle and T. Harrington, “Analysis of log periodic dipole array antennas for site validation and radiated emissions testing,” in Proceedings of the 1999 IEEE International Symposium on EMC, pp.
618-623