Comparison between Three-Antenna Method and Equivalent Capacitance Substitution Method for Calibrating Electrically Short Monopole Antenna
Masanori Ishii, Satoru Kurokawa, and Yozo Shimada National Institute of Advanced Industrial Science and Technology, National Metrology Institute of Japan, Radio-Frequency and Fields Section, Electromagnetic Waves Division AIST Tsukuba Central 3, 1-1-1, Umezono, Tsukuba, Ibaraki 305-8563, Japan [email protected]
Abstract—In low-frequency bands, monopole antennas are it can be used for measurements of the antenna factor of a generally used for measuring the electromagnetic interference monopole antenna with a high degree of accuracy. (EMI) and estimating the electric field strength. The antenna factor is an important and widely studied characteristic. Thus far, there have been a number of measurement methods proposed for II. DEFINITION OF ANTENNA FACTOR electrically short monopole antennas. A case in point is the Electric Field equivalent capacitance substitution method, which is commonly Transmission Line used for monopole antenna measurements. On the other hand, fE )( we have proposed a near-field three-antenna method for Plane Wave Z electrically short monopole antennas. These two absolute L Z 0 measurement methods are of quite different origins. In light of 0 fV )( this fact, a comparison is made between the two measurement Output Voltage Infinite Grand Plane methods by means of experiments and simulations, and the Monopole Antenna System difference observed between the antenna factors is discussed.
Z 0 : Line impedance Z : Load impedance I. INTRODUCTION L f : Frequency In the fields of electromagnetic interference and electromagnetic compatibility, it is important to measure the Fig. 1. Definition of the antenna factor of a monopole antenna. strength of the electric field originating from electric devices. For this purpose, knowledge of the antenna factor of a For the purpose of this comparison, an electric-wave receiving antenna is necessary. In this paper, we discuss two receiving system with a monopole antenna shown in Fig. 1 is different measurement methods for monopole antennas in considered. It consists of a monopole element, a coupling low-frequency bands. circuit, a transmission line, and a matched-load to the Thus far, various methods have been proposed and characteristic impedance of the transmission line (50 Ω). The investigated for measuring the antenna factor of a monopole antenna factor of a monopole antenna is defined as the ratio of antenna. These methods include standard field methods [1] [2] an incident plane electric field to the corresponding output [3], the equivalent capacitance substitution method [4] [5], voltage across the matched load [7]. The antenna factor and the three-antenna method [6]. naturally depends on the frequency. Consequently, the Among these methods, the equivalent capacitance antenna factor AF is expressed as follows: substitution method is the most well-known and commonly used method for monopole antenna measurements. In a E f previous paper, we have proposed a near-field three-antenna AF f , (1) method [6] for electrically short monopole antennas. These Vf0 two absolute measurement methods have quite different origins. Therefore, a comparison between the two where E is the electric field of the electromagnetic plane measurement methods is of great interest. Furthermore, it is wave incident on the antenna element, and V is the output expected that the comparison can contribute to the validation 0 voltage across the matched load. Ιn other words, the antenna of the two measurement methods. In particular, the equivalent factor is defined under the far-field condition. capacitance substitution method needs to be improved before
978-1-4577-0811-4/11/$26.00 ©2011 IEEE 101 EAR FIELD HREE ANTENNA ETHOD III. N - T - M (NF-TAM) [6] proposed in [8] is used. In other words, Zmn is obtained Under near-field conditions, the electric field has a through the electromotive force method (EMF). distribution parallel to the monopole antenna’s element. This We have proposed this NF-TAM for short monopole means that the strength of the electric field applied to the antennas [6]. However, the equivalent capacitance substitution antenna element is ambiguous. As a consequence, under near- method is more commonly used. Therefore, it is necessary to field conditions, it is difficult to define E in (1). In order to draw a comparison between the two methods. cope with this problem, we introduced the averaged electric field strength ( Eavg ) estimated on the basis of the mutual IV. EQUIVALENT CAPACITANCE SUBSTITUTION METHOD impedance between two monopole antenna elements. The (ECSM) [4] [5] proposed near-field three-antenna method is expressed as follows: In the NF-TAM, an electromagnetic wave is actually transmitted between two monopole antennas, and the antenna E factor is obtained on the basis of the transmission S-parameter avg measured by a vector network analyzer. In standard field AFei V0 methods [1] [2] [3], a monopole antenna is irradiated with electromagnetic waves generated by a transmit antenna, a AZZKK jk ij ki ij ki , (2) TEM cell, a G-TEM cell, a large strip line, and so on. AAij ki ZZ L jk K jk The ECSM is the most commonly used measurement method for electrically short monopole antennas. It does not ijk, , 1, 2, 3 , 2, 3,1 , 3,1, 2 , require the generation of an electromagnetic field in an open where field. Therefore, the ECSM is considered to be a very simple l m sin zlkj exp jkr measurement method. Z 0 m [ A Specifically, as a first step, the effective length of the mn 0 m sinsin8 klkl n rA monopole antenna is given according to the following exp jkr exp jkr equation: B cos2 kl 0 dz,] r n r B 0 h , (3) 2 he = tan A n zldr , 2
2 zldr , B n where is the wavelength, and h is the length of the 22 monopole antenna element. 0 zdr , Since the target frequency band is below 30 MHz, the monopole antenna works as an electrically short monopole nm ,1,3,3,2,2,1, antenna. Subsequently, the antenna impedance of the and monopole antenna is estimated on the basis of the capacitance 2 sinsin2 klklk between the monopole antenna element and the infinite K p q , ground plane. The equivalent capacitance is expressed as pq kl cos1cos1 kl p q 2 h qp .1,3,3,2,2,1, tan 55.6h C = , (4) a 2h 2 h In these equations, AF is the antenna factor of a ln 1 ei a monopole antenna; k is the wave number; AA 2312 ,, and A31 are the transmission S-parameters between monopole where a is the average radius and h the length of the antennas; is the free space wave impedance; Z is the monopole antenna element. 0 L Figure 2 shows a schematic diagram of the typical load impedance matched to the transmission line (50 Ω); configuration for the ECSM. The ECSM requires a capacitor ll ,, and l are the lengths of the monopole antennas (1 m); 21 3 with an appropriate value of capacitance Ca , obtained by and d is the distance between two monopole antennas. The means of (4). The capacitor is directly connected to the input terminal of the monopole antenna, i.e., where the monopole mutual impedance is denoted as Z mn . It should be noted that when the mutual impedance is calculated, the antenna element antenna element would normally be attached, as shown in Fig. is considered and dealt with as one segment. The current 2. distribution on both antenna elements is assumed to be sinusoidal. For the calculation of the integral in (2) the method
102 V Coax T-connector D results of the two methods differ from each other from approximately 0.8 dB to 2.0 dB. SG (50 ) Receiver 1 (50 ) Our next step is to investigate the origin of the difference C a between the NF-TAM and the ECSM. Equivalent capacitor Antenna input terminal Antenna Factor [dB(1/m)] V 100 Base unit of Antenna output L (50O系) monopole antenna 90 Receiver 2 (50 ) 80 NF-TAM Fig. 2. Schematic of the ECSM. 70 ECSM
60 With a coaxial T-connector the direct voltage (VD ) can be 50 measured with 50-Ω load applied to the output of the 40 monopole antenna and then, when the output voltage (VL ) is measured, the 50-Ω load is connected to the output from the 30 T-connector so that the source always sees the same 20 impedance; this ensures that the input voltage to the capacitor 0 5.0 10.0 15.0 20.0 25.0 30.0 is stable. Once these two voltages are measured, the antenna Frequency [MHz] factor of the monopole antenna is given by the following Fig. 3. Measured antenna factor of a 1.15–m-long passive monopole antenna expression: by the NF-TAM and the ECSM.
V AF=20log D . (5) VI. COMPARISON OF THE ANTENNA FACTOR OBTAINED BY THE VhLe NF-TAM AND THE ECSM THROUGH NUMERICAL
SIMULATION V. COMPARISON OF ANTENNA FACTOR OBTAINED BY THE NF- Through a numerical simulation, we can calculate the TAM AND THE ECSM BASED ON EXPERIMENTAL RESULTS antenna factor of a passive monopole antenna by both the NF- We have carried out measurements using a 1.15–m-long TAM and the ECSM. The ideal antenna factor can also be simple passive monopole antenna by both the NF-TAM and obtained easily. In this section, we will compare the results. the ECSM. The NF-TAM was performed for three monopole A. Antenna Factor Estimated by the NF-TAM and the Ideal antennas of the same length on an open area test site with Antenna Factor Derived from Numerical Simulations dimensions 30 m × 50 m. The distance between the antennas was 1.5 m, and the frequencies exceeded 1 MHz. The We have obtained the antenna factor of a monopole antenna sensitivity of passive monopole antennas is very low in low on an infinite ground plane by the NF-TAM. In [6], the frequency bands. Therefore, the distance was reduced to 0.5 m antenna factor of a 1.0-m-long monopole antenna has been for the frequencies below 1 MHz. On the other hand, the calculated. In this paper, we recalculated the antenna factor of ECSM is applied to one of the three monopole antennas using the 1.15-m-long monopole antenna. In addition, using the a vector network analyzer and a capacitor with a capacitance moment method, we were able to obtain the ideal antenna of 10 pF. This time, we did not fabricate a capacitor box for factor of the 1.15-m-long monopole antenna, as shown in Fig. the ECSM. Generally, the capacitor required by the ECSM 4. and the monopole antenna can be obtained together from the Monopole antenna same production company. The measurement results of the 1.15–m-long passive Eplane E monopole antenna are shown in Fig. 3. The antenna factor AF plane obtained by means of the NF-TAM was compared with the idea l V result obtained by the ECSM in Fig. 3. The frequency ranged Infinite ground plane out Vout from 9 kHz to 30 MHz. 50 In Fig. 3, the observed difference between the two Fig. 4. Ideal antenna factor of a passive monopole antenna obtained by the measurement methods ranges from approximately 0.6 dB to moment method. 2.4 dB,. That is to say, the difference is larger at the higher frequencies and the maximum corresponds to the highest frequency (30 MHz). It becomes clear that there are B. Antenna Factor Obtained by the ECSM and Numerical differences between the NF-TAM and the ECSM. In [9], a Simulations comparison is made between the ECSM and a standard field The equivalent circuit of a passive monopole antenna is method applied to a G-TEM cell. It is also shown that the shown in Fig. 5, where Vo is the open circuit output voltage;
103 Z , the input impedance of the antenna; Z , the matched- Therefore, this result shows that we need to further investigate in L the origin of the difference between the antenna factors load to the characteristic impedance of the transmission line obtained by the NF-TAM (or the ideal antenna factor) and by (50 Ω); and VL , the output voltage across the load impedance the ECSM through numerical simulations using the moment ( Z ). method. L In the next section, we will investigate the origin of the Zin difference observed in Figs. 6 and 7. Hereafter, the ideal antenna factor will be used (instead of the NF-TAM), because the ideal antenna factor and the antenna factor obtained by the Z Vo VL L NF-TAM are in good agreement, as shown in Figs. 6 and 7.
Antenna Factor [dB(1/m)] Fig. 5. Equivalent circuit of a passive monopole antenna. 100 90 In the case of the ECSM, the impedance of an antenna 80 Ideal antenna factor element is estimated on the basis of the capacitance between 70 the antenna element and the infinite ground plane. When the NF-TAM ECSM ECSM is performed for a passive monopole antenna (without 60 50 amplifier), the antenna impedance Zin is expressed as follows: 40 30 1 Z = . (6) 20 in jC 0 5.0 10.0 15.0 20.0 25.0 30.0 a Frequency [MHz]
Fig. 6. Antenna factor of a 1.15-m-long passive monopole antenna calculated Ca is obtained using (4). On the other hand, the open circuit by the NF-TAM and the ECSM as compared to the ideal antenna factor. output voltage Vo is expressed as follows: Difference [dB] 1.5 VEhoe=- . (7) 1
he is obtained using (3), and E corresponds to the incident 0.5 plane electric field to the monopole antenna. Finally, the antenna factor of the monopole antenna given by the ECSM 0 through simulations is expressed as follows: -0.5 NF-TAM － Ideal antenna factor E Z Z ECSM － Ideal antenna factor = Lin. (8) AFe -1 VhZLeL
-1.5 The results of the three simulations are shown in Fig. 6. The 0 5.0 10.0 15.0 20.0 25.0 30.0 frequency ranges from 9 kHz to 30 MHz. The differences in Frequency [MHz] the values are made more evident through a detailed Fig. 7. Differences between the antenna factor of a 1.15-m-long passive evaluation, as shown in Fig. 7. In Figs. 6 and 7, we can monopole antenna calculated by the NF-TAM and the ECSM and the ideal observe differences between the results obtained by the ECSM antenna factor. and the NF-TAM through numerical simulations as well as experiments. The differences range from approximately 0.9 dB to 1.3 dB. The difference is larger at the higher frequencies, VII. STUDY ON THE DIFFERENCE BETWEEN THE ANTENNA and the maximum value is observed at the highest frequency FACTOR OBTAINED BY THE ECSM AND THE IDEAL (30 MHz). It is evident that there is a difference between the ANTENNA FACTOR results obtained by the NF-TAM and the ECSM through The effective length of monopole antenna expressed by (3) simulations. On the other hand, the antenna factor obtained by and the equivalent capacitance expressed by (4) are the most the NF-TAM and the ideal antenna factor are in good important constituent elements of the ECSM. In this section, a agreement with each other (difference within approximately comparison is drawn between the two elements, which are 0.03 dB). Furthermore, this difference is within the also investigated separately. calculation accuracy obtained by the moment method.
104 A. Effective Length Versus Open Output Voltage Imaginary part of antenna impedance [Ohm] 0 The effective length defined by (3) and the absolute value of the open output voltage calculated by the moment method -2000 are shown in Fig. 8. The length of the monopole antenna -4000 element is 1.15 m. The number of segments is 10. The current distribution on the element is considered to be a piecewise -6000 sinusoidal current using the moment method. -8000 Antenna Impedance in ECSM Open Voltage [V] -10000 Antenna Impedance (10 segments) in ideal AF 0.61 Antenna Impedance (1 segments) in ideal AF Effective length in ECSM -12000 (AF: Antenna Factor) 0.6 Open voltage (10 segments) in ideal AF Open voltage (1 segment) in ideal AF -14000 0.59 0 5.0 10.0 15.0 20.0 25.0 30.0 (AF: Antenna Factor) 0.58 Frequency [MHz]
0.57 Fig. 9. Imaginary part of the antenna impedance.
0.56 Real part of antenna impedance [Ohm] 0.55 6 Antenna Impedance in ECSM 0.54 5 Antenna Impedance (10 segments) in ideal AF 0.53 Antenna Impedance (1 segments) in ideal AF 0 5.0 10.0 15.0 20.0 25.0 30.0 4 (AF: Antenna Factor) Frequency [MHz] Fig. 8. Effective length versus open output voltage. 3
2 In Fig. 8, it is evident that the results do not agree with each other. However, the effective length expressed by (3) also 1 originates from the piecewise sinusoidal current on the 0 antenna element. Consequently, the effective length and the 0 5.0 10.0 15.0 20.0 25.0 30.0 open output voltage for one segment are in good agreement Frequency [MHz] with each other, as shown in Fig. 8. From these results, we can conclude that the effective length expressed by (3) is rather Fig. 10. Real part of the antenna impedance. simple, even if the frequency band is very low. The current distribution on the antenna element should be assumed more Case 1: Replace the effective length defined by (3) with accurately when the ECSM has to be carried out with a high the open voltage obtained through numerical degree of accuracy. simulations (shown in Fig. 8) Case 2: Replace the antenna impedance defined by (4) B. Equivalent Capacitance Versus Antenna Impedance and (6) with the antenna impedance obtained through In the case of the ECSM, the antenna impedance is given numerical simulations (shown in Figs. 9 and 10) by (6). On the other hand, the antenna impedance used in the Case 3: Combine Case 1 with Case 2. case of the ideal antenna factor is calculated through the The results of these three cases and the ideal antenna factor moment method. The results are shown in Figs. 9 and 10. are shown in Fig. 11. Differences in their values are made The length and diameter of the monopole antenna element more evident through a detailed evaluation, as shown in Fig. are 1.15 m and 1 cm, respectively. The number of segments 12. The difference between the antenna factor obtained by the considered in the moment method is 10 or 1. From these ECSM and the ideal antenna factor, which is shown in Fig. 7, results, it is found that these results have differences and the is also shown in Fig. 12. real part of the antenna impedance is assumed to be zero in the In Fig. 12, the antenna factor for Case 3 and the ideal ECSM. In other words, it is evident that the antenna antenna factor are in good agreement with each other. It is impedance is also too simple in the case of the ECSM. also evident that both the effective length defined by (3) and the capacitance defined by (4) contribute to the differences C. Investigation of Influences on the Antenna Factor observed with the ideal antenna factor. However, it is difficult We will investigate the influence that the abovementioned to distinguish which factor (the effective length or the antenna differences have on the antenna factor. When the ECSM is impedance defined by (6)) has a greater influence on the applied through simulations, the effective length and the value performance of the ECSM, because the difference between the of the capacitance can be replaced by the value obtained by antenna factor in Case 1 and the ideal antenna factor is larger the moment method. The cases evaluated are summarized in than the difference between the antenna factor obtained the following list. through the ECSM and the ideal antenna factor. It was also
105 found that the relationship between the dependence of the case of experiments, the results show a difference between the antenna factor on the effective length and the dependence of two measurement methods; this difference ranges from the antenna factor on the antenna impedance defined by (6) is approximately 0.6 dB to 2.4 dB. In the case of numerical not straightforward. simulations, the difference ranges from approximately 0.9 dB We can perform the ECSM inside a room, and the choice of to 1.3 dB. this method is very reasonable when we want to measure the On the other hand, the antenna factor obtained by the NF- antenna factor of a monopole antenna with an error of a few TAM and the ideal antenna factor are in good agreement with decibels. If we need a measurement of the antenna factor with each other. The difference, which is less than approximately a higher degree of accuracy, the ECSM needs to be improved. 0.03 dB, is within the calculation accuracy of the moment For example, the real part of the antenna impedance should be method. Therefore, this result shows that we need to considered and so on. investigate the origin of the difference between the results of the NF-TAM and the ECSM. Antenna Factor [dB(1/m)] In this study, we have investigated the factors on which the 100 difference between the ideal antenna factor and the antenna 90 factor obtained by the ECSM through numerical simulations Ideal antenna factor 80 Case 1 (ECSM) depends, because the ideal antenna factor and the antenna 70 Case 2 (ECSM) factor obtained by the NF-TAM are in good agreement with 60 Case 3 (ECSM) each other. We found that both the principles and theory of the ECSM are accurate. However, the definitions of the effective 50 length and the antenna impedance used in the ECSM are too 40 simple for the calibration of the antenna factor of a monopole 30 antenna with a high degree of accuracy. To conclude, it is 20 evident that the ECSM needs to be improved in order to
10 obtain results that are more accurate. 0 5.0 10.0 15.0 20.0 25.0 30.0 Frequency [MHz] CKNOWLEDGMENT Fig. 11. Comparison of Cases 1, 2, and 3 with the ideal antenna factor. A This study was supported in part by the Telecom Engineering Center (TELEC), Japan. Difference [dB] 2
1.5 REFERENCES 1 [1] N. S. Nahman, M. Kanda, E. B. Larsen and M. L. Crawford, “Methodology for standard electromagnetic field measurements,” 0.5 IEEE Trans. on Instrumentation and Measurement, vol. IM-34, pp. 0 490–503, Dec. 1985. [2] M. W. Howard, “Rod calibration techniques and comparisons.” -0.5 Available: http://www.liberty-labs.com/Content/pdf_files/rod.pdf ECSM － Ideal antenna factor [3] D. A. Knight and M. J. Alexander, “Monopole calibrations in a GTEM -1 Case 1 － Ideal antenna factor cell,” Paper presented at British Electromagnetic Conference at -1.5 Case 2 － Ideal antenna factor Harrogate on 6-8 November 2001. Case 3 － Ideal antenna factor [4] CISPR16-1-4, Edition 2.1, 2008-1, Annex B. -2 [5] ANSI C63.5, “American national standard for electromagnetic 0 5.0 10.0 15.0 20.0 25.0 30.0 compatibility-radiated emission measurements in electromagnetic Frequency [MHz] interference (EMI) control-calibration of antennas (9-40 GHz),” 2006. [6] M. Ishii and Y. Shimada, “A near field 3-antenna method for short Fig. 12. Differences between antenna factor obtained through the ECSM in monopole antennas in low frequency bands,” IEEE Int. Symp. Cases 1, 2 and Case 3 and the ideal antenna factor. Electromagn. Compat., pp. 324–327, Aug. 2009. [7] T. Iwasaki and K. Tomizawa, “Systematic uncertainties of complex antenna factor of dipole antenna as determined by two methods,” IEEE Trans. on Electromagnetic Compatibility, vol. 46, pp. 234–445, May VIII. CONCLUSION 2004. We had previously proposed a near-field three-antenna [8] H. E. King, “Mutual impedance unequal length antennas in echelon,” method for measuring antenna factors of electrically short IRE Trans. on Antenna and Propagation, vol. 5, pp. 306-313, July 1957. monopole antennas. However, the equivalent capacitance [9] D. A. Knight, A. Nothofer and M. J. Alexander, “Comparison of substitution method is the most commonly used measurement calibration methods for monopole antennas, with some analysis of the method. Therefore, it is necessary to draw a comparison capacitance substitution method,” NPL Report DEM-EM 005, October between the two methods. 2004. In this study, we have compared the NF-TAM with the ECSM through experiments and numerical simulations. In the
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