2262-98-T UNIVERSITY OF MICHIGAN ENGINEERING RESEARCH INSTITUTE ELECTRONIC DEFENSE GROUP TECHNICAL MEMORANDUM NO. 26 SUBJECT: Modifications tothe Antenna System of Technical Report No. 45 to Reduce VSWR BY: B. F. Barton DATE: January, 1956 In EDG Technical Report No. 45, the results of a study of the feasibility of an efficient wide band antenna system were presented. Matching networks were obtained which were based on a somewhat idealized monopole antenna characteristic. These matching networks produced, theoretically, a match to within 1.44 db of the available generator power for a monopole of length to radius ratio 2/r = 60 over a 3.1 to 1 frequency range. Experimental results indicate that, due to matching network imperfections and the existence of what has been referred to as base capacitance, a loss approaching 2 db which corresponds to a VSWR of approximately 4 may exist in limited regions in the band. This value corresponds to a reflection by the load of 36 percent of the transmitted power. Power distributed amplifiers which might be used to drive the antenna system in certain applications, however, are commonly designed to operate with an output VSWR not greater than 2. A VSWR of 2 corresponds to a loss of.5 db. In the following discussion, compromise designs are presented in which this restriction is met, or more nearly met. The design of the antenna matching networks of Reference 1 was based on the results of Reference 2. A lowpass equivalent circuit was obtained for a monopole ~/r = 60. This circuit was the lowpass equivalant of a bandpass antenna approximating circuit which was chosen in such a way that its input impedance approximated the input impedance of a monoTHE UNIVERSITY OF MICHcIGAN ENGINEERING LIBRARY

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-3 - pole over a frequency band of interest. In Figure 1, the elements of the antenna lowpass equivalent for a monopole antenna as functions of 2/r are presented. These curves are based on the theoretical monopole impedance characteristics by Hallen.l A reduction of the VSWR can be achieved in a number of ways, among which are: (a) The use of antennas which are inherently more broadband types, such as monopoles with a smaller i/r ratio. (b) A reduction of the bandwidth covered by the individual antennas. (c) The use of more complex matching structures. The use of more complex matching structures will not be considered. It is doubtful whether increased network complexity would be beneficial in a practical structure. Referring to Figure 14 of Reference 2, it is observed that for an optimum 4-pole structure and a loss of.5 db 2 o C c 1.86 where C1 = RC of Fig. 1. Using Figure 1, it is observed that this can be achieved, choosing a monopole of f/r = 10, with coc = 2.35. Using a value of P~ = 2.7 for the center frequency of the bandpass circuit (i.e., for fl = length of antenna in radians at the midband frequency), it is found that this corresponds to coverage from ai = 1.77 to Li = 4.12. Thus, to achieve a VSWR of 2, a monopole of f/r = 10 can be chosen, and 1 See Jordan E. C., "Electromagnetic Waves and Radiating Systems," Prentice-Hall, New York, pp. 482-485, 1951. The symbol C used here is equivalent to L on the design curves. The networks discussed here are duals of the circuits on the design curves. The dual realizations are discussed in Reference 2, pp. 11-12.

-4 - coverage of 2.33 to 1 frequency ratio results. (The antennas of Reference 1 covered a frequency ratio of 3.1 to. ) Using the design curves of Reference 2, the corresponding 4 pole structure is.158.351 1/2 1,39.989 FIG 2 Raising the impedance level to 240 ohms, and converting to a bandpass circuit with normalized center frequency Pa = 2.7 38.0036 84.2.00163 120 1 286.9 1.00474 33.3 0412 240 FIG 3 The generator impedance can then be adjusted through insertion of an ideal transformer as outlined in Reference 2, producing 29.9 1,00458 128 | 63.7,00216 20.5,00669 94,4 ):(22 0474 28.9 333 0041 240 IDEAL 29,9,00416 | 63.7.00216 20.5,00669 94.4 21 I s,5^'! 928.9 33.3. _ 240 Ci ANTENNA MATCHNG CRCU ANTENNA MATCHING CIRCUIT ANTENNA APPROX CIRCUIT FIG 4

-5 -For operation over a 3.1 to 1 frequency band, and using a monopole with /r_ = 10, it is found that a loss of.93 db results, corresponding to a VSWR of 2.5. The lowpass 4-pole network is then.0938.2024 1/2.55 T 1089,989 1. fi, -i -989 FIG 5 Transforming to a 240 ohm impedance level, and converting to a bandpass network with Pi = 2.7, 22.5.00609 28,0049 20.5 *00669 94 240 CIRCUIT - - FIG 6 In this case, the insertion of an ideal transformer is unnecessar.y. To design a matching network utilizing either Figure 4b or Figure 6, it is only necessary to choose the mean radian frequency Cuo of the band to be covered. In the case of Figure 4, the derived matching networks match over a 2.33 to 1 frequency ratio, as previously stated. For Figure 6, similarly, a match is obtained over a 3.1 to 1 frequency ratio. The individual L's or C's in Figures 4 or 6 determine the elements L' and C', respectively, in the matching networks, according to

-6 - 2.7 Lt =,Do L 2.7 C' = o1 C The resulting element values are in henries and farads. It is observed that the elements of Figures 4 and 6 are not greatly different from the corresponding elements in the networks of Reference 1. However, the effective "base capacitance" may well be greatly increased with larger diameter antennas. It is probable that a larger optimum value of base spacing will be observed with larger diameter antennas than were observed previously. When used over a lossy ground plane, the Q of an antenna is reduced. For this reason, it is suggested that the above matching networks be used with an antenna of ~/r = 12 (approximately). In addition, due to the reduction in antenna resonant frequency by the "base capacitance", it is suggested that the actual monopole be made approximately 12 percent shorter than the theoretical length. REfERENCES 1. B. F. Barton, "The Design of an Efficient Wideband Antenna System," Technical Report No. 45, Electronic Defense Group, University of Michigan, 1955. 2. B. F. Barton, "The Design of Efficient Coupling Networks," Technical Report No. 44, Electronic Defense Group, University of Michigan, 1955.

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