A compact, high-power, low-loss,L-band coaxial 18-way power divider/combiner

8. T. Hinata, H. Hosono, and H. Ono, ‘‘Scattering of Electromagnetic Waves by an Axially Slotted Conducting Elliptic Cylinder in Homogeneous Medium,’’ IEICE Trans., Vol. E79-C, Oct. 1996, pp. 1364]1370. 9. M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions, Dover, New York, 1972. 10. V. P. Chumachenko, ‘‘Modified Method of Calculation of E-Plane Waveguide Mode Having a Polygonal Boundary,’’ Radiotekh. Elektron., Vol. 34, July 1989, pp. 1581]1587 Žin Russian.. 11. J. Minor and D. Bolle, ‘‘Propagation in Shielded Microslot on Ferrite Substrate,’’ Electron. Lett., Vol. 7, No. 17, 1971, pp. 502]504. 12. J. Ramakrishna, ‘‘Even-Mode Characteristics of the Bilateral Slot Line,’’ IEEE Trans. Microwa¨ e Theory Tech., Vol. 38, June 1990, pp. 760]765. Q 1997 John Wiley & Sons, Inc. CCC 0895-2477r97

A COMPACT, HIGH-POWER, LOW-LOSS, L-BAND COAXIAL 18-WAY POWER DIVIDER / COMBINER Robert Lehmensiek1 and P. W. van der Walt 2 1 Radar Division Reutech Systems P.O. Box 686 Stellenbosch 7599, South Africa 2 Faculty of Engineering University of Stellenbosch Stellenbosch, South Africa Recei¨ ed 12 June 1997 ABSTRACT: The design, construction, and measured performance of a compact, low-loss, L-band 18-way coaxial power di¨ ider is presented. Q 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 241]243, 1997. Key words: power di¨ ider; high power, coaxial structure

Figure 1

I. INTRODUCTION

An n-way power divider generally splits a signal into n equiphase, equal amplitude parts. Power divider structures may be loosely categorized into the following three groups: the corporate Wilkinson, the fork, and the radial power dividers. The corporate Wilkinson divider and the fork divider are suitable for small n. For large n, these structures become large, especially for a larger bandwidth, and the efficiency drops rapidly w1x. The radial divider w2x is suitable for larger n and higher input power levels. However, it becomes an electrically large structure, and is therefore prone to unwanted modes w3x. We have developed a more compact and much simpler structure, where the output connectors are strapped together symmetrically around the coaxial structure. Figure 1 illustrates the divider construction, and a schematic of the circuit model is shown in Figure 2. The center pins of the 18 output connectors are directly connected to the center conductor of the coaxial structure, and lie in a plane perpendicular to the axis of the coaxial system. Since all 18 outputs are strapped together symmetrically around the coaxial structure, the impedance level at the output plane is Ž50 V % 18 ports s. 2.78 V. This impedance level is transformed with a quarter-wave impedance transformer to the 50 V impedance level at the input port, with the order dependent on the required bandwidth. The two short transmission lines to the left of the output plane in Figure 1 realize a short-step short-circuit stub, which presents a high reactance at the output ports. The total length of the stubs is reduced to less than a quarter wavelength by the stepped design. Because of the divider’s compact size, no higher order resonant modes can exist provided that the number of output ports is smaller than 20. Reciprocity allows the divider to also function as an equal power combiner w3x. In general, isolation between the output ports of a power divider is achieved with isolation resistors between the output ports. Due to the physically large isolation resistors required for higher power levels, the capacitance between these resistors and the earth planeŽs. causes currents to flow through

Construction of the coaxial 18-way power divider

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Figure 2

Equivalent circuit of the coaxial 18-way power divider

these resistors, and losses become a problem. For higher power levels, the natural choice, therefore, is to use isolators at the output ports of a reactive power divider. II. DESIGN

A second-order quarter-wave Chebyshev impedance transformer w4x was designed to transform the output plane impedance level from 2.78 V to the input impedance level of 50 V with a relative bandwidth of 15%. The resulting line impedances Z02 and Z01 ŽFig. 2. followed as 5.76 and 24.1 V, respectively. The short stubs Z03 and Z04 ŽFig. 2. need to present a high reactance toward the left. The characteristic impedance Z03 was chosen equal to the characteristic impedance Z02 so that there is no step at the output port connector’s connections to the coaxial structure. Z04 was chosen as high as is practically possible. A value of 36.4 V is used. The line lengths of the Z03 and the Z04 transmission lines were initially chosen to be 22.58 long at 1.3 GHz. The characteristic impedance of a circular coaxial structure with an air dielectric is given by the following equation: Z0 s 59.959 ln

d0

Ž1.

di

where d 0 and d i are the outer and inner diameters, respectively. The outer diameters for the transmission lines Z03 , Z02 , Z01 and the Ž Z0 s.50 V coaxial line at the input were chosen to be 46 mm. This diameter was chosen for practical reasons, especially to allow an SMA torque spanner to fit between the output port connectors. The inner diameters are calculated from Ž1., and are given in Table 1. The inner diameter of the Z04 transmission line was chosen equal to the inner diameter of the Z03 transmission line to ensure that the access hole ŽFig. 1. to the center pins of the output connectors has a constant diameter. The outer diameter of the Z04 transmission line then follows as 76.7 mm. Discontinuity susceptances which occur at a step in the coaxial structure can be modeled by a lumped capacitance as shown in Figure 2. The capacitance values are determined by means of the equations given in w5x: C1 s 0.227 pF TABLE 1

III. CONSTRUCTION

The divider consists of three turned brass parts with a composition of 85% copper, 5% lead, 5% tin, and 5% zinc. At the input, a standard C-type female connector is used. A tapered 50 V impedance line ŽFig. 1. reduces the discontinuity caused by the abrupt change in line size at the input. The center pin of the C-type connector Žcaptivated by two ‘‘barbs’’. is removed for assembly. The two ‘‘barbs’’ are machined off to allow the center pin to be replaced later. The output connectors are standard SMA-type female connectors with extended dielectrics. The epoxy-captivated center pins of the SMA connectors were also removed during assembly. Solder paste was applied to all of the connection points. A jig was made to hold all of the parts together and to center the connector pins in their holes. The entire structure was then heated in an oven to reflow the solder paste.

C3 s 1.297 pF.

Dimensions for the Transmission Lines

Impedance Ž V . d i Žmm. d 0 Žmm. Length Ž8.

242

C2 s 0.758 pF

Small adjustments to the lengths of the transmission lines may be used to compensate for these discontinuity effects. The line lengths after optimization are given in Table 1 at 1.3 GHz. The predicted transmission Žincluding conductor losses. and reflection response of the coaxial divider is shown in Figure 3. Field concentrations at the impedance steps were limited by rounding the sharp edges with a radius of 0.5 mm. The power-handling capability of the divider is limited by the input connector which has a voltage rating of 1 kV rms at sea level.

Z0

Z01

Z02

Z03

Z04

50 20 46

24.1 30.8 46 87.2

5.76 41.8 46 88.5

5.76 41.8 46 20.6

36.4 41.8 76.7 21.7

Figure 3 Predicted transmission coefficient magnitude multiplied by a factor of 100 Žcross., and the predicted Žcircle. and measured Žplus. reflection coefficient magnitudes

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REFERENCES 1. G. E. Nortjie and P. W. van der Walt, ‘‘High Performance Five Way Power Divider Using Shielded Microstrip,’’ IEEErSAIEE APrMTTS-90 Proc., 1990, pp. 245]250. 2. E. J. Wilkinson, ‘‘An N-Way Hybrid Power Divider,’’ IRE Trans. Microwa¨ e Theory Tech., Vol. MTT-8, Jan. 1960, pp. 116]118. 3. P. W. van der Walt, ‘‘Compact High Power 10:1 Power Combiner,’’ IEEErSAIEE APrMTTS-93 Proc., 1993, pp. 21-1]21-6. 4. H. J. Riblet, ‘‘General Synthesis of Quarter-Wave Impedance Transformers,’’ IRE Trans. Microwa¨ e Theory Tech., Vol. MTT-5, Jan. 1957, pp. 36]43. 5. P. I. Somlo, ‘‘The Computation of Coaxial Line Step Capacitances,’’ IEEE Trans. Microwa¨ e Theory Tech., Vol. MTT-15, Jan. 1967, pp. 48]53. Q 1997 John Wiley & Sons, Inc. CCC 0895-2477r97 Figure 4 Measured transmission coefficient magnitudes from input port to all 18 output ports

IV. MEASUREMENT RESULTS

A very good performance has been measured over the 1.2]1.4 GHz frequency band with an insertion loss of less than 0.02 dB and a maximum amplitude imbalance of 0.15 dB. The magnitudes of the 18 measured transmission coefficients are shown in Figure 4. The spread in the transmission coefficient phases between the output ports is smaller than 1.38. The measured 50 V input match is better than y21 dB over the frequency band, and is also shown in Figure 3. The measured mutually reactive coupling between the output ports is shown in Figure 5. The isolation varies from about y14 dB Žfor adjacent ports. to better than y24 dB. V. CONCLUSION

A compact, low-loss, L-band 18-way coaxial power divider has been designed and fabricated. The divider presents an excellent 50 V match at the input port, low coupling between output ports, a very high efficiency, and excellent division properties, all over a 1.2]1.4 GHz frequency band.

Figure 5 Measured mutually reactive coupling between the output ports with respect to an arbitrary reference port chosen as port 1 for the frequencies 1200, 1300, and 1400 MHz

NUMERICAL AND ANALYTICAL CHARACTERISTIC MODES FOR CONDUCTING ELLIPTIC CYLINDERS G. Amendola,1 G. Angiulli,1 and G. Di Massa1 1 Dipartimento di Elettronica, Informatica e Sistemistica Universita ` della Calabria 87036 Rende (Cs), Italy Recei¨ ed 3 June 1997 ABSTRACT: In this letter, the numerical and analytical characteristic modes for perfectly conducting, elliptic cylinders are formally deri¨ ed, and a comparison between them is presented. A good agreement between numerical and analytical solutions is obser¨ ed. The analytical solution of the TM scattering from a collection of elliptic cylinders is also gi¨ en, and results for different configurations are presented. Q 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 243]249, 1997. Key words: characteristic modes; method of moments; multiple scattering; elliptic cylinders; Mathieu functions 1. INTRODUCTION

The analysis of the scattering from large-size metallic bodies is a formidable task. If the bodies are arbitrarily shaped, none of the analytical techniques can be applied, and a numerical solution has to be found by means of expensive computational resources. The standard technique employed is the method of moments, where an integral equation, arising from the boundary conditions on the surface of the scatterer, is put in a discretized form by expanding the unknown current with a set of basis functions. The choice of the expansion functions directly affects the effectiveness of the method. Entire domain functions extend over the whole surface of the scatterer; they are very efficient to represent the current induced on the surface of the bodies, but are available only for a restricted set of geometries. Subdomain basis functions are nonzero only over a part of the boundary of the scatterers; they can be applied to any kind of geometries, but they lead to a more expensive numerical solution. A particular case of the large-size problem is the scattering from a collection of bodies. In this case, the number of the objects, other than their size, becomes an important factor affecting the complexity of the solution. To overcome the problem, a number of alternative techniques with reduced computational costs with respect to the method of moments has been proposed in recent years w1]3x. Nevertheless, it can be said that, when the scatterers have equal shapes and sizes, the use of entire-

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