regression coefficients for specific attenuation calculations provided by the CCIR.3 At 11 GHz these give a ratio — = 0-886/?-° 020 where R is the rainfall rate in ram/h. At 17 GHz the ratio is A,. Thus the frequency dependence and attenuation (and therefore rain rate) dependence are indeed small. For example, at R = 50 mm/h the predicted ratios at 11 GHz and 17 GHz are 0-819 and 0-827, respectively. This rainfall rate occurs about 0005% of the time,4 and, although the weighting of the linear fit is biased to larger attenuations, it seems likely that this is very much an upper limit to the overall average rainfall rate. The same is true of the ratio derived from long-term observations in France,5 which, for this percentage of the time (equivalent to an attenuation of 30 dB), predict a ratio of 0-822, with no mention of frequency dependence. Table 1 ATTENUATION RATIOS AND STANDARD DEVIATIONS FOR VARIOUS SIGNAL PAIRS DERIVED FROM SLOPE STATISTICS OF SCATTER PLOTS Attenuation ratio ± SD Frequency pair 11-35/17-71 10-80/16-53") 1108/16-81 j 10-80/1108") 16-53/16-81J KF Kp P Number of cases (A > 18 dB) All data Data (A > 18 dB) 0-430 ±0048 0-425 ±0039 13 0-453 ±0047 0-442 ±0039 19 0-781 ±0057 0-787 ±0038 19 ameters in the present case, and, in general, results from the cumulative distribution method will be most reliable if they come from data sets strictly matched in time and use the whole span of the distributions. Conclusions: In the frequency range 11-17 GHz, the ratio of the rainfall attenuations experienced by vertically and horizontally polarised transmissions in eastern Canada is 0-79, in reasonable agreement with similar measurements elsewhere. The exponent of the frequency scaling power law over this frequency range is 1-93, in excellent agreement with computations based on observed rainfall characteristics by means of the synthetic-storm model. The exponent calculated by regression fitting to high-time-resolution scatter plots is somewhat smaller than that estimated by comparison of the cumulative distributions of attenuation, and may be of greater reliability. No statistically significant differences are seen between the results during heavy ramfall (mostly thunder showers) and the entire data set, which includes widespread frontal rain. R. S. BUTLER 17th July 1985 Communications Research Centre Department of Communications PO Box 11490, Station H Ottawa, Canada K2H 8S2 References 1 2 3 4 5 6 BUTLER, R. s.: 'Measurements of cross-polarization discrimination at 11 and 17 GHz', Ann. Telecommun., 1981, 36, pp. 465-470 BUTLER, R. s.: 'Measurements at 11 and 17 GHz of terrestrial microwave fading and depolarization'. CRC report 1358, Communications Research Centre, Ottawa, 1982 'Attenuation by precipitation and other atmospheric particles'. CCIR, XVth Plenary Assembly report 721-1, International Telecommunications Union, Geneva, 1982 SEGAL, B.: 'High-intensity rainfall statistics for Canada'. CRC report 1329-E, Communications Research Centre, Ottawa, 1979 'Propagation data required for line-of-sight radio-relay systems'. CCIR, XVth Plenary Assembly report 338-4, International Telecommunications Union, Geneva, 1982 DRUFUCA, c : 'Rain attenuation studies'. Stormy Weather Group report MW-77, McGill University, Montreal, 1973 SEGAL, B.: 'Rain attenuation statistics for terrestrial microwave links'. CRC report 1351-E, Communications Research Centre, Ottawa, 1982 The frequency-dependent ratios kF allow an estimate to be made of the exponent C in the expression commonly used for frequency scaling: 7 Combining the Kingsmere and Corkery data, the result is C = 1-93 + 0-15, which is comparable to, but of greater statistical reliability than, the value C = 1-72 over approximately the same frequency range determined by Drufuca6 for a region near Montreal, about 150 km distant from the present experiment site. The present value agrees remarkably with the rain attenuation analysis by Segal,7 based on the syntheticstorm model applied to long-term rainfall statistics at Ottawa, in which a mean value C = 1-92 is applicable on a 40 km path for probabilities of occurrence between 0 0 1 % and 0 1 % over the frequency range 8-25 GHz. The exponent C = 1-93 derived from the scatter plots may be compared with the value C = 2-16 derived from the cumulative distributions of Butler,1 for percentages of time ranging from 0006 to 007. The discrepancy has at least two sources. One is that the scatter-plot method uses all the data points during each rain event and weights each equally, while the cumulative distribution method is restricted to a fraction of the whole data range and compares equiprobable data for the entire measurement period. The other is that the cumulative distribution method is only strictly applicable if the time series are identical at both frequencies, while the event-fitting method has no such limitation. Even with the excellent time coverage at the Kingsmere frequencies, this ideal of identical time coverage is not quite met, while at the Corkery frequencies the identical time series amounts to only 80% of the total period of fading. The event-fitting method should therefore be more reliable in its estimate of frequency scaling par- MILLIMETRE-WAVE DIELECTRIC WAVEGUIDE FERRITE PHASE SHIFTER WITH LONGITUDINAL MAGNETISATION ELECTRONICS LETTERS 12th September 1985 Vol. 21 Indexing terms: Dielectrics, Phase shifters A dielectric waveguide structure, containing an NiZn ferrite as phase-shifting medium is described. By applying a longitudinal static magnetic field to the ferrite, a reciprocal phase shift is obtained. Broadband characteristics are achieved by tapering the ferrite. Experimental results in the frequency range of 60-90 GHz for the phase shift and insertion loss of the device are presented. Introduction: Electronically controllable phase shifters can be used for many purposes, e.g. phased arrays or measuring arrangements. A possible approach to controllable phase shifting is the use of ferrite materials. Reggia and Spencer1 have demonstrated first a reciprocal phase shifter at X-band consisting of a cylindrical ferrite rod located at the centre of a rectangular waveguide. By applying an axial magnetic field to the ferrite, a phase shift of the transmitted wave is obtained. At a frequency of 35 GHz, Babbitt and Stern2 used a configuration with a rectangular ferrite sample acting as a part of a dielectric waveguide, to achieve phase shifting. On the top and bottom of the ferrite, two thin plastic layers superposed by two metal plates were placed. The longitudinal magnetic field was provided by a coil wrapped around the whole structure. No. 19 827 In this letter a phase-shifting device is described, consisting of a rectangular ferrite rod embedded in a dielectric substrate without metallic components. By applying a longitudinal DC magnetic field, the phase of the transmitted wave can be adjusted. ferrite polystyrene :e r r2-55 1-55 mm current of 0-5 A, a phase shift of 620 degrees was measured. The insertion loss varies from 2-7 dB to 4-2 dB. Fig. 4 shows a plot of the insertion loss against frequency in the range 6090 GHz, demonstrating the broadband character of the phase shifter (no magnetic field was applied). During the experiments several ferrite samples with different cross-sectional dimensions were examined. A ferrite cross-section of 1 mm by 0-5 mm produced a comparable phase shift only in the upper frequency region (80-90 GHz); at lower frequencies no significant phase shift was obtained. Contrary to this, a larger crosssection of 3 mm by 1-5 mm allowed Faraday rotation of the transmitted wave in addition to the phase shift, resulting in a considerable increase of the insertion loss due to polarisation mismatch. 600 - Fig. 1 Cross-section of dielectric structure Structure of phase shifter: In Fig. 1 a cross-section of the phaser is shown. This composite dielectric structure is constituted by a rectangular ferrite with a permittivity of er = 12-5, embedded in a supporting layer of polystyrene with a lower value of er = 2-55. The ferrite is an NiZn type (TT 2-111, Trans-Tech, Inc.) with a saturation magnetisation of 398 kA/ m. Owing to the great difference between the permittivity values most of the electromagnetic energy is transported in the ferrite region. The supporting dielectric has the same cross-sectional dimensions as a WR-12 metal waveguide (31 mm x 1-55 mm), thus providing a proper transition from the dielectric structure to the metal waveguide. For evaluating the cross-sectional dimensions of the ferrite, first a theoretical approach was used. By means of the Marcatili analysis,3 modified by the effective dielectric constant method,4 the propagation constant of the fundamental mode was determined for several cross-sectional dimensions. Finally, a 2 mm by 1 mm cross-section was evaluated experimentally. In Fig. 2 a longitudinal section of the whole phase-shifting arrangement is shown. The total length of the polystyrene rod is 140 mm, including two 20 mm-long E-taper sections at both ends. Using a conical launching horn in connection with the tapered end a smooth transition is achieved. In the middle part of the polystyrene rod a groove is provided for inserting the ferrite. The total length of the ferrite is 44 mm with two E-tapers at both ends, each 9 mm long. These tapers establish a steady transition from the low permittivity waveguide to the ferrite region. Owing to the decreasing height of the ferrite, caused by the E-taper, a part of the groove remains still empty, when the ferrite is inserted. This gap is filled up with paraffin wax (er = 2-25). paraffin launching horn Polystyrene 5 00- SUoo~ 3 00 ft 200. 100- 01 02 03 coil current, A 04 |SA7/3| Fig. 3 Plot of measured phase shift and insertion loss against coil current at a frequency of 70 GHz phase shift insertion loss Conclusions: The phaser presented here is able to achieve a large phase shift, while exhibiting a moderate insertion loss. By tapering the ferrite, broadband matching in the frequency range of 60-90 GHz is possible. The variation of the insertion loss due to the variable magnetic field is limited to a value of 1-5 dB. By providing a longer taper of the ferrite, it is expected to improve the performance of the device. Further investigations for optimisation of the dielectric structure to yield a compact design of the phaser are currently in progress. ferrite 60 solenoid w i n d i n g s 1577771 70 frequency , GHz Fig. 2 Longitudinal section of phase shifter Fig. 4 Plot of insertion loss against frequency To obtain a longitudinal magnetisation of the ferrite, the whole structure is fixed on the axis of a solenoid with an inner diameter of 30 mm and a length of 20 mm. The diameter of the solenoid was found to be larger than that necessary for avoiding a distortion of the RF-field structure. By properly increasing the cross-sectional dimensions of the supporting polystyrene rod, coil wire may be wrapped around the rod for building up a solenoid, without severe perturbation of the waveguide mode. Acknowledgments: The author would like to thank Prof. H. Brand of the Institute of High-Frequency Technology for valuable discussions. The technical assistance of D. Blume during the measurements is gratefully acknowledged. Furthermore, the author wishes to thank Alpha Ind. GmbH for providing the ferrite samples and Mr. Marek, Institute of Material Science, University Erlangen-Niirnberg, for preparing the ferrite rods. Experimental results: For measuring the phase shift, controlled by a variable DC magnetic field, the phase shifter was inserted in the test-channel of a transmission bridge. The field strength of the applied magnetic field was always kept below the value necessary for saturation. In Fig. 3 the results for the phaser are plotted at a frequency of 70 GHz. The insertion loss includes also the losses of the two transitions from the metal waveguide to the dielectric structure. By applying a coil Institutf'ur Hochfrequenztechnik Universitdt Erlangen-Niirnberg Cauerstrafie 9, D-8520 Erlangen, W. Germany R. GLOCKLER 828 12th July 1985 References 1 REGGIA, F., and SPENCER, E. G.: 'A new technique in ferrite phase shifting for beam scanning of microwave antennas', Proc. IRE, 1957,45, pp. 1510-1517 ELECTRONICS LETTERS 12th September 1985 Vol. 21 No. 19 BABBITT, R. w., and STERN, R. A.: 'Millimeter wave ferrite devices', IEEE Trans., 1982,18, pp. 1592-1594 MARCATiLi, E. A. }.: 'Dielectric rectangular waveguide and directional coupler for integrated optics', Bell Syst. Tech. J., 1969, 48, pp. 2071-2102 KNOX, R. M., and TOULIOS, P. O.: 'Integrated circuits for the milli- meter through optical frequency range'. Proceedings of symposium on submillimeter waves, Polytechnic Press of Polytechnic Institute of Brooklyn, Brooklyn, NY, USA, 1970, pp. 497-516 WIDE-MARGIN JOSEPHSON-JUNCTION A/D CONVERTOR USING REDUNDANT CODING Indexing terms: Superconducting devices, Josephson junctions, Analogue/digital conversion The letter describes a Josephson-junction analogue/digital (A/D) convertor using redundant coding and balanced SQUID comparators. It is shown that application of this scheme leads to a major increase of the critical current margins (up to ~20%), eliminating the need for adjustment of each comparator. Fig. 2a shows a possible structure of a single stage D, while in Fig. 2b the logical signals participating in eqn. 1 are plotted as functions of the analogue signal la. One can see that the most critical regions of the comparator threshold curves (the vicinities of the switch points) are not used; to our knowledge, this idea was first proposed by Barker5 in application to electromechanical angle/code convertors (the K-scan method). If the recurrent process of eqn. 1 were started from exact values of the least significant bits (LSBs) bu g0, the range of possible shifts of comparator thresholds (dotted lines in Fig. 2b) would be as large as ±25%. In reality the process is started from the uncorrected values bl = Blt g0 = Go (see Fig. 1). It results in somewhat narrower margins: ±16-7% for the LSBs and ±25(1 - 22-'/3)% for the other bits (i = 2, 3, ..., n), Nevertheless, the margins obtained are drastically larger than those for the Gray code, and, practically, do not depend on the convertor accuracy n. Gi Introduction: Periodic threshold curves of SQUIDs (superconducting quantum interference devices) make it possible to construct a simple n-bit A/D convertor consisting of n identical SQUID comparators and a resistive binary divider of the input signal.1-2 A/D convertors with n = 6-8 and sampling rates up to ~4 GHz have been fabricated and tested.34 These convertors, however, have impossibly narrow relative margins for the Josephson junction critical currents: for the usual Gray coding they are as small as ±2~n (i.e. ±2% for n = 6 and +0-5% for n = 8).2 Such margins are unachievable in the present-day Josephson-junction technology; therefore special adjustments of each comparator are necessary,2 making the whole device hardly practical. The goal of the present work has been to show that much larger parameter margins can be obtained by using the redundant error-correcting code (instead of the Gray code) and balanced comparators. |518/2| I, Fig. 2 Decoder section D a Logical structure b Logical signals as functions of analogue input The regions of the curves actually used to form the output are indicated by solid lines One more bit increasing the convertor accuracy (b0) can be obtained using b0 = bx © g0. The corresponding EXOR logic gate is shown at the top of the Fig. 1. comparators decoder |5TB7i| Fig. 1 Block diagram of A/D convertor using redundant coding Redundant coding: The A/D convertor under consideration (Fig. 1) consists of the usual resistive binary divider of the input signal Ia, a comparator block with n independent double-comparator sections (C) and a decoder composed of the similar sections D. The digital outputs Bi+l, G, of the (i + l)th section C (/ = 1, 2,..., n) present the 'errorcontaminated' bits of the natural binary and the Gray codes, respectively, while the signals bi+1, g{ are their corrected values obtained in the decoder section D using the following recurrent rules: (1) Here i is the bit number, © is the EXOR logical operation (mod 2 addition) and K is the logical commutation KA(B, Q = (2) ELECTRONICS LETTERS 12th September 1985 Vol. 21 Balanced comparators: The decoding sections D of the decoder described above can be readily realised with standard Josephson logic gates.6 The comparator sections C could in principle be composed of the SQUID comparators2"4 or the SGA comparators7 reported earlier. The convertor immunity to the critical current variations can be further improved using the balanced comparators8 composed of two identical parts connected in series. Fig. 3 shows a possible design of a double-comparator section C using this principle. Each of the two comparators (denoted by B and G, after their output codes) consists of two two-junction interferometers connected in series. All four interferometers are controlled by the same analogue current Ia. The DC bias V^ provides the necessary n shift between the interferometer threshold curves in comparators as well as the n/2 shift between the comparators. The step clock voltage V^ switches the two interferometers with lower critical currents to their resistive states, while their series companions are prevented from similar switching by appropriate choice of the feed resistors R. Such a latching mode of operation provides a low aperture time of the comparators.7 No. 19 829

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