the predominant contribution to the total carrier scattering. At (ND — NA) = 1015 cm" 3 , the calculated mobility is three times larger than the measured mobility. While this calculation gives good agreement for the case of GaAs, it thus appears to fail for Gao.47Ino.53 As. Since the most obvious difference between these materials is that Ga 0 .47^053As is an alloy semiconductor, it is reasonable to ask if the discrepancy between the calculated and measured mobilities at 77 K can be attributed entirely to alloy scattering. Acknowledgment: The author acknowledges the indispensable help of N. Visentin of Laboratoire Central de Recherche, Thomson-CSF, Orsay, France, for his work on this study. T. P. PEARSALL Bell Laboratories 600 Mountain Avenue Murray Hill, NJ 07904, USA 19th January 1981 References 1 WOLFE, c. M., STILLMAN, G. E., and LINDLEY, w. T. : 'Electron mobility in high-purity GaAs', J. Appl. Phys., 1970, 41, pp. 3088-3091 2 OOSAKA, F., SUGANO, T., OKABE, Y., and OKADA, Y.: 'Scattering of electrons by potential clusters in ternary alloy semiconductors', Japan J. Appl. Phys., 1976, 15, pp. 2371-2380 10- 3 WOLFE, c. M., STILLMAN, G. E., and DIMMOCK, j . D.: ionized impurity density in n-type GaAs', J. Appl. Phys., 1970, 41, pp. 504-507 4 STILLMAN, G. E., and WOLFE, c. M.: 'Electrical characterization of epitaxial layers', Thin Solid Films, 1976, 31, pp. 69-88 5 BARDEEN, J., and SHOCKLEY, w.: 'Deformation potentials and mobilities for non-polar crystals', Phys. Rev., 1950, 80, pp. 72-80 6 EHRENREICH, H.: 'Band structure and transport properties of some III-V compounds', J. Appl. Phys., 1961, 32, pp. 2155-2166 7 MEIJER, H. J. G., and POLDER, D.: 'Note on polar scattering of conduction electrons in regular crystals', Physica, 1953,21, pp. 255-264 8 FALICOV, c. M., and CUEVAS, M.: 'Mobility of electrons in com3 10 K)1 K)1 TO1 net carrier c o n c e n t r a t o r ! 10 18 ND-NA, c m ' Fig. 1 Calculated and measured Hall mobilities in n-type GaQ.41 Ino.53As with NA/ND = 05. No alloy scattering has been included in the calculation (a) T = 11 K A Present work (b) T = 295 K O Present work A Oliver & Eastman # Oliver & Eastman 2 Brooks has given an expression for electron scattering from random spatial variations in the periodic crystal potential because of short range variations in the crystal composition: HaUoy(X, T) - - ^ - - ^ (2) where x is the mole fraction of one alloy constituent. The temperature variation of the alloy scattering mobility is simple, and if the magnitude of this mobility were known at one temperature it could be calculated for others. The alloy scattering mobility necessary to produce agreement with the measured 77 K Hall mobility would be /ifl/,o>,(77 K) ~ 60000 cm2 V" 1 s~l. The Brooks theory would then require that the 295 K alloy scattering mobility be /ia//OJ,(295 K) ~ 30000 cm2 V~ * s~!. The presence of this additional scattering would lower the calculated room temperature mobility to 9000 c m ^ - ' s ' 1 at (ND-NA)= 1015 cm" 3 and to 8500 1 c r r ^ V ' s " at {ND - NA) = 1016 cm" 3 . These calculated values would be more than 30% below measured Hall mobilities. Hence it is concluded that alloy scattering, as it is currently understood, cannot account for the temperature variation of the electron mobility in Ga o . 47 In o . 53 As. This conclusion is subject to the assumption that Matthiessen's rule can be used to combine the various contributions to the mobility. However, these results, calculated by a semianalytic approach, are in very good agreement with the mobility calculated by the Monte Carlo method, where it is not necessary to assume Matthiessen's rule. Because the analytic approach works well for closely related binary semiconductors, it is reasonable to believe that it will also work well for the ternary alloy too. In conclusion, it has been shown that the relaxation time approximation which works well for GaAs can be used to calculate the electron mobility in Gao.47Ino.53 As which is in excellent agreement with calculations made by the Monte Carlo method. The analysis of the measured Hall mobility in Gao.47Ino.53 As shows the presence of additional scattering in the low temperature electron mobility, which is probably the manifestation of alloy effects. This scattering, however, has a more complex temperature variation than that given by the Brooks formulation of alloy scattering. 170 pensated semiconductors: (ii) Theory', Phys. Rev., 1967, 164, pp. 1025-1032 9 RODE, D. L., and KNIGHT, S.: 'Electron transport in GaAs', Phys. Rev. B., 1971, 3, pp. 2534-2541 10 TAKEDA, Y., and SASAKI, A.: 'Hall mobility and Hall factor of In o . 5 3 Ga o . 2 7 As', Japan. J. Appl. Phys., 1980, 19, pp. 383-384 1 1 PEARSALL, T. P., BEUCHET, G., HIRTZ, J. P., VISENTIN, N., BONNET, M., and ROIZES, A.: 'Electron and hole mobilities in Ga o . 4 7 In O 5 3 As'. Int. Conf. GaAs and Related Compounds, Vienna 1980, (Bristol, Institute of Physics, 1981), to be published, 1981 12 OLIVER, j . D., and EASTMAN, L. F. : 'Liquid phase epitaxial growth and characterization of high purity lattice-matched Ga JC In,_ JC As on <111>B InP', J. Electron. Mat., 1980, 9, pp. 693-712 13 LEHENY, R. F., POLLACK, M. A., BALLMAN, A. A., DEWINTER, J. C , a n d NAHORY, R. E.: 'Compositional dependence of electron mobility in InGaAsP', ibid., 1980, 9, pp. 561-568 0013-5194/81/040169-02$!.50/0 EFFECTIVE CANTING ANGLE OF DISTORTED RAINDROPS ALONG EARTHSPACE PROPAGATION PATH Indexing terms: precipitation Radiowave propagation, Atmospheric The effective canting angle of distorted raindrops along an earth-space propagation path has been obtained from a oneyear phase amplitude measurement of two orthogonal components of satellite signals. It is shown that the distribution of canting angles is centred around the horizontal orientation, with the standard deviation of about 11°. Introduction: A rain depolarisation test in earth-satellite propagation path was carried out at Ibaraki, Japan, by use of the Intelsat-IV satellite with an elevation angle of 35°. Measurements were based upon the phase-amplitude detection of two orthogonal components of the satellite downlink signals at 4 GHz, and the crosspolarisation discrimination (XPD) and tilt angle of the incident polarisation (usually a fat ellipse) during rain were calculated from measured values of phase and amplitude. Although the major purpose of this experiment was to obtain the rain depolarisation statistics for satellite links, the information of the effective canting angle of distorted raindrops along an earth-space propagation path was also ELECTRONICS LETTERS 19th February 1981 Vol.17 No. 4 deduced by comparing the XPD and tilt angle of incident polarisation during rain with those in fine weather, that is, the baseline values. Formulation: Let ep0 and epl denote the ellipticity (in nepers) in clear weather and rain, respectively, related to XPD by e P o,i - 1 and 0o, 0i the corresponding tilt angles of the incident elliptical polarisation (in radians). Then the effective canting angle 9 of distorted raindrops averaged over the earth-satellite propagation path and the rain-induced differential phase shift B can be calculated by (1) d sin | sin 2(0.0-0) _x itan (2 cot" 1 < tan X — ^ry-, (2) : where cos (2 cot cos (2 cot x ep0) Since the differential attenuations of distorted raindrops are known to be negligibly small at 4 GHz, they are excluded in the above formulations. Experimental results: Fig. 1 shows the result of measurement. In this scattergram, values of 9 are plotted against the simultaneously measured values of XPD. Each data point represents • 80 an equivalent path-averaged canting angle of all distorted raindrops and does not imply the canting angle of a specific single raindrop. In the Figure, it is seen that the canting angles are centred around zero degrees (horizontal direction) with a secondary peak around —60 to —90 degrees. When the amount of rain depolarisation is small enough, a certain portion of the small fluctuations in phase/amplitude measurement, which may be due to polarisation impurity of the earth-station antenna and/or the experimental system, could result in errors in the estimates of canting angles by about 90°. When the XPD is less than 30 dB, most values of canting angle exist in the range between — 5° and 20° from the horizontal direction. So the secondary peak in this figure may primarily be due to this measurement error, but the effect of hydrometeors other than raindrops, like ice particles, may possibly play a certain role in the formation of this anomalous secondary peak. The exclusion of the collection of data around the secondary peak provides the mean and the standard deviation of the residual 'genuine' distribution of canting angles of about 2° and 11°, respectively. This result implies that most of the major axis orientations of the distorted raindrops are in approximately the horizontal direction. As for the standard deviation, the value obtained in this experiment seems to be somewhat smaller than the values previously reported, though such measurements are still insufficient. This may be because the above-mentioned value is the standard deviation of the averaged values of all distorted raindrops along the path, rather than that of the individual raindrops. Conclusion: The effective mean-path canting angle of distorted raindrops along earth-space propagation paths obtained from a phase-amplitude measurement of a satellite downlink signal showed a distribution with mean value of about 2° and standard deviation of about 11°. Since existing data of raindrop canting angles are insufficient, these values will be of help in the prediction of rain depolarisation and/or in the design of polarisation compensators. O. FURUTA M. YAMADA 15th December 1980 Research & Development Laboratories Kokusai Denshin Denwa Co. Ltd. 2-1-23 Nakameguro, Meguro-ku, Tokyo 153, Japan 60 • • 0013-5194/81/040170-02$1.50/0 • • »#. •:*• • •• • £ fc_v__.i- o &• STRAYS-INSENSITIVE SWITCHED CAPACITOR BIQUADS WITH REDUCED NUMBER OF CAPACITORS * -20 *.*. • •• • Indexing terms: Switched-capacitor networks, Filters -40 •^- -60 -80 ••*••••••••. ••• ••:: •j w 1 * * •*• * *• •! "• -90 40 A new general structure for strays-insensitive switched capacitor biquadratic cells based on an altered set of input/output conditions is proposed. Several transformations which reduce the size or number of capacitors or create a filter characteristic independent of capacitor ratios are presented. Finally, a family of biquads which realise all inverting and noninverting bilinear transformed functions for leapfrog and follow-theleader feedback filters are derived from the general structure. 1 • •• • • • 30 XPD(4GHz),dB 20 J69A7TI Fig. 1 Distribution of effective canting angles of distorted raindrops along earth-space propagation path at Ibaraki, Japan Elevation angle, 35 degrees; period, Apr 1976-Mar 1977 (Angles are measured counter-clockwise from horizon seen from earth station). Measurement frequency, 4 GHz ELECTRONICS LETTERS 19th February 1981 Vol. 17 High order filters can be realised by switched capacitor biquadratic cells connected in various topologies. Such building blocks, based on a two-integrator two-clock-phase structure, have been demonstrated previously.1'2 This letter describes a slightly different biquad structure which offers several advantages with regards to transfer function realisability and number of capacitors required. The bilinear transform allows the use of classical synthesis No. 4 171

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