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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
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.
Attenuation ratio ± SD
Frequency pair
1108/16-81 j
of cases
(A > 18 dB)
All data
(A > 18 dB)
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.
17th July 1985
Communications Research Centre
Department of Communications
PO Box 11490, Station H
Ottawa, Canada K2H 8S2
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:
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-
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
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
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
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).
launching horn
5 00-
SUoo~ 3 00
ft 200.
coil current, A
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.
solenoid w i n d i n g s
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
12th July 1985
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
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.
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.
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.
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:
Here i is the bit number, © is the EXOR logical operation
(mod 2 addition) and K is the logical commutation
KA(B, Q =
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
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