US 3500412 A Description (OCR text may contain errors) R. G. TRIGON 3,500,412 POINTING PRECISION OF AN ELECTRONIC SCANNING ANTENNA BEAM 3 Sheets-Sheet 5 NOISE GAFE' sgn our/n/m-an' ND/NG-OFF 8 con/ 0m? con urm 4-2 Fig.7 March 10, 1970 Filed April 9, 1968 1 R0l/h'DlK-0FF COMPUTER 3,500,412 POINTlNG PRECISION OF AN ELECTRONIC SCANNING ANTENNA BEAM Roland G. Trigon, Paris, France, assignor to CSF-Compagnie Generale de Telegraphie Sans Fil, a corporation of France Filed Apr. 9, 1968, Ser. No. 719,862 Int. Cl. H04b 7/06 US. Cl. 343-100 4 Claims ABSTRACT OF THE DISCLOSURE In order to overcome the drawbacks due to the quantization of the phase shifters associated to electronic scanning antennas of the so-called counter-rotative type, the phase-position law is modified and means are supplied which avoid the simultaneous jumps of the values of several phase shifters. The present invention relates to electronic scanning antennae, comprising a network of radiating elements so supplied that they radiate a beam which moves as a function of time following a periodical law. This is in particular the case with the so-called counter rotative antennae, used on board of a satellite and supplied through networks of the type of a Butler matrix or more generally a Fourier transform matrix. In all cases, the movement of the beam is effected by varying the phase shift between the successive inputs of the matrix; the desired phase shift is a function of the position number of the matrix input concerned and of the desired direction of the beam. In practice, for technological reasons, the phase shifters used are such that the above phase shifts have only certain predetermined values in arithmetical progression. Such phase shifters are called quantized phase shifters. This results in a jerky rotation and in pointing errors. This drawback is particularly aggravated by the fact that, up to now, the direction of the systematic phase errors due to quantization was chosen according to a simple law by merely rounding 013? each phase value to the nearest quantized value, irrespective of any other considerations. It follows that, for certain desired positions of the beam, simultaneous phase jumps on several phase shifters tend to enhance the jerky nature of the movement of the beam and increase the pointing error. It is an object of the invention to minimize the drawbacks caused by the quantization of the phase shifters. To this end according to the invention, there is provided a method for improving the accuracy of the pointing of the beam radiated by an electronic scanning antenna of the type comprising a plurality of radiating elements arranged on a closed surface and a plurality of controlled quantized phase shifters respectively associated therewith, and wherein, the beam pointing direction undergoing a rotation as a predetermined function of time, the theoretical phase shift values introduced by said phase shifter are computed as predetermined functions of time, said method consisting in: Modifying the theoretical values of said phase shifts so as to accelerate or delay selectively the beam rotation with respect to said predetermined rotation; Controlling the rounding off of the phase value due to the quantized operation of the phase shifter in such a manner that only the value of one phase shifter is changed at a time. For a better understanding of the invention and to show how the same may be carried into effect reference will be made to the drawings accompanying the following description and in which: States atent FIG. 1 is a basic diagram of a conventional antenna to which the invention is applicable; FIG. 2 is a basic diagram of an antenna improved according to the invention; FIGS. 3, 4 and 5 are explanatory diagrams; and FIGS. 6 and 7 show details of the diagram of FIG. 2. For the sake of clarity, the invention will be described with reference to the particular case of an antenna placed on a stationary satellite stabilized by rotation. The direction of the beam will therefore coincide with the direction of the center of the earth or form a fixed angle therewith. The beam must therefore be rotated relative to the satellite with a uniform speed equal to the rotation speed of the satellite, but in the opposite direction. The general case of an antenna with periodic scanning will be derived from this particular case, by replacing the linear variations of the phase shifts by variations following some other law. The known antenna shown in FIG. 1 is formed by radiating elements, A to A arranged in a circle around the satellite. The direction of the maximum radiation axis rotates about the axis of the circle in the plane thereof or making a constant angle therewith. The rotation of the beam is obtained, as is well known, by interposing between the input terminal T of the system and the radiating elements a circuit, known per se, comprising a power divider D, variable phase shifters Ph to Ph and a Fourier transform matrix B with n entries and n outputs. As is known, to a linear and continuous variation of the phase of the phase shifters corresponds a gradual displacement of the illuminated radiating elements along the elements A to A and therefore a uniform rotation of the beam. The phase shifts necessary at each input of the matrix are linear functions of the number determining the position of the input and of the angle of rotation desired. In practice, the phase shifters Ph to Ph are quantized. The control of the value of the quantized phase shift caused by the phase shifters Ph (i= 1, 2 n) is effected by means of a phase calculator 3, a calculator of the roundedoif values 4 and an arrangement 5 for the control of the phase shifters. The arrangement 3 receives the indication of the desired pointing angle 9 0 being the angle between the beam and a reference direction in the plane of the radiating elements, if the axis of the beam is within this plane, or the angle made by the projection of the beam with this reference direction, if the beam rotates whilst forming a constant angle with the axis of the circule along which the sources are positioned. The input which receives the signal 6 is connected, for example, to a known device 6 which senses the position of the satellite. The calculator 3 delivers at its n outputs the theoretical values of the phases of the n phase shifters. These values are compared with different quantized levels in the rounding ofi calculator 4 which determines the orders to be given to the different phase shifters. These orders are translated, for example, into control voltages in the case, which is the most common, of voltage controlled phase shifters, in the arrangement 5 which forms the phase shifter control signals. The rounding-off calculator is, for example, a simple comparator, for example a flip-flop type comparator, which involves the drawbacks mentioned above. For the sake of clarity, the n connections between the arrangements 3, 4 and 5, are shown only as two lines but it is to be understood that, for each phase shifter, there is effected a phase computation and a rounding-01f computation; a control voltage is thus provided. The antenna improved according to the invention, which is shown in FIG. 2, comprises a modified circuit for determining the theoretical phase and the quantized phase which avoids simultaneous phase jumps, on a plurality of phase shifters, i.e., substantial jerks, and on the other hand accelerates or delays the beam rotation so that it comes nearest the desired position. According to the invention, thi circuit comprises: An arrangement 7 for correcting the law p(6 which defines the phase as a function of the desired pointing direction 0 which is inserted between the signal 6 input and the phase calculator 3; and An arrangement for determining the rounded off value, which is substituted for the calculator 4, and which comprises a test circuit with a source of random signals 9. The arrangement 7 is, for example, a memory in which is recorded a set of values 6, corresponding respectively to a set of values 0 such that (6)= (0 where (0) is the phase law of the calculator 3 of FIG. 1 and 09 is the corrected law, which results in a pointing direction 0+d0, which is the desired direction. An embodiment of the arrangement 7 is described further below. The rounding off circuit is constructed with a view to avoiding the simultaneous variation on several phase shifters. To sum up, the circuit for correcting the phase law makes it possible to compensate for the average pointing error with periodical variation, by accelerating or delay ing the rotation of the beam and the circuit for determining the direction of the rounding off makes it possible to compensate for quick variations of this error. The diagrams in FIGS. 3, 4 and 5 explain the advantages of the system according to the invention. FIG. 3 shows in solid lines the variation of the phase 90, which is plotted along the ordinates as a function of the position p of the phase shifter concerned, which positions are plotted along the abscissae: for a given value 0 The theoretical variation is linear (straight solid line). Due to the quantization, the effectively followed phase law is that shown in dashed lines, it is stepwise and 1 represents the quantization step. The circuit according to the invention for determining the rounding off direction makes it possible both to reduce the pointing error caused by the rounding otf operation and to avoid sudden variations in the direction of the radiation axis by preventing simultaneous jumps of several phase shifters. To this end, the theoretical phase is compared with odd multiples of I /2; if it is equal to one of them, the choice of the direction of the rounding ofi? is determined from a random voltage 5 supplied by a noise generator associated with each phase shifter. According to whether this voltage is lower or higher than a threshold value, the rounding off is effected to the lower or higher quantized value. On the other hand, all other things being equal, due to the quantization, for a linear variation of the phase as a function of 6 a pointing error dfi is obtained which is a function of 6 such as shown, for example, at 4-1 in FIG. 4. By substituting for the linear law 09 a different law zp (0 it is possible to accelerate or to delay the rotation according to whether dH is negative or positive, and to obtain, for example, a corrected law d fiw shown at 42 in FIG. 4. FIGS. 6 and 7 are non-limiting examples of embodiments of the arrangements 7 and 8. For the sake of clarity, it will be assumed that, in the absence of any readjustment of the beam directions according to the invention, the pointing error is a sinusoidal function of the period 21r/n of the angle 6. Disregarding rapid changes of (10, caused by jumps of the value I of the phase shifters and minimized by the rounding off determination circuits, the mean error :16 has the form d6=K sin H9. The problem is therefore to determine which value of 0 to select for so calculating the phases that the beam is pointed in a desired direction 0 the value of 0 is the solution of the equation 0 :0+k sin n9 (1) which can be solved graphically, as shown in FIG. 5. The arrangement 7 may comprise a computer which solves the equation 1 and delivers for each input signal 6 the value 6 to the phase calculator 3. More simply, the arrangement 7 may consist, as shown in FIG. 6, of a memory 71 which records a certain number of values 9, corresponding to predetermined values of .9 and of an arithmetic interpolation calculator 72 which solves the equation r r! *00 )0u 0/Io where 9 is the exact value indicated by the position sensing device 6, 0' and 6",, are the two predetermined values on both sides of 0 and 9 and 0 are the values of 0 corresponding to 9' and 6" The rounding off determination circuit 8 may be a digital or an analogue circuit. FIG. 7 shows, by way of non limiting example, a first embodiment: the theoretical phase o delivered by the calculator 3, is compared in a multi le level comparator 81 with odd multiple of the quantization step, i.e. At the output of the comparator 81 appears a signal 1 if (pm is equal to one of these levels, and no signal if not. This output is connected to control inputs of two gates 821 and 822, the first of which is normally open, i.e., remains open in the absence of any control signal, and the second is normally closed. The output of the calculator is also connected to the signal inputs of these two gates. The output of the gate 821 is connected to a rounding off calculator 84, identical to the arrangement 4 of FIG. 1 which supplies the value of the quantized phase nearest to s ta- The output of the gate 822 is connected in parallel to the inputs of two gates 831 and 832 which operate in opposition. The random voltage 6 supplied for example by the noise generator 9, is compared at 810 with a threshold voltage V and, according to the result of the comparison, there appears at the output of 810 a signal 1 or 0. This output is connected to the control inputs of the gates 331 and 832. If e V the output signal of 810 is O, the gate 831 is open and the signal corresponding to em arrives at the device 841 which calculates the phase rounded off to the lower quantized value. If on the other hand e V the signal corresponding to go arrives at the calculator 842 which calculates the phase rounded off to the upper quantized value. The arrangements 84, 841, 842, of which only one is in use at a time, feed the control arrangement 5. Of course, there are as many voltages 6 and associated circuits as there are phase shifters in use. Various modifications to the circuits described may be devised. For example, the gates 822, 831 and 832 may be combined to form a single device with multiple control inputs, the essential point being that, the rule for calculating go takes into account the fact that quantized phase shifters are used, and that logical circuit inhibiting the simultaneous jumps of the phase o are used. Although the invention has been described in the foregoing with special reference to the case of an antenna mounted on a satellite, where the angle 0,, is determined by a position sensing device, the invention may be used wherever the pointing angle is a periodical function. Of course, the invention is not limited to the embodiment described and shown which was given solely by way of example. What is claimed is: 1. A method for improving the accuracy of the point ing of the beam radiated by an electronic scanning antenna of the type comprising a plurality of radiating elements arranged on a closed surface and a plurality of controlled quantized phase shifters respectively associated therewith, and wherein, the beam pointing direction undergoing a rotation as a predetermined function of time, the theoretical phase shift values introduced by said phase shifter are computed as predetermined functions of time, said method consisting in: modifying the theoretical values of said phase shifts so as to accelerate or delay selectively the beam rotation with respect to said predetermined rotation; controlling the rounding off of the phase values due to the quantized operation of the phase shifter in such a manner that only the value of one phase shifter is changed at a time. 2. An improvement to electronic scanning antennas of the type comprising a plurality of n radiating elements numbered 1 to n, arranged on a closed surface, a plurality of n controlled quantized phase shifters numbered 1 to 11 respectively associated therewith having respective control inputs coupled to a control circuit comprising in series a phase calculator computing n theoretical phase shift values according to a theoretical law, and n rounding off means which round off respectively said It phase shift values to the nearest quantized values, said improvement consisting of means connected to said calculator for modifying the law according to which said phase shift values are computed, of n test circuits respectively numbered 1 to 11 having respective control inputs and of n random signal generators respectively numbered 1 to 11 coupled respectively to said 12 test circuits, said 11 test circuits being substituted respectively for said it rounding off means, the test circuit numbered i, where i=1, 2 n operating the rounding off of the phase shift value of the phase shifter numbered i to an inferior or a superior value according to Whether the signal supplied by said random signal generator numbered 1' is lower or higher than a predetermined value. 3. An improvement according to claim 2, wherein said modifying means comprises a memory and an interpolation calculator inserted in series at the input of said phase calculator. 4. An improvement according to claim 2, wherein each said test circuit comprises a multiple level comparator having an input coupled to said phase calculator and an output; a first and a second gate, operating in opposition, having respective signal inputs coupled to said phase calculator, respective control inputs coupled to said comparator output and a first and a second output; a round ing off calculator which rounds off said phase shift to the nearest value, having an input coupled to said first output and an output coupled to said control circuit; a threshold comparator having an input coupled to said random signal generator and an output; a third and a fourth gate operating in opposition having respective signal inputs coupled to said second output, respective control inputs coupled to said threshold comparator output and respectively a third and a fourth output; and a rounding off calculator rounding off to the nearest lower value and a rounding off calculator rounding off to the nearest higher value having respective inputs coupled respectively to said third and fourth outputs and respective outputs coupled to said control circuit. References Cited UNITED STATES PATENTS 3,387,301 6/1968 Blass et a1. 34310O 3,396,394 8/1968 Kiesling 343 RODNEY D. BENNETT, JR., Primary Examiner HERBERT C. WAMSLEY, Assistant Examiner U.S. Cl. X.R, 343854 Patent Citations
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