Abstract:
A method for the optimization of the payload of a multispot telecommunication satellite is disclosed. This type of satellite allows the use of several antenna spots on board the satellite to cover contiguous geographical zones, instead of a single broad spot. The method uses the division of an amplification unit such as a travelling wave tube TWTA between several spots.

Description:
This claims priority to French Patent Application FR 07/58690, filed Oct. 30, 2007, the entire disclosure of which is incorporated by reference herein. 
   BACKGROUND 
   The present invention concerns a method for the optimization of the payload of a telecommunication satellite with several spots, known as a multispot or multibeam satellite. This type of satellite allows several antenna spots to be used on board the satellite to cover contiguous geographical zones, instead of a single broad spot. 
   Such multispot satellites allow several radiofrequency links to be established occupying the same frequency band on different spots. An example of multispot configuration is illustrated in  FIG. 1 . Signals are sent towards a satellite  3  on an uplink LM by a terrestrial station  2  such as a gateway connected to an internet backbone  5 . These signals are then processed at the level of the satellite  3  then retransmitted on a downlink LD in the form of a plurality of spots or spots SP 1  to SP 8 . 
   In addition, certain multispot satellites allow polarized transmissions to be emitted (and received): the polarization can be linear (in this case the two directions of polarization are respectively horizontal and vertical) or circular (in this case the two directions of polarization are respectively circular left or circular right). 
   It will be noted that in the example of  FIG. 1 , the uplink leaving the station  2  uses two polarizations with four channels for each polarization, respectively Ch 1  to Ch 4  for the first polarization and Ch 5  to Ch 8  for the second polarization. The eight channels Ch 1  to Ch 8 , after processing by the payload of the satellite  3  will form the 8 spots SP 1  to SP 8  (one channel being associated with one spot in this example). 
   The payload of the satellite designates the part which allows it to fulfil the mission for which it was designed, i.e. for a telecommunication satellite  3  such as that shown in  FIG. 1 , to ensure the reception, processing (frequency conversion, filtering, amplification) and re-emission of the telecommunication signals issued from the terrestrial station  2 . The payload essentially comprises the antennae of the satellite and the transponders (and not the equipment for control, propulsion or electrical power equipment which belong to the platform of the satellite). 
     FIG. 2   a  shows in a known manner a functional block diagram of an architecture of payload  10  with multispot emission on the downlink. After reception and selection of the polarization, the signal received from a gateway is amplified by a LNA low noise amplifier  12 . The signal is then separated in N s  uplink channels by a signal divider device  13 . The N s  uplink channels are then translated in frequency by a frequency converter circuit  14  generally formed by a local oscillator and are filtered by an input filter  15  (of the pass band filter type) so as to form Ns channels in accordance with the frequency plan of the downlink. The local oscillator is most often constituted by a voltage controlled quartz VCO (Voltage Controlled Oscillator) with a phase lock loop. The N s  translated frequency channels are amplified through a power amplifier  16  HPA (High Power Amplifier) generally formed by a channel amplifier  17  CAMP (Channel AMPlifier) and a travelling wave tube amplifier  18  TWTA forming N s  downlink spot signals. The channel amplifiers  17  are generally gain command amplifiers which allow the power level of the signals to be regulated at input of the travelling wave tubes  18 . The tubes  18  can be replaced by solid state power amplifiers SSPA. It is likewise possible to use more sophisticated architectures comprising devices of the MPA type (multiport amplifier) offering the advantage of flexibility. Each of the N s  spot signals is then filtered through an output pass band filter  19 , and is then sent on a feed  20  such as a feedhorn towards a reflector for the formation of a spot. According to this configuration, if the number of gateways is designated by N GW , the payload  10  comprises: 
   2N GW  low noise amplifiers  12  LNA; 
   2N GW  signal divider devices  13 ; 
   N s  frequency converter circuits  14 ; 
   N s  input filters  15 ; 
   N s  high power amplifiers  16  HPA; 
   N s  output pass band filters  19 ; 
   N s  feedhorns  20 . 
   However, such a configuration is liable to pose some difficulties. In fact, according to the architecture of  FIG. 2   a ), the number of frequency converters, input filters, channel amplifiers and travelling wave tube amplifiers is equal to the numbers of downlink spots N s . Consequently, for large-scale systems, the high number of components forming the payload becomes disadvantageous in terms of mass and the launching of the space vehicle. Of course, these disadvantgages likewise have an impact on the associated costs. 
   SUMMARY OF THE INVENTION 
   In this context, the present invention aims to provide a method for the optimization of the payload of a multispot telecommunication satellite allowing the mass of the payload to be reduced, whilst maintaining the requirements with regard to effective isotropic radiated power EIRP. To this end, the invention proposes a method for the optimization of the payload of a multispot telecommunicaton satellite, designated optimized payload, from a reference payload for the formation of N s  spots on a downlink, N s  being a whole natural number strictly greater than 1, said reference payload comprising amplification means formed:
         either by N s  first amplification units comprising an input and an output, each of the N s  first amplification units being intended to amplify a spot,   or by a first amplification equipment comprising N s  inputs and N s  outputs and intended to amplify the N s  spots,
 
said optimization being realized in response to one of the following two criteria:
   first criterion: the capacity of said reference payload is conserved and the area of the covering zone of said payload is divided by N, N being a natural whole number strictly greater than 1 so that N s  is a multiple of N;   second criterion: the area of the covering zone of said payload is conserved and said capacity is multiplied by N;
 
according to said first criterion, said process comprises the following stages:
   comparison of said number N s  of spots with a threshold number of spots N threshold  or comparison of said capacity with a threshold capacity C threshold ;   if N s  is greater than N threshold  or if said capacity is greater than C threshold :
           when said amplification means are formed by said N s  first amplification units: substitution in said optimized payload of said N s  first units by N s /N second amplification units, each of the N s /N second amplification units being intended to amplifiy N spots;   when said amplification means are formed by said first amplification equipment: substitution in said optimized payload of said first equipment by a second amplification equipment comprising N s /N inputs and N s /N outputs and intended to amplify the N s  spots distributed over said N s /N inputs;
 
according to said second criterion, said process comprises the following stages:
   
           when said amplification means are formed by said N s  first amplification units: substitution in said optimized payload of said N s  first units by N s  third amplification units, each of said N s  third amplification units being intended to amplify N spots;   when said amplification means are formed by said first amplification equipment: substitution in said optimized payload of said first equipment by a third amplification equipment comprising N s  inputs and N s  outputs and intended to amplify N×N s  spots distributed over said N s  inputs.       

   As already stated above, the payload of the satellite is understood to mean the part which allows it to ensure the reception, processing and re-emission of the telecommunication signals issued from the terrestrial station. The payload comprises essentially the antennae of the satellite and the transponders. 
   Capacity is understood to mean the band pass capacity C FWD  of the satellite expressed in Hz and defined by the following formula: 
             C   FWD     =     Min   (           P   FWD     ⁢     N   s     ⁢   G     eirp     ,       N   s     ⁢     B   spot         )           
in which:
         Min(x, y) is a function providing the smallest value of x or of y,   P FWD  is the RF power of the repeater on the feedhorn of the antenna expressed in W,   N x  is the number of spots,   G designates the gain of the antenna in dB,   eirp is the effective isotropic radiated power (also designated PIRE in French) in dBW/Hz,   B spot  is the band pass available per spot on the basis of a single polarization expressed in Hz.       
   With the invention, the sharing of a unit of amplification such as a travelling wave tube TWTA or an SSPA amplifier between several spots (or the division of an equipment of the MPA type) may be advantageously used. One can also use the sharing of an equipment of the MPA type by reducing the number of inputs/outputs of the MPA remaining at constant capacity. 
   Two criteria can be retained to determine the optimized payload:
         either the same capacity is conserved as in a standard payload such as that described with reference to  FIG. 2   a ) and the number of TWTA tubes is reduced by a factor N, thus entailing a reduction of the total mass of the payload, of the continuous power DC required and the thermal dissipation; in this case, the sharing of each tube by several spots becomes of interest when the number of spots exceeds a threshold value;   or one conserves the same covering zone area as for the payload of  FIG. 2   a ) and the same number of TWTA tubes are retained; in this case, the capacity is increased by a factor N, whilst the mass of the payload is increased by a factor less than N; in this configuration, the sharing of a tube for several spots is still more advantageous in terms of mass than the association of one spot per tube.       

   The device according to the invention may likewise present one or more of the following characteristics, considered individually or in accordance with all the combinations which are technically possible. Advantageously, the determination of the said threshold number of spots N threshold  comprises the following stages:
         determination of the mass of said reference payload as a function of the number of spots N s ;   determination of the optimized payload as a function of the spot number N s ;   determination of N threshold  when the respective masses of said reference load and of said optimized load are equal.       

   According to a preferred form of embodiment, the natural whole N is equal to 2. Advantageously, the threshold number of spots N threshold  may be greater than 15 and preferably greater than 20, these numbers being liable to evolve with the technologies which are used. According to a first preferred form of embodiment, said amplification units are formed by travelling wave tubes TWTA. According to a second, said amplification units are formed by semiconductor amplifiers SSPA. According to a preferred third form of embodiment, said amplification equipment are formed by multiport amplifiers MPA. 
   Advantageously, the method according to the invention may comprises a reduction stage of a factor N of the number of frequency converters comprised in said payload optimized by regrouping per group of N channels in the frequency plan of the downlink. Advantageously, said capacity C threshold  is greater than or equal to 5 Ghz, this number being able to evolve as a function of the technology which is used. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other characteristics and advantages of the invention will clearly emerge from the description which is given thereof below, by way of indication and in no way restrictive, with reference to the attached figures, in which: 
       FIG. 1  is a simplified diagrammatic illustration of a multispot configuration; 
       FIG. 2   a ) is a functional block diagram of an architecture of reference payload according to the prior art; 
       FIGS. 2   b ) and  2   c ) each represent a functional block diagram of an architecture of optimized payload by the process according to the invention as a function of the first criterion, respectively without and with constraint on the frequency plan; 
       FIGS. 2   d ) and  2   e ) each represent a functional block diagram of an architecture of optimized payload by the method according to the invention as a function of the second criterion, respectively without and with constraint on the frequency plan; 
       FIG. 3  represents two configurations of frequency plans of uplink and downlink; 
       FIG. 4   a ) represents an example of covering zone composed of a plurality of disjoined hexagons; 
       FIG. 4   b ) represents an approximation of the covering zone of  FIG. 4   a ) composed of a plurality of circular spots; 
       FIG. 5  represents the linear evolution of the mass of the payload as a function of the number of spots in three configurations of payload and also the evolution of the capacity as a function of the number of spots. 
   

   DETAILED DESCRIPTION 
   In all the figures, the common elements bear the same reference numbers. 
     FIGS. 1 and 2   a ) have previously been described with reference to the prior art. 
     FIG. 2   b ) represents a functional block diagram of an architecture of payload  100  with multispot emission on the downlink optimized by the method according to the invention. 
   After reception and selection of the polarization, the received signal is amplified by a low noise amplifier  112  LNA. The signal is then separated in N s  uplink channels by a signal divider device  113 . The N s  uplink channels are then translated in frequency by a frequency converter circuit  114  or  121 . The converters  114  and  121  form a pair of converters mounted in parallel so that each provides an input of an input multiplexer  115  realizing a filtering so as to form a filtered signal regrouping the two input channels. 
   The N s /2 signals with two channels of translated frequency are amplified through a high power amplifier  116  HPA generally formed by a channel amplifier  117  CAMP and a travelling wave tube amplifier  118  TWTA forming N s /2 signals regrouping two downlink spots. Each of the N s /2 signals regrouping two spots is then separated and filtered through an output demultiplexer  119  so as to form two downlink spot signals. 
   Each of the N s  downlink spot signals is then sent over a source  120  such as feedhorn which radiates towards a reflector for the formation of a spot. According to this configuration, if one designates by N GW  the gateway number, the payload  100  comprises: 
   2N GW  low noise amplifiers  112  LNA; 
   2N GW  signal divider devices  113   
   N s /2 frequency converter circuits  114  and N s /2 frequency converter circuits  121 ; 
   N s /2 input multiplexers  115 ; 
   N s /2 high power amplifiers  116  HPA; 
   N s /2 output demultiplexers  119 ; 
   N s  feedhorns  20 . 
   It will be noted that each travelling wave tube  118  drives the amplification of two spots here; even if the invention illustrates more particularly the case of a driving of two spots, the invention applies equally to a higher number N of spots driven by the same travelling wave tube. It is found that the payload  100  allows a reduction of a factor N of the number of TWTA in relation to the payload  10  of  FIG. 2   a ). 
     FIG. 3  illustrates two possible scenarios allowing an uplink frequency plan PM to be made compatible with a first downlink frequency plan PD 1  (scenario 1) or a second downlink frequency plan PD 2  (scenario 1). As in the case of  FIG. 1 , the uplink uses two polarizations with four channels for each polarization, respectively Ch 1  to Ch 4  for the first polarization and Ch 5  to Ch 8  for the second polarization. 
   According to the frequency plan PM, the channels Ch 1 , Ch 2 , Ch 3  and Ch 4  have respectively for central frequency f u1 , f u2 , f u3 , and f u4 . Likewise, channels Ch 5 , Ch 6 , Ch 7  and Ch 8  have respectively for central frequency f u1 , f u2 , f u3 , and f u4 . According to the frequency plan PD 2 , the channels Ch 1 , Ch 3 , Ch 5  and Ch 7  have for central frequency fd 1  and the channels Ch 2 , Ch 4 , Ch 6  and Ch 8  have for central frequency f d2 . Considering that the frequency spacing Δf between channels is constant, both on the uplink and on the downlink, one has the following relationship:
 
Δ f=f   u2   −f   u1   =f   u3   −f   u2   =f   u4   −f   u3   =f   d2   −f   d1  
 
   The frequency translation fTn realized by the frequency converters of the payload corresponds, for a given channel, to the difference between the uplink frequency and the downlink frequency, i.e.:
 
 f   Tn   =f   un   −f   dm  with n varying from 1 to 8 and m being equal to 1 or 2.
 
   Consequently, it is clearly apparent that according to the frequency plan PD 1 , the frequency translation is different according to each channel, such that it is necessary to have a frequency converter for each channel and each polarization. 
   On the other hand, in the case of the frequency plan PD 2 , the judicious regrouping of the channels leads to the channels  1  and  2  sharing the same frequency translation (f t1 =f t2 =f u1 −f d1 =f u2 −f d2 ) whilst the channels  3  and  4  likewise share the same frequency translation (f t3 =f t4 =f u3 −f d1 =f u4 −f d2 ) different from the translation f t1 . The same reasoning can be made respectively for the channels  5  and  6  and for the channels  7  and  8  such that:
 
f T1 =f T2 =f T5 =f T6  and f T3 =f T4 =f T7 =f T8 .
 
   Consequently, the scenario 2 (frequency plan PD 2 ) allows only one frequency converter to be used per pair of channels and allows a reduction by 2 of the number of frequency converters with respect to the scenario 1 (frequency plan PD 1 ). 
   It will be noted that the scenario 1 (without constraint linked to a regrouping in the frequency plan) involves the use of a payload architecture such as that described with reference to  FIG. 2   b ). The scenario 2 (with constraint linked to a regrouping in the frequency plan) allows a payload architecture to be used such as the payload  200  illustrated in  FIG. 2   c ). 
   After reception and selection of the polarization, the received signal is amplified by a low noise amplifier  212  LNA. The signal is then separated into N s /2 pairs of uplink channels by a signal divider device  213 . The N s  pairs of uplink channels are then translated in frequency by a frequency converter circuit  214 ; they are then multiplexed and filtered by an input multiplexer  215  so as to form N s /2 channel pairs in accordance with the downlink frequency plan PD 2 . 
   The N s /2 signals of two filtered and translated frequency channels are amplified through a high power amplifier  216  HPA generally formed by a channel amplifier  217  CAMP and a travelling wave tube amplifier  218  TWTA forming N s /2 signals regrouping two downlink spots. Each of the N s /2 signals regrouping two spots is then separated and filtered through a multiplexer and output band pass filter  219  so as to form two downlink spot signals. 
   Each of the Ns downlink spot signals is then sent on a feed  220  such as a feedhorn which radiates towards a reflector for the formation of a spot. According to this configuration, if one designates by N GW  the gateway number, the payload comprises: 
   2N GW  low noise amplifiers  212  LNA; 
   2N GW  signal divider devices  213 ; 
   N s /2 frequency converter circuits  214 ; 
   N s /2 input multiplexers  215 ; 
   N s /2 high power amplifiers  216  HPA; 
   N s /2 output demultiplexers  219 ; 
   N s  feedhorns  220 . 
   Apart from the fact that the payload  200  (like the payload  100  of  FIG. 2   b )) allows the reduction by a factor N (N=2) of the number of TWTA used with respect to the payload  10  of  FIG. 2   a ), it will be noted that the frequency constraint imposed by the scenario 2 allows the reduction by two of the number of converters  214  with respect to the configuration of  FIG. 2   b ); in the more general hypothesis of a division of N spots per tube, the downlink frequency plan can be adapted to allow the use of N s /N converters instead of N s . 
   As already mentioned above, the band pass capacity C FWD  of the satellite is defined by the following formula: 
   
     
       
         
           
             C 
             FWD 
           
           = 
           
             
               Min 
               ( 
               
                 
                   
                     
                       P 
                       FWD 
                     
                     ⁢ 
                     
                       N 
                       s 
                     
                     ⁢ 
                     G 
                   
                   eirp 
                 
                 , 
                 
                   
                     N 
                     s 
                   
                   ⁢ 
                   
                     B 
                     spot 
                   
                 
               
               ) 
             
             . 
           
         
       
     
   
   The first term represents the limitation in power, whilst the second term represents the band pass limitation. When the payload is designed, one of the objectives to be attained consists in making the two terms equal with each other. 
   The area of the covering zone of a payload can be defined by the following relationship:
 
A ser =N s A cell  
 
in which:
         A ser  designates the area of the covering zone expressed in degrees squared ( 2 °),   A cell  designates the area of a cell which one can define as the area of the covering zone supported by each of the spots.       

   In a homogeneous multispot covering zone, each cell is represented by a hexagon such that the covering zone is composed of a plurality of disjoined hexagons FH as illustrated in  FIG. 4   a ). The area of each cell is given by the formula: 
             A   cell     =       3   ⁢     3     ⁢     θ   cell   2       8           
in which θ cell  is the external dimension of the cell expressed by the angle of the satellite associated with the covering.
 
   The area of the covering zone is therefore given by the following relationship: 
   
     
       
         
           
             A 
             ser 
           
           = 
           
             
               3 
               ⁢ 
               
                 3 
               
               ⁢ 
               
                 N 
                 s 
               
               ⁢ 
               
                 θ 
                 cell 
                 2 
               
             
             8 
           
         
       
     
   
   However, the antenna spot is not capable of producing a hexagonal form; a good approximation consists in considering a plurality of circular spots FC such as represented in  FIG. 4   b ) and each having a covering surface given by the relationship: 
             A   beam     =       π   ⁡     (       θ   cell     +     2   ⁢   ɛ       )       4           
taking into account a pointing error E linked to the precision of the antenna.
 
   Generally, the gain of the antenna is given by the following formula: 
           G   =     k       (       θ   cell     +     2   ⁢   ɛ       )     2             
in which k is a proportionality constant.
 
   Consequently, the capacity can be expressed by the following formula: 
   
     
       
         
             
           
             
               
                 
                   
                     C 
                     FWD 
                   
                   = 
                     
                   ⁢ 
                   
                     
                       
                         P 
                         FWD 
                       
                       ⁢ 
                       
                         N 
                         s 
                       
                       ⁢ 
                       k 
                     
                     
                       
                         eirp 
                         ⁡ 
                         
                           ( 
                           
                             
                               θ 
                               cell 
                             
                             + 
                             
                               2 
                               ⁢ 
                               ɛ 
                             
                           
                           ) 
                         
                       
                       2 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         P 
                         FWD 
                       
                       ⁢ 
                       
                         N 
                         s 
                       
                       ⁢ 
                       k 
                     
                     
                       eirp 
                       · 
                       
                         
                           
                             θ 
                             cell 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 2 
                                 ⁢ 
                                 
                                   ɛ 
                                   
                                     θ 
                                     cell 
                                   
                                 
                               
                             
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
             
           
         
       
     
   
   Proceeding from a hypothesis where:
         the capacities are identical in a conventional architecture such as that of  FIG. 2   a ) and in an architecture with division of N spots by each TWTA tube ( FIG. 2   b ) or  2   c )),   the two architectures present the same eirp per spot and use TWTA tubes presenting the same power RF,
 
one obtains:
       

   
     
       
         
             
           
             
               
                 
                   
                     C 
                     FWD 
                   
                   = 
                     
                   ⁢ 
                   
                     
                       
                         P 
                         FWD 
                       
                       ⁢ 
                       
                         N 
                         s 
                       
                       ⁢ 
                       k 
                     
                     
                       eirp 
                       · 
                       
                         
                           
                             θ 
                             
                               cell 
                               , 
                               1 
                             
                             2 
                           
                           ( 
                           
                             1 
                             + 
                             
                               2 
                               ⁢ 
                               
                                 
                                   ɛ 
                                   1 
                                 
                                 
                                   θ 
                                   
                                     cell 
                                     , 
                                     1 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         P 
                         FWD 
                       
                       ⁢ 
                       
                         N 
                         s 
                       
                       ⁢ 
                       k 
                     
                     
                       N 
                       · 
                       eirp 
                       · 
                       
                         
                           
                             θ 
                             
                               cell 
                               , 
                               N 
                             
                             2 
                           
                           ( 
                           
                             1 
                             + 
                             
                               2 
                               ⁢ 
                               
                                 
                                   ɛ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   N 
                                 
                                 
                                   θ 
                                   
                                     cell 
                                     , 
                                     N 
                                   
                                 
                               
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
             
           
         
       
     
   
   If one assumes by a mathematical simplification that 
                 ɛ   1       θ     cell   ,   1         =       ɛ   N       θ     cell   ,   N           ,         
one therefore has: θ cell,1   2 =Nθ cell,N   2    
   The area of the covering surface (noted respectively A ser,1  for the conventional architecture and A ser,N  for the architecture with division of N spots by each TWTA tube) is therefore given by the following formula: 
   
     
       
         
           
             A 
             
               ser 
               , 
               1 
             
           
           = 
           
             
               
                 3 
                 ⁢ 
                 
                   3 
                 
                 ⁢ 
                 
                   N 
                   s 
                 
                 ⁢ 
                 
                   θ 
                   
                     cell 
                     , 
                     1 
                   
                   2 
                 
               
               8 
             
             ⁢ 
             
                 
             
             ⁢ 
             and 
           
         
       
     
     
       
         
           
             
               
                 
                   A 
                   
                     ser 
                     , 
                     N 
                   
                 
                 = 
                   
                 ⁢ 
                 
                   
                     3 
                     ⁢ 
                     
                       3 
                     
                     ⁢ 
                     
                       N 
                       s 
                     
                     ⁢ 
                     
                       θ 
                       
                         cell 
                         , 
                         N 
                       
                       2 
                     
                   
                   8 
                 
               
             
           
           
             
               
                 = 
                   
                 ⁢ 
                 
                   
                     3 
                     ⁢ 
                     
                       3 
                     
                     ⁢ 
                     
                       N 
                       s 
                     
                     ⁢ 
                     
                       θ 
                       
                         cell 
                         , 
                         1 
                       
                       2 
                     
                   
                   
                     8 
                     ⁢ 
                     N 
                   
                 
               
             
           
           
             
               
                 = 
                   
                 ⁢ 
                 
                   
                     A 
                     
                       ser 
                       , 
                       1 
                     
                   
                   N 
                 
               
             
           
         
       
     
   
   Thus, it can be noted that remaining at constant capacity, the fact of passing from a conventional architecture to an architecture with TWTA with N spots induces a reduction of a factor N of the number of TWTA and of the covering zone, the number of spots remaining constant. 
   The payloads  300  and  400  such as represented in  FIGS. 2   d ) and  2   e ) are respectively identical to the payloads  100  and  200  of  FIGS. 2   b ) and  2   c ) except that they comprise N s  CAMP (respectively 317 and 417) and N s  TWTA (respectively 318 and 418) instead of N s /2 CAMP and N s /2 TWTA, namely N times more amplifier equipment (with N=2). In other words, the number of spots provided by the payloads  300  and  400  is equal to N×N s  (with N=2). 
   Proceeding from a new hypothesis where:
         the eirp per spot are identical in a conventional architecture such as that of  FIG. 2   a ) and in an architecture with division of N spots by each TWTA tube ( FIG. 2   d ) or  2   e )),   the two architectures use TWTA tubes presenting the same power RF, one obtains:       

   
     
       
         
             
           
             
               
                 
                   
                     
                       C 
                       
                         FWD 
                         , 
                         N 
                       
                     
                     
                       C 
                       
                         FWD 
                         , 
                         1 
                       
                     
                   
                   = 
                     
                   ⁢ 
                   
                     
                       
                         
                           N 
                           
                             s 
                             , 
                             N 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               θ 
                               
                                 cell 
                                 , 
                                 1 
                               
                             
                             + 
                             
                               2 
                               ⁢ 
                               
                                 ɛ 
                                 1 
                               
                             
                           
                           ) 
                         
                       
                       2 
                     
                     
                       
                         
                           NN 
                           
                             s 
                             , 
                             1 
                           
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               θ 
                               
                                 cell 
                                 , 
                                 N 
                               
                             
                             + 
                             
                               2 
                               ⁢ 
                               
                                 ɛ 
                                 N 
                               
                             
                           
                           ) 
                         
                       
                       2 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         N 
                         
                           s 
                           , 
                           N 
                         
                       
                       ⁢ 
                       
                         θ 
                         
                           cell 
                           , 
                           1 
                         
                         2 
                       
                     
                     
                       
                         NN 
                         
                           s 
                           , 
                           1 
                         
                       
                       ⁢ 
                       
                         θ 
                         
                           cell 
                           , 
                           N 
                         
                         2 
                       
                     
                   
                 
               
             
           
         
       
     
   
   By constraining the two systems to present the same covering zone, one obtains: 
   
     
       
         
             
           
             
               
                 
                   
                     
                       N 
                       
                         s 
                         , 
                         1 
                       
                     
                     ⁢ 
                     
                       θ 
                       
                         cell 
                         , 
                         1 
                       
                       2 
                     
                   
                   = 
                     
                   ⁢ 
                   
                     
                       N 
                       
                         s 
                         , 
                         N 
                       
                     
                     ⁢ 
                     
                       θ 
                       
                         cell 
                         , 
                         N 
                       
                       2 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         N 
                         
                           s 
                           , 
                           N 
                         
                       
                       ⁢ 
                       
                         θ 
                         
                           cell 
                           , 
                           1 
                         
                         2 
                       
                     
                     N 
                   
                 
               
             
           
         
       
     
   
   The relation between the capacity C FWD,1  for the conventional architecture and C FWD,N  for the architecture with division of N spots by each TWTA tube is therefore given by: 
   
     
       
         
           
             
               C 
               
                 FWD 
                 , 
                 N 
               
             
             
               C 
               
                 FWD 
                 , 
                 1 
               
             
           
           = 
           N 
         
       
     
   
   Thus, the passage of a configuration such as that of  FIG. 2   a ) to a configuration such as that of  FIG. 2   d ) or  2   e ) allows the multiplication of the capacity by N (with N=2 in the illustrated examples). 
   According to the above, one can therefore define two criteria (criterion 1 and criterion 2) according to whether one wishes to conserve the same covering surface or the same capacity with respect to the conventional architecture of  FIG. 2   a ): these two criteria are summarized in Table 1 below: 
   
     
       
             
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
                 
                 
               Number 
               Number of 
                 
             
             
               Criterion 
               Covering zone 
               of spots 
               TWTA 
               Capacity 
             
             
                 
             
           
           
             
               1 
               Reduction of a 
               No change 
               Reduction of a 
               No change 
             
             
                 
               factor N 
                 
               factor N 
             
             
               2 
               No change 
               Increase of a 
               No change 
               Increase of a 
             
             
                 
                 
               factor N 
                 
               factor N 
             
             
                 
             
           
        
       
     
   
   The conclusions of Table 1 above are confirmed by the numeric values of Table 2 below, given respectively for a conventional payload of capacity C such as the payload  10  of  FIG. 2  a), an optimized payload of capacity C (criterion 1) such as the payload  100  or  200  of  FIG. 2   b ) or  2   c ), an optimized payload of capacity 2×C (criterion 2 with N=2) such as the payload  300  or  400  of  FIG. 2   d ) or  2   e ) and a conventional payload of capacity 2×C (not shown; this load is identical to the conventional load  10  but comprising two times more equipment, i.e. comprising 2N s  converters, input filters, CAMP, TWTA, output filters and horns). 
   
     
       
             
             
             
             
             
           
             
             
             
             
             
           
         
             
                 
               TABLE 2 
             
             
                 
                 
             
             
                 
               Conventional 
                 
                 
               Conventional 
             
             
                 
               payload 
                 
                 
               payload 
             
             
                 
               of 
                 
                 
               of 
             
             
                 
               capacity C 
               Criterion 1 
               Criterion 2 
               capacity 2C 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               Area of covering 
               9.4° 2   
               4.7° 2   
               9.4° 2   
               9.4° 2   
             
             
               zone 
             
             
               Number of spots 
               40 
               40 
               80 
               80 
             
             
               Area of a cell 
               0.24° 2   
               0.12° 2   
               0.12° 2   
               0.12° 2   
             
             
               External dimension 
               0.60° 
               0.43° 
               0.43° 
               0.43° 
             
             
               of a cell 
             
             
               Pointing error 
               0.06° 
               0.04° 
               0.04° 
               0.04° 
             
             
               Beam dimension 
               0.72° 
               0.51° 
               0.51° 
               0.51° 
             
             
               Gain of the antenna 
               44.2 dBi 
               47.2 dBi 
               47.2 dBi 
               47.2 dBi 
             
             
               Number of TWTA 
               40 
               20 
               40 
               80 
             
             
               RF power of a 
               130 W 
               130 W 
               130 W 
               65 W 
             
             
               TWTA 
             
             
               EIRP of the system* 
               76.5 dBW 
               76.5 dBW 
               79.5 dBW 
               79.5 dBW 
             
             
               Capacity 
               10.0 GHz 
               10.0 GHz 
               20.1 GHz 
               20.1 GHz 
             
             
                 
             
             
               *Corresponds to the total eirp provided by the system and not to the eirp available per spot; thus, a double capacity with respect to a reference system must provide a double eirp of this system, namely 3 dB more.” 
             
           
        
       
     
   
   Below the configuration of the different payloads described above are analyzed with reference to  FIGS. 2   a ) to  2   e ) in terms of mass balance. Concerning the reference payload as represented in  FIG. 2   a ) with a single spot by TWTA and a capacity C, the mass of this payload is expressed as follows:
 
 M   FWD,1,C =2 N   GW   m   LNA +2 N   GW   m   split   +N   s   m   FC   +N   s   m   TWTA   +N   s   m   f   +N   a   m   refl   G   1   (Relation 1)
 
   Where
         M FWD  is the mass of the payload  10 ,   m LVA  is the mass associated with the low noise amplifier  12 ,   m split  is the mass associated with the divider device  13 ,   m FC  is the mass associated with the frequency converter,   m TWTA  is the mass associated with the high power amplifier  16 ,   m f  is the mass associated with each antenna feed  20 ,   m refl  is the specific mass associated with the reflectors and with the structure of the antenna as a function of gain,   N a  is the number of antennae,   G is the gain of the antenna expressed in the form of a ratio (and not in dB).       

   It will be noted that the contribution of the filters  15  and  19  will be considered as identical in all the configurations studied below and will therefore not be taken into account in the calculations. 
   Concerning a reference payload with a single spot per TWTA and a capacity N×C, it will be identical to that of  FIG. 2   a ) but comprising N times more equipment, i.e. comprising N×N s  converters, input filters, CAMP, TWTA, output filters and horns. Consequently, the mass of this reference payload with a capacity N×C is expressed as follows:
 
 M   FWD,1,NC =2 NN   GW   m   LNA +2 NN   GW   m   split   +NN   s   m   FC   +NN   s   m   TWTA   +NN   s   m   f   +NN   a   m   refl   G   1   (Relation 1′)
 
   In the following, we will place ourselves under the hypothesis of criterion 1 mentioned above (maintained capacity C). As already described, two scenarios are possible, according to whether one introduces no frequency constraint (scenario 1 of  FIG. 2   b )) or one introduces a frequency constraint (scenario 2 of  FIG. 2   c )). 
   Criterion 1 
   Scenario 1 
   The mass of the payload of  FIG. 2   b ) is expressed as follows: 
   
     
       
         
           
             M 
             FWD 
           
           = 
           
             
               2 
               ⁢ 
               
                 N 
                 GW 
               
               ⁢ 
               
                 m 
                 LNA 
               
             
             + 
             
               2 
               ⁢ 
               
                 N 
                 GW 
               
               ⁢ 
               
                 m 
                 split 
               
             
             + 
             
               
                 N 
                 s 
               
               ⁢ 
               
                 m 
                 FC 
               
             
             + 
             
               
                 
                   N 
                   s 
                 
                 ⁢ 
                 
                   m 
                   TWTA 
                 
               
               N 
             
             + 
             
               
                 N 
                 s 
               
               ⁢ 
               
                 m 
                 f 
               
             
             + 
             
               
                 NN 
                 a 
               
               ⁢ 
               
                 m 
                 refl 
               
               ⁢ 
               
                 G 
                 1 
               
             
           
         
       
     
   
   Comparing this relation 2 with the relation 1 above ( FIG. 2   a )), the difference between the two relations gives us: 
   
     
       
         
             
           
             
               
                 
                   
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             M 
                             FWD 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             M 
                             
                               FWD 
                               , 
                               1 
                               , 
                               C 
                             
                           
                           - 
                           
                             M 
                             FWD 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   1 
                                   N 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               N 
                               s 
                             
                             ⁢ 
                             
                               m 
                               TWTA 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             
                               N 
                               a 
                             
                             ⁢ 
                             
                               m 
                               refl 
                             
                             ⁢ 
                             
                               G 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
   
   Scenario 2 
   The mass of the payload of  FIG. 2   c ) is expressed as follows: 
   
     
       
         
           
             
               
                 
                   M 
                   FWD 
                 
                 = 
                 
                   
                     2 
                     ⁢ 
                     
                       N 
                       GW 
                     
                     ⁢ 
                     
                       m 
                       LNA 
                     
                   
                   + 
                   
                     2 
                     ⁢ 
                     
                       N 
                       GW 
                     
                     ⁢ 
                     
                       m 
                       split 
                     
                   
                   + 
                   
                     
                       
                         N 
                         s 
                       
                       ⁢ 
                       
                         m 
                         FC 
                       
                     
                     N 
                   
                   + 
                   
                     
                       
                         N 
                         s 
                       
                       ⁢ 
                       
                         m 
                         TWTA 
                       
                     
                     N 
                   
                   + 
                   
                     
                       N 
                       s 
                     
                     ⁢ 
                     
                       m 
                       f 
                     
                   
                   + 
                   
                     
                       NN 
                       a 
                     
                     ⁢ 
                     
                       m 
                       refl 
                     
                     ⁢ 
                     
                       G 
                       1 
                     
                   
                 
               
             
             
               
                 ( 
                 
                   Relation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
                 ) 
               
             
           
         
       
     
   
   Comparing this relation 3 with the relation 1 above ( FIG. 2   a )), the difference between the two relations gives us: 
   
     
       
         
             
           
             
               
                 
                   
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             M 
                             FWD 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             M 
                             
                               FWD 
                               , 
                               1 
                               , 
                               C 
                             
                           
                           - 
                           
                             M 
                             FWD 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               
                                 N 
                                 s 
                               
                               ( 
                               
                                 1 
                                 - 
                                 
                                   1 
                                   N 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   m 
                                   FC 
                                 
                                 + 
                                 
                                   m 
                                   TWTA 
                                 
                               
                               ) 
                             
                           
                           - 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             ( 
                             
                               N 
                               - 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           
                             N 
                             a 
                           
                           ⁢ 
                           
                             m 
                             refl 
                           
                           ⁢ 
                           
                             G 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
   
     FIG. 5  represents the linear evolution of the mass of the payload as a function of the number of spots in the three cases mentioned above (Relation 1: reference case of  FIG. 2   a )—Relation 2: case of scenario 1—Relation 3: case of scenario 2) in the case where N=2. It will be noted that as the two first terms are identical in the three relations 1 to 3, they have been omitted in the representation of  FIG. 5 : this omission allows the representation to be made independent of the input section and entails solely a staggering according to the axis of the ordinates. 
   The intersection, respectively of the reference line and of the line linked to scenario 1 and of the reference line and of the line linked to the scenario 2, corresponds to the resolution of ΔM FWD =0 (respectively for Equation 1 and Equation 2). 
   It is consequently found that, beyond a threshold value (N threshold1  for the payload of scenario and N threshold2  for the payload of scenario 2) of the number of spots, the mass of the payload of scenarios 1 and 2 is less than the reference payload. In the case of  FIG. 5 , it is observed that N threshold1  is approximately equal to 23 and that N threshold2  is approximately equal to 18. Typically, for N=2 (two spots per TWTA) one will take threshold number of spots N threshold  greater than 15 and preferably greater than 20. Of course, the fact of imposing a frequency constraint ( FIG. 2   c )) allows the mass of the payload to be reduced more. 
     FIG. 5  likewise represents the linear evolution of the capacity as a function of the number of spots. It is found that the threshold number of spots beyond which the configurations of  FIG. 2   b ) or  2   c ) are more advantageous than the reference configuration can likewise be expressed by a threshold capacity: in the case of 20 spots for example, the threshold capacity is approximately equal to 5 GHz. 
   In conclusion, the optimization method according to the invention allows the optimization in terms of mass of a reference payload passing to a payload comprising amplifier tubes each amplifying N (N=2) spots when the capacity is greater than 5 Ghz in the example above (or when the number of spots is greater than 20). Of course, the threshold spot number or the threshold capacity depends on the different masses of the components and on the selected technology. 
   Furthermore, it should be noted that the mass could equally take into account the auxiliary equipment and also the equipment necessary to ensure redundancy functions in the case of breakdown; to simplify the presentation, these contributions have not been taken into account. However, these disregarded contributions do not alter the result which is obtained. In addition, in so far as the number of equipment items is reduced (reduction in the number of amplifiers in the case of scenarios 1 and 2, in fact the number of frequency converters in the case of scenario 2), the taking into account of the redundancy equipment would only be more advantageous in terms of mass gain. 
   Similar comparison calculations between the reference configuration and the configurations with several spots per amplifier show that the optimization allows not only a gain in terms of mass of the payload but equally a reduction in terms of power requirement DC necessary and of thermal dissipation. 
   In the following, we will place ourselves under the hypothesis of criterion 2 mentioned above (capacity C multiplied by N). As already described, two scenarios are possible, according to whether one introduces no frequency constraint (scenario 1 of  FIG. 2   d )) or one introduces a frequency constraint (scenario 2 of  FIG. 2   e )). 
   It will be noted in addition that the noted number of spots N s  below corresponds to the total number of spots of criterion 1; in the case of criterion 2, the total number of spots is N×N s , the notation of criterion 1 having been maintained to conserve a certain normalisation. 
   Criterion 2 
   Scenario 1 
   The mass of the payload of  FIG. 2   d ) is expressed as follows:
 
 M   FWD =2 NN   GW   m   LNA +2 NN   GW   m   split   +NN   s   m   FC   +N   s   m   TWTA   +NN   s   m   f   +NN   a   m   refl   G   1   (Relation 2′).
 
   Comparing this relation 2′ with relation 1′, the difference between the two relations gives us: 
   
     
       
         
             
           
             
               
                 
                   
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             M 
                             FWD 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             M 
                             
                               FWD 
                               , 
                               1 
                               , 
                               NC 
                             
                           
                           - 
                           
                             M 
                             FWD 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             ( 
                             
                               N 
                               - 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           
                             N 
                             s 
                           
                           ⁢ 
                           
                             m 
                             TWTA 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       1 
                       ′ 
                     
                   
                   ) 
                 
               
             
           
         
       
     
   
   Scenario 2 
   The mass of the payload of  FIG. 2   e ) is expressed as follows:
 
 M   FWD =2 NN   GW   m   LNA +2 NN   GW   m   split   +N   s   m   FC   +N   s   m   TWTA   +NN   s   m   f   +NN   a   m   refl   G   1   (Relation 3′)
 
   Comparing this relation 3′ with relation 1′, the difference between the two relations gives us: 
   
     
       
         
             
           
             
               
                 
                   
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             M 
                             FWD 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             M 
                             
                               FWD 
                               , 
                               1 
                               , 
                               NC 
                             
                           
                           - 
                           
                             M 
                             FWD 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             ( 
                             
                               N 
                               - 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           
                             
                               N 
                               s 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   m 
                                   FC 
                                 
                                 + 
                                 
                                   m 
                                   TWTA 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       2 
                       ′ 
                     
                   
                   ) 
                 
               
             
           
         
       
     
   
   A resolution of the equation ΔM FWD =0, for equation 1′ and for equation 2′, shows that whatever the value of the number of spots, each of the configurations of  FIG. 2   d ) or  2   e ) is more advantageous in terms of mass than the reference configuration of identical capacity N×C using one spot per TWTA tube. It is therefore found that, contrary to criterion 1, the application of criterion 2 always entails a more favourable situation on the mass balance when several spots are shared on a same tube. 
   In addition, it is important to note that passing from a reference configuration with a capacity C ( FIG. 2   a )) to an optimized configuration ( FIG. 2   d ) or  2   e )), the capacity and the number of spots are doubled without doubling the mass. In other words, the mass of optimized payload is increased by a factor less than N (N=2). Furthermore, the merit figure of the satellite on the return link is a direct function of the number of spots; consequently, this merit figure will increase considerably. 
   As for criterion 1, similar comparison calculations between the reference configuration of capacity 2×C and the configurations with several spots per amplifier show that the optimization allows not only a gain in terms of mass of the payload but equally a reduction in terms of power requirement DC necessary and of thermal dissipation. 
   Of course, the invention is not limited to the form of embodiment which has just been described. In particular, the invention has been described more particularly in the case where N is equal to 2; the method according to the invention is applicable to any natural whole number N strictly greater than 1 so that the number is spots N s  is a multiple of N. 
   Furthermore, we have more specifically described the case of a chain of amplification comprising a CAMP followed by a TWTA. However, it will be noted that the method according to the invention is equally applicable to the case of an amplifier SSPA or equipment of the MPA type. In the case of an MPA, of constant capacity and from a threshold spot number or a threshold capacity value, the reference MPA equipment comprising N s  inputs and N s  outputs and intended to amplify N s  spots is replaced by MPA equipment comprising N s /N inputs and N s /N outputs and intended to amplify N s  spots distributed over the N s /N inputs. When the capacity C is multiplied by N, the reference MPA equipment comprising N s  inputs and N s  outputs and intended to amplify N s  spots is replaced by MPA equipment comprising N s  inputs and N s  outputs and intended to amplify N×N, spots distributed over the N s  inputs. 
   Finally, any means can be replaced by an equivalent means.