attachment:fra0.c of GHTC2015

   1 // fra0.c  fraunhofer rings and low elevation SSPS rectenna.
   2 // cc -o fra0 fra0.c -lm
   3 //
   4 // This computes the path from an -5° SSPS to a rectenna at 46° N 
   5 // and 30° west.  This gives us the antenna elevation.  We then 
   6 // assume a circular aperture, and a rectenna expanded by 1/sin(elevation)
   7 // to catch diagonal beams.  
   8 //
   9 // Skolnik says 0.7dB loss at 2.5 GHz and 25 degrees elevation, 
  10 //   thus an 85% efficiency multiplier.  If the rectenna is 85% 
  11 //   efficient, and we have 91% beam capture efficiency and 95%
  12 //   electrical grid efficiency, the broadcast to load efficiency
  13 //   is 69% .  That turns 7 GW broadcast into 4.8 GW to the customer.
  14 
  15 #define	 STEP	0.001		// m q step
  16 #define  DMAX	2113.1000	// m   rectenna diameter
  17 #define	 APER	5000.0000	// m   ssps aperture diameter
  18 
  19 #define  FREQ	2.450E+09	// hz  frequency
  20 #define	 C	2.998E+08	// m/s lightspeed
  21 #define	 GEO	42164000	// m GEO radius
  22 #define  RE	6371000  	// m Earth radius
  23 #define  SOUTH	5.00    	// degrees SSPS offset latitude south 
  24 #define  LAT	46.1920  	// degrees rectenna latitude
  25 #define	 LON	30.0000		// degrees rectenna longitude west
  26 
  27 #include <math.h>
  28 #include <stdio.h>
  29 
  30 int main() {
  31    double pi   = 4.0*atan(1.0)			 ;//       pi
  32    double d2r  = atan(1.0)/45.0			 ;//       degrees to radians
  33    double r2d  = 45.0/atan(1.0)			 ;//       radians to degrees
  34    double dNS  = SOUTH+LAT			 ;// deg   northsouth
  35    double rNS  = d2r*dNS	         	 ;// rad   northsouth
  36    double wl   = (C/FREQ)			 ;// m     wavelength
  37    double rEW  = d2r*LON			 ;// rad   eastwest
  38    double rtot = acos(cos(rNS)*cos(rEW))	 ;// rad   total angle
  39    double dtot = r2d*rtot			 ;// deg   total angle
  40    double zz   = RE*sin(rtot)			 ;// m     Z
  41    double xg   = GEO-RE*cos(rtot)		 ;// m     X to geo
  42    double dist = sqrt( zz*zz + xg*xg )		 ;// m     distance 
  43    double rel  = atan(xg/zz)-rtot		 ;// rad   elevation
  44    double del  = r2d*rel			 ;// deg   elevation
  45    double d    = APER				 ;// m     aperture diameter
  46    double xsca = pi * d / (wl*dist)		 ;// 1/m   scaling argument
  47 
  48    double qs   = STEP				 ;// m     integration step
  49    double q    					 ;// m     center of annulus
  50 
  51    double i0p  = 2.0*qs/xsca*xsca		 ;// 1/m2  power scaling
  52    double pow  = 0.0				 ;//       total power
  53    double bs                                     ;//       bessel function
  54    double btest                                  ;//
  55    double rmax = 0.5*DMAX			 ;// m     rectenna diameter
  56 
  57    for( q = 0.5*qs ; q < DMAX ; q += STEP ) {
  58       bs   = j1(xsca*q)       			 ;// m2	   additional area
  59       pow += bs * bs / q			 ;// 
  60    }
  61    pow *= i0p 					 ;//
  62    double lost = 1.0 - pow                       ;//
  63    double sin1 = 1/sin(rel)                      ;//
  64    double sin2 = DMAX/sin(rel)                   ;//
  65 
  66    printf( "%10.3e    bessel\n"                  , bs    ) ;
  67    printf( "%10.7f    fractional power\n"        , pow   ) ;
  68    printf( "%10.7f    lost power\n"              , lost  ) ;
  69    printf( "%9.1f m   Rectenna diameter\n"       , DMAX  ) ;
  70    printf( "%9.1f m   SSPS diameter\n"           , APER  ) ;
  71    printf( "%9.4f°    SSPS south\n"              , SOUTH ) ;
  72    printf( "%9.4f°    Rectenna latitude\n"       , LAT   ) ;
  73    printf( "%9.4f°    Rectenna longitude\n"      , LON   ) ;
  74    printf( "%9.4f°    Rectenna total angle\n"    , dtot  ) ;
  75    printf( "%9.4f°    Rectenna elevation\n"      , del   ) ;
  76    printf( "%9.5f     Rectenna 1/sin\n"          , sin1  ) ;
  77    printf( "%9.1f     Rectenna D/sin\n"          , sin2  ) ;
  78    printf( "%10.3e m  distance\n"                , dist  ) ;
  79    return(0);
  80 }