# EW Equations and Diagrams

 Effective   Jam Power Jam Power at the Receiver Input Jam Power of a Jamming  Source Self  Screening Range Mutual Screening Range Chaff Losses (Radar)

 Effective Jam Power Equation:    PJeff    =    PJ  x  GJ     (Watt) Examble:    PJ = 200 Watt                      GJ = 6 dB (4)            200 x 4     =     800 Watt If     BWR    < then   BWJ   then    PJeff     =    PJ  x  (BWR  /  BWJ) If    BWR J    then     PJeff    =    PJ x  (BWJ  /  BWR) BWR = Bandwidth Radar BWJ = Jamming Bandwidth Jammer PJeff = Effective Jamming Power Jam Power at the RADAR Receiver Input Equation:     JPr    =     ((PJ x GJ x GR x lam2 x BWR)     /     ((4 x pi)2 x R2J x BWJ x L)) JPr        = Jam Power at Receiver (Watt) PJ         = Jammer Transmitted Power (Watt) GJ         = Antenna Gain Jammer (Figure) GR        = Antenna Gain Radar (Figure) lam       = Wavelength (m) BWR     = IF Bandwidth Radar (Hz) RJ         = Range to Jammer (m) BWJ     = Jamming Bandwidth L          = Losses BWR and BWJ are matched no Losses! PJ    GJ    GR        lam2             BWR                   pi       230 km         BWJ      L JPr    =     (200 x 4 x 3162 x 0.0083266 x 1)   /   (158  x  5.2910   x   1   x   1)   =   2.5-9 Watt or - 86 dBW Jam Power of a Jamming Source Equation:    PJ    = (JPr x (4 x pi)2 x R2J x BWJ x L)    /    ( GJ x GR x lam2 x BWR) PJ         = Jammer Transmitted Power (Watt) JPr        = Jam Power at Receiver Input (Watt) RJ        =  Range to Jamming Source (m) BWJ     = Jamming Bandwidth (Hz) L           = Losses (Figure) GJ         = Antenna Gain Jammer (Figure) GR        = Antenna Gain Radar (Figure) lam       = Wavelength (m) BWR    = IF Bandwidth Radar (Hz) JPr              pi      50km      BWJ    19dB           6dB        44dB         0.033     BWR PJ    =     (7.08-10  x 158 x 2.59 x   16  x   79)  /  (4   x   25119   x 1.09-3  x 16)     =    201.73 Watt Self-Screening Range Equation: RSS = ((PR x GR x sig x BWJ x GP)    /    (PJ x GJ x 4 x pi x BWR x S/N))0.5 RSS    = Range Self Screening (m) PR      = Radar Transmitted RF Power (Watt) GR      = Radar Antenna Gain (Figure, LOPAR Pencil Beam) sig    = Radar Cross Section of Jammer (sq. m) BWJ    = Bandwidth of Jamming (Hz) Gp     = Gain Processing (MTI, Integration etc.) PJ     = Transmitted Jamming Power (Watt) GJ     = Antenna Gain of Jammer BWR    = IF Bandwidth of Radar S/N      = Necessary Signal to Noise Ratio PR               GR       sig   BWJ     GP                PJ         GJ                   BWR      S/N RSS    = (( 1 000 000 x 3162 x  3  x  16  x  1 )  / ( 200  x   4 x 12.57 x 16    x    1  ))0.5     =  971 m Under the above conditions the LOPAR could not detect the target early enough for an engagement!

 Diagram Self Screening RangeComparison between the TTR, LOPAR & HIPAR Variables TTR SP TTR LP LOPAR HIPAR Pav 28 280 500 26000 G 44 44 35 34.8 RCS 10 10 10 10 Td 100 100 22 19 Loss Jammer 6 6 6 6 S/N 3 3 3 3 Loss Radar 22 22 20 18 G Jammer 6 6 6 6 BW Radar (MHz) 10 1 1 .3 DIAGRAM  MutualScreening Range Equation:  RS    = (( PR x GR x GR x sig x R2J  x BWJ x GP)    /     (PJ x GJ x GRJ x 4 x pi x BWR x S/N x L))0.25 RS       = Range Screening (m) PR        = Radar Transmitted RF Power (Watt) GR        = Radar Antenna Gain (Figure, LOPAR Pencil Beam) sig       = Radar Cross Section of Jammer (sq. m) R          = Range to Jammer (m) BWJ    = Bandwidth of Jamming (Hz) Gp        = Gain Processing,MTI, Integration etc.. (Figure) PJ        = Transmitted Jamming Power (Watt) GJ       = Antenna Gain of Jammer (Figure) GRJ     = Radar Antenna Gain in the Direction of Jammer (Figure) BWR   = IF Bandwidth of Radar (Hz) S/N      = Necessary Signal to Noise Ratio (Figure) L         = Jammer Losses (Figure) Examble: Target will be screened by a Jammer.  Target and Jammer are in the main beam of the LOPAR antenna. PR          GR x GR           sig       R2J        BWJ        GP                PJ       GJ    GRJ                        BWR   S/N    L RS    =    ((1 000 000 x 10 000 000 x 3 x 1.08911 x  16    x  1)  /  (1 000 x 4 x 3162 x 12.58  x  16 x 1  x  1))0.25  The Target will be visible at =   11 970 m Diagram Mutual Screening RangeComparison between the TTR, LOPAR & HIPAR Variables TTR SP TTR LP LOPAR HIPAR Pav 28 280 500 26000 G 44 44 35 34.8 RCS 10 10 10 10 Dwell Time 100 100 22 19 BW Jamming (MHz) 100 100 100 100 Range Jammer (km) 300 300 300 300 SNR 3 3 3 3 Loss Radar 22 22 20 18 G Jammer 6 6 6 6 BW Radar 10 1 1 .3 G direction of Jammer 44 44 35 34.8 DIAGRAM  ## Chaff

One CHAFF-UNIT (CU) = 50 sq. m

500 Gramm aluminium CHAFF for the
F-Band (3 - 4 GHz) consist of 1.37 million Chaff Dipols
G-Band (4 -6 GHz)         "           2.05 million Chaff Dipols
I-Band (8 - 10 GHz)        "            4.10 million Chaff Dipols

Quantity of Chaff Dipols to simulate a specific target.

Equation:   N = deltaRCS    /    0.18 x lam2
N = Number of Dipols
deltaRCS = simulated Radar Cross Section (RCS)
lam           = Wavelength (9.12 cm for the example)
deltaRCS       9.122
Example:        N    =    100    /    (0.18 x 0.0083266)    = 66 720 Dipols are needed 