How do I calculate the effective radiated power required for a communications jammer at a given range?

Calculating the effective radiated power (ERP) required for a communications jammer at a given range involves determining the power needed at the jammer's output to create a jamming-to-signal ratio (J/S) sufficient to disrupt the target communication link. The calculation uses the jammer-to-signal ratio equation: J/S = (P_j x G_j x R_t^2 x G_r_j) / (P_t x G_t x R_j^2 x G_r_s x L), where P_j is the jammer transmit power, G_j is the jammer antenna gain toward the target receiver, R_t is the range from the transmitter to the receiver (the wanted link), G_r_j is the target receiver's antenna gain toward the jammer, P_t is the legitimate transmitter's power, G_t is the transmitter's antenna gain toward the receiver, R_j is the range from the jammer to the target receiver, G_r_s is the receiver's antenna gain toward the legitimate transmitter, and L accounts for losses. For effective jamming: J/S must exceed a threshold that depends on the communication system's modulation and coding: for analog FM: J/S > 0-6 dB. For digital QPSK without FEC: J/S > 10-15 dB. For spread spectrum with PG = 30 dB: J/S > 30-40 dB (the jammer must overcome the processing gain). The required jammer ERP is: ERP_j = P_j x G_j = (J/S_required x P_t x G_t x R_j^2 x G_r_s x L) / (R_t^2 x G_r_j). For example, to jam a 10 W UHF radio at R_t = 10 km with the jammer at R_j = 20 km: ERP_j = (10 dB x 10 W x 6 dBi x (20 km)^2 x 0 dBi) / ((10 km)^2 x 0 dBi) = 400 W ERP (for J/S = 10 dB). If the target uses spread spectrum with PG = 20 dB: the required ERP increases to 40,000 W (much more challenging).