JAMMING TO SIGNAL (J/S) RATIO
CONSTANT GAIN [LINEAR] JAMMING

JAMMING TO SIGNAL (J/S) RATIO (MONOSTATIC) Gja(Rx) = The Gain of the jammer receive antenna Gja(Tx) = The Gain of the jammer transmit antenna Gj = The gain of the jammer or: 10log J/S = 10log Gja(Rx) + 10log Gj + 10log Gja(Tx) - 10log (4/2 ) or if simplified radar equations developed in previous sections are used: 10log J/S = 10log Gja(Rx) + 10log Gj + 10log Gja(Tx) - G (dB) * Keep and in same units. Note: = c/f

Target gain factor (in dB): G = 10log + 20log f1 + K2 K2 Values (dB) RCS () (units) f1 in MHz K2 = f1 in GHz K2 = m 2 -38.54 21.46 ft 2 -48.86 11.14

JAMMING TO SIGNAL (J/S) RATIO (BISTATIC) Same as the monostatic case except G will be different since RCS () varies with aspect angle.

Since the jammer on the target is amplifying the received radar signal before transmitting it back to the radar, both J and S experience the two way range loss. Figure 1 shows that the range for both the signal and constant gain jamming have a slope that is 40 dB per decade.

Once the jammer output reaches maximum power, that power is constant and the jamming slope changes to 20 dB per decade since it is only a function of one way space loss and the J/S equations for constant power (saturated) jamming must be used.

Normally the constant gain (linear) region of a repeater jammer occurs only at large distances from the radar and the constant power (saturated) region is reached rapidly as the target approaches the radar. When a constant gain jammer is involved it may be necessary to plot jamming twice - once using J from equation [1] in the J/S - Constant Power (Saturated) Section and once using the constant gain (linear) equation [4] (shown later), as in the example shown in Figure 1.

CONSTANT GAIN SELF PROTECTION DECM

Most jammers have a constant power output - that is, they always transmit the maximum available power of the transmitter (excepting desired ECM modulation). Some jammers also have a constant gain (linear) region. Usually these are coherent repeaters that can amplify a low level radar signal to a power that is below the level that results in maximum available (saturated) power output. At some radar to target range, the input signal is sufficiently high that the full jammer gain would exceed the maximum available power and the jammer ceases to be constant gain and becomes constant power.

To calculate the power output of a constant gain jammer where:
S_Rj = The Radar signal at the jammer input (receive antenna terminals)
G_ja(Rx) = The Gain of the jammer receive antenna
G_j = The gain of the jammer
_Tx = The one-way free space loss from the radar to the target
P_jCG = The jammer constant gain power output
P_j = The maximum jammer power output
L_R = The jammer receiving line loss; combine with antenna gain G_ja(Rx)

From equation [10], in the One-Way Radar Equation Section, calculate the radar power received by the jammer.

10log S_Rj = 10log P_t + 10log G_t - _Tx + 10log G_ja(Rx) (factors in dB) [1]

The jammer constant gain power output is:

10log P_jCG = 10log S_Rj + 10log G_ja [2]

and, by definition: P_jCG < or = P_j [3]

MONOSTATIC

The equivalent circuit shown in Figure 2 is different from the constant power equivalent circuit in Figure 4 in the J/S - Constant Power (saturated) Section. With constant gain, the jamming signal experiences the gain of the jammer and its antennas plus the same space loss as the radar signal.

To calculate J, the one way range equation is used twice:

[4]

From the Two-way Range Equation Section: [5]

Terms cancel when combined: [6]

Or in dB form: 10log J/S = 10log G_ja(Rx) + 10log G_j + 10log G_ja(Tx) - 10log (4/² ) [7]

Since the last term can be recognized as minus G from equation [10] in the Two-Way Radar Equation (Monostatic) Section, where the target gain factor, G = 10log (4/² ) = 10log (4 f ² /c ² ), it follows that:

10log J/S = 10log G_ja(Rx) + 10log G_j + 10log G_ja(Tx) - G (factors in dB) [8]

Target gain factor, G = 10log + 20log f1 + K2 (in dB)

K2 Values (dB) RCS () (units) f1 in MHz K2 = f1 in GHz K2 = m 2 -38.54 21.46 ft 2 -48.86 11.14

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BISTATIC

The bistatic equivalent circuit shown in Figure 3 is different from the monostatic equivalent circuit shown in Figure 2 in that the receiver is separately located from the transmitter, R_Tx does not equal R_Rx or R_Jx and G will be different since the RCS () varies with aspect angle.

To calculate J, the one way range equation is used twice:

(R_Jx = R_Rx) [9]

From the two way range equation:

(' is bistatic RCS) [10]

Terms cancel when combined: [11]

Or in dB form: 10log J/S = 10log G_ja(Rx) + 10log G_j + 10log G_ja(Tx) - 10log (4'/² ) [12]

Since the last term can be recognized as minus G from equation [10] in the Two-Way Radar Equation (monostatic) Section, where the target gain factor, G = 10log (4'/² ) = 10log (4'f ² /c ² ), it follows that:

10log = 10log G_ja(Rx) + 10log G_j + 10log G_ja(Tx) - G_'(factors in dB) [13]

Linear J/S (Monostatic) Example (Linear Power Jamming)

Assume that a 5 GHz radar has a 70 dBm signal fed through a 5 dB loss transmission line to an antenna that has 45 dB gain. An aircraft that is flying 31 km from the radar has an aft EW antenna with -1 dB gain and a 5 dB line loss to the EW receiver (there is an additional loss due to any antenna polarization mismatch but that loss will not be addressed in this problem). The received signal is fed to a jammer with a gain of 60 dB, feeding a 10 dB loss transmission line which is connected to an antenna with 5 dB gain.

If the RCS of the aircraft is 9 m² , what is the J/S level received at the input to the receiver of the tracking radar?

Answer:

10log J/S = 10log G_ja(Rx) + 10log G_j + 10log G_ja(Tx) - G

G = 10log + 20log f₁ + K₂ = 10log 9 + 20log 5 + 21.46 = 44.98 dB

Note: The respective transmission line losses will be combined with antenna gains, i.e. -1 -5 = -6 dB and -10 + 5 = -5 dB

10log J/S = -6 + 60 - 5 - 44.98 = 4.02 dB @ 5 GHz

The answer changes to 1.1 dB if the tracking radar operates at 7 GHz provided the antenna gains and aircraft RCS are the same at both 5 and 7 GHz.

G = 10log 9 + 20log 7 + 21.46 = 47.9 dB

10log J/S = -6 + 60 - 5 - 47.9 = 1.1 dB @ 7 GHz

Separate J (-73.5 dBm @ 5 GHz and -79.34 dBm @ 7 GHz) and S (-77.52 dBm @ 5 GHz and -80.44 dBm @ 7 GHz) calculations for this problem are provided in the One-Way and Two-Way Radar Equation Sections, respectively. A saturated gain version of this problem is provided in the J/S Ratio - Constant Power (Saturated) Jamming Section.