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JAMMING TO SIGNAL (J/S) RATIO  CONSTANT POWER [SATURATED] JAMMING
The following table contains a summary of the equations developed in this section.
This section derives the J/S ratio from the oneway range equation for J and the twoway range equation for S,
and deals exclusively with active (transmitting) ECM devices or systems. Furthermore, the only purpose of the ECM
considered is to prevent, delay, or confuse the radar processing of target information.
By official
definition, ECM can be either Jamming or Deception. This may be somewhat confusing because almost any type of
active ECM is commonly called "jamming", and the calculations of ECM signal in the radar compared to the target
signal in the radar commonly refer to the "jammingtosignal" ratio ("JtoS" ratio). Therefore this section uses
the common jargon and the term "jammer" refers to any ECM transmitter, and the term "jamming" refers to any ECM
transmission, whether Deception or Concealment.
Jamming: "Official" jamming should more
aptly be called Concealment or Masking. Essentially, Concealment uses ECM to swamp the radar receiver and hide
the targets. Concealment (Jamming) usually uses some form of noise as the transmitted ECM signal. In this section,
Concealment will be called "noise" or "noise jamming".
Deception: Deception might be better called Forgery.
Deception uses ECM to forge false target signals that the radar receiver accepts and processes as real targets.
"J" designates the ECM signal strength whether it originates from a noise jammer or from a deception ECM system.
Basically,
there are two different methods of employing active ECM against hostile radars:
Self Protection ECM
Support ECM
For most practical purposes, Self Protection ECM is usually Deception and Support ECM is
usually noise jamming. As the name implies, Self Protection ECM is ECM that is used to protect the platform that
it is on. Self Protection ECM is often called "self screening jamming", and also "DECM", which is an acronym for
either "Defensive ECM" or "Deception ECM". The top half of Figure 1 shows self screening jamming (DECM).
The bottom half of Figure 1 illustrates escort jamming which is a special case of support jamming. If the escort
platform is sufficiently close to the target, the JtoS calculations are the same as for DECM.
Support
ECM is ECM radiated from one platform and is used to protect other platforms. Figure 2 illustrates two cases of
support jamming  standoff jamming (SOJ) and standin jamming (SIJ). For SOJ the support jamming platform is
maintaining an orbit at a long range from the radar  usually beyond weapons range. For SIJ, a remotely piloted
vehicle is orbiting very close to the victim radar. Obviously, the jamming power required for the SOJ to screen a
target is much greater than the jamming power required for the SIJ to screen the same target.
When
factoring ECM into the radar equation, the quantities of greatest interest are "JtoS" and Burn Through Range.
"JtoS" is the ratio of the signal strength of the ECM signal (J) to the signal strength of the target return
signal (S). It is expressed as "J/S" and, in this section, is always in dB. J usually (but not always) must exceed
S by some amount to be effective, therefore the desired result of a J/S calculation in dB is a positive number.
Burnthrough Range is the radar to target range where the target return signal can first be detected through the
ECM and is usually slightly farther than crossover range where J=S. It is usually the range where the J/S just
equals the minimum effective J/S (See Section 48).
The significance of "JtoS" is sometimes
misunderstood. The effectiveness of ECM is not a direct mathematical function of "JtoS". The magnitude of the
"JtoS" required for effectiveness is a function of the particular ECM technique and of the radar it is being
used against. Different ECM techniques may very well require different "JtoS" ratios against the same radar.
When there is sufficient "JtoS" for effectiveness, increasing it will rarely increase the effectiveness at a
given range. Because modern radars can have sophisticated signal processing and/or ECCM capabilities, in certain
radars too much "JtoS" could cause the signal processor to ignore the jamming, or activate special antijamming
modes. Increasing "JtoS" (or the jammer power) does, however, allow the target aircraft to get much closer to
the threat radar before burnthrough occurs, which essentially means more power is better if it can be controlled
when desired.
IMPORTANT NOTE: If the signal S is CW or PD and the
Jamming J is amplitude modulated, then the J used in the formula has to be reduced from the peak value (due to
sin x/x frequency distribution). The amount of reduction is dependent upon how much of the bandwidth is
covered by the jamming signal. To get an exact value, integrals would have to be taken over the bandwidth. As
a rule of thumb however:
 C If the frequency of modulation is less than the BW of the tracking radar reduce J/S by 10 Log(duty
cycle).
 C If the frequency of modulation is greater than the BW of the tracking radar reduce J/S by 20 Log(duty
cycle).
For example; if your jamming signal is square wave chopped (50% duty cycle) at a 100 Hz rate while jamming
a 1 kHz bandwidth receiver, then the J/S is reduced by 3 dB from the maximum. If the duty cycle was 33%, then
the reduction would be 4.8 dB. If the 50% and 33% duty cycle jamming signals were chopped at a 10 kHz (vice
the 100 Hz) rate, the rule of thumb for jamming seen by the receiver would be down 6 dB and 9.6 dB,
respectively, from the maximum since the 10 kHz chopping rate is greater than the 1 kHz receiver BW. 
Figure 3 is radar jamming visualized. The Physical concept of Figure 3 shows a monostatic radar that is
the same as Figure 1, Section 44, and a jammer (transmitter) to radar (receiver) that is the same as Figure 3,
Section 43. In other words, Figure 3 is simply the combination of the previous two visual concepts where there is
only one receiver (the radar's).
Figure 3. Radar Jamming Visualized
J/S for DECM vs. MONOSTATIC RADARThe equivalent circuit shown in Figure 4 applies
to jamming monostatic radars with either DECM or support ECM. For DECM (or escort) v.s. a monostatic radar, the
jammer is on the target and the radar receive and transmit antennas are collocated so the three ranges and three
space loss factors (
α's) are the same.
Figure 4. Monostatic Radar ECM Equivalent Circuit
JS Ratio (Monostatic) The ratio of the power received (P
_{r1} or J)
from the jamming signal transmitted from the target to the power received (P
_{r2} or S) from the radar
skin return from the target equals J/S.
From the one way range equation in Section 43:
[1]
Note: To avoid having to include additional terms for these calculations, always combine any transmission line
loss with antenna gain.
From the two way range equation in Section 4.4:
[2]
so
[3]
* Keep R and F in the same units.
On reducing the above equation to log form we have:
10log
J/S = 10log P
_{j} + 10log G
_{ja}  10log P
_{t}  10log G
_{t}  10log σ + 10log 4
π
+ 20log R [4]
or 10log J/S = 10log P
_{j} + 10log G
_{ja}  10log P
_{t}  10log G
_{t}
 10log σ + 10.99 dB + 20log R [5]
Note: Neither f nor λ terms are part of the final form of equation [3] and equation [5].
J/S Calculations (Monostatic) Using a One Way Free Space Loss  The simplified radar
equations developed in previous sections can be used to express J/S.
From the one way range equation
Section 43:
10log (P
_{r1} or J) = 10log P
_{j} + 10log G
_{ja} + 10log G
_{r} 
α_{1} (in dB) [6]
From the two way range equation in Section 4.4:
10log (P
_{r2} or S) = 10log P
_{t} + 10log G
_{t} + 10log G
_{r}
+ G
_{σ}  2
α_{1} (in dB) [7]
10log (J/S) = 10log P
_{j}
+ 10log G
_{ja}  10log P
_{t}  10log G
_{t}  G
_{σ}
+
α_{1} (in dB) [8]
Note: To avoid having to include additional
terms for these calculations, always combine any transmission line loss with antenna gain. The 20log f
_{1}
term in G
_{σ} cancels the 20log f
_{1} term in
α_{1}.
J/S for DECM vs. BISTATIC RADAR
The
semiactive missile illustrated in Figure 5 is the typical bistatic radar which would require the target to have
self protection ECM to survive. In this case, the jammer is on the target and the target to missile receiver range
is the same as the jammer to receiver range, but the radar to target range is different. Therefore, only two of
the ranges and two of the "'s (Figure 6.) are the same.
In the following equations:
"Tx = The
oneway space loss from the radar
transmitter to the target for range R
_{Tx}"Rx = The
oneway space loss from the target to the missile receiver for range R
_{Rx}
Like the monostatic radar, the bistatic jamming and reflected target signals travel the same path from the target
and enter the receiver (missile in this case) via the same antenna. In both monostatic and bistatic J/S equations
this common range cancels, so both J/S equations are left with an R
_{Tx} or 20 log R
_{Tx} term.
Since in the monostatic case R
_{Tx} = R
_{Rx} and
α_{Tx} =
α_{Rx} , only R or
α_{1} is used in the
equations. Therefore, the bistatic J/S equations [11], [13], or [14] will work for monostatic J/S calculations,
but the opposite is only true if bistatic R
_{Tx} and
α_{Tx} terms are
used for R or
α_{1} terms in monostatic equations [3], [5], and [8].
The equivalent circuit shown in Figure 6 applies to jamming bistatic radar. For DECM (or escort) vs. a
bistatic radar, the jammer is on the target and the radar receive and transmit antennas are at separate locations
so only two of the three ranges and two of the three space loss factors ("'s) are the same.
Figure 6. Bistatic Radar ECM Equivalent Circuit
JtoS Ratio (Bistatic) When the radar's transmit antenna is located remotely
from the receiving antenna (Figure 6), the ratio of the power received (P
_{r1} or J) from the jamming
signal transmitted from the target to the power received (P
_{r2} or S) from the radar skin return from the
target equals J/S. For jammer effectiveness J normally has to be greater than S.
From the one way range
equation in Section 43:
(R
_{Jx}
= R
_{Rx}) [9]
From the two way range equation in Section 4.4:
[10]
so
[11]
* Keep R and F in the same units.
On reducing the above equation to log form we have:
10log
J/S = 10log P
_{j} + 10log G
_{ja}  10log P
_{t}  10log G
_{t}  10log σ + 10log 4
π
+ 20log R
_{Tx} [12]
or 10log J/S = 10log P
_{j}
+ 10log G
_{ja}  10log P
_{t}  10log G
_{t}  10log σ + 10.99 dB + 20log R
_{Tx}
[13]
Note: To avoid having to include additional terms for these calculations, always combine any
transmission line loss with antenna gain. Neither f nor λ terms are part of the final form of equation [11] and
equation [13].
Bistatic J/S Calculations (Bistatic) Using a One Way Free Space Loss  The
simplified radar equations developed in previous sections can be used to express J/S.
From the one way
range equation in Section 43:
10log (P
_{r1} or J) = 10log P
_{j} + 10log G
_{ja} +
10log G
_{r}

α_{Rx} (all factors dB) [14]
From the two way range equation in
Section 44:
10log (P
_{r2} or S) = 10log P
_{t} + 10log G
_{t} + 10log G
_{r} + G
_{σ}

α_{Tx} 
α_{Rx}
(all factors dB) [15]
10log (J/S) = 10log P
_{j} + 10log G
_{ja}  10log P
_{t}
 10log G
_{t}  Gσ +
α_{Tx} (all factors dB) [16]
Note: To
avoid having to include additional terms for these calculations, always combine any transmission line loss with
antenna gain. The 20log f
_{1} term in G
_{σ} cancels the 20log f
_{1} term in
α_{1}.
Saturated J/S (Monostatic) Example (Constant 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 is flying 31 km from the radar. The aft EW antenna has 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 aircraft has a jammer that provides 30 dBm saturated output if the received signal is above 35 dBm.
The jammer feeds a 10 dB loss transmission line which is connected to an antenna with a 5 dB gain. If the RCS of
the aircraft is 9 m
^{2}, what is the J/S level received by the tracking radar?
Answer: The received
signal at the jammer is the same as the example in Section 43, i.e. answer (1) = 32.3 dBm @ 5 GHz. Since the
received signal is above 35 dBm, the jammer will operate in the saturated mode, and equation [5] can be used.
(See Section 410 for an example of a jammer operating in the linear region.)
10log J/S = 10log P
_{j}
+ 10log G
_{ja}
 10log P
_{t}  10log G
_{t}  10log σ + 10.99 dB + 20log R
Note: the respective
transmission line losses will be combined with antenna gains,
i.e. 5 + 45 = 40 dB & 10 +5 = 5 dB.
10log J/S = 30  5  70  40  9.54 + 10.99 + 89.8 = 6.25 dB @ 5 GHz*
* The answer is still 6.25 dB if the
tracking radar operates at 7 GHz provided the antenna gains and the aircraft RCS are the same at both frequencies.
In this example, there is inadequate jamming power at each frequency if the J/S needs to be 10 dB or greater to be
effective. One solution would be to replace the jammer with one that has a greater power output. If the antenna of
the aircraft and the radar are not the proper polarization, additional power will also be required (see Section
32).
Table of Contents
for Electronics Warfare and Radar Engineering Handbook
Introduction 
Abbreviations  Decibel  Duty
Cycle  Doppler Shift  Radar Horizon / Line
of Sight  Propagation Time / Resolution  Modulation
 Transforms / Wavelets  Antenna Introduction
/ Basics  Polarization  Radiation Patterns 
Frequency / Phase Effects of Antennas 
Antenna Near Field  Radiation Hazards 
Power Density  OneWay Radar Equation / RF Propagation
 TwoWay Radar Equation (Monostatic) 
Alternate TwoWay Radar Equation 
TwoWay Radar Equation (Bistatic) 
Jamming to Signal (J/S) Ratio  Constant Power [Saturated] Jamming
 Support Jamming  Radar Cross Section (RCS) 
Emission Control (EMCON)  RF Atmospheric
Absorption / Ducting  Receiver Sensitivity / Noise 
Receiver Types and Characteristics 
General Radar Display Types 
IFF  Identification  Friend or Foe  Receiver
Tests  Signal Sorting Methods and Direction Finding 
Voltage Standing Wave Ratio (VSWR) / Reflection Coefficient / Return
Loss / Mismatch Loss  Microwave Coaxial Connectors 
Power Dividers/Combiner and Directional Couplers 
Attenuators / Filters / DC Blocks 
Terminations / Dummy Loads  Circulators
and Diplexers  Mixers and Frequency Discriminators 
Detectors  Microwave Measurements 
Microwave Waveguides and Coaxial Cable 
ElectroOptics  Laser Safety 
Mach Number and Airspeed vs. Altitude Mach Number 
EMP/ Aircraft Dimensions  Data Busses  RS232 Interface
 RS422 Balanced Voltage Interface  RS485 Interface 
IEEE488 Interface Bus (HPIB/GPIB)  MILSTD1553 &
1773 Data Bus 
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