How much power is received by a radar receiver located 100 km from a jammer with

Question

How much power is received by a radar receiver located 100 km from a jammer with the following characteristics? Assume that the radar antenna has an effective area of 1.2 square meters and that the main beam is pointed in the direction of the jammer. Consider only atmospheric attenuation, excluding the effects of, for example, component loss. Provide the answer of watts and dBm Jammer peak power: 100 watts Jammer antenna gain: 15 dB Atmospheric loss: .04 dB per km (one-way) Radar average sidelobe level: -30 dB (relative to the main beam)

Explanation / Answer

The one-way (transmitter to receiver) radar equation is derived in this section. This equation is most commonly used in RWR or ESM type of applications. The following is a summary of the important equations explored in this section: ONE-WAY RADAR EQUATION Peak Power at Receiver Input, So the one-way radar equation is : * keep 8, c, and R in the same units On reducing to log form this becomes: 10log P = 10log P + 10log G + 10log G - 20log f R + 20log (c/4B) r t t r or in simplified terms: 10log P = 10log P + 10log G + 10log G - " (in dB) r t t r 1 Where: " = one-way free space loss = 20log (f R) + K (in dB) 1 1 1 and: K = 20log [(4B/c)(Conversion factors if units if not in m/sec, m, and Hz)] 1 Note: To avoid having to include additional terms for these calculations, always combine any transmission line loss with antenna gain Values of K (in dB) 1 Range f in MHz f in GHz 1 1 (units) K = K = 1 1 NM 37.8 97.8 km 32.45 92.45 m -27.55 32.45 yd -28.33 31.67 ft -37.87 22.13 ______________________ Note: Losses due to antenna polarization and atmospheric absorption (Sections 3-2 & 5-1) are not included in any of these equations. Recall from Section 4-2 that the power density at a distant point from a radar with an antenna gain of Gt is the power density from an isotropic antenna multiplied by the radar antenna gain. Power density from radar, [1] If you could cover the entire spherical segment with your receiving antenna you would theoretically capture all of the transmitted energy. You can't do this because no antenna is large enough. (A two degree segment would be about a mile and three-quarters across at fifty miles from the transmitter.) A receiving antenna captures a portion of this power determined by it's effective capture Area (A ). The received e power available at the antenna terminals is the power density times the effective capture area (A ) of the receiving antenna. e For a given receiver antenna size the capture area is constant no matter how far it is from the transmitter, as illustrated in Figure 1. This concept is shown in the following equation:

Radio Frequency (RF) propagation is defined as the travel of electromagnetic waves through or along a medium. For RF propagation between approximately 100 MHz and 10 GHz, radio waves travel very much as they do in free space and travel in a direct line of sight. There is a very slight difference in the dielectric constants of space and air. The dielectric constant of space is one. The dielectric constant of air at sea level is 1.000536. In all but the highest precision calculations, the slight difference is neglected. From chapter 3, Antennas, an isotropic radiator is a theoretical, lossless, omnidirectional (spherical) antenna. That is, it radiates uniformly in all directions. The power of a transmitter that is radiated from an isotropic antenna will have a uniform power density (power per unit area) in all directions. The power density at any distance from an isotropic antenna is simply the transmitter power divided by the surface area of a sphere (4BR ) at that distance. The surface area of the 2 sphere increases by the square of the radius, therefore the power density, P , (watts/square meter) decreases by the square D of the radius. [1] P is either peak or average power depending on how P is to be specified. t D Radars use directional antennas to channel most of the radiated power in a particular direction. The Gain (G) of an antenna is the ratio of power radiated in the desired direction as compared to the power radiated from an isotropic antenna, or: The power density at a distant point from a radar with an antenna gain of G is the power density from an isotropic t antenna multiplied by the radar antenna gain. Power density from radar, [2] P is either peak or average power depending on how P is to be specified. t D Another commonly used term is effective radiated power (ERP), and is defined as: ERP = Pt Gt A receiving antenna captures a portion of this power determined by it's effective capture Area (A ). The received e power available at the antenna terminals is the power density times the effective capture area (A ) of the receiving antenna. e For a given receiver antenna size the capture area is constant no matter how far it is from the transmitter, as illustrated in Figure 1. Also notice from Figure 1 that the received signal power decreases by 1/4 (6 dB) as the distance doubles. This is due to the R term in the denominator of equation [2]. 2 Same Antenna Capture Area Range 1 Range 2 Received Signal Received Signal ONE WAY SIGNAL STRENGTH (S) S decreases by 6 dB when the distance doubles S increases by 6 dB when the distance is half S 6 dB (1/4 pwr) 6 dB (4x pwr) 2R R R S 0.5 R PD ' PtGt 4BR 2 ' (100 watts) (10) 4B (100 ft) 2 ' 0.0080 watts/ft 2 PD ' PtGt 4BR 2 ' (105mW) @ (10) 4B (3047.85cm) 2 ' 0.0086 mW/cm2 Pt (dBm) ' 10 Log Pt watts 1 mW ' 10 Log 100 .001 ' 50 dBm Gt (dB) ' 10 Log Gt 1 ' 10 Log (10) ' 10 dB 4-2.2 Figure 1. Power Density vs. Range Sample Power Density Calculation - Far Field (Refer to Section 3-5 for the definition of near field and far field) Calculate the power density at 100 feet for 100 watts transmitted through an antenna with a gain of 10. Given: P = 100 watts G = 10 (dimensionless ratio) R = 100 ft t t This equation produces power density in watts per square range unit. For safety (radiation hazard) and EMI calculations, power density is usually expressed in milliwatts per square cm. That's nothing more than converting the power and range to the proper units. 100 watts = 1 x 102 watts = 1 x 105 mW 100 feet = 30.4785 meters = 3047.85 cm. However, antenna gain is almost always given in dB, not as a ratio. It's then often easier to express ERP in dBm. ERP (dBm) = Pt (dBm) + Gt (dB) = 50 + 10 = 60 dBm To reduce calculations, the graph in Figure 2 can be used. It gives ERP in dBm, range in feet and power density in mW/cm . Follow the scale A line for an ERP of 60 dBm to the point where it intersects the 100 foot range scale. Read 2 the power density directly from the A-scale x-axis as 0.0086 mW/cm (confirming our earlier calculations).

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