ALTERNATE TWO-WAY RADAR EQUATION

In this section the same radar equation factors are grouped differently to create different constants as is used by some authors.

TWO-WAY RADAR EQUATION (MONOSTATIC) Peak power at the radar receiver input is: * Keep or c, , and R in the same units. On reducing the above equation to log form we have: or: 10log Pr = 10log Pt + 10log Gt + 10log Gr - 2 (in dB) Where: 2 = 20log f1R2 - 10log + K3 , and K3 = -10log c2/(4)3 Note: Losses due to antenna polarization and atmospheric absorption are not included in these equations.

K3 Values: (dB) Range Units f1 in MHz in m2 f1 in GHz in m2 f1 in MHz in ft2 f1 in GHz in ft2 NM 114.15 174.15 124.47 184.47 km 103.44 163.44 113.76 173.76 m -16.56 43.44 -6.24 53.76 yd -18.1 41.9 -7.78 52.22 ft -37.2 22.8 -26.88 33.12

In the last section (Two-way Radar Equation - Monostatic), we had the basic radar equation given as equation [6] and it is repeated as equation [1] in the table above.

In that section, in order to maintain the concept and use of the one-way space loss coefficient, , we didn't cancel like terms which was done to form equation [6] there. Rather, we regrouped the factors of equation [5]. This resulted in two minus terms and we defined the remaining term as G, which accounted for RCS (see equation [8] & [9] ).

Some authors take a different approach, and instead develop an entirely new single factor ₂ , which is used instead of the combination of and G.

If equation [1] is reduced to log form, (and noting that f = c/) it becomes:

10log P_r = 10log P_t + 10log G_t + 10log G_r - 20log (f R²) + 10log + 10log (c²/(4)³) [2]

We now call the last three terms on the right minus ₂ and use it as a single term instead of the two terms and G. The concept of dealing with one variable factor may be easier although we still need to know the range, frequency and radar cross section to evaluate ₂. Additionally, we can no longer use a nomograph like we did in computing and visualize a two-way space loss consisting of two times the one-way space loss, since there are now 3 variables vs two.

Equation [2] reduces to: 10log P_r = 10log P_t + 10log G_t + 10log G_r - ₂ (in dB) [3]

Where ₂ = 20log (f₁R²) - 10log + K₃ and where f₁ is the MHz or GHz value of frequency
and K₃ = -10log (c²/(4)³) + 20log (conversion for Hz to MHz or GHz)+ 40log (range unit conversions if not in meters) - 20log (RCS conversions for meters to feet)

The values of K₃ are given in the table above.

Comparing equation [3] to equation [10] in the last section, it can be seen that ₂ = 2 - G .