Electronic Warfare and Radar Systems Engineering Handbook
- Alternate Two-Way Radar Equation

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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.

In the last section, we had the basic radar equation given as equation [6] and it is repeated as equation [1] in the table below.

In section 4-4, in order to maintain the concept and use of the one-way space loss coefficient, α₁ , 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 α₁ terms and we defined the remaining term as G_σ, which accounted for RCS (see equation [8] & [9]).

Some authors take a different approach, and instead develop an entirely new single factor α₂ , which is used instead of the combination of α₁ and G_σ.

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

10log P_r = 10log P_t + 10log G_t + 10log G_r - 20log (fR²) + 10log σ + 10log (c²/(4π)³)      [2]

We now call the last three terms on the right minus α₂ and use it as a single term instead of the two terms α₁ and G_σ. 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 α₂. Additionally, we can no longer use a nomograph like we did in computing α₁ 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 Pr = 10log Pt + 10log Gt + 10log Gr - "2 (in dB)      [3]

Where α₂ = 20log (f₁R²) - 10log σ + K₃ and where f₁ is the MHz or GHz value of frequency

and K3 = -10log (c²/(4π)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 Section 4-4, it can be seen that α₂ = 2α₁ - G_σ.

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 | One-Way Radar Equation / RF Propagation | Two-Way Radar Equation (Monostatic) | Alternate Two-Way Radar Equation | Two-Way 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 | Electro-Optics | Laser Safety | Mach Number and Airspeed vs. Altitude Mach Number | EMP/  Aircraft Dimensions | Data Busses | RS-232 Interface | RS-422 Balanced Voltage Interface | RS-485 Interface | IEEE-488 Interface Bus (HP-IB/GP-IB) | MIL-STD-1553 & 1773 Data Bus |

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