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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,

α_{1} , 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

α_{1} 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

α_{2} , which is used instead of the combination of

α_{1}
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 (fR

^{2})
+ 10log σ + 10log (c

^{2}/(4

π)

^{3}) [2]

We now call the last three terms on the right minus

α_{2} and use it as a
single term instead of the two terms

α_{1} 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

α_{2}. Additionally, we can no longer use a nomograph like
we did in computing

α_{1} 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

α_{2} = 20log (f

_{1}R

^{2}) - 10log σ + K

_{3}
and where f

_{1} is the MHz or GHz value of frequency

and K3 = -10log (c

^{2}/(4

π)

^{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 K

_{3} are given in the table above.

Comparing
equation [3] to equation [10] in Section 4-4, it can be seen that

α_{2} = 2

α_{1}
- 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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