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Electronic Warfare and Radar Systems Engineering Handbook  Alternate TwoWay Radar Equation  
[Go to TOC]
ALTERNATE TWOWAY 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 44, in order to maintain the concept and use of the oneway 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}/(4π)^{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 twoway space loss consisting of
two times the oneway 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}/(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 K_{3} are given in the table above.
Comparing equation [3] to equation [10]
in Section 44, it can be seen that α_{2} = 2α_{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  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  This HTML version may be printed but not reproduced on websites.

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