Monostatic Radar Equation

The theoretical range of a radar signal can be determined from the Monostatic radar equation if the following parameters are known: The microwave dish antenna used at the transmit site, is assumed to be 65% efficient, and is for this equation, the same antenna that is used to receive the returned signal from the target. If the transmit antenna and receive antenna were of different sizes, then modifications to the given monostatic radar equation would have to be made to accommodate the different antenna capture areas. The transmit and receive antenna do not necessarily have to be co-located. If the antenna used by the receiver was not the same antenna as that used by the transmitter and was located at a different place (or even if it was located right next to the transmit antenna, then the radar would be called a bistatic radar.

If the overall noise factor of the receiver (F) is known, together with its IF bandwidth d f, and the temperature of the environment (T), the minimum receivable signal power (Pm) may be calculated. Below is the monostatic radar equation used in this applet together with the derived equations used and an explanation of the quantities and units used.

The reason why the term monostatic is used, is because it is assumed that both the source of the radar pulses, and the target are both stationary and that the antenna used by the transmitter is the same as that used by the receiver. Should the target and/or the source of the radar be moving, the monostatic radar equation must be modified to take account of doppler effects for moving targets.

THEORY

The general monostatic radar equation is given by:

The minimum receivable power Pm, is given by: Substiting this equation for the minimum receivable power into the general monostatic radar equation, above, gives the form of the monostatic radar equation which is used in this applet, that is: where;
 
Pt = The transmitter power in watts
S = Target area in square meters
Ao = Capture area of the transmitting/receiving antenna in square meters
k = Boltzmann's constant = 1.380662 x 10-23 J/K
T = Temperature of the environment in Kelvin = 273 + Centigrade
l = Wavelength of the carrier
d f = The receiver IF bandwidth in Hz
F = Noise Factor (dimensionless)

It should be noted that noise figure in dB, is 10 log (noise factor F) and the frequency f (Hz), is related to the wavelength l (m), by the speed of light c (m/s), as shown below:

APPLET

In this applet the receiver noise figure is asked for (which is in dB), as it is the more usual way of expressing this quantity in practice. Also, the transmit/receive antenna diameter D, is asked for rather than the capture area Ao or the antenna gain Ap (dBi). For convenience the temperature (T) is asked for in Centigrade, rather than in Kelvin. The IF bandwidth d f is asked for in KHz, rather than in Hz, because a bandwidth requiring Hz only would be for highly specialized equipment, and the carrier frequency f, is asked for in GHz (= 109 Hz), again because of practical considerations.

To key the parameters on the applet slidebars to the parameters used in the equations presented here, the following equivalences are used:
 
r = range of the radar (m) Pt = Transmitter power (W) = TxPwr(W)
S = Target area (m2) = TrgtA(sqm) T = Temperature in Kelvin = 273 + Temp(C)
D = Transmitting/Receiving site antenna (m) = DishD(m) F = Overall receiver noise figure = RxNF(dB)
d f = Receiver IF bandwidth (Hz) = (IFBW kHz)/1000 f = Carrier frequency (Hz) = Freq(GHz)/106. 

 

The relationship between the carrier frequency f and the carrier wavelength l , is given by:

The relationship between the diameter (D) and the capture area (Ao) for an assumed 65% efficient antenna, is given by: If the gain of the antenna (Ap) was given in dBi, then the capture area (Ao) is related by the following expression: Learning from the Applet

From the equation for the monostatic radar, it can be seen that the range is directly proportional to the dish diameter D. Set up any range with the variables, setting the dish diameter to be, say, 2 m. If the diameter only is doubled, the range should be doubled. The relationships between the range and other variables will vary according to the square root and the fourth root. By playing with these variables individually, keeping the other variables fixed at some value, a feel for the effect of a parameter on the radar range can be obtained.
 
 

The source code (version Rev.1 98/08/03) is available according to the GNU Public License.

 

 
 
 

Tony Townsend tonyart@ieee.org