Radar Basics

MaxRange

from_range_equation(Pt, Gt, Cs, Ae, Pr_min) classmethod

Method to calculate the maximum range (\(R_{max}\)) of a radar system by using the gain (\(G_t\)) and effective area (\(A_e\)) of the antenna. The maximum range can be calculated using the following equation derived from the radar range equation:

\[ \begin{equation} R_{max} = \left[ \frac{P_t \cdot G_t \cdot A_e \cdot \sigma}{(4\pi)^2 P_{r_{min}}} \right]^{\frac{1}{4}} \end{equation} \]

Where

• \(R_{max}\) is the maximum range of the radar in meters (\(m\)).
• \(P_t\) is the transmitted power in watts (\(W\)).
• \(G_t\) is the gain of the transmitting antenna.
• \(A_e\) is the effective area of the receiving antenna in square meters (\(m^2\)).
• \(\sigma\) is the radar cross-section of the target in square meters (\(m^2\)).
• \(P_{r_{min}}\) is the minimum detectable power by the radar in watts (\(W\)).

Parameters:

Name	Type	Description	Default
Pt	float	Transmitted power in watts (\(W\)).	required
Gt	float	Gain of the transmitting antenna (in \(dBi\)).	required
Cs	float	Radar cross-section of the target in square meters (\(m^2\)).	required
Ae	float	Effective area of the receiving antenna in square meters (\(m^2\)).	required
Pr_min	float	Minimum detectable power by the radar in watts (\(W\)).	required

Returns:

Name	Type	Description
R_max	float	Maximum range of the radar in meters (\(m\)).

from_antenna_gain(Pt, Gt, f, Cs, Pr_min, c=LIGHT_SPEED) classmethod

Method to calculate the maximum range (\(R_{max}\)) of a radar system by using the gain (\(G_t\)) and frequency (\(f\)) of the antenna. The maximum range can be calculated using the following equation derived from the radar range equation, note that for this equation, the TX and RX antennas are the same, so the gain is squared:

\[ \begin{equation} R_{max} = \left[ \frac{P_t \cdot G_t^2 \cdot \lambda^2 \cdot \sigma}{(4\pi)^3 P_{r_{min}}} \right]^{\frac{1}{4}} \end{equation} \]

Where

• \(R_{max}\) is the maximum range of the radar in meters (\(m\)).
• \(P_t\) is the transmitted power in watts (\(W\)).
• \(G_t\) is the gain of the transmitting antenna.
• \(\lambda\) is the wavelength of the signal, calculated as \(\lambda = \frac{c}{f}\).
• \(\sigma\) is the radar cross-section of the target in square meters (\(m^2\)).
• \(P_{r_{min}}\) is the minimum detectable power by the radar in watts (\(W\)).

Parameters:

Name	Type	Description	Default
Pt	float	Transmitted power in watts (\(W\)).	required
Gt	float	Gain of the transmitting antenna (in \(dBi\)).	required
f	float	Frequency of operation in \(Hz\).	required
Cs	float	Radar cross-section of the target in square meters (\(m^2\)).	required
Pr_min	float	Minimum detectable power by the radar in watts (\(W\)).	required
c	float	Speed of light in \(m/s\).	LIGHT_SPEED

Returns:

Name	Type	Description
R_max	float	Maximum range of the radar in meters (\(m\)).

from_effective_area(Pt, Ae, Cs, f, Pr_min, c=LIGHT_SPEED) classmethod

Method to calculate the maximum range (\(R_{max}\)) of a radar system by using the effective area (\(A_e\)) and frequency (\(f\)) of the antenna. The maximum range can be calculated using the following equation derived from the radar range equation, note that for this equation, the TX and RX antennas are the same, so the effective area is squared:

\[ \begin{equation} R_{max} = \left[ \frac{P_t \cdot A_e^2 \cdot \sigma}{4\pi \cdot \lambda^2 \cdot P_{r_{min}}} \right]^{\frac{1}{4}} \end{equation} \]

Where

• \(R_{max}\) is the maximum range of the radar in meters (\(m\))
• \(P_t\) is the transmitted power in watts (\(W\)).
• \(A_e\) is the effective area of the receiving antenna in square meters (\(m^2\)).
• \(\sigma\) is the radar cross-section of the target in square meters (\(m^2\)).
• \(\lambda\) is the wavelength of the signal, calculated as \(\lambda = \frac{c}{f}\).
• \(P_{r_{min}}\) is the minimum detectable power by the radar in watts (\(W\)).

Parameters:

Name	Type	Description	Default
Pt	float	Transmitted power in watts (\(W\)).	required
Ae	float	Effective area of the receiving antenna in square meters (\(m^2\)).	required
Cs	float	Radar cross-section of the target in square meters (\(m^2\)).	required
f	float	Frequency of operation in \(Hz\).	required
Pr_min	float	Minimum detectable power by the radar in watts (\(W\)).	required
c	float	Speed of light in \(m/s\).	LIGHT_SPEED

Returns:

Name	Type	Description
R_max	float	Maximum range of the radar in meters (\(m\)).

calc_unambiguous_range(Tp, c=LIGHT_SPEED)

Calculate the maxium radius of detection that doesn't have ambiguity between two (or more) pulses \(R_un\). The maximum radius is related with the period of pulses (or with the pulse repetition frequency \(PRF\)), based on:

\[ \begin{equation} R_{un} = \frac{T_p \cdot c}{2} \end{equation} \]

Where

• \(R_{un}\) is the maxium radius of detection without ambiguity.
• \(T_p\) is the pulse Repetition period in seconds.
• \(c\) is the light speed in the medium.

Parameters:

Name	Type	Description	Default
Tp	float	Pulse repetition period in seconds.	required
c	integer	Light speed (default \(c=299792458\)).	LIGHT_SPEED

Returns:

Name	Type	Description
run	float	Radius of maxium detection without ambiguity in meters.

effective_area(g, f, c=LIGHT_SPEED)

Calculate the effective area (\(A_e\)) of an antenna given its gain (\(g\)) and frequency (\(f\)). The \(A_e\) can be calculated using the following equation:

\[ \begin{equation} A_e = \frac{G \lambda^2}{4\pi} \end{equation} \]

Where

• \(A_e\) is the effective area of the antenna in square meters \(m^2\).
• \(G\) is the gain of the antenna (in \(dBi\)).
• \(\lambda\) is the wavelength of the signal, calculated as \(\lambda = \frac{c}{f}\).
• \(c\) is the speed of light in \(m/s\).

Parameters:

Name	Type	Description	Default
g	float	Gain of the antenna in \(dB\).	required
f	float	Frequency of operation in \(Hz\).	required
c	float	Speed of light in \(m/s\).	LIGHT_SPEED

Returns:

Name	Type	Description
Ae	float	Effective area (\(A_e\)) of the antenna in square meters (\(m^2\)).

Reference:

Merill I. Skolnik - Introduction To Radar Systems Third Edition (Pg - 18)

power_received(Pt, Gt, R, Cs, Ae)

To calculate the power received (\(P_r\)) by a radar system, we can use the radar range equation, which is given by:

\[ \begin{equation} P_r = \frac{P_t \cdot G_t \cdot \sigma \cdot A_e}{(4\pi)^2 R^4} \end{equation} \]

Where

• \(P_r\) is the power received by the radar in watts (\(W\)).
• \(P_t\) is the transmitted power in watts (\(W\)).
• \(G_t\) is the gain of the transmitting antenna.
• \(\sigma\) is the radar cross-section of the target in square meters (\(m^2\)).
• \(A_e\) is the effective area of the receiving antenna in square meters (\(m^2\)).
• \(R\) is the range to the target in meters (\(m\)).

Parameters:

Name	Type	Description	Default
Pt	float	Transmitted power in watts (\(W\)).	required
Gt	float	Gain of the transmitting antenna (in \(dBi\)).	required
R	float	Range to the target in meters (\(m\)).	required
Cs	float	Radar cross-section of the target in square meters (\(m^2\)).	required
Ae	float	Effective area of the receiving antenna in square meters (\(m^2\)).	required

Returns:

Name	Type	Description
Pr	float	Power received by the radar in watts (\(W\)).
Pr_dBW	float	Power received by the radar in decibels with respect to one watt (\(dBW\)).

Reference:

Merill I. Skolnik - Introduction To Radar Systems Third Edition (Pg - 18)