Power

power_radar_system

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

$$ egin{equation} P_r = rac{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 (\(m\)).

$$

mag_to_db(signal)

Converts the signal magnitude to a logarithmic scale (\(dB\)). The conversion process is given by the expression below.

\[ dB(x) = 20 \log_{10}\left(\frac{|x|}{x_{peak} + 10^{-12}}\right) \]

Where

• \(x\): Signal to be converted to \(dB\).
• \(x_{peak}\): Peak magnitude of the signal.
• \(10^{-12}\): Constant to avoid division by zero.

Parameters:

Name	Type	Description	Default
signal	ndarray	Array with signal data	required

Returns:

Type	Description
ndarray	Array with signal converted to \(dB\)

db_to_linear(db)

Convert dB to linear scale.

\[ \begin{equation} P = 10^{\frac{P_{dB}}{10}} \end{equation} \]

where

• \(P\) is the power in linear scale
• \(P_{dB}\) is the power in dB

Parameters:

Name	Type	Description	Default
db	float	Power in dB	required

Returns:

Name	Type	Description
P_lin	float	Power in linear scale

linear_to_db(linear)

Convert linear scale to dB.

\[ \begin{equation} P_{dB} = 10 \log_{10}(P_{linear}) \end{equation} \]

where

• \(P_{linear}\) is the power in linear scale
• \(P_{dB}\) is the power in dB

Parameters:

Name	Type	Description	Default
linear	float	Power in linear scale	required

Returns:

Name	Type	Description
P_db	float	Power in dB

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

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)