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Minimum Detectable Signal Formula

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Minimum Detectable Signal represents the minimum power level of a signal that a radar can detect reliably above the noise floor. Check FAQs

S min = \frac{P trns \cdot G trns \cdot σ \cdot A eff}{16 \cdot π^{2} \cdot {R t}^{4}}

S_min - Minimum Detectable Signal?P_trns - Transmitted Power?G_trns - Transmitted Gain?σ - Cross Section Area of Radar?A_eff - Effective Area of Receiving Antenna?R_t - Target Range?π - Archimedes' constant?

Minimum Detectable Signal Example

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Here is how the Minimum Detectable Signal equation looks like with Values.

Here is how the Minimum Detectable Signal equation looks like with Units.

Here is how the Minimum Detectable Signal equation looks like.

0.026 = \frac{100 \cdot 657 \cdot 25 \cdot 17.5875}{16 \cdot {3.1416}^{2} \cdot {289.62}^{4}}

0.026W = \frac{100kW \cdot 657 \cdot 25m² \cdot 17.5875m²}{16 \cdot {3.1416}^{2} \cdot {289.62m}^{4}}

0.026 = \frac{100 \cdot 657 \cdot 25 \cdot 17.5875}{16 \cdot {3.1416}^{2} \cdot {289.62}^{4}}

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Minimum Detectable Signal Solution

Follow our step by step solution on how to calculate Minimum Detectable Signal?

FIRST Step Consider the formula

S min = \frac{P trns \cdot G trns \cdot σ \cdot A eff}{16 \cdot π^{2} \cdot {R t}^{4}}

Next Step Substitute values of Variables

∴

S min = \frac{100kW \cdot 657 \cdot 25m² \cdot 17.5875m²}{16 \cdot π^{2} \cdot {289.62m}^{4}}

Next Step Substitute values of Constants

∴

S min = \frac{100kW \cdot 657 \cdot 25m² \cdot 17.5875m²}{16 \cdot {3.1416}^{2} \cdot {289.62m}^{4}}

Next Step Convert Units

∴

S min = \frac{100000W \cdot 657 \cdot 25m² \cdot 17.5875m²}{16 \cdot {3.1416}^{2} \cdot {289.62m}^{4}}

Next Step Prepare to Evaluate

∴

S min = \frac{100000 \cdot 657 \cdot 25 \cdot 17.5875}{16 \cdot {3.1416}^{2} \cdot {289.62}^{4}}

Next Step Evaluate

∴

S min = 0.0260001326571171W

LAST Step Rounding Answer

∴

S min = 0.026W

Minimum Detectable Signal Formula Elements

Variables

Constants

Minimum Detectable Signal

Minimum Detectable Signal represents the minimum power level of a signal that a radar can detect reliably above the noise floor.

Symbol: S_min

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Minimum Detectable Signal

Transmitted Power

Transmitted Power is the amount of power the radar system is radiating into the environment to transmit radar signals.

Symbol: P_trns

Measurement: PowerUnit: kW

Note: Value should be greater than 0.

Formulas to find Transmitted Power

Transmitted Gain

Transmitted Gain is a parameter used to describe the ability of an antenna to concentrate and direct electromagnetic energy in a specific direction when it is used to transmit signals.

Symbol: G_trns

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Transmitted Gain

Cross Section Area of Radar

Cross Section Area of Radar also called radar signature, is a measure of how detectable an object is by radar.

Symbol: σ

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Section Area of Radar

Effective Area of Receiving Antenna

Effective Area of Receiving Antenna is a fundamental parameter that characterizes the ability of the antenna to capture electromagnetic radiation and convert it into an electrical signal.

Symbol: A_eff

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Effective Area of Receiving Antenna

Target Range

Target Range is defined as the distance from the radar site to the target measured along the line of sight.

Symbol: R_t

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Target Range

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Radar and Antenna Specifications category

Go Range of Target

R t = \frac{[c] \cdot T run}{2}

Go Measured Runtime

T run = 2 \cdot \frac{R t}{[c]}

Go Maximum Unambiguous Range

R un = \frac{[c] \cdot T pulse}{2}

Go Pulse Repetition Time

T pulse = \frac{2 \cdot R un}{[c]}

How to Evaluate Minimum Detectable Signal?

Minimum Detectable Signal evaluator uses Minimum Detectable Signal = (Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Target Range^4) to evaluate the Minimum Detectable Signal, The Minimum Detectable Signal formula is defined as a signal that produces a signal-to-noise ratio of a given value m at the output. Minimum Detectable Signal is denoted by S_min symbol.

How to evaluate Minimum Detectable Signal using this online evaluator? To use this online evaluator for Minimum Detectable Signal, enter Transmitted Power (P_trns), Transmitted Gain (G_trns), Cross Section Area of Radar (σ), Effective Area of Receiving Antenna (A_eff) & Target Range (R_t) and hit the calculate button.

FAQs on Minimum Detectable Signal

What is the formula to find Minimum Detectable Signal?

The formula of Minimum Detectable Signal is expressed as Minimum Detectable Signal = (Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Target Range^4). Here is an example- 0.026 = (100000*657*25*17.5875)/(16*pi^2*289.62^4).

How to calculate Minimum Detectable Signal?

With Transmitted Power (P_trns), Transmitted Gain (G_trns), Cross Section Area of Radar (σ), Effective Area of Receiving Antenna (A_eff) & Target Range (R_t) we can find Minimum Detectable Signal using the formula - Minimum Detectable Signal = (Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Target Range^4). This formula also uses Archimedes' constant .

Can the Minimum Detectable Signal be negative?

Yes, the Minimum Detectable Signal, measured in Power can be negative.

Which unit is used to measure Minimum Detectable Signal?

Minimum Detectable Signal is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Minimum Detectable Signal can be measured.

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Minimum Detectable Signal Formula

Minimum Detectable Signal Example

Minimum Detectable Signal Solution

Minimum Detectable Signal Formula Elements

Other formulas in Radar and Antenna Specifications category

How to Evaluate Minimum Detectable Signal?

FAQs on Minimum Detectable Signal

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