Minimum Detectable Signal Calculator

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Radar & Antenna Specifications

Radar Antennas Reception

Special Purpose Radars

✖Transmitted Power is the amount of power the radar system is radiating into the environment to transmit radar signals.ⓘ Transmitted Power [P_trns]			+10% -10%
✖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.ⓘ Transmitted Gain [G_trns]			+10% -10%
✖Cross Section Area of Radar also called radar signature, is a measure of how detectable an object is by radar.ⓘ Cross Section Area of Radar [σ]			+10% -10%
✖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.ⓘ Effective Area of Receiving Antenna [A_eff]			+10% -10%
✖Target Range is defined as the distance from the radar site to the target measured along the line of sight.ⓘ Target Range [R_t]			+10% -10%

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

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Formula

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Minimum Detectable Signal

Formula

`"S"_{"min"} = ("P"_{"trns"}*"G"_{"trns"}*"σ"*"A"_{"eff"})/(16*pi^2*"R"_{"t"}^4)`

Example

`"0.026W"=("100kW"*"657"*"25m²"*"17.5875m²")/(16*pi^2*("289.62m")^4)`

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Minimum Detectable Signal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Minimum Detectable Signal = (Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Target Range^4)
S_min = (P_trns*G_trns*σ*A_eff)/(16*pi^2*R_t^4)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Minimum Detectable Signal - (Measured in Watt) - Minimum Detectable Signal represents the minimum power level of a signal that a radar can detect reliably above the noise floor.
Transmitted Power - (Measured in Watt) - Transmitted Power is the amount of power the radar system is radiating into the environment to transmit radar signals.
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.
Cross Section Area of Radar - (Measured in Square Meter) - Cross Section Area of Radar also called radar signature, is a measure of how detectable an object is by radar.
Effective Area of Receiving Antenna - (Measured in Square Meter) - 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.
Target Range - (Measured in Meter) - Target Range is defined as the distance from the radar site to the target measured along the line of sight.

STEP 1: Convert Input(s) to Base Unit

Transmitted Power: 100 Kilowatt --> 100000 Watt (Check conversion here)
Transmitted Gain: 657 --> No Conversion Required
Cross Section Area of Radar: 25 Square Meter --> 25 Square Meter No Conversion Required
Effective Area of Receiving Antenna: 17.5875 Square Meter --> 17.5875 Square Meter No Conversion Required
Target Range: 289.62 Meter --> 289.62 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_min = (P_trns*G_trns*σ*A_eff)/(16*pi^2*R_t^4) --> (100000*657*25*17.5875)/(16*pi^2*289.62^4)

Evaluating ... ...

S_min = 0.0260001326571171

STEP 3: Convert Result to Output's Unit

0.0260001326571171 Watt --> No Conversion Required

FINAL ANSWER

0.0260001326571171 ≈ 0.026 Watt <-- Minimum Detectable Signal

(Calculation completed in 00.004 seconds)

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Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

Shobhit Dimri has created this Calculator and 900+ more calculators!

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< 24 Radar & Antenna Specifications Calculators

Maximum Range of Radar

Go Target Range = ((Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Minimum Detectable Signal))^0.25

Minimum Detectable Signal

Go Minimum Detectable Signal = (Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Target Range^4)

N Scans

Go N Scans = (log10(1-Cumulative Probability of Detection))/(log10(1-Detection Probability of Radar))

Transmitted Gain

Go Transmitted Gain = (4*pi*Effective Area of Receiving Antenna)/Wavelength^2

Transmitted Frequency

Go Transmitted Frequency = Doppler Frequency*[c]/(2*Radial Velocity)

Power Density Radiated by Lossless Antenna

Go Lossless Isotropic Power Density = Maximum Radiated Power Density/Maximum Gain of Antenna

Maximum Power Density Radiated by Antenna

Go Maximum Radiated Power Density = Lossless Isotropic Power Density*Maximum Gain of Antenna

Maximum Gain of Antenna

Go Maximum Gain of Antenna = Maximum Radiated Power Density/Lossless Isotropic Power Density

Radar Antenna Height

Go Antenna Height = (Range Resolution*Range)/(2*Target Height)

Target Height

Go Target Height = (Range Resolution*Range)/(2*Antenna Height)

Probability of Detection

Go Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans)

Cumulative Probability of Detection

Go Cumulative Probability of Detection = 1-(1-Detection Probability of Radar)^N Scans

Effective Area of Receiving Antenna

Go Effective Area of Receiving Antenna = Antenna Area*Antenna Aperture Efficiency

Antenna Aperture Efficiency

Go Antenna Aperture Efficiency = Effective Area of Receiving Antenna/Antenna Area

Antenna Area

Go Antenna Area = Effective Area of Receiving Antenna/Antenna Aperture Efficiency

Pulse Repetition Frequency

Go Pulse Repetition Frequency = [c]/(2*Maximum Unambiguous Range)

Maximum Unambiguous Range

Go Maximum Unambiguous Range = ([c]*Pulse Repetition Time)/2

Pulse Repetition Time

Go Pulse Repetition Time = (2*Maximum Unambiguous Range)/[c]

Target Velocity

Go Target Velocity = (Doppler Frequency Shift*Wavelength)/2

Doppler Frequency

Go Doppler Frequency = Doppler Angular Frequency/(2*pi)

Doppler Angular Frequency

Go Doppler Angular Frequency = 2*pi*Doppler Frequency

Radial Velocity

Go Radial Velocity = (Doppler Frequency*Wavelength)/2

Range of Target

Go Target Range = ([c]*Measured Runtime)/2

Measured Runtime

Go Measured Runtime = 2*Target Range/[c]

Minimum Detectable Signal Formula

What is minimum detectable optical power?

The NEP of a detector is the optical power incident to. the detector that needs to be applied to equal the noise. power from all sources in the detector; in other words, NEP is the optical power that results in an SNR of 1

How to Calculate Minimum Detectable Signal?

Minimum Detectable Signal calculator 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 calculate 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 calculate Minimum Detectable Signal using this online calculator? To use this online calculator 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. Here is how the Minimum Detectable Signal calculation can be explained with given input values -> 0.026 = (100000*657*25*17.5875)/(16*pi^2*289.62^4).

FAQ

What is 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 and is represented as S_min = (P_trns*G_trns*σ*A_eff)/(16*pi^2*R_t^4) or Minimum Detectable Signal = (Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Target Range^4). Transmitted Power is the amount of power the radar system is radiating into the environment to transmit radar signals, 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, Cross Section Area of Radar also called radar signature, is a measure of how detectable an object is by radar, 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 & Target Range is defined as the distance from the radar site to the target measured along the line of sight.

How to calculate 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 is calculated using Minimum Detectable Signal = (Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Target Range^4). To calculate Minimum Detectable Signal, you need 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). With our tool, you need to enter the respective value for Transmitted Power, Transmitted Gain, Cross Section Area of Radar, Effective Area of Receiving Antenna & Target Range and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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