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Amplitude of Signal Received from Target at Range Formula

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Amplitude of Signal Received refers to the strength or magnitude of the echo signal that is detected by the radar receiver after it reflects off a target. Check FAQs

A rec = \frac{V echo}{\sin ((2 \cdot π \cdot (f c + Δf d) \cdot T) - (\frac{4 \cdot π \cdot f c \cdot R o}{[c]}))}

A_rec - Amplitude of Signal Received?V_echo - Echo Signal Voltage?f_c - Carrier Frequency?Δf_d - Doppler Frequency Shift?T - Time Period?R_o - Range?[c] - Light speed in vacuum?π - Archimedes' constant?

Amplitude of Signal Received from Target at Range Example

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Here is how the Amplitude of Signal Received from Target at Range equation looks like with Values.

Here is how the Amplitude of Signal Received from Target at Range equation looks like with Units.

Here is how the Amplitude of Signal Received from Target at Range equation looks like.

125.8165 = \frac{101.58}{\sin ((2 \cdot 3.1416 \cdot (3000 + 20) \cdot 50) - (\frac{4 \cdot 3.1416 \cdot 3000 \cdot 40000}{3E+8}))}

125.8165V = \frac{101.58V}{\sin ((2 \cdot 3.1416 \cdot (3000Hz + 20Hz) \cdot 50μs) - (\frac{4 \cdot 3.1416 \cdot 3000Hz \cdot 40000m}{3E+8m/s}))}

125.8165 = \frac{101.58}{\sin ((2 \cdot 3.1416 \cdot (3000 + 20) \cdot 50) - (\frac{4 \cdot 3.1416 \cdot 3000 \cdot 40000}{3E+8}))}

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Amplitude of Signal Received from Target at Range Solution

Follow our step by step solution on how to calculate Amplitude of Signal Received from Target at Range?

FIRST Step Consider the formula

A rec = \frac{V echo}{\sin ((2 \cdot π \cdot (f c + Δf d) \cdot T) - (\frac{4 \cdot π \cdot f c \cdot R o}{[c]}))}

Next Step Substitute values of Variables

∴

A rec = \frac{101.58V}{\sin ((2 \cdot π \cdot (3000Hz + 20Hz) \cdot 50μs) - (\frac{4 \cdot π \cdot 3000Hz \cdot 40000m}{[c]}))}

Next Step Substitute values of Constants

∴

A rec = \frac{101.58V}{\sin ((2 \cdot 3.1416 \cdot (3000Hz + 20Hz) \cdot 50μs) - (\frac{4 \cdot 3.1416 \cdot 3000Hz \cdot 40000m}{3E+8m/s}))}

Next Step Convert Units

∴

A rec = \frac{101.58V}{\sin ((2 \cdot 3.1416 \cdot (3000Hz + 20Hz) \cdot 5E-5s) - (\frac{4 \cdot 3.1416 \cdot 3000Hz \cdot 40000m}{3E+8m/s}))}

Next Step Prepare to Evaluate

∴

A rec = \frac{101.58}{\sin ((2 \cdot 3.1416 \cdot (3000 + 20) \cdot 5E-5) - (\frac{4 \cdot 3.1416 \cdot 3000 \cdot 40000}{3E+8}))}

Next Step Evaluate

∴

A rec = 125.816539015967V

LAST Step Rounding Answer

∴

A rec = 125.8165V

Amplitude of Signal Received from Target at Range Formula Elements

Variables

Constants

Functions

Amplitude of Signal Received

Amplitude of Signal Received refers to the strength or magnitude of the echo signal that is detected by the radar receiver after it reflects off a target.

Symbol: A_rec

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Amplitude of Signal Received

Echo Signal Voltage

Echo Signal Voltage refers to the electrical signal that is received by the radar receiver after the transmitted radar signal reflects off a target and returns to the radar antenna.

Symbol: V_echo

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Echo Signal Voltage

Carrier Frequency

Carrier Frequency refers to the constant and unmodulated radio frequency (RF) signal that is transmitted by the radar system.

Symbol: f_c

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Carrier Frequency

Doppler Frequency Shift

Doppler frequency shift is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

Symbol: Δf_d

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Doppler Frequency Shift

Time Period

Time Period refers to the total time radar takes for one complete cycle of operation, the time gap between successive pulses and any other time intervals related to the radar's operation.

Symbol: T

Measurement: TimeUnit: μs

Note: Value should be greater than 0.

Formulas to find Time Period

Range

Range refers to the distance between the radar antenna (or the radar system) and a target or object that reflects the radar signal.

Symbol: R_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Range

Light speed in vacuum

Light speed in vacuum is a fundamental physical constant representing the speed at which light propagates through a vacuum.

Symbol: [c]

Value: 299792458.0 m/s

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other formulas in Special Purpose Radars category

Go Doppler Frequency Shift

Δf d = \frac{2 \cdot v t}{λ}

Go Reference Voltage of CW Oscillator

V ref = A ref \cdot \sin (2 \cdot π \cdot ω \cdot T)

Go Amplitude of Reference Signal

A ref = \frac{V ref}{\sin (2 \cdot π \cdot ω \cdot T)}

Go Distance from Antenna 1 to Target in Monopulse Radar

s 1 = \frac{R o + s a}{2} \cdot \sin (θ)

How to Evaluate Amplitude of Signal Received from Target at Range?

Amplitude of Signal Received from Target at Range evaluator uses Amplitude of Signal Received = Echo Signal Voltage/(sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c]))) to evaluate the Amplitude of Signal Received, The Amplitude of Signal Received from Target at Range formula is defined as the amplitude required by signal to propagate efficiently. Amplitude of Signal Received is denoted by A_rec symbol.

How to evaluate Amplitude of Signal Received from Target at Range using this online evaluator? To use this online evaluator for Amplitude of Signal Received from Target at Range, enter Echo Signal Voltage (V_echo), Carrier Frequency (f_c), Doppler Frequency Shift (Δf_d), Time Period (T) & Range (R_o) and hit the calculate button.

FAQs on Amplitude of Signal Received from Target at Range

What is the formula to find Amplitude of Signal Received from Target at Range?

The formula of Amplitude of Signal Received from Target at Range is expressed as Amplitude of Signal Received = Echo Signal Voltage/(sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c]))). Here is an example- 125.8165 = 101.58/(sin((2*pi*(3000+20)*5E-05)-((4*pi*3000*40000)/[c]))).

How to calculate Amplitude of Signal Received from Target at Range?

With Echo Signal Voltage (V_echo), Carrier Frequency (f_c), Doppler Frequency Shift (Δf_d), Time Period (T) & Range (R_o) we can find Amplitude of Signal Received from Target at Range using the formula - Amplitude of Signal Received = Echo Signal Voltage/(sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c]))). This formula also uses Light speed in vacuum, Archimedes' constant and Sine (sin) function(s).

Can the Amplitude of Signal Received from Target at Range be negative?

Yes, the Amplitude of Signal Received from Target at Range, measured in Electric Potential can be negative.

Which unit is used to measure Amplitude of Signal Received from Target at Range?

Amplitude of Signal Received from Target at Range is usually measured using the Volt[V] for Electric Potential. Millivolt[V], Microvolt[V], Nanovolt[V] are the few other units in which Amplitude of Signal Received from Target at Range can be measured.

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Amplitude of Signal Received from Target at Range Formula

Amplitude of Signal Received from Target at Range Example

Amplitude of Signal Received from Target at Range Solution

Amplitude of Signal Received from Target at Range Formula Elements

Other formulas in Special Purpose Radars category

How to Evaluate Amplitude of Signal Received from Target at Range?

FAQs on Amplitude of Signal Received from Target at Range

Variable Name