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Amplitude of Signal Received from Target at Range Calculator

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Special Purpose Radars Radar and Antenna Specifications Radar Antennas Reception

✖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.ⓘ Echo Signal Voltage [V_echo]			+10% -10%
✖Carrier Frequency refers to the constant and unmodulated radio frequency (RF) signal that is transmitted by the radar system.ⓘ Carrier Frequency [f_c]			+10% -10%
✖Doppler frequency shift is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.ⓘ Doppler Frequency Shift [Δf_d]			+10% -10%
✖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.ⓘ Time Period [T]			+10% -10%
✖Range refers to the distance between the radar antenna (or the radar system) and a target or object that reflects the radar signal.ⓘ Range [R_o]			+10% -10%

✖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.ⓘ Amplitude of Signal Received from Target at Range [A_rec]

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Formula

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Amplitude of Signal Received from Target at Range

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]}))}

Example

125.8165 V = \frac{101.58 V}{\sin ((2 \cdot π \cdot (3000 Hz + 20 Hz) \cdot 50 μs) - (\frac{4 \cdot π \cdot 3000 Hz \cdot 40000 m}{[c]}))}

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Amplitude of Signal Received from Target at Range Solution

STEP 0: Pre-Calculation Summary

Formula Used

Amplitude of Signal Received = Echo Signal Voltage/(sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c])))
A_rec = V_echo/(sin((2*pi*(f_c+Δf_d)*T)-((4*pi*f_c*R_o)/[c])))
This formula uses 2 Constants, 1 Functions, 6 Variables

Constants Used

[c] - Light speed in vacuum Value Taken As 299792458.0
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(Angle)

Variables Used

Amplitude of Signal Received - (Measured in Volt) - 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.
Echo Signal Voltage - (Measured in Volt) - 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.
Carrier Frequency - (Measured in Hertz) - Carrier Frequency refers to the constant and unmodulated radio frequency (RF) signal that is transmitted by the radar system.
Doppler Frequency Shift - (Measured in Hertz) - Doppler frequency shift is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.
Time Period - (Measured in Second) - 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.
Range - (Measured in Meter) - Range refers to the distance between the radar antenna (or the radar system) and a target or object that reflects the radar signal.

STEP 1: Convert Input(s) to Base Unit

Echo Signal Voltage: 101.58 Volt --> 101.58 Volt No Conversion Required
Carrier Frequency: 3000 Hertz --> 3000 Hertz No Conversion Required
Doppler Frequency Shift: 20 Hertz --> 20 Hertz No Conversion Required
Time Period: 50 Microsecond --> 5E-05 Second (Check conversion here)
Range: 40000 Meter --> 40000 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_rec = V_echo/(sin((2*pi*(f_c+Δf_d)*T)-((4*pi*f_c*R_o)/[c]))) --> 101.58/(sin((2*pi*(3000+20)*5E-05)-((4*pi*3000*40000)/[c])))

Evaluating ... ...

A_rec = 125.816539015967

STEP 3: Convert Result to Output's Unit

125.816539015967 Volt --> No Conversion Required

FINAL ANSWER

125.816539015967 ≈ 125.8165 Volt <-- Amplitude of Signal Received

(Calculation completed in 00.004 seconds)

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Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

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< Special Purpose Radars Calculators

Amplitude of Signal Received from Target at Range

Go Amplitude of Signal Received = Echo Signal Voltage/(sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c])))

Amplitude of Reference Signal

Go Amplitude of Reference Signal = CW Oscillator Reference Voltage/(sin(2*pi*Angular Frequency*Time Period))

Reference Voltage of CW Oscillator

Go CW Oscillator Reference Voltage = Amplitude of Reference Signal*sin(2*pi*Angular Frequency*Time Period)

Doppler Frequency Shift

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

Amplitude of Signal Received from Target at Range Formula

How Does The Frequency Of The Radar Affect The Measurement?

A higher frequency provides a more concentrated narrow beam which can be useful in applications where there are obstacles present in the tank such as many-ways, agitators or heating coils.

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

Amplitude of Signal Received from Target at Range calculator 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 calculate 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 calculate Amplitude of Signal Received from Target at Range using this online calculator? To use this online calculator 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. Here is how the Amplitude of Signal Received from Target at Range calculation can be explained with given input values -> 125.8165 = 101.58/(sin((2*pi*(3000+20)*5E-05)-((4*pi*3000*40000)/[c]))).

FAQ

What is Amplitude of Signal Received from Target at Range?

The Amplitude of Signal Received from Target at Range formula is defined as the amplitude required by signal to propagate efficiently and is represented as A_rec = V_echo/(sin((2*pi*(f_c+Δf_d)*T)-((4*pi*f_c*R_o)/[c]))) or Amplitude of Signal Received = Echo Signal Voltage/(sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c]))). 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, Carrier Frequency refers to the constant and unmodulated radio frequency (RF) signal that is transmitted by the radar system, Doppler frequency shift is the change in frequency of a wave in relation to an observer who is moving relative to the wave source, 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 & Range refers to the distance between the radar antenna (or the radar system) and a target or object that reflects the radar signal.

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

The Amplitude of Signal Received from Target at Range formula is defined as the amplitude required by signal to propagate efficiently is calculated using Amplitude of Signal Received = Echo Signal Voltage/(sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c]))). To calculate Amplitude of Signal Received from Target at Range, you need Echo Signal Voltage (V_echo), Carrier Frequency (f_c), Doppler Frequency Shift (Δf_d), Time Period (T) & Range (R_o). With our tool, you need to enter the respective value for Echo Signal Voltage, Carrier Frequency, Doppler Frequency Shift, Time Period & 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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