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Echo Signal Voltage Calculator

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Special Purpose Radars Radar and Antenna Specifications Radar Antennas Reception

✖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 [A_rec]			+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%

✖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]

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Formula

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Echo Signal Voltage

Formula

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

Example

101.7281 V = 126 V \cdot \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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Echo Signal Voltage Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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

Amplitude of Signal Received: 126 Volt --> 126 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

V_echo = A_rec*sin((2*pi*(f_c+Δf_d)*T)-((4*pi*f_c*R_o)/[c])) --> 126*sin((2*pi*(3000+20)*5E-05)-((4*pi*3000*40000)/[c]))

Evaluating ... ...

V_echo = 101.728120166902

STEP 3: Convert Result to Output's Unit

101.728120166902 Volt --> No Conversion Required

FINAL ANSWER

101.728120166902 ≈ 101.7281 Volt <-- Echo Signal Voltage

(Calculation completed in 00.004 seconds)

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Created by Shobhit Dimri

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

Echo Signal Voltage Formula

What is doppler frequency shift?

The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

How to Calculate Echo Signal Voltage?

Echo Signal Voltage calculator uses Echo Signal Voltage = Amplitude of Signal Received*sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c])) to calculate the Echo Signal Voltage, The Echo Signal Voltage formula refers to the electrical voltage level of the received radar signal after it has been reflected back from a target. Echo Signal Voltage is denoted by V_echo symbol.

How to calculate Echo Signal Voltage using this online calculator? To use this online calculator for Echo Signal Voltage, enter Amplitude of Signal Received (A_rec), Carrier Frequency (f_c), Doppler Frequency Shift (Δf_d), Time Period (T) & Range (R_o) and hit the calculate button. Here is how the Echo Signal Voltage calculation can be explained with given input values -> 101.7281 = 126*sin((2*pi*(3000+20)*5E-05)-((4*pi*3000*40000)/[c])).

FAQ

What is Echo Signal Voltage?

The Echo Signal Voltage formula refers to the electrical voltage level of the received radar signal after it has been reflected back from a target and is represented as V_echo = A_rec*sin((2*pi*(f_c+Δf_d)*T)-((4*pi*f_c*R_o)/[c])) or Echo Signal Voltage = Amplitude of Signal Received*sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c])). 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, 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 Echo Signal Voltage?

The Echo Signal Voltage formula refers to the electrical voltage level of the received radar signal after it has been reflected back from a target is calculated using Echo Signal Voltage = Amplitude of Signal Received*sin((2*pi*(Carrier Frequency+Doppler Frequency Shift)*Time Period)-((4*pi*Carrier Frequency*Range)/[c])). To calculate Echo Signal Voltage, you need Amplitude of Signal Received (A_rec), 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 Amplitude of Signal Received, 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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