Amplitude of Signal Received from Target at Range Calculator

Formula Used:

\[ A_{rec} = \frac{V_{echo}}{\sin\left(2\pi(f_c + \Delta f_d)T - \frac{4\pi f_c R_o}{c}\right)} \]

Echo Signal Voltage (Vecho):

Carrier Frequency (fc):

Doppler Frequency Shift (Δfd):

Time Period (T):

Range (Ro):

Amplitude of Signal Received (Arec):

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1. What is the Amplitude of Signal Received Formula?

The Amplitude of Signal Received formula calculates the strength of the echo signal detected by a radar receiver after it reflects off a target. This calculation considers various factors including carrier frequency, Doppler shift, time period, and target range.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ A_{rec} = \frac{V_{echo}}{\sin\left(2\pi(f_c + \Delta f_d)T - \frac{4\pi f_c R_o}{c}\right)} \]

Where:

\( A_{rec} \) — Amplitude of Signal Received (V)
\( V_{echo} \) — Echo Signal Voltage (V)
\( f_c \) — Carrier Frequency (Hz)
\( \Delta f_d \) — Doppler Frequency Shift (Hz)
\( T \) — Time Period (s)
\( R_o \) — Range (m)
\( c \) — Speed of light in vacuum (299792458 m/s)
\( \pi \) — Mathematical constant pi (3.141592653589793)

Explanation: The formula accounts for the phase relationship between transmitted and received signals, incorporating Doppler shift effects and propagation delay.

3. Importance of Signal Amplitude Calculation

Details: Accurate signal amplitude calculation is crucial for radar system performance analysis, target detection probability estimation, and signal-to-noise ratio calculations in radar systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Echo signal voltage, carrier frequency, time period, and range must be positive values. Doppler frequency shift can be positive or negative depending on target motion direction.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the sine function in this formula?
A: The sine function represents the phase relationship between transmitted and received signals, accounting for both time delay and Doppler frequency shift effects.

Q2: How does Doppler frequency shift affect the received signal amplitude?
A: Doppler shift changes the apparent frequency of the received signal, which affects the phase relationship and consequently the calculated amplitude.

Q3: What are typical values for echo signal voltage?
A: Echo signal voltages typically range from microvolts to millivolts, depending on target size, distance, and radar system characteristics.

Q4: Why is the speed of light included in this calculation?
A: The speed of light is used to calculate the time delay of the signal traveling to the target and back, which affects the phase of the received signal.

Q5: Are there limitations to this formula?
A: This formula assumes ideal conditions and may need adjustments for atmospheric effects, system losses, and other real-world factors that affect radar performance.