Question

. What is the free space path loss in dB at the 2.4 GHz band?

Answer 1

Free Space Path Loss (FSPL) can be calculated using the following formula:

\[
\text{FSPL (dB)} = 20 \log_{10}(d) + 20 \log_{10}(f) + 20 \log_{10}\left(\frac{4\pi}{c}\right)
\]

Where:
- \( d \) is the distance between the transmitter and receiver in meters.
- \( f \) is the frequency of the signal in hertz (for 2.4 GHz, \( f = 2.4 \times 10^9 \) Hz).
- \( c \) is the speed of light in meters per second (approximately \( 3 \times 10^8 \) m/s).

To simplify the equation for free space, we often use a constant for \( 20 \log_{10}\left(\frac{4\pi}{c}\right) \). This value is approximately 32.44 dB when using a distance unit of kilometers and frequency in megahertz.

Using 2.4 GHz (or 2400 MHz) and assuming a distance \( d \) in kilometers, the FSPL can be simplified using the following formula:

\[
\text{FSPL (dB)} = 32.44 + 20 \log_{10}(d) + 20 \log_{10}(f)
\]

Plugging in the frequency:

\[
f = 2400 \text{ MHz}
\]

The FSPL formula becomes:

\[
\text{FSPL (dB)} = 32.44 + 20 \log_{10}(d) + 20 \log_{10}(2400)
\]

Calculating \( 20 \log_{10}(2400) \):

\[
20 \log_{10}(2400) \approx 20 \times 3.3802 \approx 67.604 \text{ dB}
\]

Therefore, the FSPL can be expressed as:

\[
\text{FSPL (dB)} = 32.44 + 67.604 + 20 \log_{10}(d)
\]

Combining the values:

\[
\text{FSPL (dB)} \approx 100.044 + 20 \log_{10}(d)
\]

To calculate the FSPL for a specific distance \( d \), you substitute the value of \( d \) (in kilometers) into the final equation. For example, for \( d = 1 \) km:

\[
\text{FSPL (dB)} \approx 100.044 + 20 \log_{10}(1) = 100.044 \text{ dB}
\]

For other distances, adjust \( d \) accordingly, using the same formula.