Free Space Path Loss Calculator | Qucs-S S-parameter Viewer Documentation

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# Free Space Path Loss Calculator

## Overview

The Free Space Path Loss (FSPL) calculator computes signal attenuation in free space based on frequency, distance, and antenna gains.

## Formula

The FSPL is calculated using:

    FSPL (dB) = 20×log₁₀(4π/c) + 20×log₁₀(f) + 20×log₁₀(d) - G_TX - G_RX

Where:

- `f` = frequency in Hz

- `d` = distance in meters

- `c` = speed of light (299,792,458 m/s)

- `G_TX` = transmitter antenna gain in dBi

- `G_RX` = receiver antenna gain in dBi

- `20×log₁₀(4π/c)` ≈ -147.55 dB (constant term)

## Input Parameters

Parameter | Range | Units Available
--- | --- | ---
Frequency | 0 to 10¹⁵ | Hz, kHz, MHz, GHz, THz
Distance | 0 to 10¹⁵ | m, km, cm, mm, ft, mi, nmi
G_TX | -50 to 100 dB | dBi
G_RX | -50 to 100 dB | dBi

## Output

The calculator displays path loss for five distance points:

- d/4 (quarter distance)

- d/2 (half distance)

- d (specified distance, highlighted)

- 2×d (double distance)

- 4×d (quadruple distance)

## Example

Input:

- Frequency: 1000 MHz (1 GHz)

- Distance: 1 km

- G_TX: 0 dBi

- G_RX: 0 dBi

Calculation:

    f = 1×10⁹ Hz
    d = 1000 m
    FSPL = -147.55 + 20×log₁₀(10⁹) + 20×log₁₀(1000) - 0 - 0
         = -147.55 + 180 + 60
         = 92.45 dB

Output Table:

Distance | Path Loss
--- | ---
250 m (d/4) | 80.43 dB
500 m (d/2) | 86.44 dB
1 km (d) | 92.45 dB
2 km (2×d) | 98.47 dB
4 km (4×d) | 104.48 dB

## Notes

- Distance doubling increases path loss by approximately 6 dB

- Higher frequencies result in greater path loss

- Antenna gains reduce overall path loss

- Invalid inputs (frequency or distance ≤ 0) display “Error”