# Demo — Free-Space Path Loss Calculator
Free-space path loss is the first thing that happens to a radar signal: it spreads and weakens with both range and frequency. This demo makes the 6 dB rules tactile — slide range or frequency, watch the loss climb, and see the band structure of the spectrum laid out.
## The relationship
With range in km and frequency in GHz,
$$
L_\text{fs,dB} = 20\log_{10}(R_\text{km}) + 20\log_{10}(f_\text{GHz}) + 92.45.
$$
Because both terms are $20\log_{10}(\cdot)$ and $20\log_{10}(2)\approx 6$ dB, **doubling either range or frequency adds 6 dB**.
## Interactive demo
Open in full screen
## Walkthrough
1. **Set frequency to 10 GHz (X-band) and range to 50 km.** Read the FSPL — about 146 dB — and the wavelength readout (~3 cm).
2. **Double the range to 100 km.** Watch the loss climb by exactly 6 dB. Double again to 200 km for another 6 dB.
3. **Reset range, then double the frequency from 10 to 20 GHz.** The loss again climbs 6 dB — frequency and range behave identically in the formula.
4. **Click the band chips (L, S, C, X, Ku, K, Ka).** Frequency snaps to each band center. Notice how much more loss the high bands carry at the same range.
5. **Watch the Plotly curves.** Each band is an FSPL-vs-range line; the vertical cursor follows your range slider so you can read all bands at once.
6. **Find a 6 dB step yourself.** Move the range cursor between any value and its double; confirm the footer's "+6 dB" indicator lights up.
## Key observations
- **Loss grows with both range and frequency**, and identically in dB — that symmetry is the whole point of the 6 dB rules.
- **High bands pay a propagation tax.** Ku/Ka give resolution and small antennas but start from a higher loss floor, which is why long-range search radars sit at L/S band.
- **This is one-way loss.** The radar round trip doubles the dB and feeds the $1/R^4$ of the next lesson's range equation.
## Source
MATLAB · code/L2_FreeSpacePathLoss.m↓
The in-class script plots FSPL versus range for the L, S, C, and X bands and verifies the 6 dB rules numerically.