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,
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#
Walkthrough#
Set frequency to 10 GHz (X-band) and range to 50 km. Read the FSPL — about 146 dB — and the wavelength readout (~3 cm).
Double the range to 100 km. Watch the loss climb by exactly 6 dB. Double again to 200 km for another 6 dB.
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.
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.
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.
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.