Lesson 3 Flashcards#
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1. Write the radar range equation for received power.
\(P_r = \dfrac{P_t G_t G_r \lambda^2 \sigma}{(4\pi)^3 R^4}\).
2. Where does the \(1/R^4\) come from?
Two-way spreading: the signal spreads as \(1/R^2\) on the way out and again \(1/R^2\) on the way back. The product is \(1/R^4\).
3. What is radar cross section (RCS)?
\(\sigma\) (m²): the equivalent area that, capturing the incident density and re-radiating it isotropically, would produce the observed echo. It encodes how strongly a target reflects.
4. Write the maximum detection range.
\(R_\text{max} = \left[\dfrac{P_t G_t G_r \lambda^2 \sigma}{(4\pi)^3 S_\text{min}}\right]^{1/4}\), equivalently \(R_\text{max} = K\,\sigma^{1/4}\).
5. By what factor must transmit power rise to double detection range?
×16 (+12 dB), because every term sits under a fourth root. The same factor applies to \(G_t\), \(G_r\), or \(1/S_\text{min}\).
6. What is \(S_\text{min}\)?
The minimum detectable signal — the smallest received power at which the radar declares a detection. It is bounded by the receiver noise floor; coherent integration lowers it somewhat.
7. Why is RCS the target's best lever despite the fourth root?
The radar's power/gain levers run into hard thermal and physical limits, while shaping and materials keep reducing \(\sigma\). Both sides are fourth-rooted, but the target's lever has room left.
8. In the worked example, what is \(R_\text{max}\) for a 1 m² target?
About 472 km (S-band, \(P_t=1\) MW, \(G_t=G_r=30\) dBi, \(\lambda=0.1\) m).
9. Dropping that target to −30 dBsm changes \(R_\text{max}\) to roughly what?
About 84 km. A 1000× RCS cut scales range by \((10^{-3})^{1/4} \approx 0.178\), i.e. ~5.6× shorter.
10. What is the effective aperture of a receive antenna?
\(A_e = G_r \lambda^2 / 4\pi\). Multiplying the echo power density by \(A_e\) gives the received power \(P_r\).
11. Why is the Detect link the most leverage-rich part of the kill chain?
The fourth-power law makes detection range extremely sensitive in operational terms: small engineering changes to \(\sigma\) reshape the entire defended volume, and detection gates everything downstream.