# Lesson 36 Flashcards — Signal-to-Noise Ratio Click a question to reveal the answer.
1. Where does noise come from?

Thermal noise from random charge motion in any conductor above absolute zero, receiver noise from the amplifiers and other electronics in your own receiver, and sky and ground noise collected by the antenna. It is there even when nobody else is transmitting.

2. Define SNR.

\(SNR = P_\text{signal}/P_\text{noise}\) — how loud you are talking divided by how loud everyone else is. It is dimensionless, often quoted in dB.

3. Give the thermal noise power equation.

\(P_\text{noise} = k\,T_\text{sys}\,BW\), with \(k = 1.38\times10^{-23}\) J/K, \(T_\text{sys}\) in kelvins, and \(BW\) the receiver's bandwidth in Hz. The result is in watts.

4. What are the two levers on the noise floor?

Bandwidth — narrower means less noise, which is why receivers filter down to just the signal — and system temperature, which is why radio astronomy cools its receivers.

5. Where does 'minimum detectable signal' actually come from?

\(P_{R,\min} = SNR_{\min} \times k\,T_\text{sys}\,BW\), where \(SNR_{\min}\) is the minimum SNR the receiver needs. It is a property of your receiver and its bandwidth, not of the transmitter.

6. When does a link close, or a radar detect?

When \(SNR \ge SNR_{\min}\). Comparing \(P_R\) with the sensitivity \(P_{R,\min}\) is the same test. A jammer adds its power to the noise and the same \(SNR_{\min}\) still decides: \(P_R/(P_\text{noise} + P_{R,\text{jam}}) \ge SNR_{\min}\).

7. Is SNR greater than 1 the test for detection?

No. \(SNR_{\min}\) belongs to the receiver's processing. A receiver that integrates many pulses, or de-spreads a spread-spectrum signal, can work with \(SNR_{\min}\) far below 1; one without that processing gain needs it above 1.

8. Write SNR for a communications link.

\(SNR = P_R/(k T_\text{sys} BW)\) with \(P_R\) from Friis. Everything that helps \(P_R\) helps SNR, plus the new lever of reducing \(BW\).

9. Write SNR for a radar link.

The same, but with \(P_R\) from the radar range equation — so the \(R^4\) carries straight through and radar SNR collapses very fast with range.

10. Why does low observability attack detection rather than the radar itself?

Because reducing the RCS, \(\sigma\), attacks the numerator of the SNR expression directly, lowering received signal against a noise floor the radar cannot reduce further.

11. Halving bandwidth improves comms range by how much? Radar range?

Comms \(P_R \propto 1/R^2\) so range improves by \(\sqrt{2}\). Radar \(P_R \propto 1/R^4\) so range improves only by \(2^{1/4} = 1.19\).

12. What is the golden rule when judging detection?

A received power means nothing alone: compare it to the noise, or to a sensitivity that already contains the noise. Detection is a signal-to-noise question.