Lesson 33 Flashcards — The Friis Equation#
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1. What is a link budget?
Bookkeeping on power from transmitter to receiver: everything in between either adds gain or subtracts loss. If what arrives meets or exceeds the receiver's sensitivity \(P_{R,\min}\), the link closes.
2. Write the Friis equation.
\(P_R = P_T G_T G_R \lambda^2/(4\pi R)^2\), with every gain a linear ratio (no units).
3. Where does the 1/R² in Friis come from?
The surface area of an expanding sphere. Transmitted power spreads over \(4\pi R^2\) — that is the one-way spreading loss.
4. What is effective aperture?
\(A_e = \lambda^2 G_R/4\pi\) — the effective area over which a receiving antenna collects power. Multiplying power density by \(A_e\) gives received power.
5. What happens to P_R if you double the transmit power? The gain?
Both double \(P_R\) — these terms enter linearly.
6. What happens to P_R if you double the wavelength?
\(P_R\) goes up by four times, since \(\lambda\) is squared. Lower frequencies travel farther for the same power.
7. What happens to P_R if you double the range?
It drops to one quarter — range enters squared.
8. Higher frequency hurts Friis but helps antennas. Explain the tension.
Free-space loss goes as \(1/\lambda^2\), but dish gain goes as \(1/\lambda^2\) too. Raising frequency costs you in propagation and pays you back in antenna gain — a real design tradeoff.
9. Give the decibel conversions worth memorizing.
\(\times 2 = +3\) dB, \(\times 4 = +6\) dB, \(\times 10 = +10\) dB, \(\times 100 = +20\) dB, \(\div 2 = -3\) dB. These are power ratios, \(10\log_{10}\); the equation sheet's \(20\log_{10}\) row is for voltage gain (Lesson 17).
10. Why do link budgets use decibels at all?
Because multiplying becomes adding, and the dynamic range involved is enormous. In this course, convert a dB value to a linear ratio before it goes into an equation.
11. How do you find the power-limited range of a link?
Solve Friis for \(R\) with \(P_R = P_{R,\min}\): \(R = \frac{\lambda}{4\pi}\sqrt{P_T G_T G_R/P_{R,\min}}\), in meters. It is the second Friis row on the equation sheet.
12. The LOS range comes out in miles and the Friis range in meters. How do you compare them?
Convert first. \(R_{LOS,mi}\) takes heights in feet and gives miles; multiply by 1.61 for kilometers. Compare the two limits only in the same unit.
13. A satellite is directly overhead. What range goes into Friis?
The difference of the two altitudes, \(R = h_\text{sat} - h_\text{aircraft}\), in meters (feet × 0.305). Straight up there is no horizon in the way, so there is no LOS limit to compute.
14. What two tests must a communication link pass?
It needs line of sight and adequate power. The maximum range is the smaller of the two limits — and either one can bind, so compute both.