Waveguides and antennas
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| guide wavelength | guide wavelength |
| Friis equation | phương trình Friis |
The pipe and its cutoff
- A hollow guide carries waves only above $f_{c} = c/2a$: WR-90 (a = 22.86 mm) cuts off at 6.56 GHz — X-band rides above. The guide wavelength stretches: $\lambda_{g} = \lambda/\sqrt{1 - (f_{c}/f)^{2}}$ = 39.8 mm at 10 GHz (λ = 30 mm).
{exercise:uni-ee0771-cutoff}
WR-90 guide (a = 22.86 mm) cuts off at about —
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fc = c/2a = 3e8/(2 × 0.02286) = 6.56 GHz — set by the WIDE dimension; halving it doubles fc, which is the 13.1 trap.
As f approaches fc, the guide wavelength —
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λg = λ/√(1 − (fc/f)²): the denominator vanishes at cutoff. At high f the zigzag vanishes and λg → λ.
The link, priced in dB
- The Friis equation: $P_{r}/P_{t} = G_{r}G_{t}(\lambda/4\pi R)^{2}$. Two 10-dBi antennas at 3 GHz: 1 m apart is −22 dB (easy); 1 km apart is −82 dB — the R² geometry that decides dish sizes.
{exercise:uni-ee0772-friis}
Doubling the link distance R changes the received power by —
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Friis has (1/R)²: doubling R costs 2² = 4× = 6 dB. From 1 m to 1 km (1000×) that is 60 dB — the dish-size driver.