l2

Lecture 2: Signal Propagation & Transmission

How electromagnetic waves travel from transmitter to receiver.

Direct path between antennas.
Used for Wi-Fi, microwave links, and satellite communication.
Maximum LOS Distance Formula: $d = 3.57 (\sqrt{K h_{1}} + \sqrt{K h_{2}})$
- $d$ : distance in km.
- $h_{1}, h_{2}$ : antenna heights in meters.
- $K$ : adjustment factor for refraction (typically $K = 4 / 3$ ).

Conductors that radiate or collect electromagnetic energy.

Isotropic Antenna: Idealized point source radiating equally in all directions.
Dipole Antenna: Half-wave dipole, standard reference.
Parabolic Antenna: High directivity, used for satellite/microwave.
Radiation Pattern: Graphical representation of antenna properties (Beam width).

The power output in a specific direction compared to an isotropic antenna.

G = \frac{4 π A_{e}}{λ^{2}}

A link budget sums all gains and losses:

P_{r} = P_{t} + G_{t} + G_{r} - L_{p}

Given:

\begin{aligned} Given: & f = 10 GHz = 10^{10} Hz, \\ P_{t} = 27.78 dBW, G_{t} = 18 dBi, G_{r} = 20 dBi, \\ B = 4 \times 10^{6} Hz, N_{0} = 2 \times 10^{- 10} W/Hz \end{aligned}

\begin{aligned} 1) Noise Power: N & = N_{0} B \\ = (2 \times 10^{- 10}) (4 \times 10^{6}) \\ = 8 \times 10^{- 4} W \end{aligned}

\begin{aligned} N_{dBW} & = 10 \log_{10} (8 \times 10^{- 4}) \\ \approx - 30.97 dBW \end{aligned}

\begin{aligned} 2) Maximum Allowable Path Loss: P_{r} & = P_{t} + G_{t} + G_{r} - L_{p} \end{aligned}

\begin{aligned} For faithful reception: P_{r} & \geq N \end{aligned}

\begin{aligned} N & \leq P_{t} + G_{t} + G_{r} - L_{p} \\ L_{p} & \leq P_{t} + G_{t} + G_{r} - N \\ L_{p} & \leq 27.78 + 18 + 20 - (- 30.97) \\ L_{p} & \leq 96.75 dB \end{aligned}

\begin{aligned} 3) Distance from FSPL: L_{p} & = 20 \log_{10} (d) + 20 \log_{10} (f) + 20 \log_{10} (\frac{4 π}{c}) \end{aligned}

\begin{aligned} 96.75 & = 20 \log_{10} (d) + 20 \log_{10} (10^{10}) + 20 \log_{10} (\frac{4 π}{3 \times 10^{8}}) \\ 96.75 & = 20 \log_{10} (d) + 200 - 147.56 \\ 96.75 & = 20 \log_{10} (d) + 52.44 \end{aligned}

\begin{aligned} 20 \log_{10} (d) & = 44.31 \\ \log_{10} (d) & = 2.2155 \\ d & = 10^{2.2155} \\ d & \approx 164.2 m \end{aligned}

Maximum faithful coverage distance \approx 164 m

Lower Frequencies: Long distance, penetrates obstacles, low data rate.
Higher Frequencies: High data rate, high attenuation, requires LOS.
Link Budget: Essential for calculating if a signal will reach its destination with sufficient power.

continue:./l3.md
before:./l1.md