Wireless Notes
Learn path loss in wireless communication with free space path loss formula, path loss exponent, log-distance model, link budget calculation, solved examples, and factors affecting signal loss for engineering students.
Hindi: Path loss ka matlab hai wireless signal ki strength (power) ka distance ke saath kam hona. Jab signal transmitter se door jaati hai, toh woh weak hoti jaati hai โ iss weakening ko path loss kehte hain. Yeh wireless system design mein sabse important factor hai.
๐ What is Path Loss?
Hindi: Path loss woh signal power ka loss hai jo tab hota hai jab signal transmitter se receiver tak travel karti hai. Distance badhne ke saath signal weaker hoti jaati hai.
Definition: Path loss (PL) is the reduction in power density of a radio wave as it propagates through space.
| Pt | โ |
|---|---|
| โ | |
| โโ | |
| โโโโ | |
| โโโโโโ | |
| โโโโโโโโโโ | |
| โโโโโโโโโโโโโโโโโ | |
| Pr | โโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ Received power |
| dโ dโ dโ dโ |
In dB:
๐ Free Space Path Loss (FSPL)
Hindi: FSPL ideal condition hai jahan koi obstacle nahi, koi reflection nahi โ sirf distance ki wajah se signal weak hoti hai. Yeh minimum possible path loss hai.
FSPL Formula:
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ โ
โ FSPL (dB) = 20logโโ(d) + 20logโโ(f) + 32.44 โ
โ โ
โ Where: โ
โ d = distance in km โ
โ f = frequency in MHz โ
โ โ
โ Alternative (d in meters, f in Hz): โ
โ FSPL (dB) = 20logโโ(4ฯd/ฮป) โ
โ = 20logโโ(d) + 20logโโ(f) - 147.55 โ
โ โ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
Key Insights from FSPL:
- Distance doubles โ 6 dB more loss (signal 4x weaker)
- Frequency doubles โ 6 dB more loss (signal 4x weaker)
- This is why higher frequencies have shorter range
FSPL Values for Common Scenarios:
| Frequency | Distance | FSPL |
|---|---|---|
| 900 MHz (4G) | 1 km | 91.5 dB |
| 900 MHz (4G) | 5 km | 105.5 dB |
| 2.4 GHz (WiFi) | 10 m | 60.0 dB |
| 2.4 GHz (WiFi) | 50 m | 74.0 dB |
| 5 GHz (WiFi) | 10 m | 66.3 dB |
| 28 GHz (5G) | 100 m | 101.3 dB |
| 28 GHz (5G) | 500 m | 115.3 dB |
๐ Path Loss Exponent
Hindi: Real world mein path loss FSPL se zyada hoti hai. Path loss exponent (n) batata hai ki environment kitna lossy hai.
| Environment | Path Loss Exponent (n) | Hindi |
|---|---|---|
| Free space | 2 | Khuli jagah (ideal) |
| Urban (LoS) | 2.7 โ 3.5 | Sheher (direct sight) |
| Urban (NLoS) | 3 โ 5 | Sheher (buildings block) |
| Indoor (same floor) | 1.6 โ 3.5 | Inside a building |
| Indoor (multi-floor) | 4 โ 6 | Multiple floors cross |
| Rural | 2 โ 2.5 | Gaanv/open area |
| Factory | 2 โ 3 | Industrial building |
Interpretation:
- n = 2: Signal follows inverse square law (ideal free space)
- n = 3-4: Typical urban environment
- n > 4: Very obstructed environment
- n < 2: Waveguide effect (corridors, tunnels)
๐ Log-Distance Path Loss Model
Hindi: Yeh practical model hai jo reference distance se path loss predict karta hai:
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ โ
โ PL(d) = PL(dโ) + 10nยทlogโโ(d/dโ) + Xฯ โ
โ โ
โ Where: โ
โ PL(d) = Path loss at distance d โ
โ PL(dโ) = Path loss at reference distance dโ โ
โ n = Path loss exponent โ
โ d = Distance to receiver โ
โ dโ = Reference distance (typically 1m or 100m) โ
โ Xฯ = Random shadowing (Gaussian, 0 mean, ฯ std) โ
โ โ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
๐๏ธ Empirical Models
Hindi: Real-world measurements se derive kiye gaye models:
Okumura-Hata Model (150 MHz โ 1500 MHz):
- Urban, suburban, rural areas
- Cell ranges of 1-20 km
- Most widely used for cellular planning
COST 231 (1500 MHz โ 2000 MHz):
- Extension of Hata model for higher frequencies
- Used for GSM/3G planning
3GPP Models (for 4G/5G):
- UMa (Urban Macro)
- UMi (Urban Micro)
- RMa (Rural Macro)
- InH (Indoor Hotspot)
๐ก๏ธ Factors Affecting Path Loss
| Factor | Effect | How Much |
|---|---|---|
| Distance | Doubles โ +6 dB loss (free space) | Major |
| Frequency | Doubles โ +6 dB loss | Major |
| Obstacles | Buildings add 10-30 dB per wall | Significant |
| Foliage | Trees add 5-20 dB | Moderate |
| Rain | Significant above 10 GHz | +1-10 dB/km |
| Indoor penetration | Outer wall: 10-25 dB | Significant |
| Floor penetration | Per floor: 10-20 dB | Significant |
| Body blocking | Human body: 5-30 dB (mmWave) | Varies |
Typical Wall/Material Losses:
| Material | Loss at 2.4 GHz | Loss at 5 GHz | Loss at 28 GHz |
|---|---|---|---|
| Drywall | 3-5 dB | 4-7 dB | 6-10 dB |
| Concrete | 10-15 dB | 15-20 dB | 25-35 dB |
| Glass | 2-4 dB | 4-8 dB | 5-10 dB |
| Brick | 8-12 dB | 10-15 dB | 20-30 dB |
| Metal | 20-30 dB | 25-40 dB | 40+ dB |
๐ฐ Link Budget
Hindi: Link budget ek calculation hai jo determine karti hai ki signal receiver tak enough power ke saath pahunchegi ya nahi.
Example Link Budget:
| Parameter | Value | Unit |
|---|---|---|
| TX Power | +23 dBm | (200 mW, typical phone) |
| TX Antenna Gain | +3 dBi | |
| Cable Loss (TX) | -1 dB | |
| Path Loss | -110 dB | (urban, 2 km, 1800 MHz) |
| RX Antenna Gain | +15 dBi | (cell tower) |
| Cable Loss (RX) | -2 dB | |
| Received Power | -72 dBm | |
| Receiver Sensitivity | -95 dBm | |
| Link Margin | 23 dB | โ Sufficient |
๐ Solved Examples
Example 1: FSPL for WiFi
Given: f = 2.4 GHz = 2400 MHz, d = 30 m = 0.03 km
Example 2: Will signal reach?
Given: TX power = 20 dBm, Path loss = 85 dB, Receiver sensitivity = -90 dBm
Example 3: Maximum distance
Given: TX = 30 dBm, Sensitivity = -100 dBm, n = 3.5, PL(1m) = 40 dB
๐ Summary
| Concept | Formula | Key Point |
|---|---|---|
| Path Loss | PL = Pt - Pr | Signal weakening with distance |
| FSPL | 20log(d) + 20log(f) + 32.44 | Minimum possible loss |
| Distance effect | Double d โ +6 dB loss | Inverse square law |
| Frequency effect | Double f โ +6 dB loss | Higher freq = more loss |
| Path Loss Exponent | n = 2 (free space) to 5+ (indoor) | Environment dependent |
| Link Budget | Must exceed receiver sensitivity | Design tool |
โ FAQ
Q: 5G mmWave ki range kyun kam hai? A: 28 GHz pe FSPL hi bahut zyada hai (101 dB at 100m). Plus obstacles bahut zyada block karte hain. Isliye dense small cell deployment chahiye.
Q: WiFi router ka signal door tak kaise le jaayein? A: Higher TX power, better antenna (higher gain), obstacles minimize, mesh system use, ya repeater lagao. Each wall 5-15 dB loss add karti hai.
Q: dBm aur dB mein kya difference hai? A: dBm absolute power measure hai (referenced to 1 mW). dB relative difference hai. Path Loss dB mein hoti hai, power dBm mein.
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