What Is a Decibel?
- A power ratio in dB:
-
- An absolute power in dBW (referenced to 1 W):
- Course notation: is linear power; is its decibel representation — brackets denote logarithmic quantities
- Try it: 1 W → 0 dBW, 10 W → 10 dBW, 100 W → 20 dBW
- What about 2 W? , so about 3 dBW (consistent with “power ×2 → +3 dB” below) (answer not on slide)
Linear Power and Decibel Power
| 1 mW | 10 mW | 0.1 W | 1 W | 10 W |
|---|
| (dBW) | −30 | −20 | −10 | 0 | 10 |
| (dBm) | 0 | 10 | 20 | 30 | 40 |
- Every +10 dB step multiplies power by 10
- Gains add; losses subtract
- (dBm is referenced to 1 mW)
Useful Decibel Relationships
| Change | Physical effect | Received power |
|---|
| Power ×2 | Twice the watts | |
| Power ×10 | Ten times the watts | |
| Range ×2 | Four times the sphere area | |
| Range ×10 | One hundred times the area | |
- Predict the sign and scale before touching the calculator
- Range enters as , so it costs per factor, while power costs (why)
Quantities and Their Units
| Quantity | Linear form | Logarithmic form |
|---|
| Power or EIRP | W | dBW or dBm |
| Antenna gain | Ratio to isotropic | dBi |
| Loss | Power ratio ≥ 1 | dB, subtracted |
| Power flux density, | W/m² | (linear form for now) |
| Effective area, | m² | (linear form for now) |
- Losses are written as positive dB numbers and subtracted in the ledger (e.g. in free-space path loss)