1. The Logic of Logarithms (10log vs 20log)
The Decibel (dB) is a logarithmic unit used to express the ratio of two values. It is essential in engineering because signals span massive dynamic ranges (from nanowatts to megawatts).
Figure 1: Comparison of Linear Power vs. Logarithmic Decibels.
- Power Rule (10 log): For quantities representing Power (Watts, Joules), the formula is $dB = 10 \log_{10}(P_2/P_1)$. A factor of 2 in power is approx 3 dB.
- Field Rule (20 log): For quantities like Voltage (V) or Current (I), power is proportional to the square ($P \propto V^2$). Therefore, $10 \log(V^2/V_{ref}^2) = 20 \log(V/V_{ref})$. A factor of 2 in voltage is approx 6 dB.
Figure 2: The Decibel "Rules of Thumb" for Quick Estimation.
2. Absolute Reference Units
dB by itself is a relative ratio. To measure absolute levels, we use a suffix to denote the reference:
- dBm: Referenced to 1 milliwatt (1 mW). $0 \text{ dBm} = 1 \text{ mW}$. Used in RF/Audio.
- dBW: Referenced to 1 Watt. $0 \text{ dBW} = 1 \text{ Watt} = 30 \text{ dBm}$. Used in High Power RF.
- dBV: Referenced to 1 Volt RMS. Independent of impedance. Used in Audio.
- dBu: Referenced to 0.775V (Voltage across 600Ω dissipating 1mW). Legacy Audio standard.
3. Free Space Path Loss (FSPL)
In industrial telemetry (SCADA radios, Wi-Fi), signals attenuate as they travel through space. The FSPL formula defines the loss based on distance ($d$) and frequency ($f$):
Figure 3: Attenuation Trend over Distance (FSPL).
Where $K$ is a constant depending on units (32.44 for km/MHz, 92.45 for km/GHz). Doubling the distance adds 6 dB of loss.
4. Impedance Mismatch in dB Calculations
When converting Voltage to Power (dBm), Impedance ($Z$) is critical. $P = V^2 / Z$.
Figure 4: Signal Propagation Chain (Gain and Loss Accumulation).
A 1 Volt signal into 50Ω (RF Standard) produces $1^2 / 50 = 20 \text{ mW} = +13 \text{ dBm}$.
The same 1 Volt signal into 600Ω (Audio Standard) produces $1^2 / 600 = 1.66 \text{ mW} = +2.2 \text{ dBm}$.
Always verify the system impedance before converting dBV to dBm.
5. FAQ & Visual Guide
10 log vs 20 log?
Use 10 log for Power ratios ($P_2/P_1$). Use 20 log for Field ratios ($V_2/V_1$). The field multiplier accounts for the squared relationship of Power to Voltage.
What is 0 dBm?
It is the absolute power level referenced to 1 milliwatt (mW). 0 dBm is the standard "quiet" anchor for most RF systems.
Impedance Effect?
A 1V signal into 50Ω yields +13 dBm, while in 600Ω it yields only +2.2 dBm. Power is the actual "work" done by the voltage.
Path Loss (FSPL)?
Signal energy spreads out in space. Doubling your distance results in a 6 dB loss as the wave covers four times the area.
Why 3 dB?
3 dB represents a factor of 2 change in power. Because decibels are logarithmic, doubling the watts always adds 3 dB.
dBi vs dBd?
dBi references a theoretical point source (isotropic), while dBd references a standard dipole. 0 dBd = 2.15 dBi.
Adding dBs?
Gains and losses can be added arithmetically (10dB amp + 3dB cable = 13dB net). Absolute levels cannot be added directly.
dBW vs dBm?
dBW is power referenced to 1 Watt. Since 1 Watt is 1000 milliwatts, there is always a 30 dB difference between dBW and dBm.
SNR & Noise?
Noise Figure (NF) represents the signal-to-noise degradation. A signals' value is only useful relative to the noise floor.
Negative dBs?
Attenuation or loss is expressed as negative decibels. This indicates that the output power is lower than the input power.