dB Calculator (Gain/Loss) & Link Analysis

Commercial-grade Signal Processing & RF Tool. Calculate Gain/Loss (dB), Absolute Power (dBm, dBW), and perform RF Link Budget Analysis (FSPL). Features precise 10log vs 20log logic and impedance corrections.

Engineering Guide: Decibels & Signal Analysis

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).

  • 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.

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 ($f$):

$$ FSPL(dB) = 20 \log_{10}(d) + 20 \log_{10}(f) + K $$

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. $P = V^2 / Z$.

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. Frequently Asked Questions (FAQ)

1. When do I use 10 log vs 20 log?
Use 10 log₁₀(P₂/P₁) for POWER ratios (Watts). Use 20 log₁₀(V₂/V₁) for FIELD quantities like Voltage (Volts) or Current (Amps). The factor of 20 comes from the fact that Power is proportional to Voltage squared ($P = V^2/R$).
2. What is 0 dBm?
0 dBm is an absolute power level referenced to 1 milliwatt (1 mW). Positive values indicate power > 1mW (e.g., 30 dBm = 1W), while negative values indicate power < 1mW (e.g., -30 dBm=1 microwatt).
3. How does Impedance affect dBV calculations?
dBV is solely a voltage reference (1V). However, if you convert dBV to dBm (Power), impedance (Z) matters critically ($P = V^2/Z$). A 0 dBV signal is +13 dBm in a 50Ω system but only +2.2 dBm in a 600Ω system.
4. What is Free Space Path Loss (FSPL)?
FSPL quantifies the loss of signal strength as an electromagnetic wave spreads out in free space. It depends on distance and frequency. Doubling the distance or doubling the frequency results in a 6 dB additional loss.
5. Why is 3 dB significant?
A change of 3 dB represents a doubling (or halving) of Power. +3 dB ≈ 2x Power. -3 dB ≈ 0.5x Power. For Voltage, a doubling is 6 dB.
6. What is dBi vs dBd in antennas?
dBi is gain referenced to an isotropic radiator (theoretical point source). dBd is gain referenced to a dipole antenna. Typically, dBi = dBd + 2.15. Industrial specs usually use dBi.
7. How do I add dB?
You can add dB values directly if they represent gains/losses in a chain (e.g., +10dB Amp - 3dB Cable = +7dB Net). You CANNOT add absolute levels (e.g., 10dBm + 10dBm is NOT 20dBm; it is approx 13dBm because 10mW + 10mW = 20mW).
8. What is the formula for dBW?
dBW is power referenced to 1 Watt. Formula: dBW = 10 log₁₀(Power in Watts). 0 dBW = 30 dBm.
9. Does this tool calculate Noise Figure?
This specific tool focuses on Gain, Loss, and Absolute levels. Noise Figure calculations involve thermal noise floors (-174 dBm/Hz) which are covered in our advanced RF suite.
10. Why is attenuation expressed as negative dB?
Gain is positive dB ($P_{out} > P_{in}$). Attenuation or Loss is negative dB ($P_{out} < P_{in}$). Sometimes 'Loss' is stated as a positive number (e.g., 'Cable Loss: 3dB' ), which mathematically means a -3dB gain.