Signal & dB Formulas
Signal and decibel formulas express gain, loss, and ratios on the logarithmic scale that engineers use every day. These calculators convert between linear ratios and decibels for both voltage and power. They are essential for amplifier design, link budgets, and audio level matching.
Signal & dB Formula Calculators
- dB (Power) dB = 10 × log₁₀(P2/P1) Reference Power 10 mW, Measured Power 22 mW → Gain = 3.424 dB
- dB (Voltage) dB = 20 × log₁₀(V2/V1) Reference Voltage 0.33 V, Measured Voltage 0.726 V → Gain = 6.848 dB
- dBm to Watts P = 10^((dBm − 30) / 10) Power (dBm) -2 dBm → Power = 0.631 mW
- dBV (Voltage Level) dBV = 20 × log10(V / 1V) Voltage 0.33 V → Level (dBV) = -9.63 dB
- dBu (Voltage Level) dBu = 20 × log10(V / 0.7746V) Voltage 0.33 V → Level (dBu) = -7.411 dB
- dBm to dBW Conversion dBW = dBm − 30 Power (dBm) 0.66 dB → Power (dBW) = -29.34 dB
- Receiver Noise Floor NF_floor = −174 + NF + 10×log10(BW) Noise Figure 0.66 dB, Bandwidth 5 Hz → Noise Floor = -166.4 dB
- Effective Number of Bits ENOB = (SINAD − 1.76) / 6.02 SINAD 0.3 dB → ENOB = -0.2425
- SINAD from ADC Bits SINAD = 6.02 × N + 1.76 Number of Bits 0.025 → SINAD = 1.911 dB
- Octave & Decade Frequency Spans octaves = log2(f2/f1), decades = log10(f2/f1) Lower Frequency 5 Hz, Upper Frequency 11 Hz → octaves = 1.138
- THD + N THD+N = √(Vharm² + Vnoise²) / V1 Harmonic RMS 10 mV, Noise RMS 22 mV, Fundamental RMS 0.33 V → THD + N = 7.323 %
- Noise-Equivalent Bandwidth (1-pole) NEB = (π/2) · f−3dB −3 dB Bandwidth 0.22 kHz → Noise Bandwidth = 0.3456 kHz
Worked result for every Signal & dB formula
| Formula | Expression | Worked result |
|---|---|---|
| dB (Power) | dB = 10 × log₁₀(P2/P1) | Reference Power 10 mW, Measured Power 22 mW → Gain = 3.424 dB |
| dB (Voltage) | dB = 20 × log₁₀(V2/V1) | Reference Voltage 0.33 V, Measured Voltage 0.726 V → Gain = 6.848 dB |
| dBm to Watts | P = 10^((dBm − 30) / 10) | Power (dBm) -2 dBm → Power = 0.631 mW |
| dBV (Voltage Level) | dBV = 20 × log10(V / 1V) | Voltage 0.33 V → Level (dBV) = -9.63 dB |
| dBu (Voltage Level) | dBu = 20 × log10(V / 0.7746V) | Voltage 0.33 V → Level (dBu) = -7.411 dB |
| dBm to dBW Conversion | dBW = dBm − 30 | Power (dBm) 0.66 dB → Power (dBW) = -29.34 dB |
| Receiver Noise Floor | NF_floor = −174 + NF + 10×log10(BW) | Noise Figure 0.66 dB, Bandwidth 5 Hz → Noise Floor = -166.4 dB |
| Effective Number of Bits | ENOB = (SINAD − 1.76) / 6.02 | SINAD 0.3 dB → ENOB = -0.2425 |
| SINAD from ADC Bits | SINAD = 6.02 × N + 1.76 | Number of Bits 0.025 → SINAD = 1.911 dB |
| Octave & Decade Frequency Spans | octaves = log2(f2/f1), decades = log10(f2/f1) | Lower Frequency 5 Hz, Upper Frequency 11 Hz → octaves = 1.138 |
| THD + N | THD+N = √(Vharm² + Vnoise²) / V1 | Harmonic RMS 10 mV, Noise RMS 22 mV, Fundamental RMS 0.33 V → THD + N = 7.323 % |
| Noise-Equivalent Bandwidth (1-pole) | NEB = (π/2) · f−3dB | −3 dB Bandwidth 0.22 kHz → Noise Bandwidth = 0.3456 kHz |
Variables used across Signal & dB formulas
- dB — Power ratio in decibels
- P1 — Reference power in watts (W)
- P2 — Measured power in watts (W)
- V1 — Reference voltage in volts (V)
- V2 — Measured voltage in volts (V)
- dBm — Absolute power level referenced to 1mW
- P — Power in watts (W)
- dBV — Voltage level referenced to 1V RMS (dB)
- V — RMS voltage (V)
- dBu — Voltage level referenced to 0.7746V RMS (dB)
- dBW — Power in decibels relative to 1 watt
- Noise Floor — Minimum noise power in the receiver (dBm)
- NF — Receiver noise figure (dB)
- BW — Receiver bandwidth (Hz)
- ENOB — Effective number of bits (dimensionless)
- SINAD — Signal-to-noise-and-distortion ratio (dB)
- N — Number of ADC bits (dimensionless)
- f₁ — Lower frequency (Hz)
- f₂ — Upper frequency (Hz)
- THD+N — Total distortion + noise ratio (fraction)
- Vharm — RMS sum of harmonic components (V)
- Vnoise — RMS noise (V)
- NEB — Noise-equivalent bandwidth (Hz)
- f−3dB — Filter −3 dB cutoff frequency (Hz)
Questions people ask about Signal & dB
- Absolute voltage level 1v — dBV (Voltage Level)
- Octave vs decade — Octave & Decade Frequency Spans
- Pi filter db/octave — Octave & Decade Frequency Spans
- Equivalent bandwidth rc — Noise-Equivalent Bandwidth (1-pole)
Related Formula Categories
Browse the full formulas index for all 32 categories.