Signal Attenuation & dB Calculator

Convert between voltage/power gain and decibels. Calculate signal attenuation in transmission lines.

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Reading Gain and Loss on the Decibel Scale

A decibel value is a logarithmic way to express a ratio, not an absolute amount of power by itself. For power ratios, GdB=10log10(Pout/Pin). A ratio above 1 gives positive dB gain, a ratio below 1 gives negative dB loss, and equal input and output power gives 0dB. The logarithm compresses very large and very small ratios into manageable numbers.

Voltage and current ratios use 20log10 only when the compared quantities refer to the same impedance, or when the impedance relationship is otherwise accounted for. The factor 20 arises because power is proportional to voltage squared for a fixed resistance: 10log(V2 ratio)=20log(V ratio). Without the equal-impedance assumption, converting a voltage ratio directly to a power ratio can be wrong.

GdB=10log10(Pout/Pin),   GdB=20log10(Vout/Vin) for equal impedances
QuantityRelationInterpretation
Power ratio10log10(Pout/Pin)+10dB means 10× power; −10dB means one-tenth.
Voltage ratio20log10(Vout/Vin)For equal impedance, +20dB means 10× voltage.
CascadedB values addMultiplication of linear ratios becomes addition of logarithms.

Attenuation is often quoted as a positive loss magnitude, such as "6dB attenuation," even though a signed gain calculation would report −6dB. Always check the convention being used. Decibels can also be attached to references, such as dBm or dBW, which then represent absolute power levels rather than dimensionless ratios.

Worked Examples

Example 1: Amplifier: P_out/P_in=100
10 log₁₀(100)
Result: 20 dB gain
Each 3dB = 2× power, 10dB = 10×
Example 2: Cascade: +26dB amp, −3dB filter, +14dB amp
Total = 26-3+14
Result: 37 dB net gain — power ratio 5012×
dB stages simply add
Example 3: One percent of the input power remains
Pout/Pin=0.01 → 10log10(0.01)
Result: −20 dB
A 100-fold power reduction is a 20dB loss. If attenuation is quoted as a positive magnitude, it would be described as 20dB attenuation.
Example 4: Voltage cut in half
Vout/Vin=0.5 with equal impedance → 20log10(0.5)
Result: −6.02 dB
With equal impedance, halving voltage makes power one-quarter, consistent with about −6.02dB.

Common Mistakes

⚠️
Using 20log for a power ratio

Power ratios use 10log10. The 20log form is for amplitude ratios such as voltage under the appropriate impedance condition.

⚠️
Assuming −3dB is exactly half voltage

−3dB is approximately half power. Under equal impedance, the corresponding voltage ratio is about 0.708, not 0.5.

⚠️
Confusing dB with dBm

dB alone expresses a ratio. dBm is referenced to 1mW and therefore represents an absolute power level.

Frequently Asked Questions

Why use dB?
Human perception is logarithmic. dB compresses huge power ratios (10⁻¹² to 10¹² W) into manageable numbers. Cascaded gain stages ADD in dB instead of multiply — simpler system analysis.
Key dB values to memorize?
±1 dB ≈ 1.26× power (subtle). ±3 dB ≈ 2× power (−3 dB = half power). ±6 dB ≈ 4× power, 2× voltage. ±10 dB = 10× power. ±20 dB = 100× power, 10× voltage.
Why do decibel gains add when stages are cascaded?
Linear power ratios multiply from stage to stage. Taking a logarithm turns multiplication into addition: 10log(G1G2)=10logG1+10logG2. This makes long gain-and-loss budgets much easier to calculate and audit.
What power ratio corresponds to −6dB?
The power ratio is 10−6/10≈0.251. So roughly one-quarter of the input power remains. Under equal impedance, the corresponding voltage ratio is 10−6/20≈0.501, or about one-half.
Can I use the voltage dB formula if input and output impedances differ?
Not as a direct power-gain statement. Since power depends on both voltage and impedance, unequal impedances require those impedances to be included. The 20log voltage-ratio shortcut is safe for power comparison only when the relevant impedances are equal or otherwise properly normalized.
Is 0dB the same as zero signal?
No. For a ratio, 0dB means output equals input because log10(1)=0. An absolute zero signal cannot be represented as a finite ratio in dB because the logarithm of zero tends toward negative infinity.

Formula Explorer connections

Interpretation: This relationship connects frequency, wavelength, speed, phase, intensity or resonance in an oscillating system. Assumption: Identify the medium, boundary conditions and reference frame. Linear waves, small amplitudes, nondispersive media or ideal resonance may be assumed.

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