Decibels Explained from Scratch
The decibel appears everywhere in radio electronics. Antenna gain is measured in decibels. Cable loss is measured in decibels. Amplifier gain, receiver sensitivity, filter rejection, the difference between a 5 W QRP station and a 100 W station — all expressed in decibels. Understanding what a decibel actually is, and being able to work with dB values in your head, is one of the most practical skills you can develop for radio work. This lesson builds that understanding from the ground up.
Why We Need Decibels
A transceiver receives signals ranging from a few tenths of a microvolt (a weak DX station) to hundreds of millivolts (a nearby station). That is a voltage ratio of more than a million to one — over 1,000,000:1. The same ratio expressed as a power ratio is over a trillion to one (1012:1). Writing and working with ratios this large on a linear scale is impractical.
The decibel takes the base-10 logarithm of the ratio, compressing enormous ranges into small, easily handled numbers. The ratio 1012:1 becomes 120 dB. The ratio 106:1 becomes 60 dB. The ratio 2:1 becomes approximately 3 dB. And crucially: gains and losses in a signal path can simply be added and subtracted. A 20 dB amplifier followed by a 3 dB attenuator gives 17 dB net gain — no multiplication required.
The decibel scale compresses a trillion-to-one power range into a 120 dB span that is easy to work with.
View LargerThe Power Decibel Formula
For a ratio of two power levels P2 and P1:
Where P2 is the output (or measured) power, P1 is the input (or reference) power, and log10 is the base-10 logarithm (the "log" key on a calculator).
dB = 10 × log10(10 / 1) = 10 × log10(10) = 10 × 1 = +10 dB
Example 2: Coaxial cable passes 25 W, input was 50 W
dB = 10 × log10(25 / 50) = 10 × log10(0.5) = 10 × (−0.301) = −3.01 dB ≈ −3 dB (a loss)
Example 3: Attenuator reduces 1 W to 100 mW (0.1 W)
dB = 10 × log10(0.1 / 1) = 10 × log10(0.1) = 10 × (−1) = −10 dB
A positive dB value means gain (the output is larger than the input). A negative dB value means loss (the output is smaller than the input). Zero dB means unity — the output equals the input.
The Voltage and Current Decibel Formula
For voltage or current ratios, the formula uses 20 instead of 10:
dB = 20 × log10(I2 / I1)
Important: this assumes both voltages (or both currents) are measured across (or through) the same impedance. If impedances differ, use the power formula instead.
dB = 20 × log10(10) = 20 × 1 = +20 dB
Example 2: Voltage divider halves the signal (Vout/Vin = 0.5)
dB = 20 × log10(0.5) = 20 × (−0.301) = −6.02 dB ≈ −6 dB
Why 20 Instead of 10?
Power is proportional to voltage squared divided by resistance: P = V2/R. This means if the voltage doubles, the power quadruples (not doubles). A voltage ratio of 2:1 corresponds to a power ratio of 4:1.
The decibel was originally defined in terms of power. To get the same dB result whether you are measuring voltage or power, the factor of 20 compensates for the squaring relationship:
Using the power formula: dB = 10 × log10(4) = 10 × 0.602 = 6.02 dB
Using the voltage formula: dB = 20 × log10(2) = 20 × 0.301 = 6.02 dB ← same result
This is why:
- A 2:1 power ratio = +3 dB
- A 2:1 voltage ratio = +6 dB
Both represent the same physical increase, just measured differently. The dB system ensures both give the same number when the underlying energy change is the same.
Key Decibel Values to Memorise
The following table shows the most important dB values. The three you must know by heart are highlighted: ±3 dB ≈ ×/÷2 power, ±10 dB = ×/÷10 power, ±20 dB = ×/÷100 power.
| dB value | Power ratio | Voltage ratio | Practical meaning |
|---|---|---|---|
| +30 dB | 1000× | 31.6× | Typical small signal amplifier chain gain |
| +20 dB | 100× | 10× | Typical LNA gain; 10× power increase |
| +10 dB | 10× | 3.16× | 10× power increase; clearly audible |
| +6 dB | 4× | 2× | Doubling voltage; quadrupling power |
| +3 dB | ≈ 2× | ≈ 1.41× | Double power; just noticeable |
| 0 dB | 1× | 1× | No change; unity gain |
| −3 dB | ≈ 0.5× | ≈ 0.707× | Half power; −3 dB point of filters |
| −6 dB | 0.25× | 0.5× | Quarter power; half voltage |
| −10 dB | 0.1× | 0.316× | One tenth of power |
| −20 dB | 0.01× | 0.1× | One hundredth of power |
| −30 dB | 0.001× | 0.0316× | One thousandth of power |
Adding and Subtracting Decibels
The key practical advantage of decibels: when signals pass through cascaded stages, you add or subtract their dB values instead of multiplying or dividing their power ratios. This makes mental arithmetic in a signal chain much simpler.
A preamplifier with +15 dB gain, followed by 6 dB of coaxial cable loss, feeding a receiver with 10 dB of internal gain.
Total net gain = +15 − 6 + 10 = +19 dB
In raw ratios that would be: 31.6 × 0.25 × 10 = 79.1 — much harder to compute mentally and easy to get wrong.
A 100 W transmitter (50 dBm) drives an antenna through 3 dB of coax loss.
Power at the antenna = 50 − 3 = 47 dBm ≈ 50 W
(Every 3 dB halves the power: 100 W → 50 W. Confirmed.)
Decibels in Signal Chains
A typical receive signal chain in a ham station might look like this, with dB gains and losses tracked at each point:
- Antenna receives a −120 dBm signal
- Coax cable: −2 dB loss → signal is now −122 dBm at the shack end
- Low-noise preamplifier: +20 dB gain → signal is now −102 dBm
- Band-pass filter: −2 dB insertion loss → signal is now −104 dBm
- Receiver input sees: −104 dBm
Signal at receiver = −120 + 16 = −104 dBm ✓
A receive signal chain with gains and losses tracked in decibels. Adding the dB values gives the net system gain.
View LargerHam Radio Applications
Real dB values you will encounter regularly in ham radio:
| Application | Typical dB value | Meaning |
|---|---|---|
| RG-58 coax loss at 145 MHz | ~3.5 dB per 10 m | About half your power lost in 10 m of cable |
| 3-element Yagi gain | 7–8 dBd | Roughly 5× power in the forward direction vs a dipole |
| Typical HF receiver MDS | −127 to −140 dBm | Minimum signal the receiver can detect |
| 5 W QRP transmitter output | 37 dBm | 37 dB above 1 mW reference level |
| 100 W transmitter output | 50 dBm | 50 dB above 1 mW; 13 dB more than 5 W |
| 400 W transmitter output | 56 dBm | 6 dB more than 100 W; 4× the power |
| Typical linear amplifier gain | ~26 dB | Approximately 400× power gain |
| Good notch filter rejection | 40 dB at notch frequency | Reduces interference to 1/10,000 of original power |
Decibel Calculators
Power Ratio to dB
Enter two power levels (in any consistent unit — both must be in watts, or both in milliwatts, etc.). Calculates the dB difference.
dB to Power and Voltage Ratio
Enter a dB value. Calculates the corresponding power ratio (P2/P1) and voltage ratio (V2/V1).
Frequently Asked Questions
Why does the formula use ×10 for power but ×20 for voltage?
Because power is proportional to the square of voltage (P = V2/R). If voltage doubles, power quadruples. A 2× voltage ratio gives a 4× power ratio. The decibel was originally defined in terms of power (it is one tenth of a Bel, a unit named for Alexander Graham Bell, used to compare power levels in telephone systems). To get the same dB result from a voltage ratio as you would from the corresponding power ratio, you need to account for the squaring relationship — which means multiplying by 20 instead of 10. Both formulas give the same result for the same physical change: 6 dB is always 6 dB, whether you calculate it from a 4× power ratio (10 × log10(4) = 6.02 dB) or a 2× voltage ratio (20 × log10(2) = 6.02 dB).
Is a 3 dB difference audible or noticeable?
In audio, the human ear can just perceive a 1 dB change in level under careful listening conditions; 3 dB is clearly noticeable. However, 3 dB represents only a doubling of power — suggesting that the ear's perception of loudness scales roughly logarithmically (which is true: the decibel was originally developed partly to match the ear's response). In RF systems, 3 dB is significant: it doubles or halves the effective transmit power, and a 3 dB improvement in receiver sensitivity means you can copy a signal that is half the strength of what you could copy before. In practice, when comparing two antennas or two receivers, a 3 dB difference is a meaningful real-world improvement.
Can I use the dB formula for any ratio, not just electronics?
Yes. The decibel is a dimensionless ratio — it can describe any ratio of the same quantity. dB is used in acoustics (sound pressure level), optics (optical power loss in fiber), seismology (Richter scale, though that uses a slightly different convention), and audio engineering. In every case, the formula is the same: 10 × log10(ratio) for power-like quantities, 20 × log10(ratio) for amplitude-like quantities. The reference level (what you call 0 dB) varies by application. In electronics, when no reference is specified, dB is always a relative quantity — a ratio between two values with no absolute level implied.
Test Your Knowledge
Answer the questions below to check your understanding of this lesson. Every answer can be found in the lesson above.