# How big is a decibel?

Say I've calculated that my feedline losses are 3dB, or I'm considering an antenna with 10dB gain, or trying to decide between a transmitter with 10dBm output power versus 16dBm (6dB difference).

I understand a decibel is a degree of change in signal quality, similar to a degree of temperature. But how much change? For example, if I increase my antenna gain by 3dB, how much better will that make my signal?

Here are some visual examples, corresponding to what you'd see receiving an analog TV transmission. I've picked an image with features of varying detail. Look for:

• the letters "IPI"
• individual jelly beans
• contrast between the beans, especially the darker ones that are very close in brightness
• reflections on the beans

Here are sets of three images side-by-side, each adjacent image some number of decibels apart in signal to noise ratio. Our eyes are good at picking out fine detail in noise, about as good as a well-designed digital mode. So this should give you an intuitive sense of the difference a decibel makes for digital modes, and also slow-scan TV.

Audio samples are past the images, if SSB is more your concern.

1dB:

1dB:

3dB:

3dB:

10dB:

10dB:

Ears don't work like eyes, so I've also generated some audio samples such as you'd hear for SSB. Again they are normalized to a constant volume like AGC would do. The numbers refer to the noise power, so -48 dB is the highest quality (lowest noise power), and -06 dB is the worst quality (highest noise power)

• It should be noted when using these images as an analog for SNR that our eyes are able to resolve FAR more subtle changes than our ears can. A reduction in volume or an decrease in SNR of 3dB is barely perceptible to the human ear (and only then if your hearing is quite good and conditions are ideal). However, a halving of contrast or effective luminosity is immediately perceptible to the eye as a significant change. Slow Scan TV is a good way of equating the two concepts. What sounds like "Arm chair copy" frequently still results in perceptible visual noise. – Hamsterdave Sep 16 '16 at 22:10
• @Hamsterdave I've added some audio samples. – Phil Frost - W8II Sep 17 '16 at 13:53
• Phil, your answers are always wonderful. – HH- Apologize to Carole Baskin Sep 22 '16 at 23:36

If your transceiver has an S-meter, one "S" has 6dB.

Is decibel small? In my sense, yes, dB is quite small: it is difficult to hear a change of 1-5dB in voice quality.

A 5-10dB change is significant, 15dB or 18dB totally changes conditions.

Few devices in the amateur market can measure a 1dB difference.

But precise "bookkeeping" of the antenna system is important: the sum contains many small numbers: +7dB antenna gain, -0.5dB lost in UC-1 connector (other name for PL-259) , 20 meters of feedline with -35dB per 100m gives a 7dB loss, another UC-1 connector: In total, this system has an effective -1dB.

Connector power loss like UC-1 (PL-259) are not measurable at home, so take it from literature (most sources give 0.5dB). Loss in longer cable can be measured in a good quality amateur testing set, or more simply read it from the manufacturer's data sheet.

In reality small changes can add up: increase antenna gain 1.5dB, install a better feedline for 0.3dB/1m, better connectors etc .... and you've made a 6dB improvement. This is a good result.

FM has a different behavior from SSB: quality is 'good' in a broad central part of scale (hard to distinguish for an untrained ear), a small drop in quality (voice+noise) near the low range, and drastic loss of quality when signal drops more and suddenly voice is totally unreadable under noise.

A decibel is a mathematical measurement of the change in the magnitude of a quantity. It uses a logarithmic scale so that a change of 10 db is an increase of 10 times, while a change of 20 db is an increase of 100 times.

The formula for computing the change in decibels between the original power $P_0$ and the new power $P$ is

$$10 \log\left(\dfrac{P}{P_0}\right)$$

where the logarithm uses base 10. There are some useful relations with decibels that are easy to remember

3 dB = 2x
6 dB = 4x
7 dB = 5x
10 dB = 10x


and because it is a logarithmic scale, you can use these together so 13 dB = 10 dB + 3 dB = 10x * 2x = 20x.

Because decibels measure change relative to some baseline value, to use them to specify absolute values, like a power of 1W, we sometimes use the unit dBm which means "decibels relative to 1 milliwatt". So $1\ W = 1000\ mW = 30\ dBm$ because 30 dB = 10 dB + 10 dB + 10 dB = 10 x 10 x 10 = 1000x.

A transmitter with 10 dBm power output puts out 10 dB more than one millwatt, or $10\ mW$. A transmitter with 6 dB more power or 16 dBm puts out 4x as much power or $40\ mW$.

• Also note that a 1 dB change in power is about 20%. This is usually not important - at least in HF communications. A change of 1 dB in an audio signal is hard to discern by ear. We use dB because your ear (and your other senses) operate more-or-less logarithmically. – Martin Ewing AA6E Sep 22 '16 at 0:40