What are decibels?

Introduction

The “bel” is a logarithmic unit named after Alexander Graham Bell – inventor, scientist and engineer. It is widely used in the electronics, audio and communication industries and is a method for expressing ratios logarithmically. The prefix, “deci” is added to subdivide the unit into tenths of a bel. When we do this, the units become “decibels” or “dB” for short.

This article will attempt to explain the meaning of decibels in a straight forward way based on the reasons below.

Decibels as a tool, not as a concept

Many websites give a conceptual or mathematical derivation of the decibel, which can be difficult to grasp for non-engineers. While interesting from a scientific viewpoint, engineers are only interested in the decibel as a tool. In other words, it isn’t essential that you understand logarithms in order to use the unit.

Decibels used outside of radio

In principle, the decibel can be applied to any varying physical quantity, for example in audio and acoustic engineering. In the audio industry, the voltage decibel is mainly used since the signals are mostly analysed in terms of voltage.

So why do we say “voltage decibel”?

Both voltage and power are valid. But due to the relationship between voltage and power, the decibels between the two do not turn out to be equal. Reading further, you can see this through the derivation of the formula.

For radio equipment, we describe the signal in terms of power more often than voltage, so the power decibel is what this article will focus on.

How radio module data sheets apply decibels instead of normal units e.g. mW.

For main parameters such as output transmission power, using watts or milliwatts is sufficient. However for quantities relating to radio performance and comparative measurements, decibels tend to be used. Here we will look at some examples.

Proportionality

A linear scale treats every interval of increase with the same respect. For example going from 1 to 2 and then 100 to 101, the increase is one in both cases. However in terms of growth, the first is an increase of 100 percent and the other is only 1 percent which makes very little difference. For data values that go from small values to large values – proportionality, rather than the difference is more important. For example humans can hear sound pressure waves ranging from 20 micro pascals, going up to thousands of micro pascals. The human perceives louder sounds in proportional (not incremental) increases in sound pressure.

Example values

Let us write some values which rapidly grow. Since this article is in the domain of radio, let’s assume these are power levels in mW.

0.007, 0.014, 0.07, 0.3, 0.5, 2, 2.4, 5, 10, 15, 200, 10000, 15000, 70000,

Plotting the values on a linear scale, the larger values are visible but we can see the lower value points are compressed into a small space. This hides any detail we wish to see.

 

With the log scale, the points are more spread out. However while the log scale is correct, not many are familiar with log scales which still makes it less than ideal.

Introducing decibels

Some points about the decibel scale:

• It expresses the ratio between two values.
• It provides a far easier to read scale with simpler numbers.
• Decibels can be added and subtracted.

Formula

$$ (dB) = 10 \times \log\frac{P_{2}}{P_{1}}$$

Where P2 and P1 are power levels.

For example if P2 / P1 is 2, in other words P2 is twice that of P1, then our result would be 3.01 dB (or just 3 dB). You can think of dB as the amount of spread between P2 and P1.

Rules of thumb

While the formula gives the exact dB result, it is not always necessary to use the formula as there are shorthand values to go by.

If your value P2 is the same as P1, then this difference is 0 dB
If your value P2 is twice that of P1, then this difference is 3 dB
If your value P2 is ten times that of P1, then this difference is 10 dB

For ratios less than 1, the dBs become negative:

If your value P2 is half that of P1, then this difference is -3 dB
If your value P2 is one tenth that of P1, then this difference is -10 dB

(Note these rules apply only to power. You can read further to see how it differs when it comes to voltage)

Advantages of the decibel in radio

Let’s go back to our previous set of values and convert them into decibels.

0.007, 0.014, 0.07, 0.3, 0.5, 2, 2.4, 5, 10, 15, 200, 10000, 15000, 70000,

Because it’s a ratio, we’ll use the lowest value as fixed point of reference for the rest and then plot them. Our lowest value is 0.007, so its ratio will be equal to one (because we are dividing by itself) or 0 dB. The highest value, 70000 is 10 million times 0.007 or 70 dB.

This gives 70 dB of span between the lowest to the highest value. Notice how we have condensed a large range into a nice readable scale spanning from 0 to 70 dB. One of the values, 0.014 which is twice 0.007 gives our 3 dB point between 0 and 10 dB. Likewise the value 0.07, its point lies at 10 dB.

Addition and subtraction of decibels

This is much more intuitive than multiplying and dividing. For example jumping from 0.007 to anywhere on the scale such as 0.07 can be done by adding 10 dB. Adding another 60 dB takes it to 70000. Subtracting 10 dB three times (-30 dB) brings it down to 70.

Why are decibels different for voltage?

The decibel unit is used to express a ratio of power levels. However, decibels can be used for voltages in the same way by adjusting the equation:

$$ \text{(dB)} =10\log\left(\frac{P_2}{P_1}\right) = 10\log\left( \frac{V_2^2/R}{V_1^2/R}\right) =10\log\left(  \frac{V_2}{V_1}\right)^2$$

$$ \text{(dB)} =20\log\left(  \frac{V_2}{V_1}\right)\ $$

The voltage decibel gives twice the value of the equivalent power decibel, so the values used in the rules of thumb would be the same, but doubled. For example:

If your value V2 is the same as V1, then this difference is 0 dB
If your value V2 is twice that of V1, then this difference is 6 dB
If your value V2 is ten times that of V1, then this difference is 20 dB

Using the correct reference

Unknown reference

When the unit “dB” is written, it only shows the ratio. This is useful for devices with input and output ports. For example an amplifier produces 10 dB gain and adding one more produces another 10 dB creating a total gain of 20 dB.

To an explicit reference

While “dB” is fine when describing relative changes in a system, all physical quantities in the real world are going to be in absolute values such as watts or volts. The problem is decibels only work on decibels and not absolute values. What we want is to express absolute values in decibel form by explicitly stating the working reference to be used. We do this by appending “dB” with the reference.

• dBW : The power relative to one watt.
• dBm: The power relative to one millwatt.
• dBV: The voltage relative to one volt.
• dBmV: The voltage relative to one millivolt.
• etc.

For example, 10 dBm means 10 dB over 1 mW. This means 0 dBm (1mW) + 10 dB = 10 dBm which is 10 mW.

Calculation tool

In order to help understand this, Circuit Design’s calculation tool allows you to convert between volts/watts and various decibel units.

Example situations where decibels are used.

Signal to Noise ratio

The signal to noise ratio is a way of expressing the amount of wanted signal to the unwanted signal (the noise) during reception. The wanted signal can be very small that it barely pushes through the noise or in the case of a strong transmitter, be many times higher than the noise. Since the decibel scale can cover a wide range, we can visualise both weak and strong signals.

You can read more about signal to noise ratios in this article “Signal to Noise ratio”

Sensitivity

The minimum level presented to the receiver in order that signal can be demodulated is the receiver sensitivity. It is one of the parameters that define the reception performance. The level is very small, usually many times smaller than a milliwatt. For example a signal originating from a transmitter with an output of a few mW, by the time it reaches the receiver, it can be at a level of -100 dBm which is 1 / 10 billionth of a milliwatt. Try expressing that as a decimal number!

In amateur radio for example, you will see sensitivity being expressed as decibel volts, because it is the equivalent voltage at the antenna input that is being expressed, not power.

You can read more about reception performance and sensitivity in the article, “Understanding receiver specifications”

12 dB SINAD

One way of measuring sensitivity of radio receivers is the 12 dB SINAD rule. It compares wanted output signal to the noise and distortion levels. The RF signal level to the antenna input is adjusted until the separation between the output signal and noise/distortion approaches 12 dB. This ratio means 25% of the total output signal is noise and distortion.

See What is 12 dB SINAD? article for more details.

Adjacent channel selectivity

Adjacent channel selectivity is the ability of a receiver to reject an unwanted signal in the adjacent channel. Specifically, it is the measure of the largest signal possible in the adjacent channel while still being able to receive the signal in the wanted channel. For example, where both signals are in dBm, this difference can be expressed in decibels by simple subtraction.

You can read more about reception performance and selectivity in the article, “Understanding receiver specifications”

Blocking

Blocking refers to the receiver’s ability to reject signals that exist in nearby bands. Similar to selectivity, the difference can also be expressed in decibels or if both signals are in dBm, this difference can be expressed in decibels by simple subtraction.

You can read more about reception performance and blocking in the article, “Understanding receiver specifications”

Antenna gain and propagation

Antenna gain is also specified in decibels relative to either an isotropic (dBi) or dipole (dBd). If propagation and other losses are also written in decibels it means we can combine them to see the loss across the entire communication link.

See Link budget, propagation and antenna gain articles for more details.

Noise figure

Every device in the radio chain introduces noise to the incoming signal. This is shown by a slight reduction in signal to noise ratio at the device output. If signal to noise ratios are in decibels, the noise figure can be expressed by subtracting the two signal to noise ratios.

$$\text{Noise Figure (dB) }= SNR_i(dB) – SNR_o(dB) $$

See noise figure article for more details.

Conclusion

The problem with explaining decibels is trying to say that it is the same as a logarithmic scale. This may confuse the issue since a logarithmic scale is just a quantity that go up and down logarithmically. An example is distance in kilometres (e.g. 1, 10, 100 km).

Decibels also do the same – but its the ratios, not the absolute values that go up and down logarithmically. Since a ratio compares two values, a point of reference needs to be established in order to work with decibels.