Decibels in electronics: dB, dBm, dBV - a guide to units

"Volume level +3 dB", "antenna gain 9dBi", "receiver sensitivity -110dBm" - decibels are a key unit for engineers and technicians. For many, however, they remain a mysterious concept because they require a different way of thinking than the usual linear units used every day. In this article, we will explore the fascinating world of the decibel - a unit that has revolutionised the design of electronic systems, presenting both its mathematical basis and its practical applications in modern technology.

• The basics of the logarithmic scale
• Decibel
• Variants of the decibel
• Practical applications
• Measurements in decibels

Basics of the logarithmic scale

The story of the decibel begins with a simple but fundamental discovery - the human senses do not respond linearly to stimuli, but logarithmically. When we light a second candle in a dark room, we notice a significant difference in brightness. However, adding one candle to the fifty already lit brings a barely perceptible change. Our hearing works in a similar way - the difference between a whisper and a normal conversation is as significant to us as between a normal conversation and a loud concert, although in terms of physical sound power these differences are incomparable.

In order to understand decibels, one must first get used to the concept of a logarithmic scale. In everyday life, we are used to linear scales: driving 2km is twice the distance of 1km, and 2 kilograms is twice the mass of 1 kilogram. In logarithmic scales, however, equal distances on the scale represent equal ratios of values, not equal differences.

The logarithm is a mathematical operation that answers the question "to what power should a fixed base be raised to get a given number?". For the decimal logarithm (with base 10), log₁₀(100) = 2, because 10² = 100. Similarly, log₁₀(1000) = 3, because 10³ = 1000.

Why have electronic engineers come to love the logarithmic scale so much? There are several important reasons for this.

Firstly, the dynamic range. In electronics, we often work with quantities that vary by many orders of magnitude. In a single circuit, we may be dealing with signals from microvolts to kilovolts or from picowatts to kilowatts. The logarithmic scale allows us to represent these extremely different values on a single graph, maintaining readability in all ranges.

Secondly, human perception. Our senses, especially hearing, operate approximately logarithmically. If the sound power increases by a factor of ten, we do not perceive the sound as ten times louder, but as approximately twice as loud. This property is particularly important in audio electronics, where we are concerned with correlating technical parameters with human experience.

Thirdly, simplification of calculations. On the logarithmic scale, multiplication turns into addition and division into subtraction. When we design complex electronic systems consisting of many components, each with a specific gain or attenuation, we can simply add decibels instead of multiplying coefficients - a huge convenience in engineering practice.

Imagine a signal passing through a circuit consisting of an amplifier (gain 100 times), a filter (attenuation 2 times) and an attenuator (attenuation 10 times). In linear units we would have to perform the operation: 100 ÷ 2 ÷ 10 = 5. In decibels it is a simple addition: ÷ 20 dB ÷ 3 dB ÷ 10 dB = ÷ 7 dB. This property is invaluable when analysing complex electronic systems.

Decibel (dB) - basic unit

Alexander Graham Bell probably never imagined that his name would forever be associated with one of the most important units in electronics. Originally, the unit was the bel (B), but it soon became apparent that this was too large for practical applications in telecommunications, so the decibel (dB) was introduced as a tenth of the unit.

Mathematically, the decibel is defined as the unit expressing the ratio of two values, according to the formulae:

• for power: dB = 10 × log₁₀(P₂/P₁);
• for voltage or current: dB = 20 × log₁₀(V₂/V₁) or dB = 20 × log₁₀(I₂/I₁).

Why is the multiplier 10 for power but 20 for voltage and current? This is due to the relationship P = V² / R (power = voltage squared divided by resistance). Since power is proportional to the square of the voltage, and the logarithm of the square is the logarithm doubled, hence the factor of 20 instead of 10. Importantly, this relationship is only accurate if the impedances are the same for the two voltages being compared.

In this case, the voltage gain in dB is exactly twice the corresponding power gain.

The decibel value is therefore a measure of the ratio between the two quantities. When the decibel is positive, we speak of signal amplification; when it is negative, we speak of attenuation. Zero decibels means that the ratio is exactly 1, i.e. the two quantities are equal.

In engineering practice, it is useful to remember a few key values:

• +3dB corresponds to approximately double the signal power;
• +10dB is a tenfold increase in power;
• +20dB is a hundredfold increase in power;
• -3dB is a halving of power;
• -10dB is a tenfold reduction in power.

These values are the foundation of the practical use of decibels. They allow us to quickly estimate how a signal will change after passing through a circuit element, without the need for complex calculations.

Let's take a practical example: we are designing a radio system where the signal passes through a transmitting antenna (gain +5dB), a free space (attenuation -80dB), a receiving antenna (gain +8dB) and an amplifier (gain +25dB). The total change in signal level is simply the sum of: +5 -80 + 8 + 25 = -42dB. So we can see that, despite the use of an amplifier and efficient Antennas, the signal is still significantly attenuated (about 16,000 times) compared to the input signal, mainly due to the high attenuation in the free space.

Decibel variants - an overview of the most important units

While the decibel (dB) itself is a relative unit, expressing the ratio of two values, in practice we often need absolute units, referring to standard reference levels. This is how a family of 'derivatives' of the decibel was created, such as dBm, dBV or dBW.

dBm - decibels relative to milliwatt

dBm is one of the most common units in radio electronics and telecommunications. The letter 'm' indicates that the reference level is 1 milliwatt (0.001W). In other words, 0dBm corresponds exactly to a power of 1mW.

The defining formula is: dBm = 10 × log₁₀(P/1mW), where P is the power expressed in milliwatts.

Imagine a typical radio transmission chain. A Wi transmitter can generate a signal with a power +20dBm (100mW). After passing through the walls of a building, the signal can be attenuated to -60dBm (exactly 10^{(-60/10) = 10}-6mW, or 1 nanowatt). Despite the huge difference in numerical values (100mW versus 0.000001mW), in decibels the difference is only 80dB, which is a convenient range to represent on a single graph.

In telecommunications practice, there are several characteristic levels expressed in dBm:

• +43dBm (20W) is the typical transmitter power of a GSM base station;
• +30dBm (1W) is the maximum transmitter power of a mobile phone;
• +20dBm (100mW) is the typical power of a Wi-fi transmitter;
• -70dBm is a good Wi-Fi signal level indoors;
• -90dBm is a weak but still usable cellular signal;
• -110dBm is the typical sensitivity of modern GPS receivers.

dBm is indispensable in RF systems where precise determination of the absolute signal strength level is crucial to the proper functioning of equipment.

dBV - decibels relative to volts

dBV is a unit mainly used in audio and measurement electronics where we measure signal voltage. The reference level here is 1 volt (V). This means that 0dBV corresponds to a voltage of 1V RMS (rms).

Formula: dBV = 20 × log₁₀(V/1V), where V is the voltage expressed in volts.

In a recording studio, we may encounter levels such as:

• +6dBV (2V RMS) is the typical maximum signal level in professional equipment;
• 0dBV (1V RMS) is the standard reference level;
• -10dBV (0.316V RMS) is a common consumer signal level;
• -20dBV (0.1V RMS) is a typical signal level from condenser microphones.

Interestingly, in professional audio we also encounter the unit dBu, where the reference level is 0.775V. This unusual value is due to the historical power standard of 1mW at an impedance of 600Ω, which was commonly used in telephony.

dBW - decibels relative to the watt

dBW is decibels relative to a power level of 1 watt. It is a unit used mainly in high-power systems such as radio or radar transmitters.

Formula: dBW = 10 × log₁₀(P/1W), where P is power expressed in watts.

The conversion between dBW and dBm is straightforward: dBW = dBm = 30, since 1W = 1000 mW and 10 × log₁₀(1000) = 30.

Example values:

• +60dBW (1MW) is the power of a large radio transmitter;
• +30dBW (1kW) is the typical power of an FM transmitter;
• 0dBW (1W) is the reference point;
• -30dBW (1mW) is the equivalent of 0 dBm.

dBi, dBd - units of antenna gain

In antenna technology we come across specific units: dBi and dBd. The first refers to the gain of an antenna compared to a hypothetical isotropic antenna (radiating uniformly in all directions). The second compares the antenna to a half-wave dipole, which is a practical reference standard.

There is a constant relationship between these units: dBi = dBd + 2.15, since a half-wave dipole has a gain of 2.15dB relative to an isotropic antenna.

In practice Wi-Fi antennas typically have gains ranging from 2dBi (embedded antennas) to 24dBi (directional antennas). Satellite Antennas can achieve gains in excess of 30dBi, allowing reception of weak signals from satellites thousands of kilometres away.

Practical applications of decibels

Decibels are not just a theoretical construct - they are a practical tool in the day-to-day work of an electronics, telecommunications or acoustic engineer. Let's take a look at how they are used in different areas of electronics.

Signal amplifiers

In amplifiers, from simple audio circuits to sophisticated microwave systems, decibels are the natural language for expressing gain. An amplifier with a gain factor of 20dB increases the power of a signal by a factor of 100 - such information is much more useful than saying that 'an amplifier increases the amplitude of a signal by 10 times'.

Operational amplifiers are an interesting example, where the typical open-loop gain is around 100dB (10¹⁰ times!). By using negative feedback, we can precisely control the actual gain of the circuit in the range of a few decibels to a few tens of decibels.

Power amplifiers in radio transmitters are characterised by what is known as the 1dB compression point (P1dB) - this is the output power level at which the actual gain drops by 1dB relative to the linear gain. It is worth noting that non-linearities in the amplifier start to appear earlier, and 1dB is the conventional point at which non-linearity becomes relevant from a practical point of view.

Attenuators

Attenuators, elements that intentionally attenuate the signal, are also characterised in decibels. An attenuator of -20dB reduces the signal power by a hundred times. Attenuators are indispensable in measurements, where we often need to attenuate the signal so as not to overdrive the meter input, and in antenna systems where we need to control the signal level precisely.

Optical attenuators used in optical fibres are an interesting example. An attenuation of -3dB means reducing the optical power by half. This is used in signal splitters, where one input signal is split into two identical output signals.

Filters

The frequency response of filters is one of the best examples of the usefulness of the logarithmic scale. In graphs of filter attenuation as a function of frequency, the Y-axis is almost always scaled in decibels and the X-axis is often on a logarithmic scale.

The standard low-pass filter has a cut-off point defined at a slope of -3dB, corresponding to a halving of power. The steepness of the filter slope is defined in dB/octave or dB/decade. A first-order filter has a steepness of 6dB/octave (20dB/decade) for signal amplitude, which corresponds to 3dB/octave for power. This means that the amplitude attenuation increases by 6dB for every doubling of frequency above the cut-off point.

These relationships would be extremely complicated to express in linear units, but decibels make them intuitive and practical.

Telecommunications

In telecommunications systems, decibels are ubiquitous. The signal-to-noise ratio (SNR), expressed in dB, is a key parameter for determining the quality of transmission. SNR = 20dB means that the signal power is 100 times greater than the noise power. The SNR required depends on the type of modulation and system - for simple analogue systems 10-15dB may be sufficient, while advanced digital modulations may require 25-30dB or more.

The noise figure (NF), also expressed in dB, determines the SNR degradation introduced by the device. A high quality low noise amplifier (LNA) in a GPS receiver may have an NF of less than 1dB, indicating minimal signal degradation.

The link budget, a comprehensive analysis of amplification and loss in a telecommunications system, is usually calculated in decibels, allowing easy addition and subtraction of individual components.

Measurements in decibels - basic information

Measurements in decibels require specialised equipment adapted to the type of signal and frequency range. Below are the most important instruments used in electronics and telecommunications.

Spectrum analyzer is a key tool in RF measurement that allows you to see the power level of a signal as a function of frequency. The results are typically presented in dBm. The dynamic range of modern analysers can exceed 160dB, which corresponds to a ratio of 10^16 (ten billion) times between the strongest and weakest measurable signal!

An RF Power Meter measures the total signal power in a specific frequency band. It is a simpler device than a Spectrum Analyzer, but often more precise for single measurements.

A vector network analyser (VNA) is a sophisticated device that measures the S (spread) parameters of electronic circuits. These parameters are expressed in dB and determine how the signal is transmitted and reflected by the circuit under test. The VNA is essential in the design of impedance matches, filters and amplifiers at high frequencies.

When interpreting measurements in decibels, it is crucial to be aware of the unit (dB, dBm, dBV) and the reference impedance of the measurement system. In RF technology the standard is 50Ω, in cable TV 75Ω, and in audio we encounter impedances ranging from 4Ω, 8Ω or 16Ω (speakers) to 600Ω (professional audio systems).

Decibels, despite their initial complexity, are an extremely elegant and practical tool in electronics. They allow huge ranges of values to be expressed intuitively, reflect the way the human senses perceive the world, and greatly simplify calculations in complex systems.

Familiarity with decibels - from the basic definition, through the different variants (dBm, dBV, dBW), to practical applications and measurement methods - is a fundamental skill for every electronics and telecommunications engineer. This logarithmic unit, although it may seem alien at first, over time becomes the natural language for describing and analysing electronic circuits.

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