# Decibels: Make them absolute levels

#### Article By : Bob Witte You can express decibels relative to many reference levels, such as one milliwatt or relative to a carrier signal.

In Decibels: Use with caution, I reviewed the concept of decibels as a ratio of two powers (and sometimes voltages). Decibels are also used to indicate absolute power and voltage levels by specifying a power or voltage reference. One of the most common reference power levels is 1 mW, indicated as dBm. As an example, one watt of power corresponds to 10 log (1/0.001) = 30 dBm. Five microwatts of power is 10 log (0.000005/0.001) = -23 dBm.

Another common power reference is 1 W, referred to as dBW. Remember to keep the ratio form of decibels separated from the absolute forms. For example, you could ask the question: What is the power at the output of an amplifier that has a gain of 12 dB with a −20 dBm signal applied to the input? In this case, the gain of the amplifier can be added to the input power to calculate the output power: −20 dBm + 12 dB = −8 dBm. Sometimes engineers will trip up by referring to the amplifier gain as 12 dBm, but that’s incorrect. The gain is a ratio of two powers, so it is expressed as 12 dB. Similarly, someone might say the output power is 8 dB, also incorrect terminology.

Absolute decibel voltages
The voltage form of the decibel equation can be used to indicate absolute voltage values by specifying a suitable reference. A common voltage reference is 1 volt, resulting in dBV. Another common reference is one microvolt. Decibels are commonly used to describe audio levels, which leads us to the topic of VU (volume unit) meters. I won’t cover that here but see Michael Dunn’s article [Ref 1] for more information on that application. Also see related articles below.

There are many other absolute decibels used in electronics. Table 1 lists some of the most common ones. See the Wikipedia entry on the decibel for a longer but still not complete list. Table 1. Common decibel references

Another category of decibels uses a reference but not one with a fixed value. For example, dBc indicates the power level relative to a carrier. The term “carrier” obviously has a communications flavor to it but dBc can be applied to any situation where a smaller signal is compared to a bigger one.

Figure 1 shows a spectrum analyzer measurement of a signal with two sidebands. The larger signal in the center is the carrier with amplitude −15 dBm and the sidebands are both at −52 dBm. So we would say that the sidebands are 37 dB below the carrier power, or −37 dBc.

Another example is shown in Figure 2. Here the amplitudes of the harmonics are measured relative to the fundamental signal. The level of the fundamental frequency is −15 dBm and the second harmonic is −55 dBm, or −40 dBc. The third harmonic has a lower amplitude of −62 dBm, or −47 dBc. Figure 2. Spectrum analyzer measurement of a signal and its harmonics shows harmonics below the amplitude of the fundamental (−15 dBm).

Decibels are also used to describe a signal level referenced to a system definition of full scale. It is common for electronic systems to have some maximum signal level, referred to as full scale, that can be handled while meeting all system specifications. The full-scale signal level may be limited by the maximum input range of a data convertor or the maximum voltage supported by an analog circuit.

Decibels relative to full scale is indicated as dBFS; they depend on the signal handling capabilities of a system. For example, if the maximum signal level supported by a system is 25 mW, this would be referred to as 0 dBFS. A 0.5 mW signal would be 10 log (0.5/25) = −17 dBFS.

The concepts of dBc and dBFS are similar but with an important difference. In common practice, dBc is referenced to the power in the carrier or fundamental, which may change depending on the specific operating conditions. On the other hand, dBFS references the level of a full-scale signal in the system, independent of actual signal level.

Watch out for how to interpret the full-scale signal level. Figure 3 shows a sine wave with peak value of 1 V, with the corresponding RMS value of 0.707 V. If RMS values are used to define the full-scale signal, the peak voltage will be ~40% higher than the RMS value. If our system can handle a maximum voltage of 1V, the full-scale signal level in dBV is 20 log (0.707) = −3 dBV.

dB\$
At one time, I suggested that some engineers balance their checkbooks using dB\$, decibels relative to one dollar. Of course, this is a bit ridiculous and, in fact, I’ve never been able to identify anyone that does this. The reason is clear: decibels are most useful when the numbers being manipulated have a high dynamic range. Most checkbooks don’t suffer from this problem. At least mine doesn’t.

But I haven’t given up on the dB\$, because I claim it has some utility. For example, we can use it to describe the average engineer’s salary of \$86,174 (source: Zip Recruiter, US average). In dB\$, this is 10 log (\$86174) = 49.3 dB\$. Now compare this to the gross domestic product (GDP) of the US, which is roughly \$21.06 trillion, or 133 dB\$. This means that the engineer salary is only about 83.7 dB down from GDP. I guess we could call that −83.7 dBgdp. See how dB\$ helps us with high dynamic range?

The next time you ask management for a raise, tell them you are only asking for a few dB.

Bob Witte is president of Signal Blue LLC, a technology consulting company.

References

1. Dunn, Michael, “Audio levels, dBu, dBV, and the gang: What you need to know,” EDN, April 2017
2. Fundamentals of Sampled Data Systems,” Analog Devices