# Understanding the decibel

**Agilent Technologies Australia Pty Ltd**

Thursday, 07 June, 2012

In the RF microwave test and measurement world, engineers often deal with the power measurement unit of dBm instead of wattage. However, engineers entering the audio measurement arena will need to understand one more measurement unit known as dBu, which is decibel relative to 1 mW into 600 Ω.

The decibel is a very commonly used yet often misunderstood unit of measurement. The “bel” in “decibel” comes from the name of Alexander Graham Bell. He was interested in the way in which the human ear responds to sound intensity. He used a logarithmic scale to express this sound intensity, in which range from the softest sound to the loudest (threshold of pain) sound is one to a billion (1012) or zero to 12 bels. The decibel is one-tenth of a bel and is abbreviated as dB.

There are two primary benefits to using dB. The first is to express very large or very small ratios in a compact way; for example, +63 dB to -153 dB is more concise than 2 x 10^{6} to 0.5 x 10^{-15}. Another advantage is apparent when comparing quantities used to multiply the gain or divide the loss of several cascaded devices. dB simplifies the mathematic process, in that multiplication of numeric gain is replaced by addition and division of numeric attenuation is replaced by subtraction.

To describe dB as an absolute value, a reference point must be known. There are a number of different reference points, as defined below:

- dBm represents the power level P1 with reference to 1 mW
- dBW represents the power level P1 with reference to 1 W
- dBV represents the power level V1 with reference to 1 Vrms
- dBmV represents the power level V1 with reference to 1 mVrms
- dBuV represents the power level V1 with reference to 1 uVrms

dBm is the most commonly used unit in power measurement. For instance, if an engineer is working in a known industry standard environment, the impedance of the test system is usually 50 Ω in RF engineering, 75 Ω in television engineering and 600 Ω in audio engineering. A conversion formula will help engineers to convert power measurement of dBm to any unit of dBV, dBmV or dBuV.

For 50 Ω system:

- dBV = dBm - 13 dB
- dBmV = dBm + 47 dB
- dBuV = dBm + 107 dB

For 75 Ω system

- dBV = dBm - 11.25 dB
- dBmV = dBm + 48.75 dB
- dBuV = dBm + 108.75 dB

For 600 Ω system

- dBV = dBm - 2.22 dB
- dBmV = dBm + 57.78 dB
- dBuV = dBm + 117.78 dB

dBu (dB relative to 1 mW into 600 Ω)

For most traditional test equipment, the source impedance uses only 50 Ω, but for audio test applications the 600 Ω source impedance is more commonly used. In audio test applications, the engineer has to consider another decibel formula in the unit of voltage measurement: dBu. dBu is defined as dB relative to 1 mW into 600 Ω. It is a logarithmic unit expressing the relative voltage measurement with reference to a voltage value of 0.7746 Vrms (voltage drops across 600 Ω that results in 1 mW of power).

The “u” in dBu comes from the word “unloaded”. It also implies that the load is unterminated or the load impedance is unspecified and is likely to be high. Thus, the 0.7746 Vrms is an open circuit source.

As mentioned earlier, 50 Ω is the most commonly used source impedance. 50 Ω source impedance can result in higher short-circuit current (for a constant voltage) and 10 times the frequency response over a given length of cable than with 600 Ω source impedance. The U8903A has the maximum voltage source for unbalanced output (Vs) of 8 V, and the following figures illustrate the maximum power transfer the U8903A can deliver into various load-impedance scenarios using the source impedance of 50 Ω or 600 Ω.

Nowadays, due to the advancement of DSP-based RF test equipments, some RF engineers are able to perform audio measurements on RF instruments and then correlate the test results with other audio instruments. Sometimes engineers encounter problems with their RF signal analyser when measuring two different sources of supply that are identical in stimulus set-up: for example, output frequency (FL) and output voltage (VL). The RF signal analyser receives very divergent measurement results that show both inputs are unequal in amplitude or bandwidth.

If an engineer sets the voltage output of an audio generator that comes with a fixed source impedance of 50 Ω, VS = 2 V (8.24 dBu), then its voltage will drop across at 50 Ω load impedance, VL = 1 V (see Figure 1).

If the engineer sets up another output of an audio generator with source impedance of 600 Ω, then in order to get the output performance similar to the previous 50 Ω system, the engineer needs to set a higher output voltage of VS’ = 13 V (24.5 dBu). Therefore, it will also deliver VL’ = 1 V to the same 50 Ω load impedance (see Figure 2).

dBu (in 50 Ω) to dBu (in 600 Ω) conversion is a technique for verifying and confirming that the source impedance of the audio analyser is the reason for the divergent measurement results in the RF signal analyser.

As a rule of thumb, dBu (in 600 Ω) = dBu (in 50 Ω) + 16.26 dB.

The U8903A comes with a switchable source impedance of 50 Ω or 600 Ω. Once the engineer has verified and confirmed the root cause, he or she just needs to modify the setting of the output source impedance in order to get the appropriate output voltage reading.

In summary, it is important for every engineer to review these concepts, understand and familiarise the measurement from time to time.

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