This article reviews the decibel units used in EMC laboratory measurements and testing. We begin by defining a decibel (dB) unit and proceed to the EMC specific units for voltage, current, power, and impedance measurements. The relationships between the units are derived when appropriate. The applicability of the dB units discussed in this paper is shown in specific EMC measurements or specifications.

Logarithm and Decibel Definition

In mathematics, base 10 logarithm of a positive number *A* is defined as log_{10}*A*. The resulting number is negative, zero, or positive according to

(1)

The only requirement in mathematics for this operation to be defined is that the number *A* is a positive number. There is no other implicit assumption about this number.

In engineering, especially in EMC, we use a unit of decibel (dB) which is related to the base 10 logarithm and defined as

(2a)

when *A* represents power ratios, or

(2b)

when *A *represents voltage and/or current ratios. In the following section we will discuss the difference between these two definitions.

Note the very important aspect of a number *A* when expressed in *dB*: it is always a *ratio of two quantities*, not just a positive number.

What if this ratio is negative? In this case we treat the negative quantity as a complex quantity with a positive magnitude and a phase of 180°,

(3)

and simply consider the magnitude only.

Power and Voltage (Current) Gain in dB

Consider the circuit shown in Figure 1 [1]. A sinusoidal source consisting of an open-circuit rms voltage *V _{S}* and source resistance

*RS*delivers a signal to an amplifier whose load is represented by

*RL*.

The input power to the amplifier is

(4a)

while power delivered to the load is

(4b)

The power gain in dB, *PGdB*, is defined as

(5a)

Using Equations 4a and 4b this gain can also be expressed as

*
* (5b)

The voltage and current gains in dB, *VGdB*, and *IGdB*, respectively, are defined as

(6a)

(6b)

Note that *if the input resistance to the amplifier equals the load resistance*, *RL = RIN* (which is often the case in practice) then the power gain in dB is the same as the voltage (or current) gain in dB.

(7)

**EMC Units and Measurements**

In EMC dB units we don’t simply express the ratios of two powers, voltages, etc., we express the ratio of a given nominal value to a base quantity, as shown in Table 1.

Often the electric and magnetic field intensities, as well as the impedance, are also expressed with respect to a base quantity, as shown in Table 2.

EMC Measurements Using dB Units

The FCC Class *B* radiated emissions limits are specified in dBµV/m and are shown in Figure 2 [2].

Figure 3 shows an example of the radiated emission measurement.

FCC and CISPR 22 Class B conducted emission limits are specified in dBµV and are shown in Figure 4.

Figures 5 shows the conducted emissions measurements on the neutral line in the regulatory frequency range.

As an example of dB µA units we present the CISPR 25 limits for conducted emissions – current probe method. This is shown in Figure 6.

Note that for Class 5 devices the limit in the FM band (and other places in the table) is negative. How can a magnitude limit be negative? At first, this does not seem right until we look at the units of measurements: dBµA. The negative limit simply means that the measured value (which is positive) must be smaller than 1µA.

Figure 7 shows the CISPR 25 Conducted emissions measurement in dBµA.

One of the most common measurement units expressed in decibels is dBm. Many spectrum analyzers display voltage amplitudes both in dBµV and in dBm, even though dBm is a unit of power. The two units are related by the impedance of the measuring equipment, namely 50 Ω.

To convert from dBm to dBµV we add 107 dB, while to convert from dBµV to dBm we subtract 107 dB:

(8)

To illustrate this relationship we used the measurement setup shown in Figure 8.

In this measurement setup we simply connected a comb generator through an attenuator to a signal analyzer and change the units from dBµV to dBm. Figure 9 shows the measurement result in dBµV while Figure 10 shows the same measurement in dBm.

Note that the measurement in dBµV is approximately 107 dB higher than the measurement in dBm, as predicted by Equation 8.

References

- Clayton R. Paul,
*Introduction to Electromagnetic Compatibility,*Wiley, 2006. - Bogdan Adamczyk,
*Foundations of Electromagnetic Compatibility with Practical Applications*, Wiley, 2017.

**Dr. Bogdan Adamczyk** is professor and director of the EMC Center at Grand Valley State University (http://www.gvsu.edu/emccenter/) where he develops EMC educational material and teaches EMC certificate courses for industry. He is an iNARTE certified EMC Master Design Engineer. Prof. Adamczyk is the author of the textbook “Foundations of Electromagnetic Compatibility with Practical Applications” (Wiley, 2017). He can be reached at adamczyb@gvsu.edu.

**Jim Teune** is a founding partner of E3 Compliance LLC which specializes in product development and EMC precompliance testing. He is an iNARTE certified EMC Engineer and Master EMC Design Engineer. Jim is an industrial partner of the EMC Center at GVSU. He can be reached at jim@e3compliance.com.

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