If you want to communicate effectively with EMC engineers, it’simportant to get comfortable with decibels (dB). Decibel notation is aconvenient way of expressing ratios of quantities that may or may not span manyorders of magnitude. It is also used to express the amplitude of various signalparameters such as voltage or current relative to a given reference level.
A power ratio, P2:P1, in dB is simply calculated as,
For example, if weare comparing a 10-watt received power to a 5-watt specification, we could saythat the received power exceeded the specification by,
If the impedance associated with two power levels is constant, then thepower is proportional to the voltage (or current) squared. In this case, we canalso express voltage (or current) ratios in dB,
or,
Antenna or amplifiergains are usually reported in dB. So are cable or filter losses. An amplifierthat receives a 1-watt signal and produces a 100-watt signal has a gain of,
A cable whose input signal has an amplitude of 3.0 volts and whoseoutput signal has an amplitude of 2.8 volts exhibits a gain of,
or a loss of,
Note that the inverse of any ratio is expressed by changing its sign indB. A ratio of 1 is 0 dB. Phase or negative values cannot be expressed in dB.
Quiz Question
A signal traveling one kilometer in a coaxial cable loses one-half itsvoltage. Express the,
A. input-to-output voltage ratio
B. input-to-output power ratio
C. input-to-output voltage ratio in dB
D. input-to-output power ratio in dB.
Of course,the input-to-output voltage ratio is 2:1, while the input-to-output power ratiois
Example 1-1: Specifying ratios in dB
Specify the following ratios in dB:
ExpressingSignal Amplitudes in dB
Signal amplitudes can also be expressed in decibels as a ratio of theamplitude to a specified reference. For example, a 100-μvolt signal amplitudecan also be expressed as,
Quiz Question
Express the following signal or field amplitudes in their normal units,
The units in parentheses following the 'dB' indicate that thequantity being expressed is an amplitude.
Each of the quantities above is simply converted as follows:
Using Decibels
Why bother expressing signal amplitudes in dB? After all, there's neverany ambiguity concerning whether a quantity is a power or voltage when theamplitude and its units are provided. The real power of working in dB iscalculating ratios.
Previously, we mentioned comparing a 10-watt receiver to a 5-wattspecification. In Equation (2), we showed that the receiver was 3 dB over thespecification. In this case, if the powers had been expressed in dB(W),
We could havecalculated the ratio as,
Rather than dividing amplitudes to determine the ratio, we can simplysubtract amplitudes expressed in dB(·). Again, as long as the impedance isconstant, it won't matter whether we are working with units of power, voltageor current.
Example 1-2: Specifying ratios in dB
Specify the following ratios in dB:
dBm
One of the most common units expressed in decibels is dB(mW) or dBrelative to 1 milliwatt. This is almost always written in the abbreviated form,dBm (i.e. without the 'W' and without the parentheses). Manyoscilloscopes and spectrum analyzers optionally display voltage amplitudes indBm. Since dBm is a unit of power, we must know the impedance of themeasurement in order to convert dBm to volts. For example, a voltage expressedas 0 dBm on a 50-Ω spectrum analyzer is,
Example 1-3: Specifying voltages in dBm
Specify the following voltages in dBm assuming they were measured with a50-Ω oscilloscope:
In this example, wecan see that doubling the voltage adds 6 dB (e.g. 13 dBm + 6 dB = 19 dBm) andincreasing a voltage by a factor of 10 adds 20 dB. This is true no matter whatunits of voltage are being used and is an example of why it is often convenientto work with decibels.
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