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Decibel Measurements
19 questions By Tony R. Kuphaldt
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Question 13 of 19
Suppose an AC signal amplifier circuit has a voltage gain (ratio) of 5. That is, Vout is five times as large as Vin:
Translate this voltage gain ratio into a decibel figure. Explain why the conversion from voltage gain ratio to decibels is not the same as conversion of a power gain ratio to decibels.
Reveal answerAV = 13.98 dB
Notes:Discuss with your students the nature of the “Bel” unit: it is fundamentally a unit of power gain, not voltage or current gain. So, representing voltage or current gains in units of either Bels or decibels means representing those voltage or current gains in terms of how much power gain they equate to.
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Question 14 of 19
Specialized forms of the decibel unit have been devised to allow easy representation of quantities other than arbitrary ratios of voltage, current, or power. Take for example these units, the first one used extensively in the telecommunications industry:
- dBm
- dBW
- dBk
Define what each of these units represents.
Reveal answer“dBm” represents the magnitude of a voltage in relation to 1 mW of power dissipated by a 600 Ω load. “dBW” and “dBk” units represent the magnitude of a voltage in relation to 1 W and 1 kW of power dissipated by the same load, respectively.
Follow-up question: how many volts is 2 dBm equivalent to?
Notes:Here we see the decibel unit being used to represent absolute quantities rather than relative ratios. Ask your students what benefit would there be in doing this. Why not just represent signal magnitudes in units of “volts” instead? Why would we want to use an obscure unit such as the decibel?
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Question 15 of 19
Calculate the overall voltage gain of this cascaded amplifier circuit, where the output of one voltage amplifier feeds into the input of another:
Also, convert the voltage gains of each amplifier into units of decibels, then convert the overall voltage gain ratio into units of decibels as well.
What do you notice about the overall gain of this circuit in relation to the individual amplifier gains, compared as ratios versus compared as decibel figures?
Reveal answerCascaded voltage gains expressed as ratios:
AV = 3 ×2 = 6 Cascaded voltage gains expressed a decibel figures:
AV = 9.54 dB 6.02 dB = 15.56 dB Notes:Besides providing practice with ratio-to-decibel conversions, the purpose of this question is for students to realize that gains multiply as ratios but add as decibels.
