(a) What is the gain in decibels of an amplifier with a...

(a) What is the gain in decibels of an amplifier with a power gain of 4 ?
(b) What is the power gain ratio of a 5-dB amplifier?
(c) Express $2 \mathrm{~kW}$ power in terms of $\mathrm{dBm}$ and $\mathrm{dBw}$.

Key Concepts

Decibel (dB) Scale

The decibel (dB) is a logarithmic unit used to express ratios, typically of power or intensity. By using a logarithmic scale, large and small values can be conveniently expressed, and multiplying gains or losses becomes a matter of addition or subtraction. This is accomplished using the formula 10 log??(P?/P?) for power ratios.

Power Gain and Its Conversion

Power gain represents the ratio of output power to input power of a system, such as an amplifier. Converting a power gain to decibels involves applying the logarithmic conversion formula, while converting from decibels back to a linear power gain ratio requires using the inverse logarithmic function.

Differentiation of dBm and dBw Units

dBm and dBw are specialized decibel measurements relative to common reference power levels. dBm is referenced to 1 milliwatt (mW), making it convenient for describing small power levels in communication systems, whereas dBw is referenced to 1 watt (W), providing a broader scale for larger power measurements.

Conversion Between Power Units and Decibel Representations

Converting between actual power values (in watts or kilowatts) and their decibel representations (like dBm or dBw) involves applying the logarithmic formula with the appropriate reference values. This process allows for direct comparisons between power levels, making it easier to understand and work with the relative strengths of signals in various engineering and physics applications.

Transcript

00:01 This problem has two parts to it.

00:03 We have, we're actually given in this equation where beta is the gain, and we have 10 times log of the power output divided by the power input.

00:15 And the first part says if your output is 135 and your input is 1 milawatt, what is the gain? so we're just going to literally plug this in.

00:27 It shouldn't be too difficult.

00:28 So we'll plug in 135 for the power out.

00:31 And then instead of just putting 1 at the bottom, we have to do 1 times 10 to the negative 3.

00:38 And the reason why is because this is milly and a milly watt is equal to 1 times 10 to the negative 3 watts.

00:49 So that's just a conversion there to get that to be what we want it to be.

00:53 When you plug that into the calculator, what you end up getting is, let's try it, 10 times log of 135 ,000 ,000.

01:02 Divided by 1 times 10 to the negative 3 gives us a decibel.

01:08 Remember this is in decibels, 51 .3 decibels.

01:14 So that's the first part of the question.

01:17 The second part says, well, what if we have 93 decibels as our gain? and that's going to equal 10 times log times.

01:26 And they give us a power output of 10 watts.

01:29 And they want to know what is the power input.

01:31 At this point, you're just going to, again, use the same equation.

01:36 You saw me plug in each step.

01:39 You know, the gain is 93 decibels, 10 times log...

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