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Chapter 9: Problem 4

Calculate the power gain in decibels for each of the following cases. a. \(P_{o}=100 \mathrm{~W}, P_{i}=5 \mathrm{~W}\). b. \(P_{o}=100 \mathrm{~mW}, P_{i}=5 \mathrm{~mW}\). c. \(P_{o}=100 \mathrm{~mW}, P_{i}=20 \mu \mathrm{W}\).

Short Answer

Expert verified
Power gains for the given cases are: \(G_{dB,1} = 10 \cdot \log_{10}(20)\) dB, \(G_{dB,2} = 10 \cdot \log_{10}(20)\) dB, \(G_{dB,3} = 10 \cdot \log_{10}(5000)\) dB.

Step by step solution

01

Calculate the power gain for the first case

Apply the formula for the power gain for the first case, i.e., \(P_{o}=100 \mathrm{~W}\) and \(P_{i}=5 \mathrm{~W}\). Thus, \(G_{dB,1} = 10 \cdot \log_{10} \left( \frac{100}{5} \right)\)
02

Calculate the power gain for the second case

Apply the formula for the power gain for the second case, i.e., \(P_{o}=100 \mathrm{~mW}\) and \(P_{i}=5 \mathrm{~mW}\). Thus, \(G_{dB,2} = 10 \cdot \log_{10} \left( \frac{100}{5} \right)\). Note even though powers are in milliwatt (mW), the powers will cancel out and will not affect the calculation.
03

Calculate the power gain for the third case

For the third case, first, express both powers in the same units, i.e., either Watts (W) or milliwatts (mW) or micro-watts (\(\mu W\)). Let's convert \(P_{i}\) to mW. So, \(P_{i}=20 \mu W = 0.02 mW\). Now apply the formula for power gain: \(G_{dB,3} = 10 \cdot \log_{10} \left( \frac{100}{0.02} \right)\).

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Most popular questions from this chapter

Two voltage measurements made across the same resistance are \(V_{1}=110 \mathrm{~V}\) and \(V_{2}=220 \mathrm{~V}\). Calculate the power gain in decibels of the second reading over the first reading.

Calculate the overall voltage gain of four identical stages of an amplifier, each having a gain of 20 .

Input and output voltage measurements of \(V_{i}=10 \mathrm{mV}\) and \(V_{o}=25 \mathrm{~V}\) are made. What is the voltage gain in decibels?

a. The total decibel gain of a three-stage system is \(120 \mathrm{~dB}\). Determine the decibel gain of each stage if the second stage has twice the decibel gain of the first and the third has \(2.7\) times the decibel gain of the first. b. Determine the voltage gain of each stage.

a. The feedback capacitance of an inverting amplifier is \(10 \mathrm{pF}\). What is the Miller capacitance at the input if the gain of the amplifier is \(-120\) ? b. What is the Miller capacitance at the output of the amplifier? c. Is it a good approximation to assume \(C_{M_{i}} \cong\left|A_{v}\right| C_{f}\) and \(C_{M_{o}} \cong C_{f} ?\)
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