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Chapter 9: Problem 9

If the applied ac power to a system is \(5 \mu \mathrm{W}\) at \(100 \mathrm{mV}\) and the output power is \(48 \mathrm{~W}\). determine: a. The power gain in decibels. b. The voltage gain in decibels if the output impedance is \(40 \mathrm{k} \Omega\). c. The input impedance. d. The output voltage.

Short Answer

Expert verified
a. The power gain in decibels is 96.8 dB. b. The voltage gain in decibels is 273.6 dB. c. The input impedance is approximately 0.208 mΩ. d. The output voltage is 19.2 MV.

Step by step solution

01

Convert input power and voltage to basic units

Transform the given input parameters into their basic units. Snce they are given in microwatts and millivolts, we should change them to watts and volts respectively. So, \(5 \mu W = 5 \times 10^{-6} W\) and \(100 mV = 0.1 V\).
02

Calculate power gain in decibels

The formula for calculating power gain in decibels is \(10 \log(\frac{output Power}{input Power})\). Plugging in our numbers, that gives us \(10 \log(\frac{48}{5 \times 10^{-6}}) = 96.8 dB\).
03

Calculate current and output voltage

First, we calculate the current using \(Current = \frac{Power}{Voltage}\). Hence, Current = \(\frac{48 W}{0.1 V} = 480 A\). Then we calculate the output voltage using \(Voltage = Impedance \times Current\), which results in \(Voltage = 40,000 \Omega \times 480 A = 19.2 \times 10^6 V\).
04

Calculate voltage gain in decibels

The formula for calculating voltage gain in decibels is \(20 \log(\frac{output Voltage}{input Voltage})\). Substituting the values obtained gives \(20 \log(\frac{19.2 \times 10^6 V}{0.1 V}) = 273.6 dB\).
05

Calculate the input impedance

The formula for calculating impedance is \(Impedance = \frac{Voltage}{Current}\). Hence, the input impedance is given by = \(\frac{0.1 V}{480 A} = 0.208 \times 10^{-3} \Omega\).

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Most popular questions from this chapter

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. \(P_{o}=100 \mathrm{~mW}, P_{i}=20 \mu \mathrm{W}\).

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

Calculate the overall upper \(3-\mathrm{dB}\) frequency for a four-stage amplifier having an individual stage value of \(f_{2}=2.5 \mathrm{MHz}\)

a. What frequency is one octave above \(5 \mathrm{kHz}\) ? b. What frequency is one decade below \(10 \mathrm{kHz}\) ? c. What frequency is two octaves below \(20 \mathrm{kHz}\) ? d. What frequency is two decades above \(1 \mathrm{kHz}\) ?

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?
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