Homework2_sol

Homework2_sol - MCE311 Homework # 2 Solution Question 1...

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Unformatted text preview: MCE311 Homework # 2 Solution Question 1 (3.1 textbook): An amplifier produces an output of 5 V when the input is 5V. What is the gain G and the decibel gain GdB? Solution: The gain is: 5 10 5. 10 The gain in dB is: 20 120 _____________________________________________________________________ Question 2 (3.2 textbook): An amplifier has a gain of 60 dB. If the input is 3mV, what is the output voltage? Solution: First we compute the gain G 60 20 60 3 We know that 10 10 By definition G is the ration of output to input: is given as 3 mv = 3.10 V 10 3.10 3 _____________________________________________________________________ Question 3 (3.4 textbook): A pressure transducer has an output impedance of 120 and is to be connected to an amplifier. What must be the minimum impedance of the amplifier if we want to keep the loading error less than 0.1%? Solution: 0.999 Loading of 0.1% implies is the impedance of the amplifier. The transducer and the amplifier impedances are in series and therefore the total impedance is: 120 Voltage across Solve for : is: 120 0.999 120 0.999 119.88 1 0.999 Therefore the minimum impedance is: 119.88 _____________________________________________________________________ Question 4 (3.5 textbook): The output of a force transducer is 5mV when measured with a multi-meter that has a 5 M input impedance. The output of the same transducer when measuring the same force is 4.8mV when it is connected to a filter with an input impedance of 10 k. What is the output impedance of this transducer? Solution: Use When 5. 10 ; 5. 10 5. 10 . . eq.(1) When 10 ; 4. 8.10 4. 8.10 eq.(2) These are two equations with two unknowns. Solve for the impedance we get 416 _____________________________________________________________________ Question 5 (3.11 textbook): Change in frequencies is often measured in decades and in octaves. a. How many octaves correspond to a decade? b. If a curve of a filter is characterized by 6 dB per octave, what is the equivalent in dB/decade? Solution: When we double f, we get twice the frequency. Double again, we get 4 times the frequency. Double again we get 8 time the frequency. Double again we get 16 time the frequency. Somewhere between 8 and 16 we get 10 times the frequency. a) log 10 3.33 10 2 log 2 b) We have 3.33 octave = decade, therefore 6 dB/octave *3.33 octave /decade = 20 dB/decade _____________________________________________________________________ Question 6 (3.13 textbook): The output of a dc generator that produces a maximum voltage of 90V is to be attenuated to 10V using a voltage divider. The attenuated signal is to be used as an input to a filter. If the output impedance of the generator is 10 and the input impedance of the filter is 100 k, specify the values of the resistors in voltage divider such that the loading error is 0.1%. Solution: First, you should establish a relationship between , , and the required voltage division, without filter impedance. This provides one equation: 10 2 90 10 Or 10 80 100 0 This equation sets the voltage across 10 (required by VD specification) across 100k Second, attach the filter to the divider and compute the voltage where 90 10 Loading of 0.1 implies that: 10 10 10 10 10 0.001 10 10 0.001 10 10 90 ; and 0.001 90 0 This provides the second equation (nonlinear) Now, we have 2 equations with 2 unknowns. Solve for the unknowns R1 = 112612 ; R2 = 8999 and Question 7 (3.18 textbook): A transducer measures a sinusoidal signal with an amplitude of 5V and a frequency of up to 10 Hz. Superimposed on this signal is 60 Hz noise with an amplitude of 0.1V. It is desired to attenuate the 60 Hz noise to les than 10% of its value using a low pass filter. Knowing that the filter gain is given by Vo Vi 1 f 1 fc 2n Determine the appropriate filter order if the cut-off frequency is 10 Hz. Solution: LP filter with Gain of 0.1 at 60 Hz 1 1 0.1 60 f 1 1 10 f 0.1 1 1 1 6 60 10 60 10 6 1 10 100 99 log 6 log 99 log 99 1.2823 2log 6 2 _____________________________________________________________________ ...
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