Concept explainers
(a)
The value of output voltage,
(a)
Answer to Problem 61E
The value of output voltage,
Explanation of Solution
Given data:
The input voltage is,
The given diagram is shown in Figure 1.
Calculation:
Mark the loop current
The required diagram is shown in Figure 2.
The conversion of
The conversion of
Hence, the value of the inductor,
The conversion of
The conversion of
Hence, the value of the capacitor,
The expression for output voltage using KVL is given by,
Substitute
Apply Fourier transform to the above expression.
The Fourier transform of
Substitute
Further solve as,
Apply shifting property for
Further solve as,
The inverse Fourier transform for the
The inverse Fourier transform for the
The inverse Fourier transform for the
Substitute
The expression for the output voltage from the figure is given by,
Substitute
Further solve as,
Conclusion:
Therefore, the value of output voltage,
(b)
The value of output voltage,
(b)
Answer to Problem 61E
The value of output voltage,
Explanation of Solution
Given data:
The input voltage is,
Calculation:
The expression for output voltage using KVL is given by,
Substitute
Apply Fourier transform to the above expression.
The Fourier transform of
Substitute
Further solve as,
The inverse Fourier transform for the
The inverse Fourier transform for the
Substitute
The expression for the output voltage from the figure is given by,
Substitute
Further solve as,
Conclusion:
Therefore, the value of output voltage,
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Chapter 17 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
- 4. Using the definition, obtain Fourier transforms of the following signals (a > 0) (a) x(t) = Ae-atu(t) (b) x(t) = ½ [8(t + 1) + 8(t + ½) + 8(t − ½3) + 8(t − 1)]arrow_forward5. With f(t) = sinc(t), Obtain Fourier transforms of the following functions. (a) (t)arrow_forwardFor each signal, find the Fourier transform, X(W), and then plot [X()| (Check your drawings using MATLAB.) 4. x(t) = cos(200t)p4(t) %3D 5. x(t)=e"cos(10t)u(t)arrow_forward
- 5. Compute the fourier Series of the following function: S(1) -7,0starrow_forwardBe able to calculate the Fourier transform of a function Find the Fourier transform of each function. In each case, a is a positive real constant.f(t)=0,t<0,f(t)=e−atsin ω0t,t≥0.arrow_forward6- Find the Fourier Transform of the following signals (4+4) x(t)- e "u(1) a>0. x(t) = 8(t) Yiu)arrow_forwardBe able to calculate the Fourier transform of a function Find the Fourier transform of each function. In each case, a is a positive real constant. f(t)=0,t>0,f(t)=−teat,t≤0.arrow_forward(i) Show that the Fourier transform of 8(t-a) = e¯jwa (ii)Prove the inverse of the above expression (iii) Prove that the Fourier transform of an impulse train is also an impulse train. 1. %3Darrow_forward2. Sketch the function r(t) and find its Fourier transform X(w). t/T, 0 0 is a constant). =arrow_forwardUse Only Direct Integration to find the Fourier Transform of the given functions a) f(t) = 8(t) b) f₂(t) = 8(1-5) c) f₂(t)= e¯at [u(t) - u(t−5)], a>0arrow_forwardQ2: Calculate the Fourier Transform F(w) for the following function f(t) = {1}] 0arrow_forward5) A linear system is described by the differential equation below, where x(t) is the input and y(t) is the output. Given that x(t) = 2sin(@t), where o =2000, find the Fourier Transform of the input and the output. You may assume zero state response. () + 2000 y(t) = 5000x(t)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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