Concept explainers
Sketch the line spectrum for the waveform shown in Figure 17.31.
Answer to Problem 15E
The line spectrum for the given waveform is sketched as shown in Figure 1.
Explanation of Solution
Given data:
Refer to Figure 17.31 in the textbook.
Formula used:
Write the general expression for Fourier series expansion.
Write the general expression for Fourier series coefficient
Write the general expression for Fourier series coefficient
Write the general expression for Fourier series coefficient
Write the expression to calculate the fundamental angular frequency.
Here,
Calculation:
In the given Figure 17.31, the time period is
The function
Substitute 0.4 for T in equation (5) to find
Applying equation (6) in equation (2) to find
Simplify the above equation as follows,
For half wave symmetry and even symmetry,
For all values of ‘n’,
Applying equation (6) in equation (3) to find the value of coefficient
Consider the function,
Consider,
On differentiating the above expression,
Equation (8) will be follows,
In the above equation, consider,
By applying linearity,
In equation (10),
consider,
Let,
Equation (11) will be as follows,
Similarly, in equation (10),
consider,
Let,
Equation (12) will be as follows,
Substitute the values of m and l in equation (10) as follows,
Substitute the value of y in equation (9) as follows,
Therefore,
On applying the limits,
Simplify the equation as follows,
Simplify the equation as follows,
Substitute the value of
Converting the equation (1) which is in angular frequency into frequency.
Substitute the value of
By considering
For
For
The sketch for the line spectrum is shown in Figure 1.
Conclusion:
Thus, the line spectrum for the given waveform is sketched as shown in Figure 1.
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Chapter 17 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
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