(a)
ToShow:
The trap filter acts to reject signals in a band of frequencies centered
(a)
Answer to Problem 55P
The trap filter acts to reject signals in a band of frequencies centered at
Explanation of Solution
Given:
The given diagram is shown below
The above circuit is a trap filter circuit. Its phasors diagram is shown below.
Calculation:
The phasor diagram for the trap filter is shown below.
Here
The projection of
Define bandwidth as
Here,
And
Output voltage
Here,
And
Now,
Substitute
Again substitute
Now,
Substitute 0 for
Conclusion:
Hence, it is shown that the trap filter acts to reject signals in a band of frequencies centered at
(b)
The way, the width of the frequency band rejected depends on the resistance
(b)
Answer to Problem 55P
The width of the frequency band rejected is directly proportional to the resistance.
Explanation of Solution
Given:
The given circuit diagram is shown below
The given circuit is a trap filter circuit. Its phasors diagram is shown below.
Calculation:
The required Phasor diagram is shown below
Here
The projection of
Define bandwidth as
And impedance of the trap as
These two will yield an expression for the bandwidth and reveal its dependence on R.
Substitute
Again,
Substitute
For
For the case,
Substitute
Conclusion:
Hence, the width of the frequency band rejected directly proportional to the resistance.
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Chapter 29 Solutions
Physics for Scientists and Engineers
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