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Passive Filter Circuits
44 questions By Tony R. Kuphaldt
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Question 13 of 44
Identify what type of filter this circuit is, calculate its cutoff frequency, and distinguish the input terminal from the output terminal:
Reveal answerThis is a low-pass filter.
fcutoff = 48.23 Hz
The input terminal is on the right, while the output terminal is on the left.
Notes:Be sure to ask students where they found the cutoff frequency formula for this filter circuit. Also, ask them how they were able to distinguish the input and output terminals. What would happen if these terminals were reversed (i.e. if the input signal were applied to the output terminal)?
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Question 14 of 44
The formula for determining the cutoff frequency of a simple LR filter circuit looks substantially different from the formula used to determine cutoff frequency in a simple RC filter circuit. Students new to this subject often resort to memorization to distinguish one formula from the other, but there is a better way.
In simple filter circuits (comprised of one reactive component and one resistor), cutoff frequency is that frequency where circuit reactance equals circuit resistance. Use this simple definition of cutoff frequency to derive both the RC and the LR filter circuit cutoff formulae, where fcutoff is defined in terms of R and either L or C.
Reveal answerfcutoff = 1 2 πR C(For simple RC filter circuits) fcutoff = R 2 πL(For simple LR filter circuits) Notes:This is an exercise in algebraic substitution, taking the formula X = R and introducing f into it by way of substitution, then solving for f. Too many students try to memorize every new thing rather than build their knowledge upon previously learned material. It is surprising how many electrical and electronic formulae one may derive from just a handful of fundamental equations, if one knows how to use algebra.
Some textbooks present the LR cutoff frequency formula like this:
fcutoff = 1 2 π L RIf students present this formula, you can be fairly sure they simply found it somewhere rather than derived it using algebra. Of course, this formula is exactly equivalent to the one I give in my answer - and it is good to show the class how these two are equivalent - but the real point of this question is to get your students using algebra as a practical tool in their understanding of electrical theory.
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Question 15 of 44
Identify what type of filter this circuit is, and calculate the size of resistor necessary to give it a cutoff frequency of 3 kHz:
Reveal answerThis is a high-pass filter.
R = 2 πf L
R = 5.65 kΩ
Notes:The most important part of this question, as usual, is to have students come up with methods of solution for determining R’s value. Ask them to explain how they arrived at their answer, and if their method of solution made use of any formula or principle used in capacitive filter circuits.
