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GR0177 #39
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Problem
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This problem is still being typed. |
Electromagnetism }Filters
High-pass filters have, for high-frequencies ( ),  .
The net impedance is given by )) .  , and thus  .
For cases I and II, ) .
For case I: )) Thus, in the regime of high, frequency, one gets  (This is a low-pass filter.)
For case II: )) , one gets  (To wit: L'Hopital's Rule can be used or this limit.)
For cases IV and III, )) .
For Case III, ))) For high-frequency,  \rightarrow 0) , and thus one has .
For Case IV, ))) . This quantity goes to 0 for high-frequency. (This is a low-pass filter.)
Hence, the only choices that work for high-freq filters are choices II and III. Choice (D).
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Comments |
istezamer
2009-10-12 23:38:09 | Actually I like how Yosun always reach for the mathematical approach to give you a profound solution that accepts no doubt!!... but at the same time I like the other approaches of the users... these are frequently time saving especially at the test when the average time you need to solve a problem is only 100 seconds!! |  | chrisfizzix
2008-09-23 08:25:58 | The easiest way to solve these kinds of questions is to remember the behavior of circuit elements in the high-frequency and low-frequency extremes.
At low frequency (aka DC), a capacitor just looks like an open circuit, while an inductor just looks like a wire.
At high frequency, a capacitor looks like a wire while an inductor looks like an open circuit.
Thus, we want the two circuits which have terminals that look like open circuits at high frequencies:
II has leads across the inductor, so that will pass HF.
III has a capacitor, which will look like a wire, and the resistor then sees all of the voltage drop.
Thus, answer D is correct.
In I, the inductor will appear open circuit ( ), so all the voltage drop will appear across the inductor and not the leads.
In IV, the capacitor will look like a wire, and no voltage drop appears across an ideal wire.
jmason86
2009-07-15 18:21:36 |
This is exactly how I did the problem. It's really quick and intuitive. Good explanation :)
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wittensdog
2009-10-09 14:41:57 |
Very much agreed. When a problem doesn't specify any numbers, I think it's generally a hint that you shouldn't be thinking too much about math. The first time I went to do this I used roughly this method, not even really remembering anything about high and low pass filters, and managed to get it right.
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| | blue_down_quark
2008-09-02 01:31:53 | A fast way to solve this problem is to note that for a high-pass filter the output will be zero if the input is DC . Only II and III fulfill this requirement. | |
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