- #1

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1/x(sqrt(R^2+1/(x^2)))

Just to show the limits as x approaches 0 and infinity, where x is frequency.

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- Thread starter houlahound
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- #1

- 906

- 223

1/x(sqrt(R^2+1/(x^2)))

Just to show the limits as x approaches 0 and infinity, where x is frequency.

- #2

BvU

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- #3

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It should equal 1 at x = 0 ie DC, open circuit for capacitor and zero for frequency approaches infinity ie capacitor is short circuit.

It can't tho cos of the first term in x goes to 1/0 ie infinite at DC.

- #4

BvU

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Kudos !Self studier here

Simple recipe: for ##\ \ x\downarrow 0\ \ ## you want to be looking at something like ##\ \ A + x\ \ ## and for ##\ \ x\rightarrow\infty\ \ ## you want something like ##\ \ B + {1\over x}\ \ ##.

To wit for ##\ \ x\rightarrow\infty\ \ ##:$$ { 1\over x \sqrt{R^2+{1\over x^2}}}$$the last term in the denominator disappears besides R

For ##\ \ x\downarrow 0\ \ ## you bring the x inside the root: $${ 1\over \sqrt{x^2 R^2+1}}$$ and now the first term disappears besides the 1.

- #5

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(1/x)*1/(stuff)

and wrongly insisted that due to the first term (1/x) that the behaviour had to blow up to infinity.

I wanted the equation to fit my expectation even tho I knew the behaviour of the low pass in advance.

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