Capacitors and resonant frequency

Oct 29, 2006 7 Replies

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meyousikmann 19 years ago

I have a problem that asks about the movement of the second plate of a capacitor in order to change the resonant frequency by 10 ppm in an LC circuit. I am getting stuck in terminology.

Here is the information given:

Area of each capacitor plate (one attached to solid nonmoving post while other can move small distances perpendicular to the plates) .01 m^2

Initial plate separation

100 micometers

Inductance

120 nH

I have found the initial capacitance and frequency, but the second part of the question says "How far must the second plate move to change the resonant frequency by 10ppm". I am not entirely sure what this question is asking for. Where does ppm fit into any of the calculations. I don't want answers, but I would appreciate if somebody can translate the question into something I might understand.

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Baron 19 years ago

Think about the definition of a capacitor ! The value of capacitance for a fixed plate area will vary in inverse proportion to the separation !

Baron:

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Charles Schuler 19 years ago

delta f = 10/1e6 x f1

fx = f1 - delta f

solve for new value of C based on fx

solve for new plate spacing based on C

(If I understand the question ;>)

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Tom Biasi 19 years ago

I believe you are being asked to determine the capacitance needed for that frequency change and then determine the plate areas that must face each other at the given distance.

Tom

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John Popelish 19 years ago

First you need to derive the relationship between capacitance and frequency (the power of proportionality).

Then you derive the relationship between plate spacing and capacitance (another power of proportionality). Then combine these two things to get 10 ppm frequency change.

10ppm is just a fraction 10/1,000,000 times the original frequency. So the original frequency must become either 1 + 10/1,000,000 of its original value, or 1 - 10/1,000,000 of it (depending on whether the plates are moved apart or together).

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Eeyore 19 years ago

It's another way of representing a small number ( as in parts per million ). Compare with per_cent for example which is parts per hundred.

Graham

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mphillipps2 19 years ago

Off the top of my head, I think it's:

100um (plate spacing) * (10 ^ -6) = 10^ -9 m = 1 nanometer

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mphillipps2 19 years ago

Wait, my last post was wrong.

f = 1/(2 * pi * sqrt(LC))

so I get 2 nanometers.

snipped-for-privacy@yahoo.com wrote:

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