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# Determining LC unknown values by using an oscillator

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#### sofer

##### Junior Member level 1
lc oscillator

Hello everybody,

I have an interesting question. Is there a way to determine the values of an inductor and a capacitor just by forming several oscillators based on them and measuring the frequency ?
Mathematically, it seems impossible. For example, let us say the I take one inductor L and two capacitors C1 and C2. By forming an oscillator using L and C1 I can measure a frequency f1=1/(2*pi*sqrt(L*C1)). Then I can form a second oscillator using L and C2 and I can measure a frequency f2=1/(2*pi*sqrt(L*C2)) and finally I can form a third oscillator using L and C1+C2 in parallel to get a third frequency f3=1/(2*pi*sqrt(L*(C1+C2))). So I have 3 equations of the form: L*C1=k1, L*C2=k2, L*(C1+C2)=k3. But the variables are not independent enough so no unique solution.
What I was wondering whether someone knows or can suggest a way to connect any number of inductors and capacitors to form any number of LC oscillators, so that just by measuring the resultant frequencies one can determine the values of the component inductors and capacitors ? It is important to state that no known components may be used, i.e., no accurate 1% capacitor of a known value or a similar inductor. All L and C components must be unknown in advance and their determination should only be done through freq. measurement. Is such a thing even possible ?

Thanks.

lc comparator oscillator

You probably could, as long as you had created enough equations as unknowns.

But there are much easier ways of doing this!

comparator lc oscillator

Hi Old Nick,

Well, it is not as simple as you think. In the example I presented, you have 3 equations and 3 unknowns but still the unknowns are correlated enough so as not to allow a single and unique solution. I tried many combinations, using 1 inductor and 2 capacitors, using 2 inductors and 2 capacitor. Connecting them in series, parallel, etc. The equations are always correlated enough so as not to yield a single solution. If you find any error in my statement (and I hope you do), please provide an example that works.

When you say that there are easier ways to do it, what would you suggest ? and please don't send me to use an LCR meter. There is a purpose to this madness and I can elaborate if you or anyone else is interested.

Thanks.

measuring a capacitor using an oscillator

I don't know whether it is possible or not, I would guess it is.

You could try connecting them all in parallel, and feeding 3 known frequencies through the circuit measuring the impeadence at the 3 frequencies. That should give you enough information.

Or an LCR meter

Having thought about it further,but not in any great depth, I'm pretty ure to get this to work you'll have to settle on one circuit, change 1 condition 3 times for 3 unknowns. If you can measure impedance then that would be the easiest way, I can't think of the top of my head how you'd do that though.

measure inductor with oscillator

Well, I was keen on measuring only frequency. But measuring impedance will sure work and give the required answer.
Let me tell you what I had in mind and what this is all for.
There is a nice LC meter design floating around the web that was cloned to death by everybody. This design uses an LC oscillator based on a comparator and a parallel LC tank and a PIC microcrontroller to measure the frequency. It measures the L and C values by inserting the capacitor in parallel with the tank and the inductor in series with the existing inductor.
The trick is calibration. The principle is that you use any regular inductor and capacitor for the parallel LC tank, but you also use a known 2% 1nF capacitor which you connect in parallel with the regular one for calibration. So you measure the frequency once without the accurate capacitor and once with it, and based on the fact that you know its value you can compute the values of L and C in the tank circuit and use it later on for the meter. Since measuring freq. can be done very accurately with the PIC, in fact, as accurate as you like, allowing enough time and memory capability to hold the counts, I figured it should be easy to devise a scheme where I can use any regular components and not need an accurate capacitor, and by connecting then just right, and measuring enough frequencies I could determine the components. Apparently, this task is not as easy as I thought, and in fact, I am almost sure it can't be done by using just frequency measurements alone. That is unfortunate, but life is often like that.
In any case, I thank you for taking an interest. :lol:
Maybe I will have a new idea someday. :idea:

Hi, just an idea: perhaps you can make a reference inductor from a plumbing tube and some wire. Formulas can be found in most text books dealing with passive components. Or just here: en.wikipedia.org/wiki/Inductor Formulae 1.

I can't seem to find anything cheaper then this.

It is not a question of price. It is a question of having an elegant and robust design that does not require "magic" accurate components for calibration.

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