Author Topic: What happens when L and C are not matched?  (Read 83 times)

Offline petespaco

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What happens when L and C are not matched?
« on: May 08, 2019, 04:42:35 PM »
Mads-
 The formula for  resonant frequency is: "Freq. = 1/(2pi X sqrt(L X C)).
This formula would imply, to me, anyway that ANY values of L and C will produce some resonant frequency.

But, I can find many references that say:
"Resonance occurs when capacitive and inductive reactances are equal to each other."
Well, that's fine, but we know that circuits DO oscillate when L and C are NOT equal.
Is this just a "play on words"?  The resonant frequency formula that I quote above doesn't seem to deal with that issue at all.

   I studied resonant circuits back in the early 1950's.  I vaguely remember that there is some negative "cost" to having L and C too far away from eachother, but I don't know why.

In my hobbyist work with the small ZVS induction heaters, I see that I can at least double capacitance or double inductance and still get the thing to oscillate.
My question:
   So what is the "cost" of "unbalanced" L and C in an oscillating circuit?

In my experiments so far, the main problem I see is reducing L and/or C so far that the oscillation frequency is  so high that the Mosfet gates can't turn on fast enough.  (This, of course, leads to overheating and failure.)
  But that still does not address that issue of "unbalanced" L and C.

Offline dexter

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Re: What happens when L and C are not matched?
« Reply #1 on: May 08, 2019, 05:45:36 PM »
Capacitive and inductive reactances depends on capacitance/inductance and frequency.
Xc=-1/(2pi X f X C)
Xl=2pi X f X L

"Resonance occurs when capacitive and inductive reactances are equal to each other."
that means: Xl=Xc
rearrange the terms and you get: Frez = 1/(2pi X sqrt(L X C))

So whenever you change the capacitance or the inductance the frequency at which Xc and Xl becomes equal (also known as resonant frequency) also changes.

Mads-
   I studied resonant circuits back in the early 1950's.  I vaguely remember that there is some negative "cost" to having L and C too far away from eachother, but I don't know why.
the energy stored in inductor and capacitor is:
Wc=0.5 x C x V^2
Wl=0.5 x L x I^2
At resonance Wc=Wl
For an inductance heater you need high current in the work coil. To achieve this a small inductance coil is used but
 a large capacitor with a high voltage rating is required. So the "negative cost" translate to a monetary cost :)

Offline Uspring

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Re: What happens when L and C are not matched?
« Reply #2 on: May 08, 2019, 05:59:59 PM »
petespaco wrote:
Quote
Well, that's fine, but we know that circuits DO oscillate when L and C are NOT equal.
If you're employing some sort of feedback, the circuit will oscillate at or near the resonance frequency. The advantage of using resonance is, that you can have a lot of energy in the tank without this energy going through your driving transistors all the time. The driving circuit has to supply only the power, that is lost either in the tank resistances or better in your sample.

When you change your tank parameters, you very likely also change the oscillating frequency. In induction heaters, there is an optimal frequency, depending on the type of sample. You can think of the sample being an almost shorted secondary loop. If the frequency is too high, that secondary loop will have a large impedance, which won't allow driving a lot of current in it. If the frequency is too low, the secondary won't generate enough voltage to generate a big current. A general rule, which follows from this is, that a better conductive sample should be heated with a lower frequency.

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Re: What happens when L and C are not matched?
« Reply #2 on: May 08, 2019, 05:59:59 PM »

 


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