High Voltage Forum
General electronics => Electronic circuits => Topic started by: petespaco 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.

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 :)

petespaco wrote:
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.

... some negative "cost" to having L and C too far away from each other, but I don't know why.
... So what is the "cost" of "unbalanced" L and C in an oscillating circuit?
Hi Pete. This is my first post here, but I'm a regular at old 4hv forum.
L and C are measured with differently shaped units, so they can't really be close or far from each other.
But let's say their numerical values in conventional units are the same.
e.g. 1 uH and 1 uF, whose reactances have the same magnitude at f = 1 MHz/2pi.
So what's wrong with 100 uH and 0.01 uF, whose resonant frequency is the same?
Undamped LC tank circuits can be characterized by resonant frequency f = 1 / 2 pi sqrt(LC), and an impedance z = sqrt(L/C).
The impedance values in example above are 1 ohm and 100 ohms. It's the ratio of peak (or RMS) voltage to peak (or RMS) current.
The design of active circuits around the LC tank depends a whole lot on the impedance. Could be an ohm or less in induction heater, or many thousands of ohms in a signal oscillator or radio receiver.
Does that help?

The OP implies a misunderstanding of the difference between reactance and either capacitance or inductance, but I think thats been covered by the replies.
WRT real world components its crucial to remember that inductors also have internal capacitance and resistance, just as capacitors have internal inductance and resistance. So while you could in theory use any combination of L and C to get a particular resonant frequency, in practice you really cant build a 20H inductor and expect it to resonate with a 10pF capacitor at 11.25kHz as the inductor probably already has 100s of pF of internal capacitance already.
This is one of the reasons you will see output filters on high frequency switchmode power supplies with 1nF, 100nF and 10uF capacitors all in parallel, which in theory seems pointless. But a real 10uF ceramic capacitor will typically be selfresonant at around 1 to 2MHz, at which point it ceases to be a capacitor and looks more inductive as the frequency goes up. Hence the 100nF and 1nF capacitors, which are there to provide filtering beyond the range of the 10uF.
Q is another consideration: as a rule of thumb bigger inductors will have poorer Q, because their resistance will be higher.