Q factor and resonant frequency

[T3sl4co1l]

Q is defined for anything you can give a definition for.

Tim

[emece67]

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[T3sl4co1l]

It's funny, isn't it?  You'll get the same sort of "nonsense" from this tool, too: https://hamwaves.com/inductance/en/index.html#input (models solenoid coils quite accurately, including resonances)

Tim

[langwadt]

It is remarkable that the datasheet linked by th OP clearly states that the self resonance frequency of the coil is 11 MHz and at the same time they plot a Q vs. f curve that seems to go to zero at such frequency.

the Q vs. f curve is surely with a load capacitor to bring the resonance to the frequency that'll be used in a charger

[emece67]

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[Siwastaja]

EDIT: later on he states that "[...] so the quality factor Q will be huge near resonance." 

Depending on series/parallel viewpoint, it's either 0 or infinity.

Again, it's more important to understand the concept than to learn one definition of the Q factor by heart then be confused about it and unable to utilize it.

[T3sl4co1l]

Cannot get it to work. Where's the "calculate" button?

It's automatic on entering a full set of parameters.  Enable JS and use a current browser.

Tim

[bob91343]

The plot thickens.  We are confusing circuit Q with component Q.  The thing that is wrong is, as mentioned above, applying formulas without understanding them.

You care about component Q when using an inductor.  Circuit Q varies all over the place and isn't a terribly useful parameter.

[SiliconWizard]

Yeah. There is an obvious difference in the definition of the Q factor for an inductor (or rather, a coil, as opposed to an ideal inductor) and for a resonant circuit, and that can be confusing.

https://en.wikipedia.org/wiki/Q_factor

[KE5FX]

Another problem with Q is that it conflates energy loss/efficiency with bandwidth and stability.  In precision timing work, it's almost an axiom that stability improves as Q increases and line width shrinks.  Not necessarily true for pendulum clocks, though.  This is an area where pendulums are more interesting than they appear at first.  On page 73, Tom suggests that we should be using P for stability and Q for energy loss, at least where pendulums are concerned. 

What are some examples where this is true in electronics?

[SiliconWizard]

A high Q factor for a resonant circuit is a double-edged sword: it improves efficiency at the exact resonant frequency, but degrades efficiency elsewhere much more so than a circuit with a lower Q factor. So in practical power transfer applications, it's often a trade-off.

[TimFox]

Going back to my earlier post about the Q for a resonant circuit and the Q of a reactive component.  I leave the actual algebra as an exercise for the reader.
1.  As  pointed out by several, for resonators in general (e.g., cavities, RLC circuits, piezoelectric crystals):  at the resonant frequency, Q is defined in terms of the energy dissipated per cycle compared with the energy stored in the resonator.
2.  From this definition, we see that Q is also the ratio of the resonant frequency to the bandwidth (at half-power, - 3 dB).  Q = (resonant frequency) / (-3 dB bandwidth).
3.  For a component such as a practical coil or capacitor, with a reactance and resistance at a given frequency (assuming the frequency of measurement is far enough from the self-resonant frequency of the component so that we can ignore the other reactance), a Q meter will measure the component Q as Q = Abs(X_s) / R_s = Abs(R_p / X_p), where the absolute value is needed since the reactance will be negative for a capacitance and positive for an inductance.  Note that the series and parallel reactances for a given component are not equal, although if Q is very high the difference is small.  For a high-Q component, the series and parallel resistances differ by a large factor, approximately Q².
4.  We now wire a practical coil and capacitor together to make a resonant circuit, with the resonant frequency well below the self-resonant frequencies of the two components for simplicity.
5.  A series circuit gives a low impedance at resonance, where the positive inductive series reactance and negative capacitive series reactance cancel.  Since both components have positive series resistance, the total impedance does not go to zero, but the current reaches a maximum at the resonant frequency when driven by a low-impedance voltage source.
6.  A parallel circuit gives a high impedance at resonance, where the positive inductive parallel reactance and the negative capacitive parallel reactance cancel.  What is left is the parallel combination of the two parallel resistances.  If the two components were lossless, which is not physically possible, then the impedance would increase without bound (infinite impedance at resonance).
7.  From this elementary circuit theory, we calculate that the Q of the resonant circuit is given by 1/Q = 1/Q_L + 1/Q_C.  Usually, the capacitor's Q is higher than the inductor's Q and the inductor Q dominates the calculation.
8.  When the resonant circuit is used to transfer power from a source to a load at a single frequency, the efficiency is reduced by the unloaded Q of the resonant circuit, where the loaded Q includes the effect of the load resistor on the circuit (series or parallel).

[emece67]

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