# Determine LC ring freq

Discussion in 'Electronic Design' started by Stuart Hall, Jul 16, 2007.

1. ### Stuart HallGuest

When I feed a squarewave into a resonant tank circuit (LC network)
what component determines the _frequency_ of the resulting ringing?

I know the Q, or persistence, relates to how well the network is
tuned. But what about the actual ringing frequency?

Stuart Hall

2. ### Phil AllisonGuest

"Stuart Hall"

** The ringing frequency seen is that of the LC network itself.

The frequency of a driving square wave is irrelevant except to the
repetition rate of the ringing behaviour - this assumes the square wave
frequency is at least several times lower than the ringing frequency.

.... Phil

3. ### Fred_BartoliGuest

Phil Allison a écrit :
More precisely, several times lower than the ringing frequency divided
by the tank Q.

4. ### Phil AllisonGuest

"Fred_Bartoli"

** Purest bollocks.

Yawn - yet again ..........

......... Phil

5. ### Fred_BartoliGuest

Phil Allison a écrit :
As you say: yawn

6. ### Phil AllisonGuest

"Fred_Bartoli"

** Make your damn point - Fred.

**** knows what the hell it is, but do have the decency to put the poor,
mangy, bedraggled thing out of its misery .... ASAP.

........ Phil

7. ### MooseFETGuest

Several can be as low as three. Three isn't quite enough. Make that
many and it will be better.

8. ### Guest

When you feed a square wave into a resonant tank circuit, the tank
circuit presents a frequency dependent impedance to the the harmonic
content of the square wave.

The square wave can be resolved into a series of sine waves, the first
having the same period (frequency) as the square wave, while the rest
are the odd harmonics of that sine wave, with frequencies of three,
five and seven (etcetera) of the first sine wave and amplitudes
decreasing in proportion to the harmonic number (one third, one fifth,
one seventh etcetra).

If one of these harmonics is close to the resonant frequency of the
tank circuit the tank circuit may appear to ring at that frequency,
but what you will see will depends on the relationship between the
output impedance of the source of the square wave and the impedance of
the tank circuit.

If the resonant peak of the tank circuits overlaps a couple of
harmonics, the waveform appearing across the tank circuit can look
rather odd.

Get hold of a copy of LTSpice (Linear Technologies Switcher Cad III)
and see for yourself.

9. ### Fred_BartoliGuest

MooseFET a écrit :
I thought several could be as low as two

The exponential factor term is Exp(-t Wo/(2Q))
Now let several be as low as two.
The exponential factor is now
Exp(-(2Q/Fo)/2 2.Pi.Fo/(2Q)) = Exp(-Pi) = 0.043
That's low enough to make all the 'strange effects' small enough.
With several as high as three, the residuals get under 1% and at
several=4 that's 0.2%.

Can we agree on many starting at three? ;-)

10. ### John LarkinGuest

Pretty close to

F = 1 / ( 2 * pi * sqrt(L * C) )

John

11. ### MooseFETGuest

No, that would be a couple or a few.

Yes, for large values of three.

While I don't dispute your math, I do suggest that you may be applying
the wrong math to what is really cared about here. The OP wanted to
measure the frequency of the ringing. For low frequency squarewaves,
this could come out quite exact.

I was thinking in terms of how well the frequency can be measured.

12. ### meGuest

snip

several is 2 to 7
a few is 3 to 11

13. ### Jim ThompsonGuest

[snip]
Is that definitive ?

...Jim Thompson

14. ### RobinGuest

If you grab hold and force a garden swing to move at some frequency,
slow or fast then it will. Likewise if you connect a "powerful" (low
impedance) squarewave generator to an LC then it will do that square
wave - the harder the drive, the more slavishly the copying.

Alternately, if you "ping" a garden swing, it will, as soon as the
push disconnects, start to move "freely" at its natural frequency.
Likewise the LC, you have to "ping" it and then let go to allow it to
move freely.

If you know the frequency of the swing then you can adjust your
pushing in sympathy for best effect. Likewise the LC if you connect a
sinusoidal generator to it but it *would* have to be just right it
there was a "direct" (low impedance) connection.

To give the LC a bit of freedom, to release it a little from the hard
grip, put a resistor in series with the sinusoidal generator,
(increase the driving impedance) now, as you swing the generator's
frequency through the LC's resonance, it is allowed to build up an
amplitude of its own. If you get it just right, the amplitude will
keep increasing (just like the garden swing) to greater than the
driving force! The greater this effect is, the greater must be the Q
i.e. the bigger the series resistance the bigger the Q.

I.e. as the resistance gets greater so the generator is less connected
to the LC and the less the generator *damps" the swing, the greater
the Q.

As the other poster says, if you use a square wave instead, then you
will be using a whole bunch of sinusoids simultaneously (because a
square wave is ~ the sum of all the odd harmonics of its fundamental
i.e. f + 3f/3 + 5f/5...) so it is likely one of these harmonics will
"rattle" the LC at the its resonant frequency - by chance.

But only if that square wave it (appreciably) below the LC's
resonance.

Robin

15. ### RobinGuest

If you grab hold and force a garden swing to move at some frequency,
slow or fast then it will. Likewise if you connect a "powerful" (low
impedance) squarewave generator to an LC then it will do that square
wave - the harder the drive, the more slavishly the copying.

Alternately, if you "ping" a garden swing, it will, as soon as the
push disconnects, start to move "freely" at its natural frequency.
Likewise the LC, you have to "ping" it and then let go to allow it to
move freely.

If you know the frequency of the swing then you can adjust your
pushing in sympathy for best effect. Likewise the LC if you connect a
sinusoidal generator to it but it *would* have to be just right it
there was a "direct" (low impedance) connection.

To give the LC a bit of freedom, to release it a little from the hard
grip, put a resistor in series with the sinusoidal generator,
(increase the driving impedance) now, as you swing the generator's
frequency through the LC's resonance, it is allowed to build up an
amplitude of its own. If you get it just right, the amplitude will
keep increasing (just like the garden swing) to greater than the
driving force! The greater this effect is, the greater must be the Q
i.e. the bigger the series resistance the bigger the Q.

I.e. as the resistance gets greater so the generator is less connected
to the LC and the less the generator *damps" the swing, the greater
the Q.

As the other poster says, if you use a square wave instead, then you
will be using a whole bunch of sinusoids simultaneously (because a
square wave is ~ the sum of all the odd harmonics of its fundamental
i.e. f + 3f/3 + 5f/5...) so it is likely one of these harmonics will
"rattle" the LC at the its resonant frequency - by chance.

But only if that square wave it (appreciably) below the LC's
resonance.

Robin

16. ### Jasen BettsGuest

few is more than several ? I would have expected it to be fewer!

Bye.
Jasen

17. ### Rich GriseGuest

I once read somewhere that there are primitive cultures that count:
"One, Two, Three, Many."

Cheers!
Rich