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
"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
Phil Allison a écrit :
More precisely, several times lower than the ringing frequency divided by the tank Q.
-- Thanks, Fred.
"Fred_Bartoli"
** Purest bollocks.Yawn - yet again ..........
........ Phil
Phil Allison a écrit :
As you say: yawn
-- Thanks, Fred.
"Fred_Bartoli"
** Make your damn point - Fred.Fuck knows what the hell it is, but do have the decency to put the poor, mangy, bedraggled thing out of its misery .... ASAP.
....... Phil
ve
Several can be as low as three. Three isn't quite enough. Make that many and it will be better.
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.
-- Bill Sloman, Nijmegen
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? ;-)
-- Thanks, Fred.
Pretty close to
F = 1 / ( 2 * pi * sqrt(L * C) )
John
wave
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.
MooseFET wrote in news: snipped-for-privacy@x35g2000prf.googlegroups.com:
snip
several is 2 to 7 a few is 3 to 11
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Is that definitive ?:-)
...Jim Thompson
-- | James E.Thompson, P.E. | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona Voice:(480)460-2350 | | | E-mail Address at Website Fax:(480)460-2142 | Brass Rat | |
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
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
few is more than several ? I would have expected it to be fewer!
Bye. Jasen
I once read somewhere that there are primitive cultures that count: "One, Two, Three, Many."
Cheers! Rich
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