current at resonance

antknee said:

Only the OP could answer that, my guess is that the first is wanted. The second could only be an academic/mathematical derivation with in my opinion little practical value and too little information to begin. In other words OP has to do that himself.

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Even though this was posted in the general chat forum and not the homework help forum, it seemed to me to have the flavor of a homework problem; this would account for the second case seeming to be an academic derivation. Even Mr. Al apparently thinks it's homework; he says, "...it often depends on the course and where they are in that course..."

MrAl said:

Hi again,


Yes it could be a trick question aimed at misleading the student into thinking that he has to use the entire circuit to calculate the 'resonant' frequency and that somehow it might be needed while it's a much simpler question.
Because the circuit as is contains two independent circuits, the resonance of the first has nothing to do with the current in the second.
I would have thought that if they wanted us to do the entire circuit then they would have specified at least some small generator resistance, but then again it often depends on the course and where they are in that course.

For example, if they were trying to exemplify how perfect sources do not have any series resistance then the circuit is to be analyzed as is, but on the other hand if they were trying to point out how most real life sources have at least some series resistance no matter how tiny, then we have to analyze the entire circuit to get the true solution. It depends a lot on what they were talking about in the course just prior to asking this question.
Interestingly, as a third possibility they might be handed a schematic from a real life device and asked whether or not the series resistance of the generator matters in that circuit...then it would be up to us to do a few calculations and decide.

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Whether or not the source has some resistance, the addition of Cp changes things. Furthermore, if Cp is not present, then the resonance frequency is the same whether you define it to be the frequency of maximum current from the source, or the frequency of zero phase angle of the source excitation.

When Cp is present, those two definitions give different frequencies. To see that this is true, I picked some arbitrary component values:

Lm = .1
Rm = 10
Cm = 1 µF
Cp = 5 µF

Then I plotted the phase angle and and magnitude of the current from the source, with an assumed voltage of 1 volt, and an internal impedance of zero. I've attached a couple of images showing the results. The phase angle is shown in red and the current magnitude in blue. I've subtracted an offset from the current magnitude so it will appear near the x-axis.

In the first plot the Cp capacitor is absent; the frequency of maximum current magnitude is the same as the frequency of zero phase angle. Either criterion will give the same resonance frequency.

In the second plot, the Cp capacitor is present. It can be seen that the frequency of zero phase angle increased, and the frequency of maximum current decreased. The resonance frequency is not the same for the two criteria, and neither is the same as the resonance frequency of the series Lm-Rm-Cm circuit alone.

There are three possible resonance frequencies that could be associated with the complete circuit, even when the source impedance is zero.

This circuit has the same topology as the spice models of quartz crystals and piezoelectric resonators. It can have a series resonant frequency and a parallel resonant frequency. Here I've plotted the current from a voltage source driving the model of a crystal that is series resonant at 10.000MHz.

The Electrician said:

There are three possible resonance frequencies that could be associated with the complete circuit, even when the source impedance is zero.

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The circuit is the electrical analog of a piezo, a piezo has 4 resonant frequencies, perhaps the 'real world effect' adds the other.

The word "piezo" by itself doesn't specify any particular device in common parlance. Numerous electrical devices use piezoelectric materials, such as ultrasonic cleaner transducers, sonar transducers, speakers, phonograph pickups, microphones, etc. What in particular are you referring to when you say "piezo"?

I use the term piezo to mean any device using the material pzt at the resonant frequency of the pzt - causing vibration. They should all have this electrical analog. Loading pzt and making it a 'piezo' will add resistance and change the compound frequency a little. However if the pzt is substantially loaded the pzt won't be able to vibrate at its resonant frequency and it is no longer a piezo.

Perhaps this is my own personal definition I've not thought about it until you asked.

The Electrician said:

Even though this was posted in the general chat forum and not the homework help forum, it seemed to me to have the flavor of a homework problem; this would account for the second case seeming to be an academic derivation. Even Mr. Al apparently thinks it's homework; he says, "...it often depends on the course and where they are in that course..."



Whether or not the source has some resistance, the addition of Cp changes things. Furthermore, if Cp is not present, then the resonance frequency is the same whether you define it to be the frequency of maximum current from the source, or the frequency of zero phase angle of the source excitation.

When Cp is present, those two definitions give different frequencies. To see that this is true, I picked some arbitrary component values:

Lm = .1
Rm = 10
Cm = 1 µF
Cp = 5 µF

Then I plotted the phase angle and and magnitude of the current from the source, with an assumed voltage of 1 volt, and an internal impedance of zero. I've attached a couple of images showing the results. The phase angle is shown in red and the current magnitude in blue. I've subtracted an offset from the current magnitude so it will appear near the x-axis.

In the first plot the Cp capacitor is absent; the frequency of maximum current magnitude is the same as the frequency of zero phase angle. Either criterion will give the same resonance frequency.

In the second plot, the Cp capacitor is present. It can be seen that the frequency of zero phase angle increased, and the frequency of maximum current decreased. The resonance frequency is not the same for the two criteria, and neither is the same as the resonance frequency of the series Lm-Rm-Cm circuit alone.

There are three possible resonance frequencies that could be associated with the complete circuit, even when the source impedance is zero.

Click to expand...

Hi again,


I never said Cp didnt change 'anything'.
The question had to do with the current through Cp didnt it?
For example, his teacher might want him to calculate the 'resonant' frequency of the RLC part and then use that frequency to calculate the current through Cp. I would then guess he wants him to use F=1/(2*pi*sqrt(L*C)) to calculate that frequency, but again im just guessing and i think he should clarify.

MrAl said:

Hi again,

I never said Cp didnt change 'anything'.

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And I never said you did say that.

MrAl said:

The question had to do with the current through Cp didnt it?

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In post #18, I indicated my awareness of that when I said: "we would need to calculate that resonance frequency, and then calculate the current in Cp at that frequency."

The calculation of the current in Cp would take into account any generator resistance as well as the frequency of resonance, however defined.

MrAl said:

For example, his teacher might want him to calculate the 'resonant' frequency of the RLC part and then use that frequency to calculate the current through Cp. I would then guess he wants him to use F=1/(2*pi*sqrt(L*C)) to calculate that frequency, but again im just guessing and i think he should clarify.

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I think you are acknowledging that we don't know exactly which resonance frequency his teacher wants him to use, and by implication that there might be more than one possibility.

In post #14 you said "Yes, if he wants the current through Cp and not Cm then the Rm,Lm,Cm circuit has nothing to do with this problem, unless of course we are to assume some small but significant generator resistance as some problems do. Then (and only then) we have to consider both parallel networks to get the right answer."

It's true that only if there were significant generator resistance, would the shunting effect of the Rm,Lm,Cm circuit affect the current in Cp. But the Rm,Lm,Cm circuit is involved in another way, because the problem asks for the current in Cp at "resonance". To find the resonance frequency, we must definitely consider the Rm,Lm,Cm circuit.

When you said "...the Rm,Lm,Cm circuit has nothing to do with this problem...", you didn't say that you were referring to the shunting effect of that branch. It took me a while to figure out what you meant, because, clearly, that branch plays a big part in determining the resonance frequency, which subsequently is used to determine the current in Cp.

I have shown that it isn't true that only when there is some significant generator resistance might we have to consider both parallel networks to get the right answer, because we have to consider effects other than the shunting effect of the Rm,Lm,Cm branch. Even with zero generator resistance, the presence of Cp causes the frequency of zero (source) phase shift to be different from the frequency of maximum source current.

Since one of those two definitions is almost always used to determine the resonance frequency, and since when Cp is present both of those frequencies (with respect to the source current and voltage) are different from the resonance frequency of the Lm-Rm-Cm branch alone, the OP's question "i want to know the current through the Cp at resonance?" is ill-posed. Perhaps in earlier course work the instructor or the text gave a definition of resonance which the OP forgot to tell us; perhaps the problem statement specified "resonance of the Lm-Rm-Cm branch", and the OP didn't tell us that.

Hey guys
Thanks all for your reply, And Am sorry for the ill-posted.
Here we are,,
The resonance is of the complete circuit, and yes it is the electrical analogy for the piezo.
I thought that the resonance frequency of the complete circuit is
ω=1/√(Lm Cm )
Because the Cp will not affects.
And i need this current so then i can determine the power at load (see the attachment) , the voltage at the diode bridge (Rectifier) terminal is same as the AC source and then i need the current at this terminals in order to find the power at the load. Am right?

Please could you please suggest for me software so that i can use it to simulate this circuit? I used Pspice but get some problems.

XL-power said:

Hey guys
Thanks all for your reply, And Am sorry for the ill-posted.
Here we are,,
The resonance is of the complete circuit, and yes it is the electrical analogy for the piezo.
I thought that the resonance frequency of the complete circuit is
ω=1/√(Lm Cm )
Because the Cp will not affects.
And i need this current so then i can determine the power at load (see the attachment) , the voltage at the diode bridge (Rectifier) terminal is same as the AC source and then i need the current at this terminals in order to find the power at the load. Am right?

Please could you please suggest for me software so that i can use it to simulate this circuit? I used Pspice but get some problems.

Click to expand...

With zero source impedance, the power at the load will be independent of your resonant circuit.
You can simulate it with LTspice.

Please give us some more information. Is this a homework problem?
If not, then is it a work problem, or a personal project problem?

As you have shown things in the full circuit, the four components making up the piezo resonator perform no function. The voltage source is shown as ideal, with no internal impedance. If the source actually has an impedance of less than 100Ω, then there will be little effect from the piezo resonator on the power delivered to R2, but R1 will represent an additional loss of the same order of magnitude as the R2 load

Why is the piezo resonator there? What is its purpose? Is it a mechanical "transformer", driven at one end and with output taken from the other end? What is the overall function of the hardware you're trying to analyze?

What kind of problem are you having with Pspice?

The Electrician said:

Please give us some more information. Is this a homework problem?
If not, then is it a work problem, or a personal project problem?

As you have shown things in the full circuit, the four components making up the piezo resonator perform no function. The voltage source is shown as ideal, with no internal impedance. If the source actually has an impedance of less than 100Ω, then there will be little effect from the piezo resonator on the power delivered to R2, but R1 will represent an additional loss of the same order of magnitude as the R2 load

Why is the piezo resonator there? What is its purpose? Is it a mechanical "transformer", driven at one end and with output taken from the other end? What is the overall function of the hardware you're trying to analyze?

What kind of problem are you having with Pspice?

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it's not a homework. it's a personal problem.
want to test,, if there is a device with Excited frequency equal to the resonance frequency of the pizo. then see how will the power
changes if we change the load.at the end i have to get a plot of power at the load versus the resistor.

problem with Pspice,, i create the netlist file (attached) to see the output power versus the resistor but am not sure of it.

Be aware that if you're simulating the circuit shown in post #28, the four components shown as modeling the piezo resonator will have no effect because you apparently have an ideal voltage source. If the source doesn't have a non-zero Thevenin impedance, then the piezo resonator will draw some current, but it will not change the voltage applied to your rectifier bridge.

You should add an impedance in series with the voltage source to represent the internal impedance of that source.

XL-power said:

if there is a device with Excited frequency equal to the resonance frequency of the pizo. then see how will the power
changes if we change the load.at the end i have to get a plot of power at the load versus the resistor.

problem with Pspice,, i create the netlist file (attached) to see the output power versus the resistor but am not sure of it.

Click to expand...

I'm not sure why you didn't say this from the start. I guessed you wanted the power of a piezo and someone corrected me because your question was phrased so badly.

Are you changing piezo's or using the same piezo and for example adding weight to it?

You can't simulate piezos in Pspice, LTspice or any other program, their behaviour is too complicated for it to be anything other than a guess, so it isn't even worth trying.

Hello again,


Electrician:
Ok no prob. I think we all agreed at that point that we need more information in order how to proceed. I was making the point of the zero resistance source or not which could have a large affect on the problem. Sometimes you have to be enrolled in the course to know what the 'teacher' is looking for, that's all i was trying to say.

XL-Power:
LTSpice is a decent simulator, and it's free so what the heck.
One thing with simulators though, just because they simulate with no math required you still have to know how to specify your real world problem circuit or else you'll still get bogus results. I wish you all the luck there.

The Electrician said:

Be aware that if you're simulating the circuit shown in post #28, the four components shown as modeling the piezo resonator will have no effect because you apparently have an ideal voltage source. If the source doesn't have a non-zero Thevenin impedance, then the piezo resonator will draw some current, but it will not change the voltage applied to your rectifier bridge.

You should add an impedance in series with the voltage source to represent the internal impedance of that source.

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sorry for keeping asking,, the main reason is that my background on piezo is poor. (if you know websites related to this topic which am asking about please let me know them)
what do mean by have no effect?
so in both case either (zero impedance or non-zero) the effect of the pizo can be ignore, in this case i can do the simulation without the pizo.

antknee said:

I'm not sure why you didn't say this from the start. I guessed you wanted the power of a piezo and someone corrected me because your question was phrased so badly.

Are you changing piezo's or using the same piezo and for example adding weight to it?

You can't simulate piezos in Pspice, LTspice or any other program, their behaviour is too complicated for it to be anything other than a guess, so it isn't even worth trying.

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i have to test the following:
1- if the pizo is fixed and the load is varying
2- if the pizo changes and the load is fixed and what is the effect on frequency

MrAl said:

Hello again,


Electrician:
Ok no prob. I think we all agreed at that point that we need more information in order how to proceed. I was making the point of the zero resistance source or not which could have a large affect on the problem. Sometimes you have to be enrolled in the course to know what the 'teacher' is looking for, that's all i was trying to say.

XL-Power:
LTSpice is a decent simulator, and it's free so what the heck.
One thing with simulators though, just because they simulate with no math required you still have to know how to specify your real world problem circuit or else you'll still get bogus results. I wish you all the luck there.

Click to expand...

yes i download the LTSpice. and i work on both the simulation and the real world problem
thanks

MrAl said:

One thing with simulators though, just because they simulate with no math required you still have to know how to specify your real world problem circuit or else you'll still get bogus results.

Click to expand...

There is an old, succinct saying about simulators that takes fewer words:

Garbage in, garbage out.

XL-power said:

yes i download the LTSpice. and i work on both the simulation and the real world problem
thanks

Click to expand...

Hi again,


Ok, that's great. You should be able to start getting some results and decide what it is you want to do with this circuit overall.

XL-power said:

sorry for keeping asking,, the main reason is that my background on piezo is poor. (if you know websites related to this topic which am asking about please let me know them)
what do mean by have no effect?
so in both case either (zero impedance or non-zero) the effect of the pizo can be ignore, in this case i can do the simulation without the pizo.

Click to expand...

If your source has zero impedance then the voltage applied to your bridge of rectifiers will be unchanged by the current drawn by the piezo resonator. If your source has some non-zero impedance, then the current drawn by the piezo resonator will cause a voltage drop in the source impedance, and less voltage will be available for the recitifier bridge.

The way to model the source impedance in spice is to simply put a resistor (possibly with some reactance as well) in series with the source.

What is the nature of your physical source? Is it a signal generator, or some kind of amplifier? Do you know what its internal impedance is?

To find out its internal resistance, set up your source to provide an output without a load and connect a voltmeter or oscilloscope to the output to measure it. Apply a resistive load, perhaps a variable resistor, and vary the resistance until the output of the source drops to 1/2 of the unloaded value. Then the value of the resistive load is equal to the internal resistance of your source.