RLC circuit question

Ratch

Joined Mar 20, 2007
1,068
count_volta,

Okay so the reason for using an amp in a circuit like this is to restore energy, rather than to amplify the output signal so that I will be able to hear it once it comes out of the speaker?
Well, you have to sustain the oscillation and make it high enough to drive the load of the speaker. Right now, I don't think you will hear too much from 7 cycles that decay to 0 in 0.01 sec if the resistance is 0.1 ohm.

How about the idea which Bill_Marsden suggested of not using a resistor at all? I'm afraid that this will cause currents which are dangerously high and damage the inductor and or capacitor.
Many components can sustain large current spikes if they are not prolonged. In this circuit, the larger the current spike, the shorter its period. A voltage of 6 volts across a 470 uf capacitor stores less than 0.01 joules. I don't think you have to worry too much.

Ratch
 

Wendy

Joined Mar 24, 2008
21,848
Part of what your missing is energy transfer. With a tank circuit the energy is transfered back and forth, which is the oscillation you are after. Try calculating the current through each component.

Try this paper experiment. Take a look at a series resonant circuit being feed its resonant frequency. Calculate the voltage across each component. It is not an illusion, but since the voltages have different phases they cancel overall.

Q is a real term, it can be thought of as quality, but it is more than that. I'm surprised you haven't been taught it. Resistance is everywhere, and it is the major factor that reduces Q.

While (in theory) energy is stored in a tank circuit there just isn't much there. It's a little like quantum physics, you look at it it changes.
 

Thread Starter

count_volta

Joined Feb 4, 2009
434
We were taught how to do phasor analysis of the steady state with an AC input, and then how to use laplace with any input and to solve the differential equation and to solve for the voltage and or current of the inductor capacitor and resistor.

I would guess in this case if I want the complete response, I would need to do a Laplace circuit using equivalent impedances. For example the inductor impedance is L*s. The capacitor impedance is 1/C*s.

Am I right?
 

Wendy

Joined Mar 24, 2008
21,848
Not sure, it's been well over 30 years for me, and while I use vector analysis for phase shift, and reactance for impedance a lot of my analysis and math is rusty.

Capacitive impedance = 1/ 2πfC
Inductive = 2πfL

The main thing is a series resonant circuit reduces it's impedance at resonance, so in theory it goes to zero. A parallel resonant circuit does the exact opposite, and goes to maximum impedance at resonance. With a parallel off frequencies are shunted through, while with series they are blocked.

Do you know how to calculate the impedance for a series resonant circuit for a specific frequency?
 

Thread Starter

count_volta

Joined Feb 4, 2009
434
Do you know how to calculate the impedance for a series resonant circuit for a specific frequency?
Well if you solve the laplace transform circuit you end up with one of a few forms, one of which is

A*cos(ωt+σ)*e^-t, where ω is the angular frequency, and σ is the phase angle. A is the magnitude. You usually do partial fractions to find A.

The poles would give you a preview of which form you need and find the coefficient ω for you.

This would be the transient response, since an RLC with a constant voltage input would give you a constant output at steady state.

The transient response is the oscillation. Thats what we learned last semester. We didn't spend too long on resonance sadly. Perhaps it will come up in future courses, like signals and systems. I can always read it in the All About Circuit book though. ;)
 

Wendy

Joined Mar 24, 2008
21,848
OK, figure what the impedance of the LC circuit at resonance, then the current through it with a source. Then calculate the voltage across each part, the capacitor and the inductor. I'm trying to lead you to something here.
 

hobbyist

Joined Aug 10, 2008
887
Well if you solve the laplace transform circuit you end up with one of a few forms, one of which is

A*cos(ωt+σ)*e^-t, where ω is the angular frequency, and σ is the phase angle. A is the magnitude. You usually do partial fractions to find A.

The poles would give you a preview of which form you need and find the coefficient ω for you.

This would be the transient response, since an RLC with a constant voltage input would give you a constant output at steady state.

The transient response is the oscillation. Thats what we learned last semester. We didn't spend too long on resonance sadly. Perhaps it will come up in future courses, like signals and systems. I can always read it in the All About Circuit book though. ;)
I'm intejecting this as a complement to ya.

WOW...
You pick up on this stuff really well, (transient analysis)

In my course from CIE we had quite a few lessons in Transient analysis, laplace transforms and such, way up into the calculas ...

I look through my notes (I took lots of them) and it boggles my mind that I understood all that at one time.

I accidentally hit somewhere at the bottom of my keyboard and I can't get off this italicize printing.

What the heck did I hit to make this italcized????

Any way keep up the good work, your going to make a good engineer someday.
 

Thread Starter

count_volta

Joined Feb 4, 2009
434
I'm intejecting this as a complement to ya.

WOW...
You pick up on this stuff really well, (transient analysis)

In my course from CIE we had quite a few lessons in Transient analysis, laplace transforms and such, way up into the calculas ...

I look through my notes (I took lots of them) and it boggles my mind that I understood all that at one time.

I accidentally hit somewhere at the bottom of my keyboard and I can't get off this italicize printing.

What the heck did I hit to make this italcized????

Any way keep up the good work, your going to make a good engineer someday.
Cool, if being a good engineer means being a math genius........... I'm not a big fan of complicated math. I just like to use it as a tool.

Concepts are awesome. Understanding what the electrons and such are doing is what I like. Remove the math and add more concepts. ;)

I will try to solve for the voltage of all elements. Wont the impedance be a complex number? How will that help me?
 

hobbyist

Joined Aug 10, 2008
887
I got out my books, and found my lessons on transient analysis, Oh man this is all greek to me now, I've been away from this for so many years I would have to start and go back to my trig. and calculus lessons just to get back up to speed on this stuff. I don't even know where tro start, in trying to get back to this, but it was fun understanding it before, it was neat being able to determine phjase angles and volt. currents at a specific time during a transient event such as the closing of a switch across a resonant circuit.

Any way here is what I found on one page of this lesson.

"the damped sinusoidal function is defined by,
f(t)=e^(-at) sin((2 pi f)+theta) for t > 0

(I spelled the greek letters out keyboard don't know greek)
 

Thread Starter

count_volta

Joined Feb 4, 2009
434
I decided to make my own inductor. 100 μH is far too small if I want to see real effects. I want it at least 20mH.

Can anyone link me to a thread or something which helps with that?

I will work on this project as long as it takes, by the end I should have good experience not only with RLC but transistors or op amps because the signal needs to be amplified. Its a good thing overall. ;)
 

hobbyist

Joined Aug 10, 2008
887
I decided to make my own inductor. 100 μH is far too small if I want to see real effects. I want it at least 20mH.

Can anyone link me to a thread or something which helps with that?

I will work on this project as long as it takes, by the end I should have good experience not only with RLC but transistors or op amps because the signal needs to be amplified. Its a good thing overall. ;)
KEEP UP THE GOOD WORK.
Working at it will introduce you to a lot of new learning experience.
Let us know how you make out with it.
 

Wendy

Joined Mar 24, 2008
21,848
Actually it doesn't matter, if the inductor is too small increase the size of the capacitor. The math works the same.
 

Thread Starter

count_volta

Joined Feb 4, 2009
434
Actually it doesn't matter, if the inductor is too small increase the size of the capacitor. The math works the same.
Yes I know that. The math and the physics. A small inductor would still take longer to charge a large capacitor and hence the period would be longer and frequency would be smaller. The largest capacitor I have is 1000μF or 1mF.

Actually doesn't the size of the capacitor and inductor only affect the frequency? And its ok if my frequency is high, so it will be a high pitched sound. Thats not a bad thing.
 

Wendy

Joined Mar 24, 2008
21,848
Frequency is all that's affected from your point of view. You need to select a pair that will resonate in the audible range. Bigger cap or bigger coil, the energy is the same.
 

Thread Starter

count_volta

Joined Feb 4, 2009
434
Oh it just hit me, can any signal produce a sound, not only a sinusoidal wave but even a square wave as long as its frequency is in the audible range?

I will probably learn about this in signal processing. It has to do with the Fourier series if I remember. Any periodic signal can be approximated by a cosine and sine of different values of k.
 

Wendy

Joined Mar 24, 2008
21,848
Yep, waveforms have different sounds, but the note is the same. I have a lot of experiments I'm writing for the experiments section of the AAC book. The AAC experiments section is a good read on its own merits.

Bill's Index

My Current Projects
 

Thread Starter

count_volta

Joined Feb 4, 2009
434
I just thought of something. No wonder I'm not getting oscillations, I used a polarized electrolytic capacitor. It doesn't work for AC, right?
 

Thread Starter

count_volta

Joined Feb 4, 2009
434
I just read most of volume 2. Especially the part about inductors, capacitors, and the tank circuit and resonant circuits. So interesting I couldn't stop reading. ;)

It didn't say anything about how long the oscillations will last in the electric pendulum circuit, but I think I'm starting to understand it. I will try to model it with spice and see what the resulting graph will be.

So to make this work I must use some sort of amp right? If I use an amplifier, the output signal of the amp will start at a higher value of voltage or current than with the battery alone, and hence take longer to die out. It will undo what the damping does. First of all, is this statement in bold correct?

But just how much do I need to amplify it in order to make the oscillations last for at least 1-2 seconds?

The op amp circuit that Bill_Marsden had before sounds like a good idea.

And also once again, is my polarized electrolytic capacitor preventing oscillations also? I used it because its big, but it blocks AC doesn't it?
 
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