# RLC circuit question

#### count_volta

Joined Feb 4, 2009
435
Hi, I have just learned about phasor and laplace analysis of RLC circuits in my engineering course.

I am trying to use my knowledge to build an RLC oscillator in real life, and create a signal that will produce an electronic sound. I understand how an oscillator works. The resulting signal is something like A*cos(ωt+σ)e^-t

The ω tells you what the frequency will be of your decaying cosine.

I also understand that the smaller the capacitance and inductance of the capacitor and inductor, the larger the frequency ω will be, because it will take less time for the capacitor to charge and the inductor to build up a magnetic field. The larger the resistance, the bigger the damping is and the signal will die out faster.

Knowing all these things I began to search for components. I have many types of capacitors, but I went to radio shack to get an inductor. The best they had is a 100μH inductor. So I built my circuit on a breadboard.

The following circuit.

So then I closed the switch. Watched the voltage of the capacitor grow to 6 volts with my multimeter. Opened the switch and watched the voltage of the capacitor decrease. As soon as that happened, I would expect the inductor to recharge the capacitor and the oscillations to begin, but I didn't see the voltage of the capacitor increase again.

So I think whats wrong is, the inductor is so tiny that its mag field was built in microseconds, too fast for me to notice or even for the meter to pick up. Is this the reason? If not what else is wrong.

Another question.

Obviously I will need to amplify my signal with a BJT before I can input it into a speaker and hear the sound. Why is that? Why will the signal be so weak? I mean how strong does a current or voltage need to be for the sound to be loud enough? It probably depends on the resistance of the speaker somewhat.

Thank you.

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#### count_volta

Joined Feb 4, 2009
435
By the way I would also like to know where I can get a larger inductor. Say 500mH? Radio Shack doesn't have them.

And please don't forget my other questions in my previous post. I think this topic is interesting, so perhaps people with more experience than me can help. Thank you.

#### Wendy

Joined Mar 24, 2008
21,929
As to the inductors, you can roll your own without too much hassle. Search DIY Inductor on this site, or Google.

The circuit will damp quickly. Three or so cycles won't be audible exactly, which is why oscillators are used with tuned circuits, to stretch out the number of cycles our ears can pick up.

#### count_volta

Joined Feb 4, 2009
435
So a resistor of 40 ohms would be overdamped? Or maybe the internal resistance of the wire and inductor and capacitor?

And what are tuned circuits exactly. What do you mean? I began reading volume 2 of the ebook but have not seen anything about this yet.

#### Wendy

Joined Mar 24, 2008
21,929
I mean a simple tank circuit can not be heard. It damps too quickly. This is why we use oscillators.

Doesn't matter what resistor you use, it will damp too fast to hear. How are you planning on connecting the speaker to it? That will also speed up the damping.

Figure any event that is less than 100ms (.1 seconds) will be more like a click.

If the freqency is 200 Hz, and it goes for 10 cycles on the ring, this will be 50ms.

Don't confuse a tuned circuit with a bell, they are similar in some ways, but electronics is always much faster (which is good).

#### count_volta

Joined Feb 4, 2009
435
I guess the speaker will be in series. Perhaps after an amplifier. So how would you suggest I extend the length of the signal? These circuits are usually used for filters I know, but since its theoretically possible to hear them, I want to try.

You see the thing is, I just finished my sophomore year in the school of engineering (first year in EE program). RLC circuits are all that I really know well. We were introduced to transistors and op amps, but thats all.

So far we have not learned anything that will produce an interesting effect. It seems that all interesting things in electronics are done with transistors, but they can get very complicated and I don't know enough about them yet. Maybe enough to try and build an amplifier. All I want to try is to build something I already know well.

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#### Wendy

Joined Mar 24, 2008
21,929
You'll need electronics, define that as gain. Get rid of any resistance, use a parallel tank circuit, and have the amp as high an input impedance as possible. You might be able to hear the ring of a tank circuit then, but I wouldn't bet money on it.

Check out the article on Sound Synthesis from Wikipedia, it relates very closely to what you're trying to do.

http://en.wikipedia.org/wiki/Sound_synthesis

If you succeed it will sound almost exactly like a bell or a gong, since a tank circuit is the electrical equivalent of the same.

#### Wendy

Joined Mar 24, 2008
21,929
Think something like this...

The op amp will need a ± power supply, since the signal will swing ± .

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#### count_volta

Joined Feb 4, 2009
435
I'm afraid to get rid of the resistor altogether because then the current through the circuit will be too high.

I tried attaching my 6 volts to the inductor for that reason to test, and it got dangerously hot.

Can I use a BJT instead of the op amp?

#### Wendy

Joined Mar 24, 2008
21,929
Yes, a high impedance BJT circuit would work, but not as well. And the switch I showed would get rid of your heat issue, the cap stores a charge, then rings when the switch is toggled.

#### count_volta

Joined Feb 4, 2009
435
OK I will try. I have an op amp chip.

Sighs. Goes back to Microelectronic circuits by Sedra Smith to the section on op amps.

Thank You.

#### Wendy

Joined Mar 24, 2008
21,929
Any op amp will work (though I expect to hear from some of our other members on this), even a 741.

#### Ratch

Joined Mar 20, 2007
1,070
count_volta,

So a resistor of 40 ohms would be overdamped? Or maybe the internal resistance of the wire and inductor and capacitor?
I plotted your circuit, and it shows no oscillation at 40 ohms and a complete energy discharge in 0.1 sec. A resistance of 0.1 ohms shows a oscillation of about 7 cycles starting with a 7 amp current and an exponential dampening down to zero energy in about 0.01 sec.

Your resonant frequency is 734 Hz and its period is .00136 sec.

Ratch

#### count_volta

Joined Feb 4, 2009
435
What value of inductor and capacitor would you recommend? As I said I bought a 100μH for \$1.30 from Radio Shack. They don't have anything larger.

I have various capacitors of different values. The tiny inductor is probably making the signal last microseconds.

#### Wendy

Joined Mar 24, 2008
21,929
Series LC generally don't oscillate, which is why I went with the tank circuit.

You will find the size of the inductor won't make much difference. The Q of the circuit is what is important, and resistance is the major facter reducing the Q. Basically this is what I've been trying to explain.

#### count_volta

Joined Feb 4, 2009
435
Q is the quality factor? We learned about that when we went over filters. And why wouldn't series LC oscillate? I don't understand the physical reason for this. The inductor recharges the capacitor, which recharges the inductor and so on until resistance causes it to stop.

#### hobbyist

Joined Aug 10, 2008
887
Q is the quality factor? We learned about that when we went over filters. And why wouldn't series LC oscillate? I don't understand the physical reason for this. The inductor recharges the capacitor, which recharges the inductor and so on until resistance causes it to stop.
In theory yes, but when you use real world components. things could change dramatically, it is the inherent component tolerances and other factors that need to be studied, and compensated for, so as to make a working circuit.

You are on the right track for learning,
by doing hands on experiments, you can seperate the theory from the practical, and learn the ins and outs of components such as there behavior under certain conditions, then using the knowledge gained from learning the theories, you can design into these circuits ways of compensating for the inherent shortcomings of these components.

#### count_volta

Joined Feb 4, 2009
435
Ok cool. So what real life phenomenon prevents series LC circuits from oscillating?

Lets think about what series means. In series resistances add. In series the current is the same in all elements.

So is it because the resistance of the inductor and capacitor add in series, the damping is still too large and hence the oscillations don't last long?

#### Ratch

Joined Mar 20, 2007
1,070
count_volta,

Ok cool. So what real life phenomenon prevents series LC circuits from oscillating?
Loss of energy

Lets think about what series means. In series resistances add. In series the current is the same in all elements.
Yes, let's think about it. At the resonant frequency, the capacitive and inductive reactance is 0.46 ohms. The resistor is 40 ohms for a Q of around 1/100. Which component is going to hog the most energy and never return it to the system? At a resistance of 0.1 ohms, we have a Q of about 4.6. The circuit oscillates, but at a peak voltage of 6 volts, the resistor is dissipating energy at a rate of E^2/R or 36/0.1 or 360 watts while at this voltage. How long do you think the system energy is going to last at that rate? My plot shows about 7 cycles.

So is it because the resistance of the inductor and capacitor add in series, the damping is still too large and hence the oscillations don't last long?
Resistance is the enemy of oscillation because it dissipates energy instead of storing it. Free oscillation depends of reducing all energy loss. If lost, it must be replace by a active element (OP amp, transistor, etc). Oscillation is the cyclic transfer of energy with a minimum of loss. Energy is the key to understanding oscillation.

Ratch