Series resonant circuit help

[chadj2]

Hi I am new to the forum. I have been studying and recently doing experiments with (LC) series resonant circuits at home. I have been referencing numerous electrical engineering books for information on series resonance, but unfortunately I have been unable to find any books that break the phenomenon down to the most basic level as to what is really going on in a series resonant circuit to reduce impedance to to zero. I have seen the vectors and the math but that really doesn't explain to me how for example the capacitor is able to interefere with the inductor's ability to control current rise in itself. All I can do is theorize that the capacitor's voltage rises at the same rate as the inductor's reactive voltage which results in no voltage drop across the the LC network. If anyone has had it explained to them or understands it more deeply and is willing to share the information please respond.

Thanks

 

[chadj2]

Like I said before I didn't mean to open a can of worms. I was just hoping to get a deeper understanding of series resonance which went into the precise interactions between the capacitor in inductor. Of course I can pass a test on what it is and the math problems concerning it. I just wanted to find out more. Right now I am referencing some old EE books from the 1940s and 1950s hoping to find more indepth coverage of the subject.

 

[Skogsgurra]

Fair enough.

But it is very simple, actually. You just have to forget about those pulses. They have very little to do with an AC circuit (except that they are a special case of the transient solution to the differential equations describing a series resonant circuit). But that, you have to leave for a little later, when you have undserstood the steady state AC solution.

So, here goes:

You have an inductor and a capacitor connected in series. Fed from an AC voltage source. Right?

There is a current flowing through this circuit. An AC current of a certain amperage. Say I amps. Right?

Now (vector diagram needed) draw one thick arrow from a point from center of a paper to the right. Make it about four inches (ten cm) long. This represents the current. Let's say it is 4 amperes.

As you know. Voltage across an inductor leads current by 90 degrees. Right? Then draw a new arrow pointing from center of paper (where current arrow starts) vertically upwards. Done?

This arrow represents the voltage across the inductor. The phase rotation in a vector diagram is always CCW. So, a leading vector is drawn 90 degrees CCW from the reference vector (the current arrow).

Now. You have half the picture. Any questions? Yes? Ah! If these arrows represent amplitude or RMS? Good question. Well, lets say for now that they represent amplitudes. More on that later.

Look at the circuit diagram. You have two elements (inductor and capacitor) in series. Voltages across the two elements sum (just like the voltage of two batteries sum). So, now you have to add the capacitor voltage to the inductor voltage. In other words, draw a new arrow (representing capacitor voltage) from the inductor voltage arrow tip.

Just one little step left for you now. Are you OK so far? Good.

As you already know (see, you actually knew all these things already!) the capacitor voltage lags the current. So, the capacitor voltage arrow shall be pointing downwards, parallel to the inductive voltage, but in opposite direction. Do that! Yes! from the top of the inductor voltage downwards.

Yes, that means going back towards where it all started.

How long? That depends. Let's say about half-way down the inductor voltage arrow.

Now, when you look at this diagram, you see a reference arrow going to the right, a voltage arrow going up and another voltage arrow going down. The sum of the voltage arrows is the distance from starting point to the tip of the down-pointing arrow. Got it? Good. What's that you said? Yes, right. This is the voltage across the circuit.

Now, resonance. That is when you have equal impedance in inductor and capacitor. Yes, same voltage drop across capacitor as across inductor. BUT DIFFERENT DIRECTIONS!

So, if you make the capacitor voltage longer. Same length as inductor voltage. What do you get? What? Nothing? Oh, yes. You mean there's no distance left between starting point and tip of capacitor voltage? Yes, that's right! No voltage across the circuit!

That is what resonance is about. Current but no voltage, Z = U/I so you have also zero impedance. Got it?

It wasn't that hard. Was it?

This is essentially what the text-books say. Only with fewer words.



There may be quite a few typos in this. I didn't have energy left to proof-read it.


Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[waross]

Look up the formulas for inductive reactance and capacitive reactance. You will see that one of the terms in both equations is frequency. A sign wave is assumed.

A resonant circuit is not universally resonant. It is only resonant at one frequency.
You may get interesting results by pulsing an L/C circuit with DC, but resonance is unlikely without a lot of math, or a little bit of trial and error.
And, by the way, the DC must reverse polarity on every pulse or the capacitor will charge and the current will stop.
respectfully.

 

[chadj2]

Skogsgurra,

Thank you for taking the time to write that explanation. It helped clarify some more things to me. I guess my big problem is that I wanted to understand how resonance occurs with a waveform resembling pulsating DC or such. As I stated before I am not an electrical engineer. My degree is in aeronautics I am actually a pilot by trade. As waross stated I was able to get parallel resonance with pulsating DC with a tiny bit of trial and error, meaning I calculated the resonance frequency and just adjusted the function generator a bit to get maximum impedance. The only difference I noticed from having an AC signal was the amplitude on the negative side was a bit lower than the positive side. When I started observing some series resonance circuits I built I was intrigued with the voltage amplification I was seeing on my scope which occurs across each component but as you stated add to zero for the total LC. I probably should have said this is not work related I just enjoy experiments with power electronics in my free time. I guess in this age of TV and video games experimenting with resonant circuits with different waveforms for fun is strange. I can understand why a lot of EE's do not like to mess with or think about this stuff when not doing it for work. I don't really like talking about flying or doing traveling during my free time either. Once again thank you for helping me get a more indepth understanding of this topic.

 

[chadj2]

P.S. I have been reading that Tesla did a lot of work on resonant circuits so I will study some of his writings.

 

[geekEE]

chad, if you're going to use square waves, you can simply consider them to be the sum of a series of sine waves (look up Fourier transform) and all of the above explanations still hold.

waross, I think the pulsating DC does not have to reverse polarity. It's all a matter of what you take to be your reference voltage (GND). You can build a filter with a positive and negative supply, or you can build it with a single supply. The only difference is that you'll have an offset with respect to ground on the single supply version.

 

[waross]

Hi geekEE;
I saw a reference to "Pulses of DC".
To me a series of pulses means an applied voltage followed by an open circuit. However from rereading the thread it appears that the OP is using a function generator which does not go open circuit but switches between two defined voltage levels (one of which may be zero).
In this case I have to agree with you.
Although the voltage does not have to reverse, I believe that the current must reverse.
respectfully

 

[Skogsgurra]

chadj,

You have to get your definitions straight. In this discipline (electric engineering) there are quite a few understood things. Like this resonance thing. It is always about sine waves (yes, sine - not sign). Square waves or whatever you are applying to your circuit are not sine waves. So you had better get hold of a simple function generator (or signal generator) and switch to sine output. Then, get an oscilloscope, then start your experimenting from there.

Applying pulses to a circuit is also a very valid and interesting excercise. But the resulting waves are a little more complex to analyze and understand. Do not expect to get a good and solid understanding of these matters without taking a formal course. It is possible, of course, for very gifted and talanted individuals to derive all these things all by themselves. If you are one of those individuals, go on. By all means. But building on knowledge that is commonly available is more practical and acquiring that knowledge is usually best done in schools.

Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[OperaHouse]

I have a little fun application. Years ago I picked up a bunch of nice German 220V muffin fans. When I put the right cap in series with one, it gives me about 180V on the motor winding. Just the speed for nice quiet operation. A novel way to generate a higher voltage from 120V easily.

 

[Skogsgurra]

Another "Free Energy" patent coming up? ;-)

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[itsmoked]

Just put one fan in front of the other and you can "harvest" all that wind!!

Keith Cress
Flamin Systems, Inc.-

http://www.flaminsystems.com

 

[OperaHouse]

When I was just a little sprout I put a capacitor in series with a 120V power transformer. I wanted to reduce the output and capacitors resist the flow of AC. The transformer went up in smoke. Lessons like that stick with you. All this low voltage stuff isn't as much fun. You just don't have the same impact looking at a scope.

Wisdom comes from knowledge.
Knowledge comes from experience.
Experience comes from bad decisions.

 

[waross]

That's ingenious Operahouse.
I once considered using a capacitor to run a DC relay on AC. When I went looking for components I found an AC relay before I found an appropriate capacitor so I didn't complete the experiment.
respectfully

 

[LionelHutz]

I'd be with waross. To me, applying a pulse means that there is a DC source available and the DC is applied to the circuit with a momentarily closed switch.

An FFT of the result when a pulse is applied is usually more telling than just looking at the waveform on a scope.