Introduction to Resonance

[Charlie_V]

The impedance the formula gives is what they call the characteristic impedance.  It is correct but with respect to the objects at hand.  The idea behind this is if you want to transmit power from one circuit to the other, you want their Zo (characteristic impedance) to match, and you get maximum real power transfer.  The more the Zo of one circuit mismatches the other circuit, then the more energy will go back and forth between circuits - aka the more oscillations you will have. 

As an example, if you could put a variable capacitor in parallel to your house's breaker box (where the power comes in from the pole) and start changing the capacitance, at some point your house's Zo will match perfectly with the Zo of the transmission line, but if you keep changing it, you can get it to a point where they are greatly mismatched and nothing in your house will turn on.  But the standing waves on the transmission line won't last long because the power companies have instruments that watch for standing waves and kill them whenever they start. 

With Tesla coils you want your primary and secondary circuit to be as greatly mismatched as possible.  There are also tricks like using an extra coil to help reduce damping that occurs when the secondary is near the primary inductor.  But all this is fine and dandy, I'm interested on how an oscillating load is useful?  If it just oscillates there and doesn't power anything in your house, what is the use?  Maybe I'm missing something?

[gotoluc]

Hi armagdn03,

I've been pulsing inductor for a while but always using square wave to trigger a transistor that pulses a DC source, since my Wavetek 234 has no real power output. On its own it can only light one LED at max output. I see that your signal generator is capable of lighting a 6 vdc flashlight bulb with sign wave. Can you or someone else please tell me what I have to do or get to be able to have a higher power output so I can do the same tests as you are doing.

Another thing I'm wondering about is, to achieve resonance in an inductor is it only possible to do it with a capacitor or is it possible to do it without one? I have noticed inductors without a capacitor have a certain frequency that the amplitude goes up. I have 2 air core inductors that at 1.64Mhz do this.

Thanks

Luc

[amigo]

Here's a page I liked that explains the impedance in relations to capacitors and inductors. I also like the two graphs of the resonance in relation to frequency and current at the bottom of the page, displaying the characteristics when LC are in series or parallel.

http://arts.ucsc.edu/EMS/Music/tech_background/Z/impedance.html

Also, regarding impedance, my understanding is that impedance is 0 at the resonance, not infinite as someone mentioned above. It has to be 0 because XL has to equal XC and in series circuit that happens when one goes to the other side of the = sign. In parallel circuit you are dividing by 0 (as XL = XC) so conditions are satisfied.

On that page right before the Transformer section it describes minimum current at resonance of parallel circuit due to two waves canceling out:

As the frequency rises, the inductor impedes, but the capacitor will take over. When the impedances of both match, you get no current flow. How is this possible?

It's because of the phase changes: the current through a capacitor is 90° ahead of the voltage, and the current through the inductor is 90° behind. When the circuit is in resonance, the two cancel out. In real circuits, series resistance tends to reduce the peaks. This is called damping, and the ratio of inductive reactance to resistance is known as Q (for quality factor).


@Charlie_V

You said that in Tesla coils, primary and secondary need to be mismatched as much as possible. Wouldn't that imply that the energy would be wasted in the primary trying to keep the oscillations going in the secondary which is out of tune?

[Charlie_V]

Also, regarding impedance, my understanding is that impedance is 0 at the resonance, not infinite as someone mentioned above. It has to be 0 because XL has to equal XC and in series circuit that happens when one goes to the other side of the = sign. In parallel circuit you are dividing by 0 (as XL = XC) so conditions are satisfied.

On that page right before the Transformer section it describes minimum current at resonance of parallel circuit due to two waves canceling out:

As the frequency rises, the inductor impedes, but the capacitor will take over. When the impedances of both match, you get no current flow. How is this possible?

It's because of the phase changes: the current through a capacitor is 90° ahead of the voltage, and the current through the inductor is 90° behind. When the circuit is in resonance, the two cancel out. In real circuits, series resistance tends to reduce the peaks. This is called damping, and the ratio of inductive reactance to resistance is known as Q (for quality factor).

I'm not sure I like this explanation.  It is wrong about getting no current flow when the impedances match, current DOES flow - always.  But there are two things going on here, the SELF inductance and capacitance make up the characteristic impedance (Zo) of a circuit.  At  resonance the self capacitance and the self inductance do cancel each other - current always flows regardless of resonance or not, but the circuit still has a characteristic impedance which is not zero.  Basically a single circuit with an inductor and a capacitor will have a frequency (resonance) in which the current and voltage will be IN PHASE with each other, for all other frequencies the voltage and current will be OUT OF PHASE.  When you have an IN PHASE case, you get maximum real power transfer through the circuit (since power is the voltage multiplied by current, when they are in phase you get the maximum value of the multiplication). 

Characteristic impedance (Zo) is only useful when you are trying to link two circuits together.  Because both circuits may share the same resonance, but REAL power will not be transmitted to the second circuit unless they both share the same characteristic impedance. 

Lets take an example: we have a radio transmitter - circuit 1.  And we have a power supply with "transmission line" aka the wires that you want to connect to the transmitter - this is circuit 2.  Now the radio has a characteristic impedance (meaning it has a capacitance and inductance based on its makeup - all electrical bodies do, whether they are really a capacitor/inductor or just a cable, transistor, etc.)  So the radio transmitter (circuit 1) has ONE frequency in which the current and voltage will be in phase, for all other frequencies it will be out of phase.  Circuit 2 (the transmission line) also has one frequency that only allows the current/voltage inphase case.  So in order to get the power from the power supply to the radio transmitter, you want both characteristic impedances to match Zo1 = Zo2.  So lets assume we did that.  Now with radio you want to "radiate" your power into the air (we'll call the air's impedance Zo3).  This means you want to make all the space/universe around us your load.  Well it turns out that space also has a characteristic impedance, this is 377 Ohms.  So if you want to radiate as much energy into space as your power source can supply, you want to make sure that Zo1=Zo2=Zo3. 

Now lets look at a Tesla coil for the reasons in the above threads.  We again have two circuits, our primary, and our secondary.  Each circuit has its own self capacitances and inductances.  And each one leads us to the characteristic impedances (Zo1 for the primary and Zo2 for the secondary).  Well, our purpose is the exact opposite to the radio transmitter above, instead of radiating our energy into space, we want to neutralize radiation and setup the strongest oscillations that we can - to send those oscillation through the ground connection (be it a wire or the earth or whatever the bottom terminal of the secondary is connected).  Well typically in Tesla coils, the primary is made of a relatively large capacitance and a pretty low inductance at some frequency determined by those two quantities.  The secondary is an inductor of much larger inductance with a capacitance (normally the toroid, sphere at the top with respect to ground) which is very low.  So the primary is maybe microfarad capacitor and microhenry inductor and the secondary is millihenry inductor and pecofarad capacitor, so Zo1 is usually very small and Zo2 is normally VERY big - we get maximum mismatch here so no REAL power flow.  BUT, the resonant frequency of the primary matches the secondary.  So both circuits will oscillate at the same frequency and slosh the power input to them back and forth between each other, developing very large oscillations - maximum REACTIVE power, but no real power. 

By now looking at the formulas posted on the website that armagdn03 gave, you should realize that a Tesla coil can be made into a radio transmitter very easily.  Make the capacitance in the primary match the capacitance in the secondary, and make the inductors in the two equal each other as well.  This will match Zo1 and Zo2 and the resonant frequencies of both circuits will be the same.  If you match those values with that of free space (377Ohm) you'll have yourself a good little radiator.  Tesla said he invented a knife, with a dull edge and a sharp edge, you can cut butter with both sides.  Unfortunately, mankind decided it was going to use the dull edge and completely ignore the sharp one!

You said that in Tesla coils, primary and secondary need to be mismatched as much as possible. Wouldn't that imply that the energy would be wasted in the primary trying to keep the oscillations going in the secondary which is out of tune?

I think my above rant explained this but to reiterate, the energy wasted in the system is wasted on the resistance in the wires.  Those are what damps the system.  Both secondary and primary are IN TUNE with each other, they both share the same resonant frequency, with their self capacitance and inductance canceled in each individual circuit (1 and 2), but their characteristic impedances are greatly different - so the energy is just sloshed back and forth between them.

@armagdn03
What I really want to know is how you can use a "load" that just oscillates.  A vibrating tuning fork may look pretty but what is it going to do?  How can we use it, how can we convert the energy to power our resistive loads WITHOUT damping the system.  That's the real trick I want to learn here.  I'm still very intent on finding out!!!

[amigo]

I'm not sure I like this explanation.  It is wrong about getting no current flow when the impedances match, current DOES flow - always.  But there are two things going on here, the SELF inductance and capacitance make up the characteristic impedance (Zo) of a circuit.  At  resonance the self capacitance and the self inductance do cancel each other - current always flows regardless of resonance or not, but the circuit still has a characteristic impedance which is not zero.

Yes you are right, I think the parallel resonance graph from the page I linked is much better as a depiction than its text. The graph shows that the dip is still above the X axis so there's current flowing, just minimal amount.

Tesla said he invented a knife, with a dull edge and a sharp edge, you can cut butter with both sides.  Unfortunately, mankind decided it was going to use the dull edge and completely ignore the sharp one!

Thank you for that quote, I got a good chuckle from it.

I think my above rant explained this but to reiterate, the energy wasted in the system is wasted on the resistance in the wires.  Those are what damps the system.  Both secondary and primary are IN TUNE with each other, they both share the same resonant frequency, with their self capacitance and inductance canceled in each individual circuit (1 and 2), but their characteristic impedances are greatly different - so the energy is just sloshed back and forth between them.

Sorry I didn't really read the above yet, I usually go backwards and when I see large posts I tend to go back and read them in one sitting with sufficient attention and focus so that I don't miss something important.

So basically if we had a superconductor we would have no resistance and there would be no end to oscillations, otherwise we have the Q factor due to resistance?

What I really want to know is how you can use a "load" that just oscillates.  A vibrating tuning fork may look pretty but what is it going to do?  How can we use it, how can we convert the energy to power our resistive loads WITHOUT damping the system.  That's the real trick I want to learn here.  I'm still very intent on finding out!!!

I thought we'd need another transformer there in the secondary circuit to actually hook up the load. Wasn't it all going through the ground in Tesla's case so you would tap the ground to get the good stuff and would not need another transformer ? I guess the other component were Longitudinal Waves which were instantaneous (propagating at c^2 iirc from Eric Dollard's lecture).