Greetings, colleagues. Once I made the movie about the standing waves in the transformer Tesla, but I noticed it is absent on this channel.
Therefore, I consider it necessary to fill this gap and talk about this interesting topic.
The most frequently asked question on the Internet - whether Tesla coil to produce more power than it consumes. The answer - definitely NO. Whatever load you have connected to the output winding, how would you have agreed it, the output power of Tesla transformer is always less than consumed. No exception in the history of this instrument was. Consequently, the efficiency of the transformer is within the unit.
Another thing - the voltage gain. Transformer Tesla - one of the best devices for EHV. Many see this as even a paradox, because the resulting voltage is more than obvious calculation based only on the transformation ratio.
The point is that the transformation ratio - is just one of the factors of increasing voltage in the Tesla transformer.
Let us look at all the phenomena, thanks to which Tesla transformer manages to reach unimaginable increase in voltage.
1. The first of these we have named - is the transformation ratio.
We will not dwell on it, I think we all know that the transformation ratio is the ratio of the number of turns of the winding
k = U1 / U2 = w1 / w2
2. The second point is much more interesting.
RESONANCE.
The primary winding of the transformer Tesla is part of the oscillating circuit.
The amplitude of the current in the resonant circuit the Q (quality factor) times greater than the amplitude of the current supply circuit.
Then, an oscillation circuit generates a magnetic field Q times larger than the coil without resonance binding
. An increase in the amplitude of the alternating magnetic field will cause an increase in EMF in the secondary winding.
Thus, due to the resonance achieved an even greater increase in the voltage at the output of the Tesla transformer.
And one more thing: the secondary winding - it is also an oscillating circuit.
Winding itself - is the circuit inductance and capacitance is at the top of the coil (top cover) and the earth - the lower side.
If the frequencies of the primary and secondary circuit coincide, the amplitude increases not only Q1 times, but also Q2.
3. And now, the most interesting and probably the most important.
Secodary coil as a long line.
Long line - a conductor, the geometric dimensions of which are comparable with the wavelength of oscillation.
Tesla coil secondary wire is a long line.
In a long line is possible such a phenomenon as the superposition of direct and reflected waves.
In the picture you can see a secondary winding of the transformer, as well as the image of the direct and reflected waves moving in the wire, which is wound the secondary winding.
Direct wave - this oscillation induced in the secondary circuit from the primary.
Direct wave moves from the lower to the upper end of the winding.
When the direct wave reaches the end of the secondary winding wire, it is reflected.
The reflected wave continues its movement downward.
This results in the imposition of direct and reflected waves.
At certain points we get the maximum amplitude - antinodes, and between them - minima or nodes.
In the picture for ease of perception of the wavelength is shown smaller than the length of wire, many wavelengths are placed in the coil.
In reality, the wavelength is usually greater than the length of wire, but the process of adding the direct and reflected waves is not affected.
When the direct and reflected waves are added in the phase a maximum amplitude (or antinode) is formed,
when added in the opposite phase - the minimum (or node).
The best result is achieved when the wire length is ¼ wavelength fluctuations.
Then it is a classic case of a standing wave.
Also suitable length of wire equal to 3/4, 5/4, and any odd number of quarter wavelength.
But rationally, of course, to use one quarter.
When the wire length is equal to ¼ wavelength at the upper end of the winding, we obtain maximum voltage at a minimum current.
And at the grounded end - maximum current at low voltage.
How many times can the voltage be increased due to the addition of direct and reflected waves?
And here is the fun part!
The amplitude of the oscillation can be increased exactly as many times as the direct and reflected waves summarized.
For example, if the oscillation frequency is 1 MHz, and discharge frequency is 1 kHz, before each discharge the wave is summarized 1000 times.
And we get a thousandfold increase in voltage due to the addition of the waves.
Let's calculate what should be the length of the wire of the secondary winding at a frequency of 1 MHz for example, to accurately hit a quarter wave.
Wavelength is λ = c / F.
Since we need a quarter wave length of the wire should reach l = λ / 4 = c / 4F = 3 * 10 ^ 8/4 * 10 ^ 6 = 75 (meters).
Only 75 meters.
The length of the wire coil is quite small.
What happens if we overdo and wound more than a quarter of the wavelength?
The image shows the degenerate case when the length of the wire of the secondary winding is 2/4 wavelength.
In this case, when the length of the waveguide is an even number of quarter-wavelength, waves are added in antiphase, and the output voltage of the coil will tend to zero.
Avoid such cases.
Strive to ensure that the secondary winding has been set up simultaneously as the oscillation circuit in resonance with the primary circuit and as a quarter-wave vibrator at the same frequency.
Then you get a significant voltage gain.
Now let's calculate exactly what the output voltage of Tesla coil we can get with given parameters:
Input voltage Ui = 100 V, The Q-factor of the primary circuit Q1 = 20, Magnetic coupling coefficient k = 0.5, The Q-factor of the secondary circuit Q2 = 5 Coefficient of superposition of waves = 1000 (it is almost the same as SWR) We accept that the system is set up perfectly - frequencies are equal. F1 = F2 = Fres, --- Find Vout
Solution Vout = Vin * Q1 * k * Q2 * КНВ= 100 * 20 * 0.5 * 5 * 1000 = 5000000 Volt
Thus, a small Tesla coil with a good setting may produse several million volts at supply voltage of one hundred volts.
These are the figures we get in practice, when we manage to set up good circuits.
Let's summarize.
What advice we can give on setting up Tesla transformer.
1. Firstly, we approximate the natural frequencies of the primary and secondary circuits.
Adjust the frequency of the primary circuit by selection of capacity and configuration of the winding inductance.
The frequency of the secondary circuit can be changed by increasing or decreasing solitary capacitance at the top of the structure.
When setting the frequency of the secondary winding also consider the capacity of the coil.
2. Secondly, choose the desired length of the wire of the secondary.
Try to be equal to ¼ wavelength of the oscillations, but not longer.
On this, perhaps, will be brief.
Let me remind you that everybody can download video lectures "Electricity" by clicking on this link or on the link in the description.
If you have questions about today's video, you can ask them in the comments, I will try to answer.
I wish you a successful New Year.
Best regards Timur Garanin