Fringe Experiments With VTA Style POCs

Hey Marcel,

My Friend, you are absolutely spot on on everything!

I have worked with a lot of different people over the years, you are definitely in the top ten best researchers I have worked with! You are very good at studding, putting the dots together and making sense of the topic and then making this work on the bench! Well done My Friend!

We have covered before, but again may be somewhat useful:

There's a fundamental relationship between the number of turns on a coil (N), the current flowing through them (I), and the core reluctance ($\mathcal{R}$) that determines the magnetic field, or magnetic flux density (B), inside the core. This is the core principle behind the design of electromagnets and inductors.

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🧲 Relationship Between Parameters

The relationship is governed by the magnetic circuit equivalent of Ohm's Law, often called Hopkinson's Law:

$$\mathcal{F} = \Phi \mathcal{R}$$

Where:

• $\mathcal{F}$ is the Magnetomotive Force (MMF), the driving force for magnetic flux.
• $\Phi$ is the Magnetic Flux (in Webers, Wb), which is the total "gated" magnetic field.
• $\mathcal{R}$ is the Magnetic Reluctance (in Ampere-turns per Weber, At/Wb), which represents the opposition to the magnetic flux.

 

1. Magnetomotive Force ($\mathcal{F}$)

The MMF is directly determined by the coil design and current:

$$\mathcal{F} = N I$$

($N$ is the number of turns, $I$ is the current in Amperes, and $\mathcal{F}$ is in Ampere-turns, At).

 

2. Magnetic Flux ($\Phi$) and Flux Density ($B$)

The total magnetic flux ($\Phi$) is the magnetic flux density ($B$) multiplied by the core's cross-sectional area ($A$):

$$\Phi = B A$$

($B$ is in Tesla, T, or Weber per square meter ($\text{Wb}/\text{m}^2$). 800 Gauss = 0.08 Tesla).

 

3. Magnetic Reluctance ($\mathcal{R}$)

The reluctance of a uniform magnetic path (like a core) is determined by its geometry and material:

$$\mathcal{R} = \frac{l}{\mu A} = \frac{l}{\mu_r \mu_0 A}$$

• $l$ is the mean length of the magnetic path (m).
• $A$ is the cross-sectional area ($\text{m}^2$).
• $\mu$ is the absolute permeability of the core material (H/m).
• $\mu_0$ is the permeability of free space ($\approx 4\pi \times 10^{-7} \text{H/m}$).
• $\mu_r$ is the relative permeability of the core material (dimensionless). Silicon steel has a high $\mu_r$ (typically in the thousands, but it varies non-linearly with $B$).

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📐 Coil Design Calculation Example

To "gate" (or establish) a magnetic flux density of 800 Gauss ($0.08 \text{ T}$) in your laminated Silicon Steel core, you can combine the equations above to solve for the required Ampere-Turns ($NI$).

$$\mathcal{F} = \Phi \mathcal{R}$$ $$N I = (B A) \left(\frac{l}{\mu_r \mu_0 A}\right)$$

Notice that the cross-sectional area ($A$) cancels out in the ideal case of a closed core with a uniform field:

$$N I = \frac{B l}{\mu_r \mu_0}$$

 

Step-by-Step Calculation

1. Define Target Flux Density ($B$):

$$B = 800 \text{ Gauss} = \mathbf{0.08} \text{ Tesla (T)}$$

2. Determine Core Geometry:

• Cross-Sectional Area ($A$): $10 \text{ cm} \times 4 \text{ cm} = 40 \text{ cm}^2 = \mathbf{0.004} \text{ m}^2$. (This is needed if the $A$ didn't cancel out, or for a more rigorous calculation, or for the core loss calculation).
• Mean Magnetic Path Length ($l$): This requires knowing the overall shape of the laminated core (e.g., E-core, toroid, simple rectangle). You must estimate this length (e.g., $l$ could be $\approx 2 \times (10 \text{ cm} + 4 \text{ cm}) = 28 \text{ cm}$ for a simple rectangular loop, or more depending on the geometry of the winding leg). Let's assume $l = 0.3 \text{ m}$ for this example.

3. Determine Relative Permeability ($\mu_r$):

• For Silicon Steel, $\mu_r$ is highly variable and non-linear. You need the **magnetization curve (B-H curve)** for the specific grade of laminated silicon steel at $B=0.08 \text{ T}$.
• As an approximation, let's assume a typical high $\mu_r$ value of $\mu_r \approx 4000$ at this flux density.

4. Calculate Required Ampere-Turns ($NI$):

Use $\mu_0 = 4\pi \times 10^{-7} \text{ H/m}$.

$$N I = \frac{0.08 \text{ T} \times 0.3 \text{ m}}{4000 \times (4\pi \times 10^{-7} \text{ H/m})}$$ $$N I \approx \frac{0.024}{0.0050265} \approx \mathbf{4.77} \text{ Ampere-Turns (At)}$$

 

5. Design the Coil

Once you have the required $NI$, you can choose a suitable combination of turns ($N$) and current ($I$):

• Option 1 (Few turns, High current): $N=10$ turns, $I = 4.77/10 \approx \mathbf{0.477} \text{ A}$.
• Option 2 (Many turns, Low current): $N=50$ turns, $I = 4.77/50 \approx \mathbf{0.095} \text{ A}$.

Your choice will depend on:

1. Available power supply voltage and current.
2. Maximum allowable coil resistance (to limit power loss and heating, $P = I^2 R$).
3. Winding space available on the core.

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Key Considerations

• Non-Linearity: The biggest challenge is that **$\mu_r$ is not constant**; it changes with $B$. For accurate design, you must use the B-H curve for your material to find the **Magnetic Field Strength ($H$)** corresponding to your target $B=0.08 \text{ T}$. Then, the required MMF is $\mathcal{F} = H l$, where $H$ is in $\text{At/m}$. $$\mathbf{N I = H l}$$
• Air Gaps: If there is any air gap in the core assembly, its reluctance ($\mathcal{R}_{\text{air}} = l_{\text{air}} / (\mu_0 A)$) will be much higher than the core's reluctance and will **dominate the total required MMF**. A rigorous design must include the reluctance of both the steel and the air gap(s).
• Gating: Your term "gating" often implies a control mechanism, possibly involving **saturation** (where $\mu_r$ drops sharply) or a **flux-gate** configuration, which would require a different, more complex analysis involving two or more windings. The calculation above provides the basic $NI$ to achieve the desired $B$.

I want to ask you one thing at the moment, please keep this experiment as is, don't change it, and keep coming back to this experiment, make sure you don't change anything! It may be a week, or a month, maybe even six months, but you will see why I said this later on.

The effect: "Amplitude Increase", please study this, its very important as we have been through a few times. This is linked directly to the VTA Internal Working and how and what's required to move forward! "Amplitude Increase" is linked to NI, the Ampere Turns and the statement by Walt Rosenthal:

The VTA "likes" to always see a minimum load of 25 watts.

You should be very proud of yourself, of all the researchers I have seen, and the ones I haven't, I am going to say, you are the closest to having the VTA Replication completed, than any other researcher, ever!

The fact that we, here at above unity dot com, can work together, towards a common goal, without the negative, silly, jealous, bickering, that floods the other forums, means we have another Huge Feather in our cap, an advantage that they could never appreciate because of their Neanderthal Brain power, and approach. Here we show the proof, that Humanity can be better, if given the chance, and not infiltrated by Neanderthal Shills!

Well Done My Friend!

   Chris