Facebook
Google
GitHub
Linkedin
I've started a while ago trying to better understand electric fence energisers, both as a case to learn more about electronics and to perhaps build a portable one myself that could run off of 2 D cell batteries. It would only have to energise a single paddock for a horse to be used during trail-riding/camping.
I've seen some existing models available on the market that work off batteries (although often still at 6 - 12 V) that have a charge energy of 0.05J, so I figured this should be enough charge for such a small paddock as well. I've been able now to create a constant current boost converter that would be able to charge an 80uF capacitor to 40V in a little less then a second. This equates to about 0.06J which I figured should make for a decent enough shock.
The aim is to discharge this into the primary of a transformer, to step it up to 3 - 4kV and apply it to the fence. This is where it starts to become difficult, as I'm not sure what the required specifications would be for the transformer. Mainly: what core size is needed and how many turns would I need on the primary (I understand these are dependent on each other)?
I have learned that saturation of the magnetic core needs to be prevented and can find many formulas relating to this, derived from Faraday's law. What I've found is that:
\[ \epsilon = -N \frac{\delta \phi}{\delta t} \]
\( \epsilon \) = EMF
N = number of turns
\(\phi\) = flux
From this it is often derived, for an AC waveform on the primary, that:
\[ N_{min}=\frac{V}{4,44*f*B_{max}*A} \]
f = frequency
A = core area
However, this is based on the sine wave that is present in the AC waveform. The next thing I figured is perhaps to look at a square wave instead. For this I found a formula similar to the above:
\[ N_{min}=\frac{V}{2*\pi*f*B_{max}*A} \]
V = voltage
B = magnetic field strength
This seems more sensible, but I'm not sure that the "frequency" is of discharging a capacitor into the primary would be. I could look at the oscillation of the LCR circuit, but that doesn't intuitively make sense as the frequency component.
The next step I took is trying to derive a formula myself, based on Faraday's law and the fact that I know how the current through the primary would change if I applied th 40 volts. I've disregarded the decay of the voltage in this. We start at the equation for the magnetic field in a cored solenoid:
\[ B = \mu_0*\mu_r*n*I \]
n = number of turns per unit of length
I = current
The flux in the solenoid is then:
\[ \phi = N*B*A = \mu_0\mu_r*\frac{N*n*I*A}{l} \]
l = the length of the solenoid.
Then if we want to know the rate of change of this flux, we differentiate. Since the current is the only time dependent part, we get:
\[ \frac{\delta\phi}{\delta t} = \mu_0\mu_r*\frac{N*n*A}{l} \frac{\delta I}{\delta t} \]
We also know that the current in a coil changes according to:
\[ \frac{\delta I}{\delta t} = \frac{V}{L} \]
If we combine the above two, we get:
\[ \frac{\delta\phi}{\delta t} = \mu_0\mu_r*\frac{N*n*A}{l} \frac{V}{L} \]
If we combine this with Faraday's law, we get:
\[ \epsilon = -N \frac{\delta \phi}{\delta t} \]
\[ \frac{\delta\phi}{\delta t} = \frac{\epsilon}{N}=\mu_0\mu_r*\frac{N*n*A}{l} \frac{V}{L} \]
\[ \epsilon=\mu_0\mu_r*\frac{N^2*n*A}{l} \frac{V}{L} \]
I'm a little unsure on whether this is correct and, if it is, how to interpret this, though. The epsilon is often substituted for V in the derivations of Faraday's law, so if they're the same, then the whole equation becomes independent of V. I'd love to hear if I'm making some mistakes here and/or if I should be looking in a completely different direction for designing this transformer.
I know btw that there are designs for this using ignition coils and such, but my main aim is to learn and understand. Just pulsing an ignition coil doesn't get me the same amount of understanding.
I've seen some existing models available on the market that work off batteries (although often still at 6 - 12 V) that have a charge energy of 0.05J, so I figured this should be enough charge for such a small paddock as well. I've been able now to create a constant current boost converter that would be able to charge an 80uF capacitor to 40V in a little less then a second. This equates to about 0.06J which I figured should make for a decent enough shock.
The aim is to discharge this into the primary of a transformer, to step it up to 3 - 4kV and apply it to the fence. This is where it starts to become difficult, as I'm not sure what the required specifications would be for the transformer. Mainly: what core size is needed and how many turns would I need on the primary (I understand these are dependent on each other)?
I have learned that saturation of the magnetic core needs to be prevented and can find many formulas relating to this, derived from Faraday's law. What I've found is that:
\[ \epsilon = -N \frac{\delta \phi}{\delta t} \]
\( \epsilon \) = EMF
N = number of turns
\(\phi\) = flux
From this it is often derived, for an AC waveform on the primary, that:
\[ N_{min}=\frac{V}{4,44*f*B_{max}*A} \]
f = frequency
A = core area
However, this is based on the sine wave that is present in the AC waveform. The next thing I figured is perhaps to look at a square wave instead. For this I found a formula similar to the above:
\[ N_{min}=\frac{V}{2*\pi*f*B_{max}*A} \]
V = voltage
B = magnetic field strength
This seems more sensible, but I'm not sure that the "frequency" is of discharging a capacitor into the primary would be. I could look at the oscillation of the LCR circuit, but that doesn't intuitively make sense as the frequency component.
The next step I took is trying to derive a formula myself, based on Faraday's law and the fact that I know how the current through the primary would change if I applied th 40 volts. I've disregarded the decay of the voltage in this. We start at the equation for the magnetic field in a cored solenoid:
\[ B = \mu_0*\mu_r*n*I \]
n = number of turns per unit of length
I = current
The flux in the solenoid is then:
\[ \phi = N*B*A = \mu_0\mu_r*\frac{N*n*I*A}{l} \]
l = the length of the solenoid.
Then if we want to know the rate of change of this flux, we differentiate. Since the current is the only time dependent part, we get:
\[ \frac{\delta\phi}{\delta t} = \mu_0\mu_r*\frac{N*n*A}{l} \frac{\delta I}{\delta t} \]
We also know that the current in a coil changes according to:
\[ \frac{\delta I}{\delta t} = \frac{V}{L} \]
If we combine the above two, we get:
\[ \frac{\delta\phi}{\delta t} = \mu_0\mu_r*\frac{N*n*A}{l} \frac{V}{L} \]
If we combine this with Faraday's law, we get:
\[ \epsilon = -N \frac{\delta \phi}{\delta t} \]
\[ \frac{\delta\phi}{\delta t} = \frac{\epsilon}{N}=\mu_0\mu_r*\frac{N*n*A}{l} \frac{V}{L} \]
\[ \epsilon=\mu_0\mu_r*\frac{N^2*n*A}{l} \frac{V}{L} \]
I'm a little unsure on whether this is correct and, if it is, how to interpret this, though. The epsilon is often substituted for V in the derivations of Faraday's law, so if they're the same, then the whole equation becomes independent of V. I'd love to hear if I'm making some mistakes here and/or if I should be looking in a completely different direction for designing this transformer.
I know btw that there are designs for this using ignition coils and such, but my main aim is to learn and understand. Just pulsing an ignition coil doesn't get me the same amount of understanding.
