N87 core for a project

[Neukyhm]

Hi forum, I need advice with this. I have to choose a ferrite core for the following transformer:

Air gap: 1.5mm (this means an Ae=381nH for ETD59 N87)
Primary: 3+3 turns
Secondary: 250 turns (for ~4kv output)
Desirable power: 150-200w
Freq: 320kHz (I know, it's high, but it's the only way I know to reduce primary current below core saturation)
Magnetic flux density caused by primary: ~220mT

I think that I could use a ETD59 N87 core from Epcos, but I'm not sure how to read the part of the datasheet that talks about core losses.

Here you have the core datasheet and N87 material datasheet:

http://docs-europe.electrocomponents.com/webdocs/13c0/0900766b813c0f43.pdf

https://en.tdk.eu/download/528882/325211356745925075927e79bdc2b163/pdf-n87.pdf

Thank you in advance.

Edit: I forgot to say: this machine is intended to run for a few seconds every few minutes only.

[orolo]

I'm not very experienced, so take this with a grain of salt until someone really knowledgeable comes around.

First, a sanity check:

Starting with the core datasheet. The datasheet claims less than 5.2 Watts of core loss at 100mT, 100kHz, 100ºC.

Turning to the material datasheet, relative core losses vs frequency graph (pag. 5/17), it is claimed that for 100kHz, 100mT, 100ºC, the material has core loss equal to about 100kW/m^3. Since the core has a volume of 51200mm^3 = 5.12e-5 m^3, we would expect 100e3*5.12e-5  = 5.12 Watts core loss. It indeed falls within tolerance. Let's call this a pass in the sanity check.

Now, for your operating conditions:

Now, turning again to the relative core losses vs frequency graph. For about 300kHz, 200mT, 100ºC, it is near 2300kW/m3, and at the limit of the plotted data. So the losses expected are 2300e3 * 5.12e-5 = 117.76 Watts. At 25ºC the relative power is more like 3000kW/m3, so the power would be around 150W.

It looks like a lot of power to me.

[Neukyhm]

It looks like a lot of power to me.

Yeah, It's a lot. The problem here is frequency. The power supply that will use that transformer is a DC-DC converter 48V to 4kV driven by a regular ZVS board with a 10nF capacitor. Frequency will be high because the capacitor and current in primary will be below saturation.

Maybe I should consider running the ZVS with 12-24V with usual 0.33uF capacitor, frequency will be much lower, current in primary may exceed saturation and I would have to add more turns to secondary coil.

If you guys had to design a ZVS driven 4kV PSU, what would you do?

[Neukyhm]

Hey what if I just use air as core, no hysteresis, no saturation, whatever frequency I want. Right now I would like to be an electric engineer, but I'm a physicist.

[orolo]

In this blog entry there is a project similar to yours, but with less power. If you use air cores, the size of the inductors will increase, the coupling will be worse, and the magnetic field won't be as confined as with a core.  On the other hand, it won't saturate, you can use whatever wire gauge, and you can compute the inductance and coupling from first principles.
Here you have a very good calculator for air core coils. To get about 13uH for your primary, you would need a coil of 10cm diameter with 10 turns, and a length of 2.5cm; not that big, after all. The series resistance is 0.12 ohms. Then you'd need about 420 turns for your secondary.

[Neukyhm]

What I don't really understand is why the core datasheet says one thing and material datasheet says a different thing.

[orolo]

What I don't really understand is why the core datasheet says one thing and material datasheet says a different thing.

Where do the datasheets disagree?

[Neukyhm]

What I don't really understand is why the core datasheet says one thing and material datasheet says a different thing.

Where do the datasheets disagree?

In core losses? I think.

I have simulated the entire circuit (remember it's a ZVS) and I have a large current on primary, like 5A at 300kHz. Being the primary 3.45u+3.45u inductors, magnetic flux is high but below saturation.

[Neukyhm]

Maybe I'm calculating something wrong. Let's say you have an inductor of N turns, and a gapped ferrite core with a known AL value and a saturation of 300mT, how do you calculate the maximum current across the inductor?

[orolo]

The core losses agree for both datasheets: about 5.2W for 100mT, 100kHz. But the core datasheet says nothing about the material at 200mT, 300kHz, so there you need to use the material information. First check both datasheets agree for a known datapoint, then extrapolate to your working conditions.

In this third datasheet you have the formulae for inductance and magnetizing current. Let us work at 25ºC, and define k1= 508.0, k2=-0.708, k3=812.0, k4=-0.796.

For a coil of N=100 turns:

The \$A_L\$ value for a gap \$s\$ is:  \$\displaystyle A_L\ = \ k_1\,s^{k2}\$
And the DC current \$I_{DC}\$ at which \$A_{L}\$  drops by 10%, marking the onset of saturation, is given by: \$I_{DC} \ = \  \displaystyle\left(\frac{0.9\cdot A_{L}}{k_3}\right)^{1/k_4}\$

So, let us assume you have a gap of s=1.5mm. Then, AL = (1.5**-0.708)*508.0 = 381, which exactly agrees with the datasheet.
Then, the magnetizing current for saturation is: Idc = (0.9*381.0/812.0)**(1.0/-0.796) = 2.95 A, near 3A.

Now, these formulas are for N=100 turns. If you want 3.45uH in each winding, since \$L = A_{L}\cdot N^2\$, then \$N =\displaystyle \sqrt{L/A_{L}}\$ (in nanohenries!), so N = sqrt(3450.0/381) = 3, ok.

I think that in your circuit the 3+3=6 turns work as a single inductor, so the DC current for 10% saturation at 25ºC should be 2.95*100/6 = 49 A. I think you are safe enough at 5A max.

Be warned, though, that I'm neither an EE, but a mathematician.

[Neukyhm]

So, maybe everything was fine after all. See the circuit and current vs time, the circuit is intended to be a 60kV power supply, using voltage multiplier. Current peaks are stable but very high (+20A) so I thought that the core would saturate, but if formulas agree that saturation current is far bigger then good.

So, if saturation current is that big, then I can use a bigger capacitor, so I can lower frequency below 100kHz.

Thank very much orolo, you have helped a lot.

[T3sl4co1l]

I doubt you'll get that high frequency, at that number of turns.  A resonant or quasi-resonant controller may be very helpful.

Tim

[Neukyhm]

I doubt you'll get that high frequency, at that number of turns.  A resonant or quasi-resonant controller may be very helpful.

Tim

I knew that it would be difficult to reach that frequency, but now I can leave the capacitor to usual value (0.6u) because primary current (although big) will not saturate the core.

I have updated parameters in Orcad and frequency is now 50kHz, with 3+3 turns primary and 36 peak amps across it. I will use the ETD59 core with 1.5mm gap.

48V is a big voltage to run a ZVS, but if I drive the MOSFETs gates with another 12V PSU, I think everything will be fine.

[orolo]

About your simulation: I think the choke L4 is not meant to be coupled. Also, shouldn't the inductors be 3.45uH each, instead of 6.858u? Also, the diodes going from the gates are ideal/generic? If that is the case, perhaps you should use an ultrafast model, like UF4001. I've simulated the circuit in LTSpice, and with 12 Ohm resistors it wouldn't start oscillating. Replacing them with 470 ohms ones did the trick.

After replacing the resistors (not the inductances), the oscillation frequency was about 40kHz and the peak current 20Amp, as in your case.

[Neukyhm]

About your simulation: I think the choke L4 is not meant to be coupled. Also, shouldn't the inductors be 3.45uH each, instead of 6.858u? Also, the diodes going from the gates are ideal/generic? If that is the case, perhaps you should use an ultrafast model, like UF4001. I've simulated the circuit in LTSpice, and with 12 Ohm resistors it wouldn't start oscillating. Replacing them with 470 ohms ones did the trick.

After replacing the resistors (not the inductances), the oscillation frequency was about 40kHz and the peak current 20Amp, as in your case.

Yes, the inductor L4 is not coupled, it's the usual inductor in any ZVS to limit current. The 12 ohms resistor have this value to allow MOSFETs gates to charge very fast. Oh and the inductors are 3.45u each one, the circuit picture was taken before modifications.

I don't know why replacing the resistors with 470 ohms makes the difference, this should only limit gate current.

The diodes I'm using are ideal. I'm not sure what diodes I should pick for MOSFET gates. I already have the diodes for the multiplier, 2CL2FM fast 20kV diodes.
The other thing that is ideal in my simulation is the coupling. I'm using the ideal K_linear. I have found a model for the ETD59 core, but I don't know how to use that model in my circuit.

[orolo]

I don't know why replacing the resistors with 470 ohms makes the difference, this should only limit gate current.

My guess is that, if the resistance is too low, the low impedance to 12V will not allow the gate to discharge through the diode reliably: the diode will be instead discharging the 12V supply. Check in your simulation if the mosfets switch at the correct time and don't miss cycles. Also, the waveform for I1 you posted doesn't look right: with the correct resistance, it should look like a smooth sinusoid. Maybe a resistance of  about 100 ohms would be a good compromise?

Another thing: if you are going to wind the secondary in a the pot core, you might want to use isolating tape from primary to secondary, and over each layer of the secondary. I wouldn't trust magnet wire enamel to isolate 4kV.

Good luck with the project!