Switched Mode Power Supply

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Rich Feldman
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Re: Switched Mode Power Supply

Post by Rich Feldman » Sat Jun 17, 2017 4:52 am

Sounds good, Niels and Dennis.

For others who want to roll their own transformers, beware of turns-count formulas based on RMS voltage of sinusoidal AC. The RMS voltage of square wave AC is the same as its "peak" voltage, and is substantially less than the RMS (much less the peak) voltage of a sinusoid with same frequency and Bmax on the same core and coil.

As a checkpoint, here is a data point figured independently from fundamentals. It's supposed to show everyone that there's nothing to be afraid of in there.

Many modern SMPS cores have Bmax = 0.2 T as an ordinary design point on the datasheet, so let's use that.
If we change your core diameter from 1.600 cm to 1.596 cm, its area becomes exactly 2 cm^2, and the other numbers all end up nice and round.

The associated flux swing is exactly 80 microwebers. The product of core area in m^2, flux density Bmax in teslas, and 2 (for operation between negative and positive extremes).

As a linear ramp over 10 microseconds, dF/dt is 8 webers/second and induces 8 volts per turn.
For example, 200 volts on a 25-turn primary, and 10000 volts on a 1250-turn secondary.

That would fit an operating frequency of almost 50 kHz. Cycle period includes 10 us for flux ramp up, 10 us for flux ramp down with reversed voltages, and some switching time and/or dead time.
The core area and adopted Bmax dictate a limit of 80 volt-microseconds per turn, per half-cycle, regardless of frequency or waveshape.

The obligatory picture is snipped from an app note by West Coast Magnetics. http://wcmagnetics.com/wp-content/uploa ... .28.10.pdf
Maybe it's already among your references. It has lots of practical information about winding and insulation issues for real commercial designs, not to mention references to some of those Ferroxcube materials you've become familiar with.
wcm_cores.PNG
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Garrett Young
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Re: Switched Mode Power Supply

Post by Garrett Young » Sat Jun 17, 2017 5:04 am

Rich,

Is your primary turns based on a half or full bridge at 200V DC rail (and 0.2T in a 2cm^2 core)? 25 Turns is correct for a full bridge but not half. Likely the secondary would need more turns to account for leakage inductance (which is usually quite high for high voltage secondaries because of isolation requirements).

The math isn't hard ... it's the doing.
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Rich Feldman
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Re: Switched Mode Power Supply

Post by Rich Feldman » Sat Jun 17, 2017 6:25 am

Yup, that analysis omits lots of real-world complications, to quickly show the physics behind turns-count formulas. Given a frequency and a volt-microseconds limit, it was trivial to get the maximum square wave voltage per turn. Optional exercise: get the sine wave voltage per turn.

And yes, it was sort of assuming a full bridge (H-bridge). It does say "200 V across 25 turn primary for not more than 10 us, then 200 V the other way for the same amount of time".

With a DC bus voltage of 200 volts, rail to rail, the inverter's output can get +200 V or -200 V, measured between symmetrical "hot" terminals. The switches can also be set to deliver 0 volts with low impedance. That state happens for a chosen fraction of each half-cycle in "modified sine wave" 60 Hz inverters. A DC motor, driven reversibly with an H-bridge, stops faster in the 0 volt drive state than the high-impedance drive state.

I think that ordinary (non-resonant) half bridge drivers switch just one end of the load back and forth between the DC rails. The other end of the load is held at an intermediate voltage by at least one relatively large-value capacitor. That voltage will automatically match the average voltage on the switched side.

In the example with 200 volt DC bus, a half bridge would put +100 V or -100 V on the primary winding. For the same frequency and flux density, the primary could get by with only half as many turns.

Have I got that right, Garrett?

The Spellman -70 kV power supplies extensively discussed on these forums in late 2016 have the half-bridge topology. I never got around to powering mine up after replacing a diode and capacitor. Should talk less and do more.

Another isolated converter topology with only two switches uses a center-tapped primary. Flyback converters are isolated and need only one switch, but they aren't really transformers. Good for low power SMPS, CRT anode power, and small engine ignition.
Last edited by Rich Feldman on Sat Jun 17, 2017 6:47 am, edited 1 time in total.
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Garrett Young
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Re: Switched Mode Power Supply

Post by Garrett Young » Sat Jun 17, 2017 6:36 am

You are correct, Rich.

I'm partial to the half bridge topology, since I think it's a good balance between cost, efficiency, and complexity.
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Re: Switched Mode Power Supply

Post by John Futter » Sat Jun 17, 2017 8:33 am

I hate half bridge as you have to allow even more headroom so that core flux walking doesnt suddenly give saturation on a half cycle
Poof more beach sand (SiO2).
It can take a long time to catch the conditions that cause core flux walking ie product out in the real world with unexplained high number of failures under warranty
Only exception to this is current fed current mode which was basically invented to get around flux walking in the core in half bridge designs. CFCM has the switches overlapping in on time and it makes for a very clean output with fewer artifacts so snubbing becomes alot easier. you can take this even further with resonant CFCM so everything looks like sine waves making EMI mitigation much easier.

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Re: Switched Mode Power Supply

Post by Garrett Young » Sat Jun 17, 2017 2:01 pm

Between a "stiff" centerpoint and current mode control they usually behave nicely ...
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Re: Switched Mode Power Supply

Post by Niels Geerits » Thu Jun 22, 2017 11:27 am

Thanks for the info Garret and Rich. I am going to go get some parts (might need to order) this weekend. I agree that winding the transformer properly seems tough with regards to tightness and insulation. I plan to use a single MOSFET and an arduino to create a square wave going from 0 to roughly 300 V (max output of the variac). The AC to DC conversion happens later in the multiplier. I could create a square wave that goes from -300V to 300V, which means I would have a higher peak to peak to work with, but also requires more semiconductor devices. To me the purely positive square wave seems like a simpler project for a beginner. Unless someone knows a reason why that would be a terrible idea?

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Re: Switched Mode Power Supply

Post by Rich Feldman » Thu Jun 22, 2017 5:55 pm

It's good to hear that you are getting your hands dirty, Niels.

How will you get a 0 to +300 volt drive with one MOSFET? An open switch is not the same as driving 0 volts.

Don't forget that the voltage averaged over a whole cycle needs to be the same on both ends of a transformer primary winding. If the switched end is alternately driven to 0 V and +300 V (using two MOSFETs), with equal ON times, the other end should be at +150 V. This is the half-bridge topology spoken of previously.

With just one MOSFET, you could experiment with the flyback converter topology. As a lab exercise you don't need a special (gapped) core, but you do need a secondary winding and at least one diode connected to it.

Do you have an oscilloscope?

Do you have a good grasp on the concept of electric current? Suppose an electric circuit is isolated within a box. A hole in the box gives you access to one wire of the circuit. The wire will have a current, possibly zero, which you could measure. But the "voltage" of that single wire is undefined, right? Nothing to measure (not counting any small IR drop between different places on the wire).
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Niels Geerits
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Re: Switched Mode Power Supply

Post by Niels Geerits » Fri Jun 23, 2017 1:27 pm

Rich right you are! That was embarassing on my part of course an open switch is not the same as driving at 0V, I was thinking a bit too quick there.

I looked up the conventional half bridge circuit diagram:
Image
And I am probably wrong but it seems like the loop V_dc - C1 - C2 - V_dc is shorted out. So I simulated it (falstad circuit simulator) and put a small resistor in that loop. I did indeed get a square wave output, but it was nowhere near 100V DC I put in in my test. To be honest I do not think that the falstad circuit simulator is working properly. I should be getting some components soon so I can play around with it (got some extra MOSFETS in case I ruin one).

I don't have an oscilloscope. I could arrange to use the one at my university every once in a while should I need it.

As for the thought experiment. A Voltage is a potential difference the wire itself has not change in potential and therefore no voltage drop (unless you look at its resistance). It does have a current which depends on the impedance of the other components. Basically voltage is potential energy, resulting from an electric field. The electric field creates a force on charged particles which causes them to move. Technically with no resistance anywhere the electons would accelerate until they reach the lowest potential. However in a conductor the electrons scatter against the lattice (comparable with friction) which causes an equilibrium velocity of the electrons to settle in. From this velocity the charge the electron density (material property I guess) and the area of the conductor one can optain the equilibrium current. Btw each scattering event in the conductor can be seen as a voltage drop, because the electron loses its kinetic energy.

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Re: Switched Mode Power Supply

Post by John Myers » Fri Jun 23, 2017 11:52 pm

Doesn't look like a conventional H bridge to me, at least what I'm use to seeing.
The low side output ( point O) will be half Vdc. It creates a positive and negative voltage swing with point O as the common.

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