Inductor Voltage Calculations

[hanzdolo30@gmail.com]

This is probably a stupid question, but please bear with me, as this is all still theoretical to me.
I'm making a boost inductor and I just wanted to make sure I'm calculating for the voltage correctly.

EDIT: I forgot to mention that the input voltage is unfiltered(no filter cap), rectified mains voltage with a V_PK ranging from 100-340VDC @ 100-120Hz to output 400VDC. I will be using 2 boost inductors operating in opposite phase of each other to minimize output ripple and maximize power output. A sample voltage will be taken from the output and fed to a comparator in order to modify duty cycle as needed to maintain a smooth 400VDC output, ideally able to power a +/-1kW load (full bridge DC-DC conversion topology).

Switching will begin @ zero crossing, where the MOSFET switching voltage will be gradually increased from V_TH to 12V over a period of 200-250ms to keep current spikes to a minimum. Duty cycle will be limited to a maximum of 75%, switching at 100kHz. I'll be using 2 E42/21/15 PC40 ferrite cores where I may introduce an air gap at the center leg if absolutely necessary(I'd prefer not to due to fringing).

Is the equation:

N = Vx10⁴
      4fA_eB

Or does that only apply to transformer windings(i.e. mutual inductance)?

If it does apply to inductors, should  V = V_boost or rectified, unfiltered, 100-120Hz V_in?

[Paul Price]

Got a detailed breakdown of  your formula or a circuit/schematic to apply your formula to?

[T3sl4co1l]

Ew, cgs units...

Anyway, V is the square wave peak voltage.  The 'input' side of the inductor is held constant at +V, and the other side is pulled down to 0V then clamped at 2*(+V) (for a 50% duty cycle).

Note that V / f has units of flux (volt*sec).  The 1/4th is because flux rises and falls, averaging zero, throughout the square wave.

This further assumes that DC current is zero, because if DC current were nonzero, flux would be nonzero (inductance is the conversion factor between flux and amps -- just as resistance is the conversion factor between volts and amps; and both obey Ohm's law, as long as they are linear components).

A boost converter obviously does not have zero DC, so the equation needs to be modified.

If you are in DCM (discontinuous current mode: inductor current returns to zero after the flyback pulse, and before the switch turns on again), then change the factor of 4 to 2.  (Flux doesn't average zero, but it returns to zero, so you're using the positive half of the total available flux.)

But it would be more appropriate to work from another equation directly.  Understand that flux is:
Phi = V/f = V*s
and when you are applying a constant voltage to an inductor, you are applying a flux over time.  That flux is simply the applied voltage times the pulse width.

But even better would be to not work with flux at all.  Your peak current mode converter should only turn on until the inductor current reaches a critical value, then turns off.  This prevents the current build-up that is the curse of a voltage-mode (i.e., feeding fixed PWM into an inductor) controller.  The circuit is just as simple, yet you obtain short circuit protection and power limiting for free!  (Reference: UC3842.)

In that case, you use the inductor equation:
V = L * dI/dt
dI is the rise in current during the pulse, and dt is the pulse length.

You only need to work with B (flux density) when selecting and gapping a core, and to check that you're not saturating it.

Tim

[hanzdolo30@gmail.com]

I've provided a bit more detail on the project. Based on your answer, I think you were under the assumption that I was building a normal boost converter. 

[T3sl4co1l]

Well, that hasn't changed anything, you still are...

Also, it's better to add information in a reply, otherwise it breaks thread order.

Some errors:

Switching will begin @ zero crossing, where the MOSFET switching voltage will be gradually increased from V_TH to 12V over a period of 200-250ms to keep current spikes to a minimum.

No -- once the MOSFET cooks off, current will spike once, massively, and whatever protective device is in place (hopefully a fuse, else the breaker) opens.

This is not how you reduce current spikes -- you control current by controlling current!  Always make sure the MOSFET is switching sharply, otherwise it will get very hot, very quickly.

Turn on the transistor until it's carrying the current you need, then turn it off.  Simple as that.  BCM PFC controllers exist, which handle this for you -- example:
http://www.onsemi.com/pub/Collateral/NCP1608-D.PDF
Note the resistor in series with the MOSFET source, sensing current.  You must do this first -- turn on the switch until the current reaches a threshold, then turn it off, and repeat after some time.

The result will be PWM, but PWM is not the goal, it is the side effect of controlling current.

You'd use a different controller, like UCC28010 or whatever, to handle the biphase timing and stuff, and also to get better efficiency at 1kW.

Also, 1kW is quite a lot of power -- please do build (or purchase a demo board) a lower power level one first!

Duty cycle will be limited to a maximum of 75%, switching at 100kHz. I'll be using 2 E42/21/15 PC40 ferrite cores where I may introduce an air gap at the center leg if absolutely necessary(I'd prefer not to due to fringing).

Other error -- the air gap is were energy is stored, so the core must be gapped -- or, if not, it must be about a hundred times larger, which is ridiculous.   You can also get core materials with a low permeability, that do not need an external gap.

You are quite correct that fringing fields are dangerous -- you'll need to use Litz wire here.

To use cheaper (but also much bigger) inductors, you'll need to consider a CCM controller, which has added complexity over the simple BCM type PFC controllers.  These are not general-purpose parts, so you're better off following the manufacturer's recommended design.

Tim

[hanzdolo30@gmail.com]

No -- once the MOSFET cooks off, current will spike once, massively, and whatever protective device is in place (hopefully a fuse, else the breaker) opens.

This is not how you reduce current spikes -- you control current by controlling current!  Always make sure the MOSFET is switching sharply, otherwise it will get very hot, very quickly.

I'm not arguing the point, because you are obviously well versed on the topic, where this is my first high voltage application of a boost converter. I just want to make sure you're understanding me as well as me obtaining a better understanding of the magnetics of the circuit. I really appreciate the time taken to assist me.

I was referring to gradually increasing the pulse voltage from V_TH(about 4.5V) to 12V, over a period of 200ms, not just linearly increasing the voltage at the gate. I'm aware that would desolder the MOSFET or worse(I've had it happen before ). The circuit as described seems to work in well in simulation. In LTSpice I saw a gradual increase in current when I did that, otherwise I saw an 80A spike when I started it up at 12V. Due to a lack of available IC models, I used an NE555 with a whole lot of auxiliary circuitry(what a headache that was  ), the PWM being controlled by the comparator via the CV pin. In that simulation I had the V_BOOSTED attached to a 129 ohm load resistor.

I've built boost converters for low voltage applications that operated at 200W attached to the 12V rail of an ATX PSU (Good Corsair 1000W supply), using a BJT astable, without tripping the PSU's protection circuitry.  I was using a toroid with some litz wire that I made using some 30AWG magnet wire I had lying around. The operating frequency was at about 150kHz (I'm sure you know BJT astables aren't the most reliable oscillators).

Turn on the transistor until it's carrying the current you need, then turn it off.  Simple as that.  BCM PFC controllers exist, which handle this for you -- example:
http://www.onsemi.com/pub/Collateral/NCP1608-D.PDF
Note the resistor in series with the MOSFET source, sensing current.  You must do this first -- turn on the switch until the current reaches a threshold, then turn it off, and repeat after some time.

The result will be PWM, but PWM is not the goal, it is the side effect of controlling current.

You'd use a different controller, like UCC28010 or whatever, to handle the biphase timing and stuff, and also to get better efficiency at 1kW.

Also, 1kW is quite a lot of power -- please do build (or purchase a demo board) a lower power level one first!

I have a variety of PFC and offline SMPS controllers from Fairchild (Now On-Semi), but I thought it was a lot of fun using the NE555s for something that they are totally not designed for.

Other error -- the air gap is where energy is stored, so the core must be gapped -- or, if not, it must be about a hundred times larger, which is ridiculous.   You can also get core materials with a low permeability, that do not need an external gap.
You are quite correct that fringing fields are dangerous -- you'll need to use Litz wire here.
To use cheaper (but also much bigger) inductors, you'll need to consider a CCM controller, which has added complexity over the simple BCM type PFC controllers.

I'm aware of the existence of distributed gap cores and skin effect. I actually got that equation from a powder core manufacturer as a calculation for inductors, I noticed it was too much like the transformer winding equation, so I had to ask someone more knowledgeable on the topic.

I just wanted to use what I have on-hand. I figured I could just calculate for B_MAX to avoid core saturation.
While I was testing the LCR meter I just got, I noticed the gap doesn't have to be very big to cause a dramatic drop in inductance/increase in reluctance.

I'm currently reading "Transformer and Inductor Design Handbook", so I do know all of the equations for gapping the core and increasing reluctance (R_M). It seems, adding a gap to an MMF circuit is equal to using a resistor in an EMF circuit, it's just that fringing that I'm worried about.

[hanzdolo30@gmail.com]

Ew, cgs units...

Anyway, V is the square wave peak voltage.  The 'input' side of the inductor is held constant at +V, and the other side is pulled down to 0V then clamped at 2*(+V) (for a 50% duty cycle).

Note that V / f has units of flux (volt*sec).  The 1/4th is because flux rises and falls, averaging zero, throughout the square wave.

This further assumes that DC current is zero, because if DC current were nonzero, flux would be nonzero (inductance is the conversion factor between flux and amps -- just as resistance is the conversion factor between volts and amps; and both obey Ohm's law, as long as they are linear components).

A boost converter obviously does not have zero DC, so the equation needs to be modified.

If you are in DCM (discontinuous current mode: inductor current returns to zero after the flyback pulse, and before the switch turns on again), then change the factor of 4 to 2.  (Flux doesn't average zero, but it returns to zero, so you're using the positive half of the total available flux.)

But it would be more appropriate to work from another equation directly.  Understand that flux is:
Phi = V/f = V*s
and when you are applying a constant voltage to an inductor, you are applying a flux over time.  That flux is simply the applied voltage times the pulse width.

But even better would be to not work with flux at all.  Your peak current mode converter should only turn on until the inductor current reaches a critical value, then turns off.  This prevents the current build-up that is the curse of a voltage-mode (i.e., feeding fixed PWM into an inductor) controller.  The circuit is just as simple, yet you obtain short circuit protection and power limiting for free!  (Reference: UC3842.)

In that case, you use the inductor equation:
V = L * dI/dt
dI is the rise in current during the pulse, and dt is the pulse length.

You only need to work with B (flux density) when selecting and gapping a core, and to check that you're not saturating it.

Tim

I just wrapped my head around the math, Faraday's equation. It's so simple I missed it the first time around. I guess I will have to gap the core (I wouldn't want an inductor the size of my kitchen table  ), which is a little tricky because it's pretty difficult to sand a mm of core down perfectly, let alone two equally, Yikes!
I may just shell out a couple bucks for a pair of Cool mu toroids. It's probably not worth the hassle just to end up with 2 totally dissimilar inductors.

Thanks again.

[T3sl4co1l]

I was referring to gradually increasing the pulse voltage from V_TH(about 4.5V) to 12V, over a period of 200ms, not just linearly increasing the voltage at the gate. I'm aware that would desolder the MOSFET or worse(I've had it happen before ). The circuit as described seems to work in well in simulation.

I understood correctly, then.  

Understand what you are doing:
By reducing Vgs(on), you are reducing the switching capacity of the MOSFET.  That is, it turns on, and pulls the voltage down, then the voltage goes back up, while it's still on.  The transistor is sinking, say, a few amperes, at full supply voltage, thus dissipating hundreds or thousands of watts!

A simulation will show this working just fine, but so too, it will show the "80A inrush" version working just fine.  There's no smoke in SPICE.

It's your responsibility, as the creator of the model, to make it representative of the thing you actually want to build -- to "model" it!

In LTSpice I saw a gradual increase in current when I did that, otherwise I saw an 80A spike when I started it up at 12V. Due to a lack of available IC models, I used an NE555 with a whole lot of auxiliary circuitry(what a headache that was  ), the PWM being controlled by the comparator via the CV pin. In that simulation I had the V_BOOSTED attached to a 129 ohm load resistor.

Gosh...  You should familiarize yourself with more basic building blocks!

In SPICE, there are ideal everythings!

It is, in turn, your responsibility to use these carefully -- as ideal elements, they don't have limited bandwidth, or time delay, or bounded output ranges.  You need to put those aspects in, yourself.

But, that said: controlled sources allow you to amplify, scale, isolate, and put functions on any voltage or current, or combination thereof, you like.  This is Turing complete (on the condition that memory -- state -- is limited by size of the circuit, which can't be modified during runtime), so you can truly build anything!

A good replacement for a 555 is a couple flip-flops or gates, comparators, a switch and a buffer.  Comparators convert analog to digital, and you then use the digital signal with logic gates.  (There is a distinction between analog and digital, in SPICE: XSPICE and other extensions provide a true event-driven digital logic simulation, which has to be interfaced with the analog side with converters.  The converters are usually implicit, but be mindful that they exist -- sometimes they screw up!  https://www.seventransistorlabs.com/Images/AltiumDigGlitch.png )

Comparators: recommend using a proper model like LM339 (mind the open collector output) or whatever (driven logic output) type is equivalent or better.

Switches: use transistors.  There is a SPICE switch, but they can be unstable (they're implemented by an ideal dependent resistance and nothing else, so can behave very unrealistically), and a transistor will capture real limitations like finite gain, bounded voltage and current, and speed.

Simple logic functions can also be done with transistors.  AoE2 called this "Mickey Mouse logic" (in the context of glue logic when you happen to need a couple transistors' worth), but it's easily tossed to the corner of a schematic sheet in SPICE.

Everything else, current sources, ramp generators, that sort of thing: use capacitors, resistors, inductors, transistors, sources, whatever works.

Nice thing about PFC in SPICE: you can make the multiplier and divider section trivial and perfect, no faffing about with PWM conversion or ADC-MDAC or analog multiplier sections!

I've built boost converters for low voltage applications that operated at 200W attached to the 12V rail of an ATX PSU (Good Corsair 1000W supply), using a BJT astable, without tripping the PSU's protection circuitry.  I was using a toroid with some litz wire that I made using some 30AWG magnet wire I had lying around. The operating frequency was at about 150kHz (I'm sure you know BJT astables aren't the most reliable oscillators).

BJTs are better than they're given credit for, but they aren't as "logical" as MOSFETs -- namely, you need to drive them with the right combination of voltage and current, and that it takes more current (the base input impedance is simply lower), whereas driving a MOSFET requires little more than a big fat logic buffer.

Tim

[jbb]

I guess I will have to gap the core (I wouldn't want an inductor the size of my kitchen table  ), which is a little tricky because it's pretty difficult to sand a mm of core down perfectly, let alone two equally, Yikes!
I may just shell out a couple bucks for a pair of Cool mu toroids. It's probably not worth the hassle just to end up with 2 totally dissimilar inductors.

Oh yes, trying to work ferrite is horrible.  However, there are 2 options you could look at: firstly, can you buy a pre-gapped core set?  Secondly, remember that (for e.g. an E core) you can just gap all three legs.  It's not quite ideal but very many power electronics prototypes are made this way.

On Kool Mu: remember to look at the loss density vs. frequency.  Kool Mu may be too lossy at high frequency.

On Vgs supply: T3sl4co1l is dead right.  Use of low Vgs supply is the wrong solution to your problem and greatly increases the risk of blowing MOSFETs.

Got a detailed breakdown of  your formula or a circuit/schematic to apply your formula to?

Maybe with a schematic (e.g. from LTSpice) someone could help you work out why the inrush is happening and suggest a remedy.

For example: you're building a two-phase interleaved boost PFC rectifier.  Boost PFC rectifiers are known to have a large inrush current when AC power is first applied because the bulk DC capacitor starts off empty.  This has nothing to do with the switching MOSFETs.

[hanzdolo30@gmail.com]

By reducing Vgs(on), you are reducing the switching capacity of the MOSFET.  That is, it turns on, and pulls the voltage down, then the voltage goes back up, while it's still on.  The transistor is sinking, say, a few amperes, at full supply voltage, thus dissipating hundreds or thousands of watts!

A simulation will show this working just fine, but so too, it will show the "80A inrush" version working just fine.  There's no smoke in SPICE.

It's your responsibility, as the creator of the model, to make it representative of the thing you actually want to build -- to "model" it!

For me this is one of those situations where the more you learn, the more you realize you don't know. 
 
 I was actually ill advised by someone on stackexchange. Thank you for the correction. I thought he was correct, being the MOSFET wasn't on for the entire time period it could handle the pulses of current, gradually charging the inductor over 1/5 of a second rather than just hard switching at the full 12V. However now that I've actually done the calculations since reading your reply, the heat dissipation would probably cause the MOSFET to explode violently.

My original idea was to engineer a soft start by gradually increasing positive pulse width (which I think a youtube I saw video recently confirmed) until the V_BOOSTED arrived at the peak voltage of 400V, then the comparator would modify the duty cycle to keep it at that point. That's actually a simplified rundown because it doesn't just increase the duty cycle like that. There's a bit of transistor logic and RC timing incorporated into that circuit. Once I've removed that bad advice from the original schematic, I'll post it.

Would you say that's a step in the right direction?   

Gosh...  You should familiarize yourself with more basic building blocks!

In SPICE, there are ideal everythings!

It is, in turn, your responsibility to use these carefully -- as ideal elements, they don't have limited bandwidth, or time delay, or bounded output ranges.  You need to put those aspects in, yourself.

But, that said: controlled sources allow you to amplify, scale, isolate, and put functions on any voltage or current, or combination thereof, you like.  This is Turing complete (on the condition that memory -- state -- is limited by size of the circuit, which can't be modified during runtime), so you can truly build anything!

A good replacement for a 555 is a couple flip-flops or gates, comparators, a switch and a buffer.  Comparators convert analog to digital, and you then use the digital signal with logic gates.  (There is a distinction between analog and digital, in SPICE: XSPICE and other extensions provide a true event-driven digital logic simulation, which has to be interfaced with the analog side with converters.  The converters are usually implicit, but be mindful that they exist -- sometimes they screw up!  https://www.seventransistorlabs.com/Images/AltiumDigGlitch.png )

Comparators: recommend using a proper model like LM339 (mind the open collector output) or whatever (driven logic output) type is equivalent or better.

Switches: use transistors.  There is a SPICE switch, but they can be unstable (they're implemented by an ideal dependent resistance and nothing else, so can behave very unrealistically), and a transistor will capture real limitations like finite gain, bounded voltage and current, and speed.

Simple logic functions can also be done with transistors.  AoE2 called this "Mickey Mouse logic" (in the context of glue logic when you happen to need a couple transistors' worth), but it's easily tossed to the corner of a schematic sheet in SPICE.

Everything else, current sources, ramp generators, that sort of thing: use capacitors, resistors, inductors, transistors, sources, whatever works.

Nice thing about PFC in SPICE: you can make the multiplier and divider section trivial and perfect, no faffing about with PWM conversion or ADC-MDAC or analog multiplier sections!

Oh, I'm aware that LTSpice will allow a 2N2222 to operate at 1000V with 50A going through it with no problem .
For instance I designed a simple phase shift oscillator in SPICE that worked like a charm, but on the breadboard I had to add 3 more resistor, capacitor stages then it actually worked, I even added a schmitt trigger and made a square wave output with a variable duty cycle. SPICE was wrong about the oscillating frequency as well  . In fact SPICE let me put just about any resistor or capacitor values in and still worked.

I took a look at that link and Yikes!

I am pretty familiar with basic circuit building blocks. It's magnetics that I've been having issues with, but I seem to be getting the equations under control. Such as, air gaps, Fringe Flux Factor, etc.. I see an air gap is absolutely necessary to maintain a proper B-H curve.

I'm actually waiting on UPS to deliver some LM339s among others, as I'm writing this.

BJTs are better than they're given credit for, but they aren't as "logical" as MOSFETs -- namely, you need to drive them with the right combination of voltage and current, and that it takes more current (the base input impedance is simply lower), whereas driving a MOSFET requires little more than a big fat logic buffer.

I totally agree. However when I post a schematic with a bunch of BJTs in it, I get people telling me that the schematic is convoluted and I should just use ICs. If I can't find an IC that does exactly what I want and IC's will almost always take up more space in my case (simple logic gates, etc. and I don't have the many of the requirements for surface mount components), so why not use BJTs? I'm using breadboards(never for power conversion) and perfboard.

I actually enjoy working with BJTs. They're quite logical as long as their operating parameters are understood, Q-point, saturation point, etc.. It's kinda like coding in hardware(I'm a programmer), lol .

I was referring to the astable multivibrator circuit itself being a bit difficult to use as far as implementing a voltage controlled duty cycle. It seems I would have to use current sources which can be a bit imprecise from BJT to BJT of the same value due to things as simple as ambient temperature and a number of other factors (of course in SPICE everything is peaches). 

The boost converter I made worked great, it's just that I would have liked to have better control over the output current with load detection rather than using a trim-pot to manually compensate. You know once it sees a voltage drop below the the 60V, increase duty cycle, but limited it to no more than 70% on time. I believe that's the point where ICs become absolutely necessary. 

[hanzdolo30@gmail.com]

Oh yes, trying to work ferrite is horrible.  However, there are 2 options you could look at: firstly, can you buy a pre-gapped core set?  Secondly, remember that (for e.g. an E core) you can just gap all three legs.  It's not quite ideal but very many power electronics prototypes are made this way.

On Kool Mu: remember to look at the loss density vs. frequency.  Kool Mu may be too lossy at high frequency.

On Vgs supply: T3sl4co1l is dead right.  Use of low Vgs supply is the wrong solution to your problem and greatly increases the risk of blowing MOSFETs.

I just got a digital caliper and a set of diamond grit files, so I may be able to get away with grinding down the center legs. I just have to calculate the l_g, and hope I don't shave off too much.

Maybe with a schematic (e.g. from LTSpice) someone could help you work out why the inrush is happening and suggest a remedy.

For example: you're building a two-phase interleaved boost PFC rectifier.  Boost PFC rectifiers are known to have a large inrush current when AC power is first applied because the bulk DC capacitor starts off empty.  This has nothing to do with the switching MOSFETs.

I'll post a schematic once I remove the bad advice that was given to me from the schematic. I think I may have been confused as to what a soft start really is. I was put under the impression that it was a gradual voltage increase, where on youtube I saw a soft start on someone's oscilloscope and seemed to be a gradual increase in duty cycle .  It was one of those terrible videos with no explanation, but I think it was pretty obvious.
 
I think the reason I saw an insane amount of inrush current is because I had a 129 resistor attached as a load from startup.   In the actual circuit that wouldn't be the case. There would be no load but a small flyback that will be used to power the primary circuit and even that wouldn't start switching until the PFC stage reached it's peak voltage of 400V. Once the flyback has has reached it's peak voltage, then the main full bridge transformer would begin switching to power the actual 1kW load, where each switching cycle would begin at zero crossing.

Does that sound about right?     

[T3sl4co1l]

For me this is one of those situations where the more you learn, the more you realize you don't know. 

Excellent!  Once you begin to get a flavor for how little you might actually know, you can begin to fill in those gaps, however small a piece at a time.

I was actually ill advised by someone on stackexchange. Thank you for the correction. I thought he was correct, being the MOSFET wasn't on for the entire time period it could handle the pulses of current, gradually charging the inductor over 1/5 of a second rather than just hard switching at the full 12V. However now that I've actually done the calculations since reading your reply, the heat dissipation would probably cause the MOSFET to explode violently.

My original idea was to engineer a soft start by gradually increasing positive pulse width (which I think a youtube I saw video recently confirmed) until the V_BOOSTED arrived at the peak voltage of 400V, then the comparator would modify the duty cycle to keep it at that point. That's actually a simplified rundown because it doesn't just increase the duty cycle like that. There's a bit of transistor logic and RC timing incorporated into that circuit. Once I've removed that bad advice from the original schematic, I'll post it.

Would you say that's a step in the right direction?   

Yes.  But more to the point: what are you really controlling?

If you're charging an inductor, and when the charge (current) gets too high the transistor blows up...... why not just stop charging when it's "full"?

In other words, measure the switch current, and turn off the switch when it reaches some peak value.

The circuit is an RS flip-flop connected to the transistor (with gate driver).  An oscillator periodically pokes S, turning on the transistor.  A comparator monitors current, relative to a threshold, and hits R when triggered.

Even if the inductor current stays high between pulses, the transistor will never stay on longer than the propagation delay of the comparator, f/f, driver and switch.  Which can be on the order of 100ns, nowhere near enough time to destroy the transistor (at least, from just one hit).

Bonus: as you vary threshold voltage, the peak current, and therefore output power, varies proportionally.  Well isn't that handy?

Suppose you control it so that input current is proportional to input voltage -- now you have your basic PFC!

(There are some added tricks to realize a full PFC: you need an outer voltage feedback loop, which varies the gain of the inner current loop, gradually (a time constant of several line cycles), so the output voltage can be stabilized without interfering with the ripple that the PFC section has to create.  Feedforward compensation is normally used as well, to keep the loop stable over wide changes in input voltage.)

Oh, I'm aware that LTSpice will allow a 2N2222 to operate at 1000V with 50A going through it with no problem .

Hmm, well -- depends.  SPICE is capable of modeling breakdown voltage (though not the latching avalanche breakdown that can occur in BJTs), and the hFE reduction at high current.

Not all models are made equally.  And cheap or shitty parts tend to have shitty models.  Nevermind that they've made, I don't know, a billion dollars worth of that part over the last half a century.

For instance I designed a simple phase shift oscillator in SPICE that worked like a charm, but on the breadboard I had to add 3 more resistor, capacitor stages then it actually worked, I even added a schmitt trigger and made a square wave output with a variable duty cycle. SPICE was wrong about the oscillating frequency as well  . In fact SPICE let me put just about any resistor or capacitor values in and still worked.

You say "worked like a charm", I say "didn't model reality worth diddly squat".   It's ultimately your responsibility to verify the models you put into your simulations, that they behave reasonably, and that your whole simulation is realistic.

You can easily build a bunch of chaotic nonsense with dependent sources, but that doesn't make it real.

Here's another model:



The left side is what I built.  It happens to be an oscillator!  Q4 collector voltage wiggles around maybe 0.5V at 30MHz (pretty fast for a TIP31, huh?).  (Oh FYI, MJD31C is the SMT version of TIP31C, and C is just the voltage grade in the TIP31 family.  Pretty much same things electrically, other than that.)

The right hand stuff is what I had to do to the circuit to make it "behave".  The inductances and capacitances correspond to lead inductances and device capacitances; except that, the inductances are far too large to be representative (by about 5 times), and the model already has capacitance parameters in it, so I shouldn't need to add more outside!

I suspect the problem is a transport (charge diffusion) effect inside the TIP31, causing real delay or something like that, which is enough to shift the poles into the right half plane.  SPICE doesn't do this.  Notoriously, SPICE has no support of transport phenomena, besides one-dimensional transmission lines, which are something of a hack anyway.  Instead, SPICE represents charge as a dependent capacitor.  But a capacitor can be discharged instantly, and has no delay (it adds a derivative, but not a time displacement), while a junction cannot.

Other times, I've had overly optimistic results: this amplifier https://www.seventransistorlabs.com/Images/WidebandAmp.png showed 300MHz bandwidth (-3dB) in SPICE, albeit with no particular attempt at replicating real parasitics (likely, trace capacitance is a pF or two on most nodes, resulting in not quite half the bandwidth).  The real one measures 100MHz, though.

IIRC, noise did come out okay though.  (The figure shown is measured.)

I totally agree. However when I post a schematic with a bunch of BJTs in it, I get people telling me that the schematic is convoluted and I should just use ICs. If I can't find an IC that does exactly what I want and IC's will almost always take up more space in my case (simple logic gates, etc. and I don't have the many of the requirements for surface mount components), so why not use BJTs? I'm using breadboards(never for power conversion) and perfboard.

Haters to the left...

To be fair, drawing everything out, discrete, is tedious and not very productive.  I might explore a circuit that way, or breadboard it, but where simple functions are needed (amps, comparators, logic), I always reach for ICs when it's time to implement it for real.

Tim

[hanzdolo30@gmail.com]

Excellent!  Once you begin to get a flavor for how little you might actually know, you can begin to fill in those gaps, however small a piece at a time.

Yes I've noticed, that's usually the case, lol.

Yes.  But more to the point: what are you really controlling?

If you're charging an inductor, and when the charge (current) gets too high the transistor blows up...... why not just stop charging when it's "full"?

In other words, measure the switch current, and turn off the switch when it reaches some peak value.

The circuit is an RS flip-flop connected to the transistor (with gate driver).  An oscillator periodically pokes S, turning on the transistor.  A comparator monitors current, relative to a threshold, and hits R when triggered.

Even if the inductor current stays high between pulses, the transistor will never stay on longer than the propagation delay of the comparator, f/f, driver and switch.  Which can be on the order of 100ns, nowhere near enough time to destroy the transistor (at least, from just one hit).

Bonus: as you vary threshold voltage, the peak current, and therefore output power, varies proportionally.  Well isn't that handy?

Suppose you control it so that input current is proportional to input voltage -- now you have your basic PFC!

(There are some added tricks to realize a full PFC: you need an outer voltage feedback loop, which varies the gain of the inner current loop, gradually (a time constant of several line cycles), so the output voltage can be stabilized without interfering with the ripple that the PFC section has to create.  Feedforward compensation is normally used as well, to keep the loop stable over wide changes in input voltage.)

Now that's where I get a little confused. Because I thought that by feeding back a reference voltage from the boosted output to the comparator and dropping the CV pin of the NE555s to 0V, stopping oscillation did exactly as you described. No charging unless output voltage drops below 400v, then it starts back up again. At least it seems logical . However I've only done high voltage boost in simulation where as you describe it, sounds a lot safer and you've obviously done this before.

You say "worked like a charm", I say "didn't model reality worth diddly squat".   It's ultimately your responsibility to verify the models you put into your simulations, that they behave reasonably, and that your whole simulation is realistic.

You can easily build a bunch of chaotic nonsense with dependent sources, but that doesn't make it real.

I actually got the original schematic from a working example on youtube, using all of the same component values and for some reason it still didn't work in real life, until I added those 3 stages.

I've made my share of chaotic nonsense in spice that I tried to manifest in reality. I have a charbroiled breadboard that I keep around to remind me to make sure my calculations are on point .
I also have a BJT astable that I blew up, as a constant reminder that earth ground IS NOT the same as the 0V at the rectifier. Ground is a reference point never to be confused. 

Haters to the left...

To be fair, drawing everything out, discrete, is tedious and not very productive.  I might explore a circuit that way, or breadboard it, but where simple functions are needed (amps, comparators, logic), I always reach for ICs when it's time to implement it for real.

Now that I actually know how to use them, I usually just use the BJTs for simple amplification where an Op-Amp would be overkill, driving MOSFETs, simple logic gates and switching parts of the circuit on or off based on reference voltages. These guys I'm talking about always want to see a canned product in use for damned near everything. For me at this point, it's more about the learning experience. Anybody can follow directions on a datasheet. The old school guys can usually appreciate the use of BJTs in conjunction with IC's. I also use them in simulation for the sake of making the simulations run faster. When I add an IC model to a schematic, the SG3525 for example, which I have Fairchilds version of, and plan to really use with the Hi/Low side drivers, it really slows things down tremendously. It's faster when I put together a crazy circuit with NE555s (insert deadtime  ) and a charge pump in SPICE rather than use the IC models, which perplexes me. Though the IC models of the SG3525 and driver ICs come from weird places and the NE555 is native to LT.   

[T3sl4co1l]

Now that's where I get a little confused. Because I thought that by feeding back a reference voltage from the boosted output to the comparator and dropping the CV pin of the NE555s to 0V, stopping oscillation did exactly as you described.

Output voltage != switch current!

That's a hysteretic converter, which is no better than MC34063 (which is similarly in my class of "people use it because they don't know better" parts), and completely unlimited on switch current.  They're typically bad at ripple, and depend on stable capacitor ESR.

Tim

[MrAl]

This is probably a stupid question, but please bear with me, as this is all still theoretical to me.
I'm making a boost inductor and I just wanted to make sure I'm calculating for the voltage correctly.

EDIT: I forgot to mention that the input voltage is unfiltered(no filter cap), rectified mains voltage with a V_PK ranging from 100-340VDC @ 100-120Hz to output 400VDC. I will be using 2 boost inductors operating in opposite phase of each other to minimize output ripple and maximize power output. A sample voltage will be taken from the output and fed to a comparator in order to modify duty cycle as needed to maintain a smooth 400VDC output, ideally able to power a +/-1kW load (full bridge DC-DC conversion topology).

Switching will begin @ zero crossing, where the MOSFET switching voltage will be gradually increased from V_TH to 12V over a period of 200-250ms to keep current spikes to a minimum. Duty cycle will be limited to a maximum of 75%, switching at 100kHz. I'll be using 2 E42/21/15 PC40 ferrite cores where I may introduce an air gap at the center leg if absolutely necessary(I'd prefer not to due to fringing).

Is the equation:

N = Vx10⁴
      4fA_eB

Or does that only apply to transformer windings(i.e. mutual inductance)?

If it does apply to inductors, should  V = V_boost or rectified, unfiltered, 100-120Hz V_in?

Hi,

To add a little here, that voltage is the voltage across the inductor winding.  It's the same for a transformer primary.  That "4" in the denominator tells us it is the formula that considers the drive wave shape to be rectangular, not sinusoidal.  If you see "4.44" instead that is for sine waves.

Also, a gap basically just reduces the total construction permeability so that the core does not saturate with the expected operating current.  Since many magnetic materials used for these applications have roughly the same saturation flux density spec and the drive current needs to be at a certain level in order to satisfy the application requirements, when we add a gap we effectively raise the level of current we can get away with in a given application.  However, since lowering the permeability is the main goal (higher current before we reach saturation) we can simply use a lower permeability core.  Creating a precision gap requires some decent machinery so if we use a lower permeability core we might get away without needing a gap.  Of course the overall inductance lowers, but since the inductance decreases in proportion to the permeability and the inductance increases with the square of the turns ratio, when we add more turns to compensate we end up with the same inductance but with a higher saturation current level.  With a low mu core we might be able to reach our goal without needing a gap.

In spite of this information it is still better to purchase an inductor that fits the bill.  There are a lot of inductors out there for sale that might work in this application and they are fully spec'd so you can pick and choose just what you want.  That is the most sure way to get this up and running in the least amount of time.  You can always go back and try to recreate the purchased inductor later if you need it for some production run or something.

[hanzdolo30@gmail.com]

Output voltage != switch current!

That's a hysteretic converter, which is no better than MC34063 (which is similarly in my class of "people use it because they don't know better" parts), and completely unlimited on switch current.  They're typically bad at ripple, and depend on stable capacitor ESR.

Tim

That completely makes sense, because (correct me if I'm wrong here) with a hysteretic converter, if the load begins to draw more current than the source can supply, it can still result in core saturation and too much current going through the MOSFET anyway (FET goes BOOM! ). However if the actual current is being monitored as well as the output voltage (giving switch current priority over output voltage of course), we end up with a PFC stage that won't have the potential of an exploding MOSFET or worse.     

[hanzdolo30@gmail.com]

Hi,

To add a little here, that voltage is the voltage across the inductor winding.  It's the same for a transformer primary.  That "4" in the denominator tells us it is the formula that considers the drive wave shape to be rectangular, not sinusoidal.  If you see "4.44" instead that is for sine waves.

Also, a gap basically just reduces the total construction permeability so that the core does not saturate with the expected operating current.  Since many magnetic materials used for these applications have roughly the same saturation flux density spec and the drive current needs to be at a certain level in order to satisfy the application requirements, when we add a gap we effectively raise the level of current we can get away with in a given application.  However, since lowering the permeability is the main goal (higher current before we reach saturation) we can simply use a lower permeability core.  Creating a precision gap requires some decent machinery so if we use a lower permeability core we might get away without needing a gap.  Of course the overall inductance lowers, but since the inductance decreases in proportion to the permeability and the inductance increases with the square of the turns ratio, when we add more turns to compensate we end up with the same inductance but with a higher saturation current level.  With a low mu core we might be able to reach our goal without needing a gap.

In spite of this information it is still better to purchase an inductor that fits the bill.  There are a lot of inductors out there for sale that might work in this application and they are fully spec'd so you can pick and choose just what you want.  That is the most sure way to get this up and running in the least amount of time.  You can always go back and try to recreate the purchased inductor later if you need it for some production run or something.

Since the Initial post, I've acquired quite a bit of knowledge on the topic, realizing that there are a number of factors involved in building an inductor core (too many equations to write down here without mathjax). Just to name a few, there's calculating the appropriate gap size for the application, B_MAX , N (being exactly as you've described it),  fringe flux factor, etc.. 

Theres one thing that I still haven't figured out, that the books don't explain. Where does that factor of 4 for square waves or 4.44 in the denominator for sine waves come from?
Does it have to do with the angle of the wave form? I was guessing it did until a few people on other forums told me to use a factor of 2, which totally confused me. 

At this point, I'd prefer not to use a "canned" product, because I feel it would not aid me in the learning process.  I'm learning as much I can about electrodynamics and, I find magnetic theory particularly fascinating.

I very much appreciate the time taken to assist me. Thank you!

[T3sl4co1l]

That completely makes sense, because (correct me if I'm wrong here) with a hysteretic converter, if the load begins to draw more current than the source can supply, it can still result in core saturation and too much current going through the MOSFET anyway (FET goes BOOM! ). However if the actual current is being monitored as well as the output voltage (giving switch current priority over output voltage of course), we end up with a PFC stage that won't have the potential of an exploding MOSFET or worse. 

Precisely, current must take priority in all [switched inductor] converters.  Ultimately, whatever you are doing, you have an inverter or switch, driving current through an inductor, and that current is the state variable of the inductor.  It's what it does, period.  Applying voltage causes a change in current, but only a change, it doesn't set the absolute value.  So the inductor current is independent of the applied voltage (and consequently, PWM% or whatever).  Then, the inductor current drives a change in voltage elsewhere (usually across a filter capacitor and load resistance), a second state variable.

Once you recognize the state variables, and wrap controllers around each one, you can easily design an indestructible converter with nearly the best possible dynamics.  You can't exceed switch/inductor current, because the current setpoint simply can't be commanded higher than whatever its input is designed to saturate at.  (You can make a variable current limit supply by clamping the setpoint current to an adjustable voltage!)  The inner current loop is easily compensated because it's a single pole, and the same is true of the outer voltage loop (given that the capacitor time constant is made longer than the current loop time constant, so that the poles don't interact much*).

*The boundary condition would be if you can adjust it so the poles interact just the right amount, giving a 3rd or 4th order, say, Bessel or Butterworth filter response: whichever condition is optimal for the application.

Tim

[hanzdolo30@gmail.com]

Precisely, current must take priority in all [switched inductor] converters.  Ultimately, whatever you are doing, you have an inverter or switch, driving current through an inductor, and that current is the state variable of the inductor.  It's what it does, period.  Applying voltage causes a change in current, but only a change, it doesn't set the absolute value.  So the inductor current is independent of the applied voltage (and consequently, PWM% or whatever).  Then, the inductor current drives a change in voltage elsewhere (usually across a filter capacitor and load resistance), a second state variable.

Once you recognize the state variables, and wrap controllers around each one, you can easily design an indestructible converter with nearly the best possible dynamics.  You can't exceed switch/inductor current, because the current setpoint simply can't be commanded higher than whatever its input is designed to saturate at.  (You can make a variable current limit supply by clamping the setpoint current to an adjustable voltage!)  The inner current loop is easily compensated because it's a single pole, and the same is true of the outer voltage loop (given that the capacitor time constant is made longer than the current loop time constant, so that the poles don't interact much*).

*The boundary condition would be if you can adjust it so the poles interact just the right amount, giving a 3rd or 4th order, say, Bessel or Butterworth filter response: whichever condition is optimal for the application.

Tim

Tim, YOU ARE THE MAN! ,

Thank you for getting me through that issue and teaching me how to make my converters "bulletproof"   

You've actually inadvertently answered a few questions I had in mind. Using my imagination, I can see a few situations where those methods can be applied.  Thanks to you, I'm gonna make some KICKASS converters!

I don't even really need canned control IC's, I can do it all with Op-Amps and proper comparators (of which I have plenty), using some simple analog control logic.
I have a bunch of silicon carbide semiconductors  that I'd love to put into use, which is why I was talking kilowatt converters at the beginning .

I'll show you the schematic once I've totally revamped it, being I've been doing it almost, all wrong. 

Though, I'd probably want to incorporate an MCU later on, so I can come up with some advanced control schemes. I think I told you before, I'm a programmer so that's right up my alley.

Thanks again Tim.

Gilbert

[jbb]

Unfortunately YouTube isn't a good source for power electronics. There's not a lot of explanation of circuit operation, and unfortunately they tend to be complex.

And a PFC circuit isn't a gentle introduction to the field, either.

Now that you've worked out why the power stage is going bang with inrush, you can move on to new and exciting ways to go bang.

One software suggestion: keep an eye on the DC output voltage. If it goes significantly above your target voltage, the converter should cease operation (I.e. turn MOSFETs off) and not restart until you command it.

Might I make some suggestions for safety:
- make sure you have galvanic isolation between the power stage and yourself or any PC/laptop
- add a drain resistor to the DC link cap to make sure it will eventually discharge
- I suggest you place a transparent lid over the converter so you don't accidentally touch anything
- try to set up all your test leads before turning on the main power, and not move them while power is applied
- eye protection can be good. MOSFETs and diodes can explode into sharp fragments.

[hanzdolo30@gmail.com]

Unfortunately YouTube isn't a good source for power electronics. There's not a lot of explanation of circuit operation, and unfortunately they tend to be complex.

Yeah, I know. There's this one video where a guy was telling people to make boost converters with an esaki oscillator. That had to be one of the most dangerous things I've ever seen..No let me correct that.
There was that one video where a guy made a step up push-pull alternator using an astable multivibrator to power a stereo system, like it was a great idea! .
There are a lot of videos on youtube that teach the uninformed how to commit suicide . There are also the videos that'll show you a topology and give you no detail as to how to implement it.
I've learned that it's best to watch the video and do further research on the topic. I tend to avoid anything that doesn't provide detailed formulae. 
There are a few good channels like iLecture Online (he provides detailed formulae on everything, which can be tedious, but you'll have a full understanding of anything he teaches) , The Post apocalyptic Inventor (started a great SMPS video series, with all of the math, but never finished it), EEVblog of course (which is how I ended up here) and Afrotech Mods (great for the basics), just to name a few. 

And a PFC circuit isn't a gentle introduction to the field, either.

This isn't exactly my first rodeo. Aside from some low voltage projects with MCUs (Not arduinos, I hate canned food,  ), I have made boost converters, charge pumps, isolated step up converters (30V max), using ATX PSU's as a source, so I actually did start out with a general understanding of the process. However, I've noticed that when working with mains power, there is very little margin for error before you end up with fireworks going off on your workbench.
 

Now that you've worked out why the power stage is going bang with inrush, you can move on to new and exciting ways to go bang.

That load resistor was just a dumb ass move on my part. Which is why coffee is absolutely not a good replacement for a well rested mind .  As I was reading your comment on the inrush, I thought about the circuit and realized  
T3sl4co1l helped me work through the current measurement so hopefully there won't be anymore BANGs!
 

One software suggestion: keep an eye on the DC output voltage. If it goes significantly above your target voltage, the converter should cease operation (I.e. turn MOSFETs off) and not restart until you command it.

I actually have a comparator taking care of that. Once the voltage arrives at 400V it pulls the CV pin on the NE555s down to 0V, essentially shutting the MOSFETs off. However, it seems the current across the FET is really the deciding factor. As I may see a voltage drop below my target voltage, the current can still be excessive, if the load device draws too much for some reason.

I'm not sure I like the software, it lies to you. All of the successful projects I've had, were prior to using simulation software. Perhaps the late Bob Peas was correct when he said "I program in solder!" , but like you said PFC isn't gentle.

Might I make some suggestions for safety:
- make sure you have galvanic isolation between the power stage and yourself or any PC/laptop
- add a drain resistor to the DC link cap to make sure it will eventually discharge
- I suggest you place a transparent lid over the converter so you don't accidentally touch anything
- try to set up all your test leads before turning on the main power, and not move them while power is applied
- eye protection can be good. MOSFETs and diodes can explode into sharp fragments.

That list of safety measures I should probably print in BIG BOLD letters and tape them to the wall above my workbench, lol.
Thanks for that.

[jbb]

Remembered another safety suggestion: attach a multimeter to the main DC cap at all times.  That way it won't lie in wait, charged and dangerous!

[hanzdolo30@gmail.com]

Remembered another safety suggestion: attach a multimeter to the main DC cap at all times.  That way it won't lie in wait, charged and dangerous!

I usually use an indicator LED on a high value resistor to let me know when the circuit goes completely dead, but that's a good idea!
Thanks for that! 

[MrAl]

Hi,

To add a little here, that voltage is the voltage across the inductor winding.  It's the same for a transformer primary.  That "4" in the denominator tells us it is the formula that considers the drive wave shape to be rectangular, not sinusoidal.  If you see "4.44" instead that is for sine waves.

Also, a gap basically just reduces the total construction permeability so that the core does not saturate with the expected operating current.  Since many magnetic materials used for these applications have roughly the same saturation flux density spec and the drive current needs to be at a certain level in order to satisfy the application requirements, when we add a gap we effectively raise the level of current we can get away with in a given application.  However, since lowering the permeability is the main goal (higher current before we reach saturation) we can simply use a lower permeability core.  Creating a precision gap requires some decent machinery so if we use a lower permeability core we might get away without needing a gap.  Of course the overall inductance lowers, but since the inductance decreases in proportion to the permeability and the inductance increases with the square of the turns ratio, when we add more turns to compensate we end up with the same inductance but with a higher saturation current level.  With a low mu core we might be able to reach our goal without needing a gap.

In spite of this information it is still better to purchase an inductor that fits the bill.  There are a lot of inductors out there for sale that might work in this application and they are fully spec'd so you can pick and choose just what you want.  That is the most sure way to get this up and running in the least amount of time.  You can always go back and try to recreate the purchased inductor later if you need it for some production run or something.

Since the Initial post, I've acquired quite a bit of knowledge on the topic, realizing that there are a number of factors involved in building an inductor core (too many equations to write down here without mathjax). Just to name a few, there's calculating the appropriate gap size for the application, B_MAX , N (being exactly as you've described it),  fringe flux factor, etc.. 

Theres one thing that I still haven't figured out, that the books don't explain. Where does that factor of 4 for square waves or 4.44 in the denominator for sine waves come from?
Does it have to do with the angle of the wave form? I was guessing it did until a few people on other forums told me to use a factor of 2, which totally confused me. 

At this point, I'd prefer not to use a "canned" product, because I feel it would not aid me in the learning process.  I'm learning as much I can about electrodynamics and, I find magnetic theory particularly fascinating.

I very much appreciate the time taken to assist me. Thank you!

Hello again,

The factor 4.44 comes from sqrt(2)*pi.  This comes out after starting with the equation for flux using sine waves.  I'd really have to look up the derivation at this point as it's been a long time for me now since i did that, but this 4.44 appears in many magnetic handbooks also including the literature from the old Magnetics Inc. company.
As n harmonics are added to this sine wave on the way to a square wave (each with amplitude 1/n) the core will saturate a little more easily with a given voltage, which means the flux density must go up with a square wave of equal amplitude.  If all the significant harmonics are considered, the flux density goes up by approximately 4.44/4 so the factor in the denominator changes to 4.  This is also in the Magnetics Inc. literature.
https://www.mag-inc.com/

[hanzdolo30@gmail.com]

Hello again,

The factor 4.44 comes from sqrt(2)*pi.  This comes out after starting with the equation for flux using sine waves.  I'd really have to look up the derivation at this point as it's been a long time for me now since i did that, but this 4.44 appears in many magnetic handbooks also including the literature from the old Magnetics Inc. company.
As n harmonics are added to this sine wave on the way to a square wave (each with amplitude 1/n) the core will saturate a little more easily with a given voltage, which means the flux density must go up with a square wave of equal amplitude.  If all the significant harmonics are considered, the flux density goes up by approximately 4.44/4 so the factor in the denominator changes to 4.  This is also in the Magnetics Inc. literature.
https://www.mag-inc.com/

Thank you for that . I wish the books would just explain things like that, instead of giving me a number factor that I have no idea where it comes from.

I've only been learning EE, summed up, for about 4 months. I took a very long break after frying a 4K monitor that was plugged in on the same power strip as a circuit with an improperly designed flyback converter that blew up like fireworks, because LTSpice said it would work . Which is why I'm very careful about calculating my magnetics.

Non-magnetic magnetic passive components, semiconductors and ICs are simple and logical. I can use them with great proficiency, both in simulation and on the breadboard/circuit board, but when it comes to magnetics . Those handbooks can be really confusing. For instance, I learned that u₀ = 4*pi^-7, then this one stupid book tells me it's unity (u₀=1) which totally threw me off, , and they put the actual u₀ in a weird format; l_g = 0.4*pi*N*I^-8/B_DC, which I didn't even catch on to until I found a good book where everything is in SI units, and u₀ is used in place of 0.4*pi^-8 . In those handbooks they use strange variable names and values all the time. It's so annoying . Where's the consistency? Should I be studying physics instead?  In the physics of it, there seems to be no inconsistencies, no matter the source. They just seem to take the long route about everything and I'm not designing core materials (for now ), I just want to make a pair of inductors quickly, using stuff I already have on hand, that will definitely work.

Sorry about the rant  , it's just that I would have probably had the equations worked out in a day if it hadn't been for all of the inconsistencies, and one book lacking in something that the other didn't. It's so irritating .
Can you recommend a book or a few?

I have 3 questions that I hope you don't mind answering.

1. The book doesn't go into detail about varying input voltages and inductance. When I calculate for the inductance of a PFC boost inductor, should I be calculating for the highest possible input voltage, V_RMS*sqrt(2), (my guess is yes, but you'd know better)?

2. Rather than calculating for fringe flux factor, couldn't I just avoid it entirely by calculating for the radius of the flux (it being proportional to l_g), and put a few layers of teflon over the l_g region of the bobbin or perhaps the entire bobbin length for the sake of even winding?

3. This question is about the MOSFETS and output voltage. I understand that the higher the output voltage, the lower your transformer current will be at a given power output, reducing the risk of saturation(correct me if I'm wrong).   If you were building the converter to operate with a P_OUT >= 1kW and you had FCH023N65S3L4(same as next, 4 legs, 1-Drain 2-Power Source, 3-Kelvin Source, 4-Gate), FCH023N65S3_F155(650V, 75A, 23 m ), FCH060N80_F155(800V, 58A, 60m ), SCT30N120(1200V, 45A, 90 m SiC), MOSFETS and FFSH40120ADN_F155 (1200V 40A SiC), FFSH30120ADN_F155(1200V 30A SiC) Schottky rectifier diodes.
What would be the ideal output voltage for the PFC application and which of the aforementioned components would you use at the chosen voltage, using a EE55/55/21, PC40 transformer core in a full bridge topology?

Thank you for your time and patience .