Half bridge DC-DC converter topology

There is a thread in=20

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which suggests a half-bridge DC-DC converter with the following = topology:
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Originally I thought it was only useful for low power applications like=20 phone chargers, and I think the capacitor in series with the primary is=20 superfluous because of the two series capacitors across the DC bus. I = found=20 a similar topology here:

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I modeled the converter using LTSpice and it seems to work quite well = with=20 reasonable components, and it seems to have less problem with transients =

than my direct drive push-pull topology. It also seems to be fairly = tolerant=20 of imbalance and it does allow the use of PWM, although it works best at =

50%.

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The simulation ASC file is there also:

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In this case, it is a high power step-down DC-DC converter. Apparently = many=20 EVs use a separate 12V battery for accessories so they can use the same=20 components as wiring as the original ICE donor (or transplant recipient) =

car. The 144V is typical for a battery pack and the DC-DC converter uses =

power from that to keep the battery charged and run the lights, fans,=20 wipers, and other usual accessories. But apparently some of the = commercially=20 available converters are not very reliable or efficient, and just using = an=20 ordinary switching supply and/or charger such as are available from=20 Mean-Well are prone to failure in an automotive environment.

I may try a similar design for my purposes, which is essentially the=20 reverse. I want to use 24-48 VDC from batteries and boost it to 320 VDC = or=20

640 VDC for a VFD and three-phase motor. I have the previous push-pull=20 design modified with a capacitor precharge circuit and adjustable PWM = but it=20 has become complicated, and this topology seems simpler and perhaps = better.=20 There seem to be many more drive ICs and complete controllers for=20 half-bridge than for push-pull, so maybe it's the way to go.

Thanks,

Paul=20

Reply to
P E Schoen
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The reason it works better is because it has a choke input filter. Although you still get nasty inrush current with a voltage-mode controller, at least without a lot of precautions. Current mode control is best.

Tim

-- Deep Friar: a very philosophical monk. Website:

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Originally I thought it was only useful for low power applications like phone chargers, and I think the capacitor in series with the primary is superfluous because of the two series capacitors across the DC bus. I found a similar topology here:

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I modeled the converter using LTSpice and it seems to work quite well with reasonable components, and it seems to have less problem with transients than my direct drive push-pull topology. It also seems to be fairly tolerant of imbalance and it does allow the use of PWM, although it works best at

50%.

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The simulation ASC file is there also:

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In this case, it is a high power step-down DC-DC converter. Apparently many EVs use a separate 12V battery for accessories so they can use the same components as wiring as the original ICE donor (or transplant recipient) car. The 144V is typical for a battery pack and the DC-DC converter uses power from that to keep the battery charged and run the lights, fans, wipers, and other usual accessories. But apparently some of the commercially available converters are not very reliable or efficient, and just using an ordinary switching supply and/or charger such as are available from Mean-Well are prone to failure in an automotive environment.

I may try a similar design for my purposes, which is essentially the reverse. I want to use 24-48 VDC from batteries and boost it to 320 VDC or

640 VDC for a VFD and three-phase motor. I have the previous push-pull design modified with a capacitor precharge circuit and adjustable PWM but it has become complicated, and this topology seems simpler and perhaps better. There seem to be many more drive ICs and complete controllers for half-bridge than for push-pull, so maybe it's the way to go.

Thanks,

Paul

Reply to
Tim Williams

The topology that you are admiring works well in the application because the primary voltage is high. The half bridge lends an automatic reduction in turns ratio. It will not work as well, if the primary voltage is reduced by an order of magnitude, to produce a high voltage output, because it pushes the turns ratio in the wrong direction - away from the ideal unity.

If you examine the circuit and imagine active switches on the low voltage side, you will see that the low voltage end of the admired circuit becomes a current-fed push pull topology. If you wanted to maintain the utility in reverse power transmission, you should try to preserve this form, as it can function naturally as a boost converter if low voltage switch conduction overlaps.

The issue of inrush is not avoided, however. If you expect it to operate into low voltage loads it must be manipulated to run without an overlap on the low voltage side, with some allowance for energy transfer in the non-overlapping period. Some kinds of switched snubber have been employed to do this successfully, although the added switches do tend to increase component count and cost.

This is not an issue if you're charging batteries with terminal voltages that don't reduce to abnormally low values - so you should decide whether this thing is intended to operate without batteries early on. In an automotive application, it would be highly abnormal to expect anything to run without the fuel source.

RL

Reply to
legg

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It looks like the series version of Peter Baxandall's Class D oscillator.

Jim Williams popularised the parallel version (though he didn't credit Peter Baxandall and probably never knew that Peter Baxandall had described it first in

1959).

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--
Bill Sloman, Nijmegen
Reply to
Bill Sloman

I redesigned the circuit for 24V to 320V, and it is not a battery = charger,=20 but a source of high voltage from a small battery pack.. I had some = problems=20 with some extremely high short duration (40 nSec) power surges in the=20 MOSFETs at turn-off, and I found that most large capacitors for the = center=20 tap had fairly high ESR so that they were eating up about 40 watts each. = So=20 I found that I could use much smaller value capacitors which are = actually=20 polypropylene film, with ESR of 2-4 mOhms, and things worked much = better. I=20 had put some hefty snubbers in the circuit but they may not really be=20 needed. It seems like this should work OK for about 1 kW and hopefully = up to=20

2 kW or so. Maybe 5 kW, although for that I might use 36 or 48 VDC = input. I=20 want to keep the battery current under 100 amps.

So, here is the simulation:

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and the ASC file:

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I might see if I can fix my existing push-pull DC-DC converter pretty = much=20 as-is but adding the precharge and some series inductance to lower the=20 inrush. I'll see if I can get it to work at 16 kHz with the iron core=20 toroid. That should be interesting.

The new design uses 50 kHz and a ferrite transformer. I need to = implement a=20 precharge and/or current limit as well. I'll package it in a smaller box = and=20 add some hooks for measurement and datalogging. I may actually build it = in a=20 couple of weeks.

Thanks,

paul=20

Reply to
P E Schoen

If you examine your simulation more closely, you'll find some difficulties exist that are being glossed over.

The power train ripple current, determined by the output inductor, could not be larger (producing AC losses in the internal source impedance of over 400W). 20uH is a very small value for the forward topology at 300V.

Source internal loss can be reduced by two orders of magnitude if the output inductor value increases by one order. This is not normally the major design criteria in choosing an output filter inductor, but it's a good indication that you don't know enough about this design process to proceed.

I suggest more reading and comprehension, with less bravado, in future 'work'. I doubt your simulations will ever accurately predict behavior in any low voltage, high current, high frequency circuit, unless some attempt is made to introduce the physical strays of wiring inductance and leakage inductance accurately. This requires at least physical model for first estimation. Admittedly, these precautions were more commonly enforced in the past, when real hardware, real expense and real safety were involved.

RL

Reply to
legg

I don't really see how the source losses come into play. I was getting = close=20 to 90% efficiency at about 1 kW power level so there can't be any more = than=20

100W total losses. And I can see that most of that is in the MOSFETs and = the=20 capacitors. Do you calculate the source losses by using I(in)^2 * R(in)?

I increased the value to 100 uH and then 50 uH, and both seemed to work=20 well, although output voltage and total power dropped. I will need to = look=20 at practical inductors to see what would be a good fit. I also tried=20 increasing the resistance of snubber resistors R3 and R4, from 0.1 ohm = to 1=20 ohm or 10 ohms, and the higher values produced short duration power = surges=20 of 1 to 2 kW. A 0.2 ohm value brings it down to about 500W, which may be =

safe, depending on the actual MOSFETs I use.

I understand some of the basics but I don't have a strong background in=20 mathematics and magnetism, so my design process tends to be more=20 "instinctive" and determined largely by trial and error simulation. I = also=20 don't have much experience in high frequency circuits, which is probably = why=20 I have had problems with some designs when I have committed them to a = PCB.=20 The information about skin effect and high frequency AC resistance was = an=20 eye-opener. There is an incredible amount to learn in order to be truly=20 proficient, and there's a limit to how much I can learn by reading and=20 comprehension.

When the explanation becomes peppered with calculus my mind shuts down. = I=20 seem to do better by running a simulation and trying to observe effects = that=20 I did not expect, I look for probable causes and make changes to see if=20 there is an improvement. It may not be the best way to proceed, but I = have a=20 feel for what will happen in real world circuits and usually they have=20 worked about as expected. My problems have usually been due to ignoring = the=20 start-up transients, and when I deal with them, I think it will be = reliable.

These circuits are more or less on a hobby level at this time. I'm using =

them for my own electric tractor project and I'm trying to apply what I=20 learn to larger systems such as electric cars and trucks, in the DIY = market.=20 There are some things that I am still learning from the experiences of=20 people on that forum, but I can also see that they often do not have a = solid=20 understanding of some basic principles. It's quite a leap from my own=20 projects of 2 kW or so, to some of their projects which usually involve=20

20-50 kW and in some cases into the megaWatt range. I'm used to dealing = with=20 such power at line voltage levels and 60 Hz, and AC currents in the 10k = to=20 100k range, but their use of high capacity batteries and exotic motors = and=20 controllers is something else. Mistakes at that level, especially in=20 automotive use, can be costly and dangerous, especially when so many = DIYers=20 do not really understand what they are dealing with and what they are=20 measuring.

Thanks,

Paul=20

Reply to
P E Schoen

There is nothing shameful about working with circuits below 1KW. It's the most practical method of developing preliminary physical models and prototypes.

The principles involved apply at all power levels. What changes is the physical limitations of materials and methods, when scaled. Your circuit is a good example. Try running the simulation with reduced transformer Lp, while maintaining turns ratio. Even with a coupling coefficient of 0.99, your current values are dominating permissible Di/Dt in the power transfer, due to leakage terms.

In real life, Lp will be selected only to be high enough so that magnetizing energy doesn't dominate function unintentionally and copper losses are minimized, so long as core losses remain manageable.

Another example - see what happens when 50nH is present in battery lead wiring....

Neither of these factors would be so noticeable at 100w. One of the major purposes of modeling in software is that these effects can be predicted before hardware is constructed.

There's usually not much calculus required, it's usually just basic algebra, with a little trig thrown in.

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DIYers may try to use readily available subassemblies and materials from similar, if not directly related applications. It's just as important to understand the potential and limitations of these materials as it is when developing from scratch.

RL

Reply to
legg

This IR driver chip is pretty nice:

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at least for fixed duty cycle.

Reply to
John Larkin

I have some similar products, IR2104, IR2136, IRS2001, IRS24531. The=20 IRS2153D

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= seems=20 similar to the IR21531 and in fact the added 1 on the part number = signifies=20 a smaller deadband. I like the idea of the built-in timer for=20 self-oscillation although I also like to drive with a PIC for more = accurate=20 frequency.

The topology of your application shows the transformer primary driven=20 through capacitors, and that might be even better than what I have with = a=20 center tap between two capacitors. It seems to me that an output voltage =

control of sorts could be done by adjusting the frequency of the square=20 wave. And the start-up surge would be easily controlled by starting with = a=20 small duty cycle and ramping up to 50%. That would require a bridge = driver=20 like the IRS2001 which has separate high and low drivers.

For my low voltage high power application the capacitors would need to = be=20 able to handle high ripple current with low ESR. Those are somewhat rare = and=20 expensive. Here is a 22,000 uF 63V cap with 20A ripple for $38.

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731

For a 24V system with half-bridge I figure that's about 12V RMS so for =

1000=20 watts I need about 80 amps. So four of those would be $150.

It seems better to use polypropylene film. Here is a 10uF 300V capacitor =

with 2.9mOhms ESR and 15A ripple, for $3.51ea/10:

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The high voltage is "wasted" but the cost is much better. 6 in parallel = is=20 still reasonable, $21. And I can easily go to a 48V system or even = higher=20 with no worries. In the EV world it would be very useful to have a =

144V-144V=20 booster to get 288V for a 240 VAC motor drive. Probably about 20 kW. And =

probably best to build with multiple 2 kW units in parallel. $50/kW = would be=20 an acceptable selling price.

Thanks!

Paul

Reply to
P E Schoen

If you need a lot of filter cap, center-tapping the filter caps makes sense. My 24 volt input is already DC, so I didn't need a lot of filtering.

It seems to me that an output voltage

The center-tapped filter cap is interesting in that it reduces DC inrush surge. The low side of the primary powers up at V+/2. Of course, you still have to charge the caps on the load side.

Full bridge operation mitigates some of those problems. I think.

Reply to
John Larkin

My application will be powered by batteries, so very little filtering is =

needed. Mostly for high frequency current surges to compensate for cable =

inductance and battery ESR.

They also draw a huge surge on the line side from the battery. The = series=20 capacitor draws nothing until the output of the half-bridge starts=20 oscillating. I tried using a 5% duty cycle and I got 65 VDC output. = Should=20 work to ramp up the duty cycle for a soft start, or for output = regulation.

Well, yes, I think so. Or I could go back to the direct drive push-pull = CT=20 topology. So there are trade-offs, and direct coupling may be best. But = it=20 seems that the series capacitance helps reduce the spikes. Maybe a full=20 bridge with a capacitor in series with the primary? Could there be a = problem=20 with resonance?

Thanks,

Paul

Reply to
P E Schoen

There's an interesting thread in the DIYelectricCar forum that shows how =

much battery lead and motor lead wiring inductance and resistance can = affect=20 the waveforms and operation of a rather simple but high-power PWM DC=20 traction motor controller. I tried to give some advice, but I think much = of=20 the difficulty is the OP's lack of understanding as well as poor wiring = and=20 measurement techniques:=20

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The transformer design seems to be the major problem, especially at = higher=20 frequencies. I need to rethink my original method of using thicker wire, = and=20 go to a bifilar winding with multiple smaller strands in parallel. But I =

don't know just how to determine leakage inductance, and I'm not sure if = my=20 LCR meters are good enough to measure it after building one. I just = guessed=20 at the 0.99 for the coupling. I know everything works better if I set it = to=20

1.00, but that's unrealistic. I have sometimes added external inductance = to=20 the model, and that seems to work a little better. And I also guessed = the=20 magnetizing inductances shown in this simulation, but I used measured = values=20 for my previous simulations for the toroid transformer at 2 kHz.

Those are some excellent references. You're right, it's not that hard to =

understand. But it will take some time to grasp all the pros and cons of =

various topologies.

Yes, but it's probably a good idea to see what is commonly available, = such=20 as the cores and bobbins I have seen on eBay. I have some ferrite cores = and=20 bobbins that I picked up from who knows where, and even where the parts = that=20 have markings I've had a hard time finding data. For a much smaller (2W) =

DC-DC transformer I was able to get samples from Lodestone Pacific and=20 Cosmo, but they have rather high minimum order levels.

I think there are two approaches to engineering and design, with one = extreme=20 (perhaps the Tesla method) being a very careful and specific design = process=20 which should produce a product that works pretty much as specified, to = the=20 other extreme (perhaps the Edison method), where you might make 99 = mistakes=20 running simulations and building actual units, and with good measurement =

techniques and some experience and "instinct", coming up with a winner = on=20 try #100. I admire Tesla, and others who can use a very solid = theoretical=20 approach, but I find the Edison method more to my liking.

Thanks,

Paul=20

Reply to
P E Schoen

Did you actually try either of the suggestions in your model?

Rest assured, both magnetizing and leakage inductance are directly measurable, using basic inductance meters, or indirectly, using simple calculations based on recorded transient current waveforms, at easily developed power levels. Their ratio produces the coefficient of coupling required for more accurate simulation at higher power levels.

An unaltered winding pair will have the same leakage inductance, with respect to each other, regardless of the core material or other external environmental factors.

The effects of leakage on power transfer and Di/Dt is most easily demonstrated in low power flyback circuits.

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The same Di/Dt limitation occurs in power transfer where the winding polarity and direction of current flow is expected to reverse.

The point is - if your leakage is mistakenly made artificially high or low in the simulation, you'll get effects that aren't reproduceable in real life. Choosing a high coupling coefficient should produce low leakage in the simulation - but by picking an unrealistically high magnetizing inductance, you also ballooned the associated leakage term out of the ballpark for a low turns count, high frequency construction.

Look for dead equipment that previously performed at roughly the same high frequency power level. This stuff is marketed by weight as non-ferrous scrap. You're looking for re-usable core assemblies. Preformed bobbins aren't often used at this power level - ground insulation and formers being constructed as required.

The issue here is the

Reply to
legg

AKA litz wire. Suggested by many already.

I've told you once...

What are they? What specification? You might be pleasantly surprised. Most commercial LCR meters should be up to the job.

Don't guess - measure.

How do you know that try #100 is the optimal solution, without calculation?

Whose electrical distribution system is almost universally used today?

Edison's, or Tesla/Westinghouse ?

--
"For a successful technology, reality must take precedence 
over public relations, for nature cannot be fooled."
                                       (Richard Feynman)
Reply to
Fred Abse

..

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ect=20

of=20

nd=20

r=20

and=20

Litz wire is multiple small strands in parallel, but it's supposed to be br= aided rather than twisted, so that each wire sees exactly the same field - = averaged over the whole length of the winding. If the various wires see dif= ferent fields, hooking them together makes a sort of shorted turn.

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could be interesting reading

The standard technique is to measure the inductance of one winding with ano= ther winding shorted. You can do better with an impedance bridge, by allowi= ng for the resistance of the shorted winding, but an inductance meter is of= ten good enough.

ed=20

We got 0.98 for a heavily gapped RM14 core (Al 160nH/T^2), and expect close= r to 0.999 for an ungapped RM14 core.=20

to=20

=20

ues=20

=20

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h=20

nd=20

hat=20

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EPCOS and Ferroxcube parts are widely available in Europe - I've got EPCOS = parts from Farnell without much trouble - they did once ship me some 10-pin= parts as if they were the 12-pin parts that I'd actually ordered, but they= sorted it out within a couple of days. The Farnell website connects you di= rectly to EPCOS data sheets, which are pretty detailed. =20

eme=20

ss=20

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The Edison appraoch turns into the Tesla approach when you've done it often= enough to have the kind of feel for what's going on that you can turn into= mathematical models. LTSpice now allows you to use the John Chan model to = simulate real inductors with hysteresis. The one part that we modelled and = tested suggests that the model works pretty well.

--=20 Bill Sloman, Nijmegen

Reply to
Bill Sloman

I tried the 50 nH in series with the battery with minimal observed = change. I=20 also rewound the ferrite core transformer I plan to use as a first=20 approximation to see what to expect. The core is about 2" square and =

1/2"=20 thick. I have two layers of 36 turns #16 AWG each followed by two = bifilar=20 windings each consisting of 3 parallel windings of #16 AWG. So the total = 72=20 turn winding is 19.95 mH and the six turns reads 0.10 mH. It should be a = 12:1 ratio but the ratio of the square roots of the inductance comes to=20 14.14. Probably an error in the measurement.

But previously I read 8.38 mH for the 72 turns, so either there was more = of=20 a gap previously or there had been some shorted turns. I had used 10 = turns=20 of #12 AWG and I had to squash it to fit the core around it.

So I'm hoping to get 5 to 10 volts per turn at 50 kHz, and with 12 V P-P =

square wave on the 3 turn primary I should get about 288 V P-P on the=20 secondary. I figure the transformer has 3.8 uH/sqrt(turns) so 3 turns = should=20 be about 35 uH. That should be about 11 ohms at 50 kHz so I'll have = about 1=20 amp magnetizing current. Since I expect up to 50 amps at 12V for 600 = watts=20 that's only 2% so it seems OK. This is where I usually just put it on = the=20 test bench and run the voltage up and see where the current starts = rising=20 faster than voltage and shows saturation. And I can also look at the = current=20 waveform. Otherwise I'd need to go through the calculations, and since I =

don't really know what material this is I still have to wing it.

I do have a better LCR meter with a 10kHz signal, but I haven't used it = for=20 awhile. I realize I can measure the magnetizing and leakage inductance = but I=20 wasn't sure how to calculate it by the physical construction of the=20 transformer.

Does a coupling factor of 0.99 mean that the leakage inductance is 1% of = the=20 magnetizing inductance? And is it analogous to the regulation of the=20 transformer? Our high current 60 Hz transformers typically have a = regulation=20 of 5-10% which means that they will put out 20x to 10x of their normal=20 rating into a short, which is essentially how we use them. However, the = open=20 circuit current draw is probably 1/10 that at the normal output current, = so=20 that would indicate the leakage inductance would be about 1% of the=20 magnetizing inductance.

For instance, we may have a transformer rated at 480V input and 4.8 = volts=20 output at 1000 amps. The open circuit current draw might be 1 amp, while = it=20 would draw 10 amps at its rated 4.8 kVA output, and 100 amps into a = short=20 circuit. Thus the magnetizing inductance would be 785 mH. The leakage=20 inductance would be 7.85 mH. Does this sound about right?

For one-off designs that's a good idea, but I want to be able to order = the=20 right materials so that once it works, it will be reproducible and=20 manufacturable. The cores don't seem to be terribly expensive. But maybe =

it's useful to see how such transformers are made.

I wish I had the time and energy to devote to learning all the details = of=20 such designs, but I have many more irons in the fire and I need to=20 concentrate on those, where I know a bit more what I'm doing and mostly = I=20 just need to attend to some details.

Thanks for everyone's help.

Paul=20

Reply to
P E Schoen

The leakage inductance is independent of the presence of the core, so if you just calculate the mutual inductances of the windings as air-cored coils you can deduce the leakage inductances.

Sort of. Look at the transformer equation

No. That's mostly driven by winding resistance and core losses. There's no loss mechanism directly associated with leakage inductance, though if leakage inductance induces huge switching spikes it can indirectly increase your losses.

Not remotely correct. Thinks about what's happening when the transformer is driving a short - with large currents flowing through the internal resistances.

--
Bill Sloman, Nijmegen
Reply to
Bill Sloman

You should se a 20Vppk waveform on 'in' and primary current exhibiting a dual slope. V'in' will show up on the driven end of L1.

With a magnetic Xsection of 144mm, estimated for a core of this size (eg E40/16/12), your 50KHz drive waveform on a three turn winding produces core flux excursions of +/-140mT, and typical total core losses of 1.4W. This will vary with input voltage, as the circuit is unregulated.

When fully wound, this core's surface temperature will rise 50degC under a total loss burden of ~4.2W in free air.

With a 24V source, the drive voltage is approximately 24Vppk, approximately 12Vpk. It's the peak voltage that is produced on the full wave output rectifier, but only if the total input voltage is reflected accurately.

Look at the output voltage of your simulation, before the choke. You'll see that the voltage there only goes positive about a third of the conversion period. The rest of the time, the voltage is dominated by the leakage inductance of the simulated transformer during phase reversal. This loss of conduction period shows up as reduced filtered output voltage, in spite of expectations due to turns ratio.

This is mostly the effect of leakage inductance occuring in your model.

While the effect is real, the scale of this effect in your simulation is masking realistic performance.

RL

Reply to
legg

change.

Well, V(in) is more like a distorted sine wave with peaks of 27V and = valleys=20 of 20V. And it does form the upper waveshape of the driven end of L1, so = I=20 can see where battery lead inductance is a major factor.

I was a bit surprised at how much inductance a length of wire can have. = I=20 used an inductance calculator and found that a 36" length of battery = cable=20

0.25" diameter has 1025 nH of inductance.
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But when I used that in the simulation it actually seemed to improve the =

operation. V(in) varies from 25.5 to 20.5 volts (looks like a rectified = sine=20 wave) and the DC output actually seems to increase. The peaks seem to be =

shifted to the center of the conduction cycle and the current in the = primary=20 L1 looks almost like a sine wave.

Sounds reasonable. Do you know of a calculator that can obtain these=20 figures? The following seem to be pretty good:

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With the higher battery lead inductance of 1025 nH, the voltage at the=20 output of the bridge only briefly drops to a minimum of 89V, has a peak = of=20

413V, an average of 306V, and RMS of 315V. I get input power of 1.03 kW = and=20 output of 939W for an efficiency of 91%.

With an (unrealistic) lead inductance of 1 nH, the input power is 963 W = and=20 output is 872 W, for 90.5% efficiency. It is interesting and useful to = know=20 that realistic battery lead inductance may actually help the operation. = I'm=20 still using the 0.99 coupling factor.

Thanks for the tips. I can see that, at these power levels, everything = needs=20 to be modeled as accurately as possible. But in the end I will still = need to=20 build it and test it.

I still don't know what the problems are for the OP in the thread:

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It may very well be battery and motor lead inductance, which should be=20 minimized by using twisted or bundled pairs. But I think the main = problem is=20 measuring the waveforms using a cheap USB scope with long, unshielded = leads=20 within a giant loop that may be seeing current surges of 100 amps or = more at=20

8 KHz.

I'm trying to give advice on ways to check what's really happening and = ways=20 to reduce the problem, but I think there is a lack of understanding and=20 experience. Maybe on my part as well, but I have encountered similar = bogus=20 waveforms and I have been able to reduce the effects considerably by = keeping=20 measurement leads tightly twisted and outside of the magnetic loop.

Paul=20

Reply to
P E Schoen

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