QCW buck converter choke, switching frequency and gate supply

How closely a buck follows its PWM depends on three things: the inductance, the switching frequency and the output capacitance. Raising the frequency looks like the cheap fix, but it costs gate-drive power. The choke is the expensive part, and under DC bias it runs well below the inductance in its catalogue. The reference choke below reads 793 µH on an LCR meter and works out to about 341 µH at 102 A.

What it is and how it works

A buck chops its input, and the choke turns the chopping back into a level. Current through an inductor cannot step. While the switch is closed it ramps up, while it is open it ramps down through the freewheel path, and the output is an average with a triangle riding on it. The capacitor behind the choke takes most of that triangle off the voltage. Inductance, switching frequency and capacitance together set how small it ends up.

A choke for this job is usually wound on a powder core: iron, or an iron alloy, ground fine and pressed with a binder. The gaps between the grains act as the air gap, spread through the whole ring instead of cut into one face. That is how these cores hold their inductance under a bias that would drive a solid ferrite flat.

A maker publishes three figures for a core: permeability, saturation and loss density. All three are measured under conditions that are not yours. That matters more for the choke than for any other part in the converter, because it carries a large steady current with only a small wobble on top. It always sits at a bias the catalogue was not measured at.

What it does in a coil, and what you decide

The knob that looks cheapest

inductor ripple
  dI = V_in · D(1-D) / (L · f_pwm)

output ripple
  dV = dI / (8 · C · f_pwm)
  so dV goes as 1 / (L · C · f^2)

Frequency enters the output ripple squared and inductance only linearly, so it is tempting to raise the frequency first. Look at what it does before counting the cost. Doubling the frequency divides dV by four, exactly as much as quadrupling the choke. On the current ripple it is weaker: dI goes as 1/(L·f), so quadrupling the choke quarters it and doubling the frequency only halves it. The current ripple is the one that matters here, because the threshold that breaks the ramp is dI/2. Frequency gets you the same output ripple with silicon instead of copper and window space. That is a real saving, but it does less for the threshold, and it costs gate power as well.

The gate supply nobody budgets for

The buck's own switch has to be driven. The average gate current is Q_g · f, so the gate power is Q_g · f · the rail-to-rail swing, and it rises with frequency. Gao's buck switch is an FF300R12KS4 half bridge module (loneoceans) and Infineon's datasheet for it gives QG = 3.20 µC at VGE = -15 V to +15 V, which is the ±15 V column here. Every row is Q_g · f and Q_g · f · swing on it [derived]:

• 20 kHz: 64 mA. 0.96 W on +15/0, 1.52 W on +15/-8.7, 1.92 W on ±15.
• 30 kHz: 96 mA. 1.44 W, 2.28 W, 2.88 W.
• 40 kHz: 128 mA. 1.92 W, 3.03 W, 3.84 W.
• 60 kHz: 192 mA. 2.88 W, 4.55 W, 5.76 W.

Only the top end of the frequency band can be computed. On that brick a two watt module runs out at about 21 kHz on ±15 V, about 26 kHz on +15/-8.7 V and not until about 42 kHz on +15/0 [derived from the rows]. The choke worked through below runs at 22 kHz, which on ±15 V is just over that limit at 2.11 W [derived], so changing the rail is cheaper than changing the frequency. The bottom of the band is a matter of preference, and every kilohertz you give up has to be made up in inductance.

What actually breaks the ramp

Ripple is usually tolerable. The real problem is discontinuous conduction. When the inductor current reaches zero inside a chopping cycle, the gain rises above the duty cycle and starts to depend on the load. At nearly no load the filter output floats up towards the bus at any duty at all. At that point the duty no longer sets the voltage.

This is a failure of the freewheel buck, one switch and a diode. The diode passes current one way, so when the inductor current would go negative it stops instead. A synchronous buck puts a second switch where the diode was and lets the current run negative, so it never leaves continuous conduction. If you freewheel through the body diode of a half bridge's bottom device, the usual shortcut, shorting that gate to its emitter is not enough. It needs an active Miller clamp or a very short gate loop.

The threshold is dI/2, the load current below which it happens, and that is the figure to read rather than the ripple. CJ runs 100 µH, 40 µF and 25 kHz on the 420 V he states in the same post. That is 42 A of ripple, 5.3 V of output ripple and discontinuous below 21 A [derived, all three, at the worst case duty of a half], on a machine that makes 94 inches of arc, 2.39 m in our units and not his. The ripple is fine. The 21 A means much of every ramp runs in the non-linear region.

Inductance cures it. Frequency moves the threshold too, at the gate-power cost above. Bench it on ten ohms rather than thirty: on a high resistance the current goes discontinuous and you see a nonlinearity the coil will never show you.

Reading the catalogue the core came out of

Four habits close the gap between what a maker measured and what you are about to build. Three of them change a number and the fourth changes the shortlist. Three families of powder turn up in QCW buck chokes, and they are not interchangeable:

iron powder        cheap, lossy, the red and yellow rings
Sendust, FeSiAl    lower loss, sold as Kool Mu
SiFe               best inductance retention under bias, sold as XFlux

Ferrite is missing from that list for a reason you can put a number on. Magnetics' own Chinese handbook tabulates seven ferrite materials at 4200 to 5000 gauss, which is 0.42 to 0.50 T [derived], and gives Kool Mµ in the same document as "磁感应强度高（10,000 高斯）", 1.0 T. The trade publisher 世纪电源网 states 1050 mT independently, agreeing to five per cent. A Sendust ring carries about twice the flux of a ferrite one. They also give way differently, since ferrite goes over a cliff where powder sags. Those are two sources, a maker and a trade publisher, and neither is the builder whose choke you are copying.

The same trade publisher turns that ratio into a core size and states the design point it applies at. It compares Kool Mµ against gapped ferrite. That is the right comparison, because a ferrite choke carrying DC has to be gapped. In their words: "假设特定的50％下降设计点，铁硅铝(KoolMμ)的磁通量是间隙铁氧体的2倍以上,这使磁芯的 尺寸可缩小35％，设计时可以把磁芯的尺寸缩小30%至35%", at a specified 50 per cent roll-off design point Kool Mµ carries more than twice the flux of gapped ferrite, which lets the core shrink by 35 per cent, and in practice you design for a 30 to 35 per cent smaller core.

Note the condition. Their design point is where the inductance has fallen to half. That is a roll-off point, well short of saturation. The measured example above sits on the same axis: the stock Sendust ring at 350 µH static and 170 µH at 17.5 A, 49 per cent left. A builder who wound to that number and an industrial designer who specified to it are working at the same point, though neither says so.

The same page lists three more differences. The last is easy to miss:

• Gapped ferrite has to be designed inside the safe part of its curve, while powder is designed within the controlled roll-off. The soft curve is a form of fault tolerance, and it matters most at high power.
• Ferrite's capability moves with temperature and Sendust's much less. That is why ferrite suppliers publish 25 °C and 100 °C figures side by side.
• A gap has fringing loss and a powder core has none. Flux escaping around the gap couples into the nearest winding and heats it. That cost of gapping does not appear in any B_sat comparison, and on a choke wound tight to the core the winding takes it.

The figures below come from two catalogues: KDM's 合金磁粉芯样本 of June 2026, whose grades and names are on its product page, and Magnetics' Chinese catalogue of 2015. Both are PDFs, so what follows is a paraphrase and not a quotation you can follow, and most of the figures are ours [derived], worked out from those catalogues' own equations.

A ranking is not a fact until you say at what field it was read

A catalogue's comparison table is read at a field the maker chose, and at your field the order can be different. These are effective permeabilities at 26 µ, from one maker's own curve equations [derived]:

                    100 Oe  200 Oe  308 Oe  400 Oe  500 Oe
High Flux, KH-HT      25.7    24.1    20.2    16.1    11.9
High Flux, KH-HP      25.7    24.0    20.4    16.6    12.7
SiFe,      KSF-HT     24.9    22.3    19.0    16.3    13.7
Sendust,   KS         20.8    13.8     8.8     6.3      -

Read across the range and the leader changes. SiFe passes both High Flux grades at about 423 Oe [derived, straight-line between the 400 and 500 columns]. The two High Flux grades cross somewhere between 200 and 308 Oe, and the data cannot place it closer than that. Nothing changed except the current. At the low end there is hardly a ranking at all. At 100 Oe the column spans 24 per cent from best to worst, 25.7 against 20.8, and at 400 Oe it spans 163 per cent, 16.6 against 6.3 [derived, both spans]. A comparison at 100 Oe answers a different question from the one you have at 400, and 100 Oe is where comparison tables tend to sit.

Both spans come from one material falling away while the rest stay close. Drop the worst and the other three sit within 3 per cent of each other at 400 Oe, and within 3 per cent at 100 Oe as well [derived, both]. The one decision the column makes is whether to use that one material, and at 100 Oe it looks like 24 per cent when it is really 163. This is also one vendor at one permeability, so it shows how the materials stand against each other, not what a given grade will do.

Work out your own field first, from H = 0.4π·N·I/l_e with l_e in centimetres and H in oersteds, and read every curve at that number. If the catalogue does not plot that far, its comparison does not cover your part. The reference choke below works at 427 Oe, a few oersteds past the SiFe crossing.

The loss column is not your loss, and the bias is on your side

Core loss comes from the AC excitation only. A DC bias of any size produces none of it. Magnetics states this directly and then puts a number on it. One inductor, twenty turns, the same 8 A of ripple at 100 kHz, run once at 20 A of DC and once at none. The peak flux is 0.06 T with the bias and 0.11 T without it, both figures theirs, because the bias has pushed the permeability down and a lower permeability makes a smaller swing out of the same ripple current. Through the loss exponent their worked example implies, that is more than three times the loss with no bias at all [derived; the flux figures are theirs, the exponent is fitted to the two loss figures printed beside them]. So the bias that costs you inductance gives some of it back in loss, and a loss figure quoted at no bias is pessimistic for a choke that runs deep in bias.

This reverses part of the ranking above. The same maker, at one geometry and 60 µ (so not the same column as before), prints peak core loss beside retention:

                 retention at 100 Oe    core loss, max
High Flux             73.6 %             300 mW/cm3
Neu Flux              67.2 %             600
SiFe                  67.2 %             750
Nanodust              60.7 %             250
Sendust               56.1 %             370

Read the two columns together and only two parts are in contention. High Flux is best on bias and second on loss. Nanodust has the lowest loss on the list and pays for it in bias. Every other part is beaten on both counts by one of those two, and SiFe is the expensive one here, with two and a half times High Flux's loss at the same retention. That is the opposite of the ordering higher up, for the reason already given. This retention column is read at 100 Oe, where retention decides nothing.

The exponent depends on what you are holding still

Losing permeability shrinks the flux swing, which cuts the loss. How much it cuts depends on what you hold fixed while comparing:

same core, same turns, swap material     swing tracks retention
                                         loss goes as retention squared

same core, same inductance               fewer henries per turn means more
at the operating point                   turns, and more turns make a smaller
                                         swing at the same ripple
                                         loss goes as retention, first power

The second is what a designer actually does, and it halves the exponent. On the 60 µ table above, where retention runs from 73.6 per cent to 56.1, the loss multiplier across that spread is 1.7 times in the first reading and 1.3 in the second [derived from those two retentions, squared and not]. A material that sags makes up part of its own loss through the extra turns.

Both multipliers are read at 100 Oe, the field warned about above, because that table has no other column. "First power" also holds only to within the exponent. The step halves whatever the material's loss exponent is, and the only one we have is about 2.0 [derived], back-fitted to the core in Magnetics' worked example because only that value turns their 260 into the 900 they print, where 2.3 gives 1050. The halving holds either way, since it depends on neither.

Under bias the shortlist grows, and nothing falls off it

Take one slice at a single permeability and a single field, so retention and loss are in the same units, and multiply each part's loss by its own retention. On two such slices at 308 Oe, seven parts at 60 µ and sixteen at 26 [derived from that catalogue's fit equations, both counts]:

                      best parts on the catalogue    ...and once biased
7 parts at 60 µ            3                              4
16 parts at 26 µ           2                              4

At neither permeability does any part drop off. The list only grows, by admitting the parts that sag. Multiplying loss by retention rewards a material for losing permeability, because losing it is what shrinks the swing that makes the loss. The catalogue's ranking is fine as far as it goes. It just rejects some parts that are reasonable once the bias is real, and does not say which.

What that leaves you buying

Anders Mikkelsen recommends a SiFe powder in the permeability 40 to 60 range, on one ground: these hold their inductance under bias better than Sendust does, and bias is the main problem in a choke carrying a hundred amps of DC with a small ripple on top. The cost is loss, higher except in the newest formulations, and he warns it can grow excessive with switching frequency and input voltage. Take "40 to 60" as a range of stock parts rather than an optimum. XFlux is sold in seven grades, 19, 26, 40, 60, 75, 90 and 125, so that names two adjacent catalogue parts, and the choice between them comes down to which you can buy in the size you need. Other builders choose on other grounds, most often saturation flux. That does not contradict him, because this choke never reaches a cliff before its permeability has halved.

Sizing one

First, which current. Not the primary current. The choke sits on the bus side and carries (2/π)·I_primary, the average the bridge draws rather than the peak the tank circulates. On the 160 A primary of the reference machine that is 102 A [derived]. Check which current somebody else's figure refers to. Gao's 100 A of primary current is about 64 A through the choke as a peak and about 90 A as an RMS figure, which he does not say [derived, both].

The current the catalogue prints is something else again. On a powder toroid the quoted saturation current is where the inductance has fallen to 90 per cent of its initial value. That is where sag starts to show, long before anything gives out. One core maker works it through end to end on a Sendust 60µ part, l_e of 10.74 cm and 60 turns, whose curve puts 90 per cent at 11.6 Oe: 11.6 x 10.74/(0.4π x 60) = 1.65 A, at 437 µH of its

1. Both are the vendor's own figures and both reproduce. Keep that 0.4π. The law is also printed as N·I/l_e, which returns ampere-turns per centimetre rather than oersteds, one of them being 1.2566 Oe, and only the form with the 0.4π lands on the maker's stated 1.65 A. Read the other into a curve plotted against oersteds and you are at four fifths of your real field.

The path length l_e is not always on the sheet. The three numbers are not independent, since A_L = µ₀·µ_r·A_e/l_e, so the path length follows from the area and the inductance factor as l_e = µ₀·µ_r·A_e/A_L. It checks out against a maker's own table. On a toroid listing where an A_e of 0.114 cm², an l_e of 3.12 cm and a permeability of 26 sit in the same row as the part's inductance factor, it returns 11.94 nH/N² against the 12 printed (KDM's product page). It also works as a cross-check, and on Gao's published figures it catches an error. His permeability of 10, A_L of 22.8 nH/N² and A_e of 1.68 cm² give a path of 9.3 cm against the 19.8 cm the same page prints [derived from those three figures]. The area is the number at fault. 1.68 cm² and the 12.7 mm height listed beside it are the single-height T300-2, while the core he wound is the taller D. With the section doubled the law comes back to about 21 nH/N² against the 22.8 he quotes.

Now the reference choke, by the same definition. Its datasheet publishes two points and 90 per cent is not one of them. The lower is 80 per cent at 215 Oe, which on 108 turns and a 32.4 cm path is 51 A [derived]. The 90 per cent point comes off the fit those two points set, µ/µ_i = 1/(1 + (H/380)^2.43), at 154 Oe and so 37 A [derived, an extrapolation below both published points, which is why it is quoted beside the 51 rather than instead of it]. Either way the rating is between a third and a half of the 102 A the choke carries. The rating sits at four fifths or more of catalogue inductance and the working point at 43 per cent. The rating describes a different part of the curve from the one the choke works on.

The catalogue inductance is therefore not the working inductance. A ring sold as 800 µH quotes A_L near zero current. Wound to 108 turns it measures 793 µH on an LCR meter, and the permeability curve puts it at 341 under 102 A of bias [derived, not measured]. Design the ripple at 793 and you get twice what you planned.

793 uH catalogue
  x 0.43 permeability left
= 341 uH working

The sag and the permeability loss are the same effect. L = A_L·N² and A_L is proportional to permeability, so the fraction of inductance you lost and the fraction of permeability you lost are the same number, and there is only one check to run. Read the fraction off the permeability curve at your own field and multiply the catalogue inductance by it. Here 102 A through 108 turns on a 32.4 cm path is 427 Oe, and a curve giving 80 per cent at 215 Oe and 50 at 380 puts that at 43. This is the method Anders Mikkelsen gives on the forum. Working it through flux formulas answers a transformer's question about a part that is not being used as a transformer.

The flux check is a second method and does not replace this one. B = L·I/(N·A_e) wants the chord permeability, total flux against total current, and neither L you have is that. The catalogue A_L overstates the flux. The derated figure is the incremental permeability, the slope at the bias point, and understates it. They are 2.3 times apart on this core [derived from 793 and 341] with the chord value in between, so that is the width of the bracket and not the error in either end. What you can state is the pair of bounds: if both clear you are clear, and if they straddle you have computed nothing. Here both clear, so the droop check decides the design and the flux check only has to pass.

Anders quotes the pair rather than the catalogue figure too. Sizing a choke for somebody else he gives a 0078912A7 pair at 32 turns as 116 µH at zero bias and just above 40 at 150 A, two thirds of it gone, in the same breath as the first number. A powder-core inductance only means something with a current next to it.

The wound value also differs from the computed one. Gao calculated 99 µH for his 66 turns and measured 113.6, fourteen per cent over before any bias at all, and puts it down to imperfect winding (loneoceans). Part of that gap is not his hands. Magnetics states the tolerance on a powder core outright: nominal and actual A_L may differ by "±8%", every core is tested and "按每隔2%的公差分档", sorted into two per cent bins, and designers wind a slightly different turn count to land within ±2 per cent of nominal. Up to eight of his fourteen points could be in the core before anybody touches the wire. Fourteen is still more than eight, so his explanation still covers the rest, and the practical advice stays the same with two reasons behind it. The two errors run opposite ways, the winding high and the bias low, so they partly cancel. That makes the error harder to see, because the sign of a winding error depends on your hands. Measure the ring you wound, at the current you will run it at.

Past a point you can compute, more turns stop helping. L goes as N² and H goes as N, so each turn pushes you further down the curve as it raises the count. Write the fade as µ ∝ H^-a and the exponents subtract, L ~ N^(2-a). Below 2, turns add inductance. Above it they cost you. a climbs with the field, and on the fit used here it reaches 2 at 715 Oe, which on this core is 181 turns:

turns    H      mu     L
 108   427 Oe  43%   340 uH
 181   715     18%  ~395  <- here
 300  1186      6%  ~365

Getting there is poor value anyway: 108 to 181 turns gives 16 per cent more inductance for 68 per cent more wire. The rows past the first are rounded because they come off a curve read past its published points. A powder core has an inductance ceiling set by the material rather than the window, and only a different core gets past it. Copper runs out first: 108 turns of 7 AWG fills about 30 per cent of a 4710 mm² window, and 50 per cent at 181. The limits are heat and wire rather than window space, the opposite of what transformer experience suggests.

Then check that it stays continuous. At 341 µH, 22 kHz and a 650 V bus:

Vout    dI      DCM at   bus I   margin
 40 V   5.0 A    2.5 A   12.5 A   5.0x
325 V  21.7 A   10.8 A  101.9 A   9.4x

It is continuous everywhere, with five times the margin at its worst, and 4.9 V of ripple at the top on 25 µF. No extra capacitance is needed to carry the doubler, which a smaller winding would have demanded. A doubler does not threaten the start of a ramp either. The input enters the ripple only through a ratio, and at small duty it cancels: doubling 325 V to 650 moves the ripple at 30 V out from 3.6 A to 3.8, and at 300 V out from 3.1 A to 21.5 [derived, all four]. A doubler moves the top of the ramp, and at the top capacitance fixes it.

What will get you

The tables in the catalogues are less reliable than the text. In the Magnetics catalogue the printed loss equation does not reproduce the loss printed on the same page: its constant is off, though its exponent is right. In both catalogues the worked examples and the prose held up under checking and the tables did not, so every figure above comes from a worked pair rather than a formula.

A part at 26 µ and a part at 60 µ are not two points on one axis. Grades are separate products with separate curves, and a table that mixes them shows the grade ladder rather than the material. Two vendors are not directly comparable either. Worked through both catalogues above, KDM's figures come out optimistic against Magnetics on bias retention and low on loss density. We have not established how far apart they are, so only the direction is known. A comparison holds inside one catalogue and has to be redone across two, where the winner can change.

The heating is continuous, and the peak figure does not tell you how much. The 262 W of copper in the sizing widget is the figure at the top of the ramp, and the ramp only runs part of the time. Two factors come off it and they multiply. Over a rise that is linear to that peak, the mean of I² is a third of the peak's. This machine's ramp is 25 ms at five bangs a second, or 12.5 per cent of the time. The average copper loss is nearer 11 W than 262 [derived, 262 W over 3, times that 0.125], and at half a hertz nearer one watt. Size the cooling for the average and the wire for the peak.

What goes wrong

• The ramp starts higher than the duty says, and the gain follows the load. This is discontinuous conduction at the bottom of the ramp, where there is no arc to load it. Set the starting step under real load.
• The choke measures right on the LCR and the ripple is twice what was designed. The catalogue value was used instead of the value under bias. They are the same number multiplied by the permeability you have left.
• The core was chosen on a comparison table and comes out lossy. The table was read far below the working field, where the top of the column cannot be told apart and the one material that is genuinely worse looks only slightly so.
• The core was chosen on saturation and the inductance still collapsed. A powder core has no cliff anywhere you will be working, and its rated current is defined at a ten per cent drop, where sag becomes visible.
• A part was rejected on its loss figure and would have been the right one. The figure was the catalogue's, at no bias, on a material whose permeability was going to halve at the working point and take the loss down with it.
• Everything measurable looks fine and something is running warm. Watch the freewheel diode, the choke and the bank, not the resistors. The choke takes continuous heating in both copper and core, while gsch.labs's 300 W input transformer was too weak and showed up as a sagging top of ramp instead.

Where next

• The buck is the ramp, the converter this choke sits in, and the synchronous variant with no discontinuous region.
• The gate supply is a power supply, the other half of the frequency cost.
• The DRSSTC bus capacitor bank: loop, ripple and the volts it sees, for the bank behind all of this.

The QCW diagram draws the buck as its parts, a switch, a choke, a freewheel diode and a capacitor, because without the choke a QCW would have no ramp.