QCW buck choke, switching frequency and the gate supply

Three things set how well a buck follows its PWM: the inductance, the switching frequency and the output capacitance. They do not cost the same, the one that looks cheapest has a second price nobody budgets for, and the expensive one is a part whose catalogue number is not the number it runs at.

What it is and how it works

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

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

What a maker publishes about one is a permeability, a saturation figure and a loss density. All three are true, and all three are measured under conditions that are not yours. That distance is the difficulty, because this is the one part in the converter that runs with a large steady current and only a small wobble on top: it never leaves the 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 reaching for it first is the obvious conclusion, and a trap before the money is counted. Doubling the frequency does exactly as much for the output ripple as quadrupling the choke and no more, since both divide dV by four, and on the current ripple it is strictly the weaker: dI goes as 1/(L·f), so quadrupling the choke quarters it where doubling the frequency only halves it. That is the number this page cares about, since the threshold that breaks the ramp is dI/2. Frequency buys the same output ripple in silicon rather than in copper and window space, which is a real saving, and it does not buy the same threshold. It has a second price on top.

The gate supply nobody budgets for

The buck's own switch has to be driven, and the average gate current is Q_g · f, so the power is Q_g · f · the rail-to-rail swing and it climbs 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.

So only one end of the frequency band can be computed, and it is the top one. On that brick a two watt module is spent 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 below runs at 22 kHz, over the symmetrical ceiling rather than under it at 2.11 W [derived], so the rail is the cheaper knob. The bottom of the band is a preference, since every kilohertz you give up comes back as 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 depending on the load, and at nearly no load the filter output floats up towards the bus at any duty at all. The relationship between duty and voltage does not merely distort. It stops existing.

The threshold is dI/2, the load current below which it happens, and it 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, which 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 tolerable; the 21 A means much of every ramp is spent in the non-linear region.

The cure is inductance, and frequency moves the threshold too at the price 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 change a number and the fourth changes the shortlist. Three families turn up in a QCW buck choke 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

And ferrite is not on that list for a reason worth having as a number. 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. So a Sendust ring carries about twice the flux a ferrite one does before anything else is argued, and that is before the difference in how each gives way: ferrite goes over a cliff where powder sags. Two sources, a maker and a trade publisher, and neither of them is the builder whose choke you are copying.

The same trade publisher turns that ratio into a size, and states the design point it holds at. Comparing Kool Mµ against gapped ferrite, which is the comparison that matters because a ferrite choke carrying DC has to be gapped: "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.

Read the condition, because it is the whole reason this page exists. Their design point is where the inductance has fallen to half. Not a saturation limit, a roll-off. That is the same axis the measured example above sits on, the stock Sendust ring at 350 µH static and 170 µH at 17.5 A, which is 49 per cent left, so a builder who wound to that number and an industrial designer who specified to it are standing in the same place without either saying so.

Three more differences from the same page, and the last is one this section had not accounted for at all:

• 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 fault tolerance rather than a defect, and it is the property that matters most at high power.
• Ferrite's capability moves with temperature and Sendust's much less, which 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 whatever winding is nearest and heats it. That is a cost of gapping which does not appear in any B_sat comparison, and on a choke wound tight to the core it is the winding that pays.

Two catalogues stand behind the figures below and both are named, because this section is about to ask catalogues for exactly that: 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 rather than a quotation you can follow, and most of the figures are ours [derived], out of those catalogues' own equations.

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

The comparison table in a catalogue is taken at a field of its maker's choosing, and the ordering it shows is not the ordering you will get. These are effective permeabilities at 26 µ, out of 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 it across the range and the leader changes. SiFe takes the lead from both High Flux grades at about 423 Oe [derived, straight-line between the 400 and 500 columns], and the two High Flux grades cross somewhere between 200 and 308 Oe, closer than that being a number the data cannot carry. Nothing moved but the current. Worse, at the low end there is barely 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 is not a gentler version of the answer. It is a different question, and 100 Oe is where comparison tables like to sit.

What to 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, the comparison does not reach 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 says so in as many words, and then prices 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 smaller 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 current ruining your inductance pays some of it back, and a loss figure quoted at no bias is the pessimistic end for a choke that runs deep in one.

Which 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 worth arguing about: High Flux, best on bias and second on loss, and Nanodust, lowest loss on the list and paying for it in bias. Everything else is beaten on both axes at once by one of those two, and SiFe is the expensive one here, carrying two and a half times High Flux's loss for the same retention. Which is the opposite of the ordering higher up, for the reason the habit above gives: 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 depends on what stays fixed while you compare:

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 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 pays part of its own way out in copper.

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 currency, 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

Nobody is displaced, at either permeability. 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. So a catalogue does not rank wrongly. It rejects outright some parts that are reasonable once the bias is real, and never says 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 whole problem in a choke carrying a hundred amps of DC with a small ripple on top. The price is loss, higher except in the newest formulations, and he warns it can grow excessive with switching frequency and input voltage. Read "40 to 60" as a shelf and not as an optimum: XFlux is sold in seven grades, 19, 26, 40, 60, 75, 90 and 125, so that names two adjacent catalogue parts and what decides between them is which you can buy in the size you need. Other builders pick on other axes, saturation flux most often, and are not arguing with him: this choke never reaches a cliff before its permeability has halved.

Sizing one

Which current. Not the primary's. 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, which on the 160 A primary of the machine this site draws is 102 A [derived]. Mind the qualifier on somebody else's figure: 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].

And the current the catalogue prints is not that one. On a powder toroid the quoted saturation current is where the inductance has fallen to 90 per cent of its initial value: where sag becomes visible, not where 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 486, both figures the vendor's own and both reproducing. 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.

And 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. The law checks out against a primary table rather than against somebody's arithmetic: on a maker's own 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 is also a cross-check, and on Gao's published figures it catches something. 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, and with the section doubled the law comes back to about 21 nH/N² against the 22.8 he quotes.

Now the reference choke through that 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], and 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, at four fifths or more of catalogue inductance while the working point is at 43 per cent: not a conservative working point but a measurement of a different part of the curve.

So the catalogue inductance is 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 is not a second effect. L = A_L·N² and A_L is proportional to permeability, so the inductance you lost and the permeability you lost are one number written twice, which kills the idea of two checks. The one to run is the permeability curve: read the fraction off the plot 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. Which is the method Anders Mikkelsen gives on the forum, rather than deriving it through flux formulas that answer a transformer's question about a component nobody is using as a transformer.

Quoting the pair rather than the catalogue figure is Anders' habit 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 is not a value, it is a value and a current.

And the wound value is not the computed one either. 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, that nominal and actual A_L may differ by "±8%", that every core is tested and "按每隔2%的公差分档", sorted into two per cent bins, and that designers wind a slightly different turn count to land within ±2 per cent of nominal. So up to eight of his fourteen points could be sitting in the core before anybody touches the wire. Fourteen still exceeds eight, so his explanation is not displaced, only shared, and the practical instruction is unchanged and now has two reasons behind it rather than one. The two errors run opposite ways, a winding high and a bias low, so they partly hide each other rather than add up, which is worse than either alone because the sign of a winding error is whatever your hands made it. Measure the ring you wound, at the current you will run it at.

And turns stop helping, at a point you can compute. L goes as N² and H goes as N, so turns push you further down the curve as they raise the count. Write the fade as µ ∝ H^-a and the exponents subtract, L ~ N^(2-a): below 2 turns buy inductance, above it they cost. a climbs with the field, and on the fit this page uses 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

The approach is poor value anyway, 108 to 181 buying 16 per cent more inductance for 68 per cent more wire, and 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 and not by the window, and only a different core breaks it. Copper runs out first: 108 turns of 7 AWG fills about 30 per cent of a 4710 mm² window, and 50 at the 181. What limits you is heat and wire, not room, the opposite of a transformer's intuition.

Then check 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

Continuous everywhere, five times the margin at its worst, and 4.9 V of ripple at the top on 25 µF, so no extra capacitance is needed to carry the doubler, which a smaller winding would have demanded. Nor does a doubler threaten the start of a ramp, since 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]. It is the top of the ramp that a doubler moves, and the top is where capacitance fixes it.

What will get you

Trust the prose, check the tables. In the Magnetics catalogue the printed loss equation does not reproduce the loss the same page prints: its constant is out and its exponent is exact. In both catalogues the worked examples and the prose survived checking where the tables did not, which is why every figure above comes off a worked pair rather than a formula.

Two comparisons that look like one. 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. Nor are two vendors in one currency. Worked through both catalogues above, KDM's figures come out optimistic against Magnetics on bias retention and low on loss density, and how far apart is not established here, so what stands is the direction: a comparison holds inside one catalogue and has to be re-derived across two, where the winner can change.

And the heating is continuous, which the peak figure does not tell you. The 262 W of copper in the sizing widget is what it takes at the top of the ramp, and the ramp is only there for 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, and this machine's ramp is 25 ms at five bangs a second, or 12.5 per cent of the time. So the average copper 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, the wire for the peak.

What goes wrong

• The ramp starts higher than the duty says, and the gain follows the load. 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, and 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 resolved 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 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 price.
• 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 what is inside it, a switch, a choke, a freewheel diode and a capacitor, because the choke is the reason a QCW has a ramp at all.