Circuit Response
every model has an edge, and the figure carries it
Two windings, and the band between them

Interleaving is a choice, not an improvement

Splitting a transformer's windings into six sections divides its leakage inductance by 21.4 and multiplies its winding-to-winding capacitance by 11.0. The product of the two — which is what sets the frequency the part stops being a transformer at — moves by 1.94, and the resonance it decides goes from 1.804 to 2.515 megahertz for all that work. What interleaving really changes is the winding's characteristic impedance, 95.2 ohms down to 6.2, and nobody quotes it.
15 min read 7 figures The parasitic is the componentEvery model has an edgeMeasured, not tabulated

Assumes: The other half of the same window · The band a turns ratio holds over · The assumption that is a geometry

Interleaving a transformer — splitting each winding into sections and stacking them alternately rather than one on top of the other — is the standard cure for leakage inductance, and it works. The inductance that is a shape measured what it is worth on a real window rather than in the expression usually quoted, and found it worth a factor of three rather than the four that is always claimed.

That essay could not say what it costs, because pricing the cost needs the window’s other parameter and the other half of the same window is where that parameter came from. With both solved on the same cross-section, on the same cells, the trade can be read in both currencies at once — which turns out to be necessary, because the two move in opposite directions and neither moves the way the count suggests.

The trade, in the plane where both halves of it live. computed by solving, not by drawing. Leakage inductance across, interwinding capacitance up, both solved on the same cross-section with the same cells. The faint diagonals are lines of constant leakage-times-capacitance, so a design action that runs along one of them has bought nothing and only moved where the energy is kept. Interleaving runs at slope -0.78, which is nearly along them: six sections cut the leakage 21.3 fold and multiply the capacitance 11.0 fold, and the product moves by 1.94. What it does change is the winding's characteristic impedance, 95 ohms down to 6.2 — a factor of 15. Thickening the interlayer instead runs at -4.8, steeply across the diagonals, and moves the product 5.2 fold over the same sweep. It is the cheaper action by that measure and it is not free either: the millimetre it spends is a millimetre of window that is not copper.
Fig. 1 The plane both halves of the trade live in: leakage inductance across, winding-to-winding capacitance up, every point a solve of the same copper in a different arrangement. The faint diagonals are lines of constant leakage-times-capacitance. Interleaving runs at a slope of −0.78, which is very nearly along them; thickening the interlayer instead runs at −4.8, steeply across.

What the count actually buys

Take a six-layer primary and a six-layer secondary and split them into one, two, three and six sections. The leakage falls hard: 8.399 microhenries a metre, then 2.384, 1.184, and 0.393 — a factor of 21.4 across the sweep, and 3.52 for the first split alone.

The winding window solved electrostatically, interleaved 2 wayscomputed by solving, not by drawing. The same cross-section the loss solve reads, read with ∇·(ε∇φ) = 0 instead. Two things are the opposite way round from the magnetic problem and both are the whole difference. The iron is now a Dirichlet boundary rather than a Neumann one — an earthed core is an equipotential, so the field meets it at right angles instead of running along it — and a conductor carries a prescribed potential rather than a prescribed current. The thin curves are equipotentials, which are contours of φ, so equal spacing is equal potential step and crowded curves are a strong field. The copper is shaded by the potential each foil sits at, which rises along the winding rather than being one number. Winding to winding this window is 2780.8 picofarads a metre, and 84 per cent of the energy is inside insulation that occupies a fraction of the window.6+6 foils, 2 sectionswindow184 × 75 cellsP–S interfaces3winding to winding2780.8 pF/m…each winding to core272.1 pF/mequivalent at terminals1346.2 pF/mprimary's self C1729.8 pF/menergy in insulation83.7%leakage, same window2.384 µH/mtwo routes agree to1.2e-14equipotentials are contours of φ: equal spacing is equal voltssolved, then checked — Dirichlet iron, not Neumann2781 pF/m across 3 interfaces
Fig. 2 Two sections. The primary is split in half with the secondary between, so the ampere-turns build up and come back down twice instead of once, and the field energy in the window — which is what leakage inductance is — falls by 3.52. The equipotentials tell the other half of the story: there are now three primary-to-secondary interfaces where there was one.

That last sentence is the whole mechanism of the cost, and it is worth stating as arithmetic rather than as a warning. One section puts one interface between the two windings. Two sections put three. Three sections put five, and six sections put eleven. Each interface is the same area of the same insulation at the same separation, so each is worth the same capacitance.

Interleaving multiplies interfaces, and the capacitance counts them. computed by solving, not by drawing. Splitting a six-layer primary and a six-layer secondary into 1, 2, 3, 6 sections puts 1, 3, 5, 11 interfaces between the windings. Each is the same area of the same insulation, so the interwinding capacitance is the count times one interface — 926.9 picofarads a metre — and the constant holds to 0.09 per cent across the whole sweep. That is the cost interleaving is never quoted with: 927 picofarads a metre becomes 10187. The other two curves are what a designer actually feels. The capacitance the terminals see FALLS, 1980 to 359, because the same split that multiplies the interfaces divides the voltage across each of them — and that only holds for one particular way of connecting the windings, which the next mode is about. The primary's own self-capacitance rises the whole time.
Fig. 3 The capacitance against the number of primary-to-secondary interfaces the arrangement has. One interface is 926.9 picofarads a metre; eleven of them are 10,187, which is 926.1 per interface — the constant holds to 0.09 per cent across the whole sweep. There is no subtlety in the cost at all: interleaving multiplies interfaces and the capacitance counts them.

So the two headline numbers are a division by 21.4 and a multiplication by 11.0, and a designer who has only ever seen the first of them is working with half the arithmetic.

The reduction is not the one the count predicts either

Before the cost is priced it is worth checking the benefit, because the benefit has a closed form that is quoted as confidently as the cure itself and it is wrong in the same direction every time.

Splitting into p sections is said to divide the leakage inductance by p², and the reasoning is clean: the magnetomotive force in the window builds to 1/p of its full height instead of to all of it, the energy goes as the square of the field, and there are p portions of it. Against this window’s own solves that expression is high at every count and increasingly so.

The winding window solved electrostatically, interleaved 6 ways. computed by solving, not by drawing. The same cross-section the loss solve reads, read with ∇·(ε∇φ) = 0 instead. Two things are the opposite way round from the magnetic problem and both are the whole difference. The iron is now a Dirichlet boundary rather than a Neumann one — an earthed core is an equipotential, so the field meets it at right angles instead of running along it — and a conductor carries a prescribed potential rather than a prescribed current. The thin curves are equipotentials, which are contours of φ, so equal spacing is equal potential step and crowded curves are a strong field. The copper is shaded by the potential each foil sits at, which rises along the winding rather than being one number. Winding to winding this window is 10187.2 picofarads a metre, and 36 per cent of the energy is inside insulation that occupies a fraction of the window.
Fig. 4 Six sections. The primary is in four pieces and the secondary in three, alternating, and the field between them builds and collapses six times across the window instead of once. Leakage 0.393 microhenries a metre against one section’s 8.399 — a factor of 21.4 where p² predicts 36.

Two sections measure 3.52 against a predicted 4, which is 13.5 per cent optimistic. Three measure 7.09 against 9, 26.9 per cent. Six measure 21.4 against 36, and the expression is now 68.4 per cent high. The error is not noise and it does not average out; it grows monotonically with the thing the expression is being used to justify.

The reason is the same one the assumption that is a geometry found in the loss expression, arriving in the other parameter. The p² argument assumes the field is parallel to the layers and confined between them, so that dividing the stack divides the field height cleanly. Every section boundary is a place where that assumption is least true — the field has to turn round there, it does so through the insulation and the end regions, and the energy in those turns is not divided by anything. More sections means more boundaries, so the part of the energy the expression cannot see is a larger share of a smaller total each time.

Which puts the benefit and the cost on the same footing. The reduction is real and large and 68 per cent smaller than advertised; the cost is real, large, and not advertised at all.

The product barely moves, and it is the product that sets the frequency

Neither number is what a circuit responds to. A leakage inductance in series with an interwinding capacitance is a resonance, and a resonance depends on the product. This is the same reduction two numbers are a frequency and an impedance makes: of all the ways two reactive quantities could combine, a circuit only ever forms their product and their ratio.

The product across the sweep goes 7,785, 6,630, 5,487, 4,004 in units of microhenry-picofarads. It falls by a factor of 1.94 while its two factors move by 21.4 and 11.0 in opposite directions. Turned into the quantity a data sheet would print, the resonance moves from 1.804 megahertz to 2.515 — thirty-nine per cent, for a winding operation that changes the whole construction of the part, adds interconnections, and makes it harder to insulate.

That is the finding, and it is why the slope of −0.78 on the trade plane matters. A line of constant product has slope −1. Interleaving runs at −0.78, close enough to that diagonal that most of what it does is move energy from one store to the other rather than reduce the total. It is nearly a lateral move in the only plane where the two quantities can be compared.

Thickening the interlayer is not. The same plane shows it running at −4.8 — steeply across the diagonals rather than along them — and moving the product by 5.2 over its sweep, against interleaving’s 1.94. By the measure that decides the band edge it is the better action by a factor of nearly three, and it is the one nobody describes as a technique. It is not free either: the millimetre it spends is a millimetre of window that is not copper, and the copper that makes it worse is about what happens to a winding’s losses when its copper is squeezed.

What interleaving does change, by a factor of fifteen

If the product barely moves, the ratio must move a great deal, and it does. The characteristic impedance √(L/C) of this winding goes 95.19 ohms at one section to 6.21 at six — a factor of 15.3, monotone, and by far the largest effect interleaving has on anything.

That is not a curiosity. Below the resonance a transformer is a turns ratio; above it, it is a piece of transmission line, and this is the impedance of that line. Every fast disturbance that arrives at a winding — a switching edge, a discharge, the common-mode step the millimetre that becomes common mode is about — is divided between the source and this impedance, and dropping it from 95 ohms to 6 changes what the winding does with such a disturbance far more than the 39 per cent change in the frequency does.

An interleaved transformer is therefore not a less parasitic transformer. It is a differently parasitic one: much stiffer, much more tightly coupled at high frequency, and much better at passing a common-mode edge straight through from one winding to the other. Whether that is an improvement depends entirely on which of those a design is failing on, which is exactly the shape of question every model has an edge is written about — the same change is a repair in one variable and a defect in another, and the only way to tell is to have both.

The screen, and where its bill arrives

The standard answer to interwinding capacitance is an electrostatic screen: an earthed foil in each primary-to-secondary interface, thin enough to fit inside insulation that had to be there anyway. It does exactly what it is sold as doing.

What an electrostatic screen interrupts, and what it charges for it. computed by solving, not by drawing. An earthed foil in each primary-to-secondary interface, thin enough to fit inside the interlayer insulation that was there anyway. Pale dots are the winding without it, solid ones with. It does exactly what it is sold as doing: the winding-to-winding capacitance falls from 927 picofarads a metre to 5.10, a factor of 182, and the leakage inductance moves by 1.8 per cent because it costs no window. What it does not do is remove the capacitance. The primary now faces an earthed plate at the range its neighbour used to be at — 2460 picofarads a metre to the screen alone — so its own self-capacitance rises from 1364 to 2655 and the equivalent capacitance at the terminals goes UP, 1980 to 3422. A screen redirects a displacement current to earth. It does not abolish it, and the bill arrives on a different line.
Fig. 5 The same window with an earthed foil in the interface. Winding-to-winding capacitance falls from 926.9 picofarads a metre to 5.10, a factor of 182, and the leakage inductance moves by 1.8 per cent because the screen costs almost no window. Pale dots are the winding without it, solid ones with.

And then the bill arrives on a different line. A screen does not abolish a displacement current; it redirects one, and the current it redirects has to have somewhere to go and something to leave from. The primary now faces an earthed plate at the range its neighbour used to be at — 2,460 picofarads a metre to the screen alone — so the primary’s own self-capacitance rises from 1,364 to 2,655 picofarads a metre, and the equivalent capacitance the terminals present goes up, 1,980 to 3,422.

What an electrostatic screen interrupts, and what it charges for it. computed by solving, not by drawing. An earthed foil in each primary-to-secondary interface, thin enough to fit inside the interlayer insulation that was there anyway. Pale dots are the winding without it, solid ones with. It does exactly what it is sold as doing: the winding-to-winding capacitance falls from 10187 picofarads a metre to 46.92, a factor of 217, and the leakage inductance moves by 6.8 per cent because it costs no window. What it does not do is remove the capacitance. The primary now faces an earthed plate at the range its neighbour used to be at — 27057 picofarads a metre to the screen alone — so its own self-capacitance rises from 3705 to 9795 and the equivalent capacitance at the terminals goes UP, 359 to 17674. A screen redirects a displacement current to earth. It does not abolish it, and the bill arrives on a different line.
Fig. 6 The same screen in the six-section winding, where there are eleven interfaces to screen rather than one. Winding to winding it is spectacular: 10,187 picofarads a metre down to 46.9. At the terminals it is a catastrophe: 359 up to 17,674, a factor of 49, because eleven earthed plates interleaved through the windings is an enormous capacitance to earth however little of it goes across.

The pair of those figures is the argument in its sharpest form. Interleaving and screening are both described as improvements, they are routinely specified together, and applied together on this window they take the winding-to-winding capacitance to a fiftieth of a screened single section while multiplying the capacitance the circuit actually sees by fifty. Neither technique is at fault. What is at fault is that each is quoted in the currency it improves.

Which capacitance the answer is in

That last paragraph is only meaningful because the two capacitances are different quantities, and it is worth saying plainly which is which, because a bridge reads a third thing again.

Winding to winding is what a screen and an isolation specification are about: the displacement current that crosses from one circuit to the other, which is a safety and an interference quantity and has nothing to do with the transformer’s own response.

At the terminals is what the circuit sees: the single capacitance that, put across the winding, stores the same energy at the same terminal voltages. That is the one in series with the leakage inductance, the one that sets the resonance, and the one that loads whatever drives the winding.

They are computed from the same solved potential and they move in opposite directions under both of the actions above. A screen divides the first by 182 and multiplies the second by 1.73. Interleaving multiplies the first by 11.0 and divides the second by 5.5. There is no arrangement of this window in which both are small, and the question a design has to answer first is which of the two it is failing on — a measurement condition being part of the answer, exactly as it is in the capacitance that is not one number.

The band edge, computed rather than fitted

There is a way to check all of this against something the collection already measured independently, and it is worth doing because it is the only external check available.

The band a turns ratio holds over measures a transformer’s two band edges from the netlist and finds the lower one nearly immovable while the upper one moves by three decades with the coupling. That upper edge is where the leakage inductance and the winding’s own capacitance stop being negligible against the load — and until both could be computed from the cross-section, the capacitance in that model was a number chosen to make the model fit rather than a property of the part.

It is now a property of the part, and it moves the way the arrangement says it should: 1.804 megahertz at one section, 1.955 at two, 2.149 at three, 2.515 at six. That the numbers are close together is the finding restated — but they are now predictions from a geometry rather than parameters, and a prediction that barely moves is a much stronger statement than a parameter that was never varied.

It also says something about which of the two edges a designer should expect to be able to shift. What coupling buys and where found the same asymmetry from the circuit side: the two ends of a transformer’s band are not equally available, and effort spent on the one that does not move is effort spent. Interleaving is that effort in its most concentrated form.

What the crossing capacitance is in amperes

The winding-to-winding number is easiest to feel as a current, because that is what it is: a displacement current that leaves one circuit and arrives in the other, and it is the quantity a common-mode measurement reads.

An edge of ten volts a nanosecond across 926.9 picofarads a metre draws 9.27 amperes per metre of turn while the edge lasts. Interleaved into six sections it is 102 amperes a metre. Screened, it is 51 milliamperes a metre at one section and 469 at six. Those are not small numbers arrived at by exaggeration — ten volts a nanosecond is an ordinary edge, and the four arrangements span a factor of two thousand in what crosses.

The current has to return, and where it returns is not in this cross-section at all. It goes out through whatever earth the far circuit has and comes back through whatever earth the near one has, which is the loop where the current comes back is about — and that essay’s finding is that the return path is chosen by the geometry rather than by the schematic, at a frequency the geometry decides.

That is the practical reason the two capacitances have to be kept separate rather than added. The terminal capacitance is a load: it draws current from the winding’s own driver, round a loop the designer drew. The winding-to-winding capacitance is a leak: it draws current round a loop nobody drew, through an earth system whose impedance is not in any model of the transformer. A part whose terminal capacitance is five times too large is slow. A part whose crossing capacitance is five times too large fails a measurement in a chamber, and the arrangement that fixes the first makes the second worse.

Where the energy went

One more reading explains why the capacitance counts interfaces so exactly, and it is the one that says the result is not an artefact of this particular window.

At one section, 56.5 per cent of the electric energy is in the enamel between adjacent foils of the same winding and 32.3 per cent in the interlayer tape between the two windings. At six sections there are almost no adjacent same-winding layers left to have enamel between them, and 63.9 per cent of what remains is in air. The total energy at one volt falls from 0.990 to 0.180 nanojoules a metre even as the winding-to-winding capacitance rises elevenfold, because the two quantities are answers to different questions asked of the same field.

That is the reconciliation, and it is a check rather than a story: the interface count, the terminal capacitance and the energy distribution are three readings of one solve and they have to be consistent, which they are.

The one number Dowell gets right, and the one it gets wrong the other way. computed by solving, not by drawing. Dowell's expression has no window in it: the same layer count and the same foil thickness give 16.382 whatever share of the bobbin the copper covers, which is the flat line. The solved ratio falls to 9.001 at 25 per cent fill — the closed form is 82 per cent high — while the actual loss goes the other way, from 0.2322 to 0.5278 watts per metre, because the same current is in less copper. A designer reading the ratio alone reads an improvement. The loss is least at 92 per cent fill and not at a hundred, by 1.8 per cent — over that narrow range the ratio falls faster than the direct-current resistance rises, and past it the trade reverses.
Fig. 7 The magnetic half of the same window, from the solve that measured it. The leakage inductance every number above is traded against is twice the energy in this picture under equal and opposite ampere-turns — the same cells, the same copper, the same films, and a different equation.

What this does not say

It does not say interleaving is a mistake. A converter whose switching loss is set by leakage inductance has a real problem that interleaving really solves, and 21.4 is a large number. It says that the reason usually given — that it reduces the parasitics — is not what it does, and that a design which interleaves to fix a resonance has bought 39 per cent for a great deal of work.

It does not extend to three dimensions, and the end regions of a real winding are where an interleaved construction is hardest and where its interconnections live.

And it does not price the safety constraint, which is often what decides the arrangement before any of this arithmetic is reached. Reinforced insulation between primary and secondary is not negotiable and it is thick, which is the interlayer axis of the trade plane being set by something that is not a trade at all.

The number worth carrying

A division by 21.4 and a multiplication by 11.0 whose product is 1.94, and a characteristic impedance moved by 15.3 that nobody quotes.

The habit that goes with it is the one this rung exists for. Two parasitic quantities of the same object, computed by different people from different models, cannot be traded — and for as long as this collection had a solver for one of them and an expression for the other, every statement it could make about interleaving was a statement about half the answer. What made the trade computable was not a better model of either quantity. It was solving both on the same cells, so that the two numbers belong to one window rather than to two accounts of one.

The generalisation is worth stating because it is not about transformers. A technique acquires a reputation in the currency it was invented to fix, and then keeps that reputation in every other currency by default, because nobody who measures the first one is set up to measure the second. Interleaving was invented against leakage inductance and is excellent against leakage inductance. It is quoted as reducing parasitics, which is a different and false claim, and the only thing that separates the two is a second solve of a cross-section somebody had already meshed.

Part 2 on winding capacitance

One argument about Winding capacitance, and one of 2 essays on it so far, each part numbered by how much of the idea it assumes. What sits either side of it:

The winding window solved electrostatically, in two portions. computed by solving, not by drawing. The same cross-section the loss solve reads, read with ∇·(ε∇φ) = 0 instead. Two things are the opposite way round from the magnetic problem and both are the whole difference. The iron is now a Dirichlet boundary rather than a Neumann one — an earthed core is an equipotential, so the field meets it at right angles instead of running along it — and a conductor carries a prescribed potential rather than a prescribed current. The thin curves are equipotentials, which are contours of φ, so equal spacing is equal potential step and crowded curves are a strong field. The copper is shaded by the potential each foil sits at, which rises along the winding rather than being one number. Winding to winding this window is 926.9 picofarads a metre, and 89 per cent of the energy is inside insulation that occupies a fraction of the window. The other half of the same window Part 1 — The two-dimensional solve that settled what a winding's alternating-current resistance really is computed one of the window's two parameters and never mentioned the other. Read with Laplace instead of the vector potential, the same cross-section returns 926.9 picofarads a metre — and 89 per cent of that energy sits inside films that occupy 14.1 per cent of the window. The instrument agrees with a layered slab to three parts in ten thousand billion and converges on a real winding at order 1.34, and the reason for the shortfall is not the arithmetic but the corner of a conductor.

Where this goes next

The winding window solved electrostatically, in two portions. computed by solving, not by drawing. The same cross-section the loss solve reads, read with ∇·(ε∇φ) = 0 instead. Two things are the opposite way round from the magnetic problem and both are the whole difference. The iron is now a Dirichlet boundary rather than a Neumann one — an earthed core is an equipotential, so the field meets it at right angles instead of running along it — and a conductor carries a prescribed potential rather than a prescribed current. The thin curves are equipotentials, which are contours of φ, so equal spacing is equal potential step and crowded curves are a strong field. The copper is shaded by the potential each foil sits at, which rises along the winding rather than being one number. Winding to winding this window is 926.9 picofarads a metre, and 89 per cent of the energy is inside insulation that occupies a fraction of the window. The other half of the same window The two-dimensional solve that settled what a winding's alternating-current resistance really is computed one of the window's two parameters and never mentioned the other. Read with Laplace instead of the vector potential, the same cross-section returns 926.9 picofarads a metre — and 89 per cent of that energy sits inside films that occupy 14.1 per cent of the window. The instrument agrees with a layered slab to three parts in ten thousand billion and converges on a real winding at order 1.34, and the reason for the shortfall is not the arithmetic but the corner of a conductor. Where a transformer's leakage inductance actually is. computed by solving, not by drawing. Both windings carry the same ampere-turns in opposite directions, which is the short-circuit condition a leakage measurement is made under, so the flux drawn here is the flux that fails to link the two — the leakage field, and nothing else. It is largest in the insulation between the portions, where the magnetomotive force is at its full value and there is no copper to be in. The energy in this window is 2.058 microjoules per metre, which is 4.116 microhenries per metre referred to the primary against a closed form of 5.213. The inductance that is a shape Leakage inductance is the one transformer parameter that belongs to the geometry rather than to the material: twice the magnetic energy in the window under equal and opposite ampere-turns, divided by the square of the current. Solved as a field it is 3.086 microhenries a metre against a closed form's 3.128 when the copper fills the window, and 4.608 against 6.255 when it fills half of it. Interleaving is worth 3.11 times and not the four it is quoted as, and the missing 0.89 is the insulation nobody puts in the formula. The winding window solved in two dimensions, copper filling 100% of it. computed by solving, not by drawing. The grey frame is iron of infinite permeability, which in this formulation is a Neumann boundary — flux enters it at right angles and pays nothing. The thin curves are flux lines, which are contours of the vector potential, so equal spacing is equal flux. The copper is shaded by its own share of the loss. At 100 per cent fill the solved ratio is 16.280 against Dowell's 16.382, and the difference is entirely the flux that curls round the ends of the foils — which the one-dimensional model has no way to hold. The assumption that is a geometry Every alternating-resistance number this collection has computed for a winding rests on one sentence — the field is parallel to the layers everywhere — and the sentence has never been tested, because testing it needs a field. Solved as one, a portion of foils that fills its window returns Dowell's expression to 0.155 per cent; the same copper filling a quarter of it returns 9.00 against the expression's 16.38, and dissipates 0.528 watts a metre against 0.232. The ratio falls by 45 per cent and the loss more than doubles. A 1:1 transformer at k = 0.99, and the band it is a turns ratio over. computed by solving, not by drawing. Two 10 mH windings coupled at 0.99, driven from 50 Ω into 50 Ω, with 0.5 Ω of winding resistance and 100 pF across the secondary. The response is flat at 0.4901 — which is 98.02% of the 0.5000 an ideal transformer of this ratio would give, and that shortfall is the coupling itself: the flat part is k times the turns ratio, times what the two winding resistances leave of the loop, to four figures at every k on the slider — between 400 Hz and 81.3 kHz, which is 2.31 decades. Both edges are bisected on the solved network. Below the first, the magnetising inductance is a short across the source; above the second, the leakage inductance is in series with the load. The slider moves the coupling, and it moves the upper edge only. The band a turns ratio holds over Every model this collection has drawn is right below a number or above one. A transformer is the first that is wrong at both ends and right in the middle, and the flat part is not the turns ratio either — measured on the solve it is the turns ratio times the coupling, times what the two winding resistances leave of the whole loop — and the first version of that last factor was a coincidence that held for every coupling and broke at a different load. What 1.5 mm of length mismatch does to a differential pair. computed by solving, not by drawing. Two lines of the same impedance and different lengths, driven differentially. The solid rising curve is what arrives as common mode; the dashed one beside it is sin(ωΔτ/2), which is what a lossless pair gives and is the same curve until the null. The flat curve at the top is the differential signal, and it is the point: at 3.04 GHz a tenth of the launched amplitude is common mode and the differential has lost 5011 parts per million of itself. The conversion is first order in the skew and the loss is second order, so the error is not missing from the signal — which is why a pair can pass its own eye and fail an emissions test. At 95.3 GHz the closed form has a null and the real pair does not: the longer conductor is also the lossier one, and an amplitude imbalance has no null in it. The millimetre that becomes common mode A pair carries two modes rather than two signals, and a length mismatch between its halves converts one into the other. A millimetre and a half of skew is ten picoseconds, a tenth of the signal is common mode by three gigahertz, and the differential signal has lost five thousand parts per million of itself getting there — so the error is not missing from the signal, which is why a pair can pass its own eye and fail an emissions test. The product in the answer is ωΔτ, which is what the instruments field's rejection corner is one over.

The objects named here

The third axis, after the field and the idea: the things themselves, and every essay that touches each one.

Characteristic impedanceDesign tradeoffEnergy-storageField solutionInterwinding capacitanceLeakage inductanceMeasurement conditionModel rangePermittivityReturn current