Three ways to dim a lamp

A dimmer has one control and one apparent meaning: less light. Three technologies implement it, all three are in ordinary use, and the instruction produces three different colours — one of which is exactly the colour it started at, one of which drifts, and one of which travels eighteen hundred kelvin.

The claim #

A light level is not a specification, because the three ways of reaching it are ΔE00 26 apart.

• Duty-cycle dimming is exactly colour-preserving. Switching the source on and off above fusion scales the spectrum and changes nothing else, so the chromaticity moves by 7 × 10⁻¹⁴ ΔE00 from full output to one per cent. That is floating point, not a small number.
• Current dimming is not. The die’s peak moves with band filling and the junction cools because it is dissipating less, so all three thermal slopes run backwards: ΔE00 3.7 across the range, almost all of it perpendicular to the locus rather than along it.
• A filament travels furthest and stays on the locus exactly. From 2,856 K at full power to 1,013 K at one per cent — 1,843 K — with a Duv of 2.8 × 10⁻¹⁶ at every level, because a blackbody at any temperature is on the Planckian locus by definition.
• And at ten per cent output the three are ΔE00 0.3, 25.9 and 26.2 apart in the three pairings. One instruction, three colours, no specification that distinguishes them.

Why each method does what it does #

Duty cycle. The source is driven at full current and switched on and off far faster than anybody can see; the average power falls with the duty ratio. Every wavelength is scaled by the same factor, so the chromaticity cannot move — the spectrum’s shape is untouched by construction. This is the only one of the three whose exactness is a theorem rather than a measurement.

What it buys instead is a waveform. A lamp modulating at a kilohertz is a hundred times past fusion and plainly visible during any glance across a room, as a dotted trail, because motion turns a temporal frequency into a spatial one. So the method with perfect colour has the worst temporal behaviour, and the trade-off is not one a colorimeter can see either way.

Current. Reducing the drive current does two things and the second is the larger. Band filling moves the die’s peak to longer wavelengths as the current falls, by a couple of nanometres per decade. And the junction cools, because it is dissipating less — so the peak-wavelength, efficiency and converter-yield slopes that the warm-up essay is about all run backwards at once. The two emitters slide relative to each other and the mixture changes.

A filament. There is no spectrum to move: a tungsten filament is a blackbody at whatever temperature the electrical power leaves it at, and Planck’s law gives the whole spectrum from that one number. The temperature follows the power as T ∝ P^n with n quoted between 0.20 and 0.25 — a consequence of tungsten’s resistivity and the Stefan–Boltzmann law rather than a fit. At one per cent power the exponent puts the filament at about a third of its full temperature.

What was computed, and how #

The exactness of duty-cycle dimming is asserted rather than assumed, at 10⁻⁹, and it is the kind of assertion that catches an implementation error rather than a physical one: a version that renormalised the spectrum after scaling, or that recomputed the colour temperature from a rounded chromaticity, would fail it immediately.

The filament’s Duv is asserted at 2 × 10⁻³ and comes out at 3 × 10⁻¹⁶, which is a much stronger result than the bound and is left loose deliberately — a tolerance set at floating point would fail on a change of search algorithm rather than on a change of physics.

The colour-temperature search floor had to be dropped to 800 K. cct searches 1,200 to 25,000 by default and a filament at one per cent power is below that, so the search clamps at the floor and reports the clamp’s distance from the target as a Duv. The first version of this sweep gave a blackbody a Duv of 0.039 for exactly that reason — a number that looks like a finding and is a boundary condition.

And the three methods share one lamp. The LED methods start from the same device as the beam essay — a pump at 452 nm, a broad converter at 565 with red nitride at 630 — at 4,044 K on the axis; the filament starts at 2,856 K, which is illuminant A. That the two start at different colour temperatures is a fact about the technologies rather than a choice, and it is why the essay’s comparisons are of travel rather than of endpoints.

Why the exact one is exact #

The claim that duty-cycle dimming preserves colour exactly deserves a moment, because “exactly” is a strong word and the site uses it sparingly.

Above the fusion frequency, a flickering light matches a steady one of the same time average. That is Talbot’s law, it is exact for a linear system, and this site has asserted it to floating point already. So the perceived stimulus from a source switched on for a fraction d of each cycle is the full-power spectrum multiplied by d — every wavelength scaled by the same number.

A chromaticity is a ratio of integrals of the spectrum. Multiplying the spectrum by a constant multiplies every integral by the same constant, and the ratios are unchanged. There is no approximation anywhere in that argument, which is why the assertion holds at 7 × 10⁻¹⁴ rather than at some small but structural value.

The two conditions it rests on are worth naming, because both can fail. The switching must be above fusion, or Talbot’s law does not apply and the observer sees a flicker rather than a colour. And the source’s spectrum must not depend on how long it has been on — which is true for an LED at constant current and is emphatically false for a filament, whose thermal mass would have to be enormous for the temperature not to fall during the off period. Duty-cycle dimming a filament is not colour-preserving at all; it is a different lamp at a lower temperature, badly.

What it costs #

The warm dim is a feature and a liability. A filament’s fall down the locus is the effect people are used to and often want: dimming toward candlelight is what an evening is supposed to look like, and a great deal of lighting design assumes it. LED luminaires now advertise “warm dim” as a feature, implemented by driving two channels of different colour temperature in a programmed ratio — which is to say, by simulating the filament’s behaviour with hardware whose natural behaviour is to do nothing at all.

A specification that names a light level has said nothing about colour. Two rooms at the same illuminance, one dimmed by duty cycle and one by filament, are ΔE00 26 apart in their illuminant. Every surface in them differs correspondingly, no measurement of illuminance distinguishes them, and the person writing the specification usually does not know which technology will be installed.

And a proofing booth is a specification of exactly this kind. The lamp in the shop decides whether a match holds, and a booth’s specification names an illuminant and an illuminance. If the booth is dimmable — and many are — the illuminant clause is only true at one setting, and which setting it is true at depends on the dimming technology.

Where the model stops #

The current-dimming slopes are data-sheet quantities and they vary between devices. Band filling at two nanometres per decade and a junction rise of fifty-five kelvin at full drive are representative rather than universal, and a device with a better thermal path would move less. What does not vary is the direction: dimming by current cools the junction, and cooling the junction moves the two emitters in opposite senses.

The filament exponent is quoted and the answer scales with it. Between 0.20 and 0.25 the temperature at one per cent power runs from about 1,140 K to 900 K, so the endpoint of the largest travel in this essay is uncertain by a couple of hundred kelvin. The path’s shape — straight down the locus, Duv zero throughout — is exact and does not depend on the exponent at all.

And there is no fourth method. Real dimmers combine techniques — phase-cut supplies with switching regulators behind them, hybrid schemes that use duty cycle at the top of the range and current at the bottom to avoid audible switching — and a hybrid’s path is a blend of two of these, which is worse than either for anybody trying to predict it.

The one comparison that is fair #

Comparing three technologies is easy to do unfairly, so it is worth naming the trap. The filament starts at 2,856 K and the LED at 4,044; if the essay quoted endpoints it would be reporting that a filament is warmer than an LED, which is a fact about which lamps were chosen and not about dimming.

Everything above is therefore a travel: how far each method’s colour moves between full output and the level being asked about, measured against that method’s own starting point. Travel is the quantity a dimmer is responsible for, it is invariant to which lamp was installed, and it is what a specification naming a light level fails to constrain.

The one place endpoints are compared is the patch figure, and there the three are normalised to the same luminance and quoted with their own colour temperatures beside them, so a reader can see what is a starting difference and what is a dimming difference. The largest gap there — 25.9 units — is mostly travel: the filament’s own start is 1,188 K from the LED’s, and the dimming adds another 1,843 in the same direction.

The filament’s ladder, and where it is steep #

The five temperatures the blackbody figure is drawn at reproduce exactly from one exponent. Taking T = 2856 · P^n and solving from the endpoint gives n = 0.2251, and that exponent returns 2091, 1701, 1456 and 1013 at a quarter, a tenth, a twentieth and a hundredth — the figure’s own numbers, to the kelvin. So the exponent the sweep used is the midpoint of the quoted 0.20-to-0.25 range, and the whole path is one parameter.

Converting the path into the unit the rest of the essay argues in, with every level normalised to one luminance so only colour is compared:

At a quarter output — the setting the essay itself says a room dimmer spends most of its life at — the filament has already moved 8.9 ΔE₀₀ from its own full-power colour. That is nine times a print tolerance and it is reached at a level nobody would describe as dim. The extreme setting is not doing the work in this argument, which is the useful thing to know about it.

Nine tenths of the current-dimming shift is in the last decade #

The three distances quoted at ten per cent output — 0.3, 25.9 and 26.2 — add exactly: 0.3 + 25.9 = 26.2. The current-dimmed white lies on the segment between the unchanged LED and the filament, in the ΔE₀₀ sense, which is what makes the three figures a ladder rather than a triangle.

The 0.3 is the interesting entry. Current dimming is said to move ΔE₀₀ 3.7 across the range, and at ten per cent output it has moved 0.3 — eight per cent of its total travel, with the other ninety-two per cent falling in the single decade from a tenth to a hundredth.

That reverses the practical reading of the whole essay. Across the range a room dimmer is actually used, current dimming is nearly as colour-preserving as duty cycle: two of the three methods are within a third of a unit of each other at a tenth output and closer still at a quarter. The instruction dimmed to a quarter does not name three colours in practice; it names two, and the split is between a filament and everything else.

The 26 units the claim list leads on is therefore a filament-versus-LED number wearing a three-technology label. Both halves of that matter — the number is real and a specification really does fail to constrain it — but the freedom being exercised is a choice of lamp technology rather than a choice of dimmer, and the dimmer’s own contribution is 3.7 at its very largest.

Mostly travel, but only just, and at the wrong level #

The fair-comparison section decomposes the 25.9 as the filament’s own start is 1,188 K from the LED’s, and the dimming adds another 1,843 in the same direction — and 1,843 is the travel to one per cent while 25.9 is measured at ten.

At ten per cent the filament sits at 1701 K, so it has travelled 1,155 K — which is less than the 1,188 K that separated the two lamps before anybody touched the dimmer. By kelvin the gap at that setting is 49 per cent travel and 51 per cent starting difference, which is not “mostly” in the direction the sentence claims.

In ΔE₀₀ the answer comes out differently, and this is the honest version. The starting gap is worth about 10.8 units and the dimming to a tenth about 14.2, so travel is 57 per cent of the sum — mostly, by a bare majority rather than by a wide margin. The two units disagree because a kelvin near 1700 is worth more colour than a kelvin near 3500, so the same temperature interval buys more at the bottom of the path than at the top.

Which is a reason to quote the decomposition in ΔE₀₀ rather than in kelvin, and the essay has the right instinct three sections earlier when it says only one of the three paths can be summarised by a colour temperature at all. A colour temperature is a poor ruler even along the locus, where it is exact — because it is exact about which blackbody and says nothing about how far apart two of them look.

The generalisation #

The sentence worth carrying is: an instruction that names an output does not name a path, and the paths differ.

This site has met the same shape in the ink. A separation is not unique: four inks matching three numbers leave a family, and its members differ in ink cost and shadow stability while matching identically. Four primaries have a choice: the same freedom in an additive device, spent on observer robustness or not spent at all.

Dimming is the same structure with the freedom exercised by a purchasing decision instead of a driver. Three implementations of “less light”, each colorimetrically distinct, and the choice made by whoever specified the fixture — usually on cost and flicker grounds, and usually without anybody computing what it does to the light.

The surprising connection is with fusion. The only exactly colour-preserving method works by modulating faster than anybody can see, so its correctness depends on a property of the observer rather than of the lamp. Below fusion it is not colour-preserving at all — it is a flicker. The exactness in the assertion is a fact about the time-average spectrum, and Talbot’s law is what converts a fact about an average into a fact about an appearance.

Who found it, and when #

The filament’s behaviour has been known for as long as filaments have been dimmed, and it is the reason the phrase “warm dim” needed inventing when the behaviour stopped being automatic. Theatrical lighting has worked with it since the resistance dimmer: a scene dimmed on tungsten goes amber, and lighting designers compensate with gel selection rather than fighting it.

Duty-cycle dimming arrived with switching supplies and its colour behaviour was understood immediately, because it follows from Talbot’s law and Talbot published in 1834. What arrived with it, and was not understood immediately, was the stroboscopic and phantom-array literature — flicker metrics for dimmed LED lighting are a recent regulatory subject and are still moving.

The current-dimming shift is a data-sheet quantity that manufacturers publish because customers ask, and the two mechanisms behind it — band filling and junction temperature — belong to different literatures, one semiconductor physics and one thermal engineering.

And nobody specifies which method a fixture uses in a colour specification, because a colour specification is written by somebody thinking about the light and a dimmer is chosen by somebody thinking about the wiring. That is not an oversight anybody is responsible for; it is a gap between two documents that have never had a reason to reference each other.

What the pictures cannot show #

They cannot dim. Every patch here is drawn at a fixed luminance and normalised so the comparison is of colour alone, which is the only fair comparison and is not what a dimmed room looks like. A dimmed room is also darker, and darkness moves appearance by more than the colour shifts measured here.

And they cannot flicker. The one property of duty-cycle dimming that matters and is not colour cannot be shown on a page at all — a printed or displayed figure has whatever temporal behaviour the reader’s display has, which is itself usually a duty cycle.

Where the ladder goes next #

The nearest unfinished piece is the hybrid. Real drivers switch strategies partway down their range, so a real installation’s path is two of these joined at a kink, and the kink’s position is a property of the driver rather than of the lamp. Nothing about a fixture’s documentation would let anybody predict where it is.

The second is the rendering index along the path. A dimmed filament’s colour rendering is essentially perfect at every temperature, because it is a blackbody and the reference for a blackbody is a blackbody. A current-dimmed LED’s is not constant, because the ratio of its two emitters changes — and by how much is one call to the fidelity machinery this site already has.

And the third is the join with the eye. A room dimmed over a few seconds is a stimulus changing while the observer’s own gains are still moving, on time constants this site has three of now. What somebody sees during a dim is not the settled appearance of any point on these paths, and nothing here computes the transient.