Divide a switchable film into zones and the zones do not behave independently: driving one of them puts a real voltage across the others. This is often described as the film “leaking” — and we use that shorthand elsewhere on this site too, because it is the easier picture — but nothing actually conducts sideways through the film. The coupling runs through the electrode the zones share — and that single fact predicts how far it reaches.
The short answer
| What you change | How far the interference reaches | What it costs you |
|---|---|---|
| Higher drive frequency f | Shorter, as 1/√f | More power, more droop inside the zone |
| Higher sheet resistance Rs | Shorter, as 1/√Rs | More droop inside the zone |
| Higher capacitance per area cA | Shorter, as 1/√cA | More power, more droop inside the zone |
Every parameter that confines the interference makes the film worse in the other direction. That symmetry is not a coincidence — as shown below, one and the same product ωRscA governs both. You can move the problem between two places by choosing a film; you cannot make it go away by choosing a film.
A PDLC film is two PET sheets, each coated with a transparent conductor, with a thin liquid-crystal/polymer layer between them. Electrically it is a parallel-plate capacitor with a slightly lossy dielectric.
When such a film is divided into zones, the pattern is normally cut into one of the two conductive coatings. The other one stays as it was: a single continuous sheet spanning the whole film, fed from a busbar at an edge. That is the arrangement we use in our own verification work as well — the three-zone sample on our Smart Glass System page is an off-the-shelf PDLC film with its rear common electrode left as one continuous sheet.
So the zones share a conductor. Everything below follows from that, plus one more fact: a transparent conductor is not a wire. ITO on PET is typically specified in the region of tens to a few hundred ohms per square. It is a resistive sheet, not an equipotential plane.
Consider two adjacent zones, A and B. The controller drives A and holds B at its reference potential — B is supposed to stay opaque.
Driving A means pushing an alternating current through A’s capacitance. That current has to return, and its return path is the common electrode. It flows sideways through the common sheet, from under zone A towards the busbar. A resistive sheet carrying current develops a potential gradient along it, so the common electrode is no longer at the reference potential everywhere: it is lifted locally, most under the driven zone, less further away.
Now look at zone B. Its own segment electrode sits at the reference potential, but the common electrode underneath it has been lifted. The voltage across B’s liquid-crystal layer is the difference between the two — and that difference is exactly the local rise of the common electrode. Zone B is being driven, by the return current of zone A.
This is worth stating plainly, because it changes where you look for a fix: if the common electrode had zero resistance, there would be no interference at all. The liquid crystal is not conducting sideways; the polymer is not at fault; the film is not defective. The zones are coupled through a shared resistive node, which is an entirely ordinary circuit phenomenon.
The common electrode and the film capacitance are not lumped components — they are distributed over the area. Write Rs for the sheet resistance of the common electrode (Ω/sq) and cA for the film capacitance per unit area (F/m²). Current spreading in the sheet and current leaking away through the capacitance give, under an undriven zone,
∇²V = jωRscA · V
where V is the local potential of the common electrode — which, as we just saw, is the voltage appearing across that undriven zone. This is the same equation that describes an RC transmission line, and it has the same kind of solution: the disturbance decays exponentially with distance, with a characteristic length
λ = √( 2 / (ω · Rs · cA) ) where ω = 2πf
At a distance λ from the driven zone the induced voltage is down to about 37% of its value at the boundary; at 2λ, to about 14%. Everything in the table at the top of this page is read off this one expression.
Strictly, the propagation constant is complex, so the disturbance is shifted in phase as well as attenuated, and the decay is not a pure exponential close to the boundary. λ is the length that sets the reach; it is not a hard edge.
It is tempting to hope that λ is small — that the interference is a border effect confined to a few millimetres either side of the cut. It is not, and this can be shown without knowing anything about a specific film.
The same product ωRscA also sets how large a single zone can be. Current fed from a busbar has to travel across the zone, and the voltage at the far edge is lower than at the busbar; that is the droop that limits the distance from the busbar to the far edge of a zone (our published figure is on the order of a metre, for a film around 100 Ω/sq driven at 60 Hz). Droop grows with the square of that distance L and in proportion to ωRscA. Writing δ for the droop fraction you are willing to accept,
δ ≈ k · ωRscAL² → λ ≈ L · √(2k / δ)
with k a factor of order one that depends on the feed geometry. The point does not depend on k: δ is by definition a small fraction — a few percent, or you would see the unevenness — so √(2k/δ) is necessarily several. In other words, for any film whose droop is good enough to be usable, the reach of the interference is several times the largest zone you can build. It cannot be a border effect.
That is precisely what is observed. On our own page the six-zone illustration of the problem shows the neighbouring zone almost fully clear and the remaining zones, further away, still unintentionally clear. The pattern — strong next door, weaker with distance, but present across the whole film — is what an exponential decay with λ several times the zone pitch looks like.
There is a genuine border effect as well, and it is a different mechanism: at the gap between two segment electrodes, the field fringes. Its range is set by the geometry of the gap and the thickness of the film — tens of micrometres, not centimetres — and it appears as a soft edge along the cut rather than as a whole zone changing state.
The two look different and respond differently, so it is worth deciding which one you are seeing before acting on it. A soft line at the boundary is fringing, and is largely a matter of how the film was patterned. A whole neighbouring zone drifting towards clear is the shared-electrode mechanism, and no amount of patterning refinement will remove it.
Interference is usually noticed by eye, which is the least reliable way to quantify it. Transmittance is a strongly non-linear function of applied voltage: below the threshold of the film almost nothing happens optically, and just above it a small increase in voltage produces a large change. A zone sitting at, say, a third of its threshold looks perfectly opaque and yet is one step away from visibly changing.
Collecting the results: the interference is not a property of the film material but of the electrode network the zones share; its reach is set by √(2/ωRscA); and that reach is necessarily larger than a single zone for any film with acceptable droop. Selecting a different film moves the difficulty between crosstalk and uniformity, in one direction or the other, but the product ωRscA appears in both, so no film setting escapes the trade.
Which is why we treat it as a drive problem rather than a film problem. Our Multi-Zone Smart Glass System holds each zone at the transmittance it was set to on ordinary, unmodified PDLC film with a continuous common electrode — the case described above. The method is patent pending in Japan, so we will not go into it here, but the photograph and the six-zone example on that page show the result on real hardware.
We offer an evaluation kit so you can check multi-zone control on the switchable film you already work with. We are happy to discuss sheet resistance, drive frequency and zone layout for a specific project.
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