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I'm currently designing a board and one of the SMD components has a particularly small package of 1.5x2.5 mm (CYSJ106C datasheet).

It doesn't have a recommended landing pad in the datasheet and these general solder pad recommendations from TI seem very large compared to the pins. For example, the pins have a length of 0.5 mm and from the minimums listed (toe + heel) the pads would have length 0.5 + 0.5 + 0.4 = 1.4 mm.

What would be the best way of designing the landing pad for a component of this size?

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Solder pads for SMD components with leads (i.e. SOIC, SOT, QFP, etc) should in general be a little wider than the component's leads and quite substantially longer. The extra length allows excess solder to go somewhere, makes the bond stronger (due to the solder fillets at either side) and makes hand-soldering the part possible in the first place (since you wouldn't be able to get solder under the lead otherwise).

Go with TI's recommendation, an SMD pad 3x the length of the lead's contact area with the PCB is perfectly reasonable. I'd use 0.5mm x 1.5mm actually.

Here's a QFP footprint by Toshiba that demonstrates this. Note the very high aspect ratio of the pads.

You might also want to take a look at this answer that goes into more detail on how to actually place the pads. While this answer is about QFPs, it applies to your chip as well.

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