CPI Linked Bonds

Let’s take the following example: If the CPI increases by 2%, then the principal amount increases to $1,020 but the coupon payment does not change.

Does this apply to all bonds linked to some sort of an index, e.g. the S&P 500? i.e. is it always the principal that changes and the coupon rate always remains constant?

In fact, the coupon payment does change (it increases by 2%); the coupon _ rate _ doesn’t change, but it’s now applied to a higher principle.

I don’t know, but probably. It’d be weird otherwise.