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On-chip components are the components built on the chip (IC) itself i.e on the same silicon substrate like transistors ,resistors ,capacitors ,coils...etc .
Off-chip components are discrete components that are not built on the chip .
Usually, off-chip components are used for coils ,capacitors and resistors of high values that are impractical to implement on the chip or for components that are required to operate at higher voltage level and power than the chip can handle .
On-chip components can provide good matching (can achieve accurate ratios between values) and doesn't consume size (not bulky) and reduces connections required on the PCB .