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Acquisitions, Divestitures and Licensing Transactions - Narrative (Details) - USD ($) $ in Millions				3 Months Ended			9 Months Ended		12 Months Ended
	Jun. 25, 2018	May 08, 2018	Nov. 29, 2017	Sep. 28, 2018	Jun. 29, 2018	Sep. 29, 2017	Sep. 28, 2018	Sep. 29, 2017	Dec. 31, 2017
Business Acquisition [Line Items]
Goodwill				$ 932.5			$ 932.5		$ 916.9
Gain on divestiture of business				0.4		$ 12.5	5.0	$ 12.5
Licensing income recognized				1,541.7		$ 1,390.9	4,375.2	$ 4,165.6
SensL
Business Acquisition [Line Items]
Percentage acquired		100.00%
Purchase price of acquisition		$ 71.6
Initial estimated purchase price allocation		$ 71.4		71.6
Developed technology, weighted-average useful life (in years)		7 years
Goodwill		$ 15.2		18.9			18.9
Other acquired intangibles | SensL
Business Acquisition [Line Items]
Intangible assets		30.4		31.4			31.4
Developed technology | SensL
Business Acquisition [Line Items]
Intangible assets		$ 30.0
Developed technology, weighted-average useful life (in years)		7 years
IPRD | SensL
Business Acquisition [Line Items]
Intangible assets		$ 25.0		$ 20.0			20.0
Present value, discount rate used (as a percent)		30.00%
Disposal Group, Disposed of by Sale, Not Discontinued Operations | Transient Voltage Suppressing Diodes
Business Acquisition [Line Items]
Proceeds from divestiture of business	$ 5.6
Gain on divestiture of business							$ 4.6
HIDM
Business Acquisition [Line Items]
Proceeds from divestiture of business									52.5
Deferred licenses revenue									$ 10.0
Proceeds from license fees received					$ 10.0
QST Co.
Business Acquisition [Line Items]
Proceeds from license fees received			$ 13.0
Proceeds from other fees			$ 8.5
License and Service | QST Co.
Business Acquisition [Line Items]
Licensing income recognized					$ 18.0

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