Weighted average amortization period of finite-lived intangible assets acquired either individually or as part of a group of assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (a)(3)
-URI http://asc.fasb.org/extlink&oid=66006027&loc=d3e16265-109275

+ Details

Name:	us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_BusinessAcquisitionLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The amount of identifiable intangible assets recognized as of the acquisition date.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 55
-Paragraph 37
-URI http://asc.fasb.org/extlink&oid=121600890&loc=d3e2207-128464

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=121647850&loc=d3e4845-128472

+ Details

Name:	us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_BusinessAcquisitionAxis=syna_DisplayLinkCorporationMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=syna_BroadcomMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_DevelopedTechnologyRightsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=syna_CustomerContractsAndRelatedRelationshipsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_InProcessResearchAndDevelopmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_TradeNamesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=syna_LicensedTechnologyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis=us-gaap_OrderOrProductionBacklogMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Acquisitions, Divestiture and Investment - Summary of Preliminary Estimate of Intangible Assets (Detail) - USD ($) $ in Millions			12 Months Ended
	Jul. 17, 2020	Jul. 02, 2020	Jun. 26, 2021
Business Acquisition [Line Items]
Estimated Weighted Average Useful Lives in Years			5 years 1 month 6 days
Display Link Corporation [Member]
Business Acquisition [Line Items]
Intangible assets	$ 193.0
Broadcom
Business Acquisition [Line Items]
Intangible assets		$ 123.0
Developed Technology Rights [Member] \| Display Link Corporation [Member]
Business Acquisition [Line Items]
Estimated Weighted Average Useful Lives in Years	3 years
Intangible assets	$ 82.0
Developed Technology Rights [Member] \| Broadcom
Business Acquisition [Line Items]
Estimated Weighted Average Useful Lives in Years		6 years
Intangible assets		$ 93.0
Customer Contracts And Related Relationships [Member] \| Display Link Corporation [Member]
Business Acquisition [Line Items]
Estimated Weighted Average Useful Lives in Years	3 years
Intangible assets	$ 54.0
Customer Contracts And Related Relationships [Member] \| Broadcom
Business Acquisition [Line Items]
Estimated Weighted Average Useful Lives in Years		6 years
Intangible assets		$ 18.0
In Process Research And Development [Member] \| Display Link Corporation [Member]
Business Acquisition [Line Items]
Intangible assets	$ 51.0
Trade Names [Member]
Business Acquisition [Line Items]
Estimated Weighted Average Useful Lives in Years			5 years 1 month 6 days
Trade Names [Member] \| Display Link Corporation [Member]
Business Acquisition [Line Items]
Estimated Weighted Average Useful Lives in Years	4 years
Intangible assets	$ 3.0
Licensed Technology [Member] \| Display Link Corporation [Member]
Business Acquisition [Line Items]
Estimated Weighted Average Useful Lives in Years	2 years 6 months
Intangible assets	$ 3.0
Order Backlog [Member] \| Broadcom
Business Acquisition [Line Items]
Estimated Weighted Average Useful Lives in Years		6 months
Intangible assets		$ 12.0