Income Taxes - Additional Information (Detail) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
Mar. 27, 2021	Mar. 28, 2020	Mar. 27, 2021	Mar. 28, 2020
Income Tax Disclosure [Line Items]
Benefit for income taxes	$ 10.4	$ 10.2	$ 16.4	$ 17.3
Unrecognized Tax Benefits, Period Increase (Decrease)			0.8
Gross unrecognized tax benefits	22.9		22.9
Interest and penalties accrued related to unrecognized tax benefits	1.7		1.7
Increase (decrease) in interest and penalties accrued related to unrecognized tax benefits			(0.2)
Maximum
Income Tax Disclosure [Line Items]
Estimated increase in unrecognized tax benefit in next twelve months	$ 3.1		$ 3.1

Income tax disclosure.

No definition available.

Name:	syna_IncomeTaxDisclosureLineItems
Namespace Prefix:	syna_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Increase (Decrease) in unrecognized tax benefit income tax penalties and interest accrued.

+ References

No definition available.

+ Details

Name:	syna_IncreaseDecreaseInUnrecognizedTaxBenefitIncomeTaxPenaltiesAndInterestAccrued
Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB TOPIC 6.I.7)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32672-109319

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 22
-Subparagraph (h)
-URI http://asc.fasb.org/extlink&oid=120311839&loc=d3e8736-108599

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h))
-URI http://asc.fasb.org/extlink&oid=120395691&loc=d3e23780-122690

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 250
-SubTopic 10
-Section 50
-Paragraph 9
-URI http://asc.fasb.org/extlink&oid=109234566&loc=d3e22663-107794

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 20
-Section 45
-Paragraph 2
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=120385591&loc=d3e38679-109324

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 220
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-04(9))
-URI http://asc.fasb.org/extlink&oid=120400993&loc=SL114874131-224263

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 250
-SubTopic 10
-Section 50
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=109234566&loc=d3e22658-107794

+ Details

Name:	us-gaap_IncomeTaxExpenseBenefit
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of increase reasonably possible in the next twelve months for the unrecognized tax benefit.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 15
-Subparagraph (d)(3)
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32718-109319

+ Details

Name:	us-gaap_IncreaseInUnrecognizedTaxBenefitsIsReasonablyPossible
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of unrecognized tax benefits.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 45
-Paragraph 10B
-URI http://asc.fasb.org/extlink&oid=120406818&loc=SL37586934-109318

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 15A
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=84230637&loc=SL6600010-109319

+ Details

Name:	us-gaap_UnrecognizedTaxBenefits
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount accrued for interest on an underpayment of income taxes and penalties related to a tax position claimed or expected to be claimed in the tax return.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 15
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32718-109319

+ Details

Name:	us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of increase (decrease) in unrecognized tax benefits attributable to uncertain tax positions taken in tax returns.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 15A
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=84230637&loc=SL6600010-109319

+ Details

Name:	us-gaap_UnrecognizedTaxBenefitsPeriodIncreaseDecrease
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: