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Revenue Recognition - Additional Information (Detail) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Dec. 30, 2023	Sep. 24, 2022	Dec. 30, 2023	Dec. 24, 2022	Jun. 24, 2023
Revenue Recognition, Milestone Method [Line Items]
Account receivable bad debt			$ 0.0
Contract asset	$ 1.2		1.2		$ 1.3
Contract liability	22.3		22.3		18.7
Refund liability	38.4		38.4		$ 39.8
Revenue recognized related to contract liabilities	$ 0.5	$ 1.0	$ 2.9	$ 2.8

X

- Definition

Account receivable bad debt charge.

+ References

No definition available.

+ Details

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

X

- Definition

Amount, after allowance for credit loss, of right to consideration in exchange for good or service transferred to customer when right is conditioned on something other than passage of time.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479837/606-10-45-3

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479837/606-10-45-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479806/606-10-50-8

+ Details

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

X

- Definition

Amount of obligation to transfer good or service to customer for which consideration has been received or is receivable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479837/606-10-45-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479806/606-10-50-8

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479837/606-10-45-2

+ Details

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

X

- Definition

Amount of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479806/606-10-50-8

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount of liability for consideration received or receivable from customer which is not included in transaction price, when consideration is expected to be refunded to customer.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 27
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479777/606-10-55-27

+ Details

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

X

- 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

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