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Balance Sheet Components - Schedule of Other Non Current Assets (Details) - USD ($) $ in Millions	Mar. 30, 2024	Jun. 24, 2023
Other Assets, Noncurrent [Abstract]
Prepayment of intangible assets	$ 116.5	$ 0.0
Deferred tax assets	77.9	68.0
Other	34.3	41.1
Non-current other assets	$ 228.7	$ 109.1

X

- Definition

Other Noncurrent Assets

+ References

No definition available.

+ Details

Name:	syna_OtherNoncurrentAssets
Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Prepayment Of Intangible Assets

+ References

No definition available.

+ Details

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Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Amount after allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences and other assets expected to be realized or consumed after one year or normal operating cycle, if longer.

+ References

No definition available.

+ Details

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

X

- Definition

Amount of noncurrent assets classified as other.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(17))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

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Namespace Prefix:	us-gaap_
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Period Type:	instant

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- References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	na
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