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Fair Value Measurements (Additional Information) (Details) - USD ($) $ in Millions | 12 Months Ended
--- | ---
Jun. 25, 2022 | Jun. 26, 2021
Defined Benefit Plan Disclosure [Line Items] |  |
Cash held in bank | $ 811.9 |
Level 1, 2 or 3 Member |  |
Defined Benefit Plan Disclosure [Line Items] |  |
Asset transfer | $ 0.0 | $ 0.0

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- Definition Cash held in bank + References No definition available. + Details
Name: | syna_CashHeldInBank
Namespace Prefix: | syna_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
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
Name: | us-gaap_DefinedBenefitPlanDisclosureLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Definition Amount of transfer of financial instrument classified as an asset into (out of) level 3 of the fair value hierarchy. + References No definition available. + Details
Name: | us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Details
Name: | us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel12And3Member
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |