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<!-- DFIN New ActiveDisclosure (SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2022-05-05T17:07:27.4199+00:00 -->
<!-- Copyright (c) 2022 Donnelly Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="syna_LineOfCreditFacilityAllowableRequestsForAdditionalBorrowing" name="LineOfCreditFacilityAllowableRequestsForAdditionalBorrowing" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="syna_LineOfCreditFacilityRepaymentDateDescription" name="LineOfCreditFacilityRepaymentDateDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_Lossonissuanceofcommonstockfromtreasurystock" name="Lossonissuanceofcommonstockfromtreasurystock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="syna_LossOnRedemptionOfConvertibleNotes" name="LossOnRedemptionOfConvertibleNotes" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="syna_MaximumAccountsReceivableFinancings" name="MaximumAccountsReceivableFinancings" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="syna_MaximumPermittedLeverageRatio" name="MaximumPermittedLeverageRatio" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="syna_MinimumInterestCoverageRatio" name="MinimumInterestCoverageRatio" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_NonconvertibleDebtBorrowingRate" name="NonconvertibleDebtBorrowingRate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="syna_NumberOfProductCategories" name="NumberOfProductCategories" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_PaymentForCostMethodInvestment" name="PaymentForCostMethodInvestment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="syna_PaymentForPayrollTaxesForDeferredStockAndMarketStockUnits" name="PaymentForPayrollTaxesForDeferredStockAndMarketStockUnits" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="syna_PaymentForRedemptionOfConvertibleNotes" name="PaymentForRedemptionOfConvertibleNotes" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="syna_PaymentOnLineOfCreditBorrowingsAndDebt" name="PaymentOnLineOfCreditBorrowingsAndDebt" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="syna_PayrollTaxesForDeferredStockUnits" name="PayrollTaxesForDeferredStockUnits" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="syna_Percentageofnonvotingcapitalstock" name="Percentageofnonvotingcapitalstock" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_PercentageOfPotentialPayout" name="PercentageOfPotentialPayout" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_PercentageOfPrincipalAmountOfNotesEqualToRepurchasePrice" name="PercentageOfPrincipalAmountOfNotesEqualToRepurchasePrice" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_PercentageOfVotingCapitalStockOfCertainForeignSubsidiariesCollateralized" name="PercentageOfVotingCapitalStockOfCertainForeignSubsidiariesCollateralized" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_PermittedLeverageRatioPriorToAmendment" name="PermittedLeverageRatioPriorToAmendment" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="syna_PotentialPayoutAdjustmentRatio" name="PotentialPayoutAdjustmentRatio" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_Priorleverageratiopermitted" name="Priorleverageratiopermitted" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="syna_ProceedsFromIssuanceOfConvertibleDebt" name="ProceedsFromIssuanceOfConvertibleDebt" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="syna_RedemptionOfConvertibleDebt" name="RedemptionOfConvertibleDebt" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="syna_Redemptionofprincipalamountpercentage" name="Redemptionofprincipalamountpercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_RefundableDepositPaidToVendor" name="RefundableDepositPaidToVendor" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="syna_ReturnOfDepositReceivedFromVendor" name="ReturnOfDepositReceivedFromVendor" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="syna_RevenuePerformanceObligationPaymentTerms" name="RevenuePerformanceObligationPaymentTerms" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_SaleLeasebackTransactionsOtherPaymentsRequired" name="SaleLeasebackTransactionsOtherPaymentsRequired" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="syna_SeniorDebtRepaymentDateDescription" name="SeniorDebtRepaymentDateDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_ShareBasedCompensationArrangementByShareBasedPaymentAwardIntrinsicValueClosingPrice" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardIntrinsicValueClosingPrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="syna_ShareBasedCompensationAttributableToAcquisition" name="ShareBasedCompensationAttributableToAcquisition" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="syna_ShortTermInvestmentsTerm" name="ShortTermInvestmentsTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_ThresholdPercentageOfEarningsPerShareToTriggerPayOut" name="ThresholdPercentageOfEarningsPerShareToTriggerPayOut" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_BasisOfPresentationLineItems" name="BasisOfPresentationLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_IncomeTaxDisclosureLineItems" name="IncomeTaxDisclosureLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_AmendedAndRestatedCreditAgreementMember" name="AmendedAndRestatedCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_AudioAndVideoTechnologyMember" name="AudioAndVideoTechnologyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_BacklogMember" name="BacklogMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_BankDepositMember" name="BankDepositMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_BroadcomMember" name="BroadcomMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_BusinessAcquisitionMember" name="BusinessAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_CustomerAMember" name="CustomerAMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_CustomerBMember" name="CustomerBMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_CustomerCMember" name="CustomerCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_CustomerContractsAndRelatedRelationshipsMember" name="CustomerContractsAndRelatedRelationshipsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_DisplayDriverTechnologyMember" name="DisplayDriverTechnologyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_DisplayLinkCorporationMember" name="DisplayLinkCorporationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_DspgAcqusitionMember" name="DspgAcqusitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_DspGroupIncMember" name="DspGroupIncMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_EmployeeSeveranceAndBenefitsMember" name="EmployeeSeveranceAndBenefitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_EmployeeStockPurchasePlanMember" name="EmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_FiscalTwoThousandTwentyOneRestructuringPlanMember" name="FiscalTwoThousandTwentyOneRestructuringPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_FiscalTwoThousandTwentyRestructuringPlanMember" name="FiscalTwoThousandTwentyRestructuringPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_FiscalTwoThousandTwentyTwoRestructuringPlanMember" name="FiscalTwoThousandTwentyTwoRestructuringPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_ForFourFiscalQuartersEndingAfterDateOfMaterialAcquisitionMember" name="ForFourFiscalQuartersEndingAfterDateOfMaterialAcquisitionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_FourPointZeroPercentConvertibleSeniorNotesDueTwoThousandTwentyNineMember" name="FourPointZeroPercentConvertibleSeniorNotesDueTwoThousandTwentyNineMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_FourYearPerformanceMember" name="FourYearPerformanceMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_InternetOfThingsProductApplicationsMember" name="InternetOfThingsProductApplicationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_LicensedTechnologyAndOtherMember" name="LicensedTechnologyAndOtherMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_MarketStockUnitsMember" name="MarketStockUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_MobileProductApplicationsMember" name="MobileProductApplicationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_OtherForeignCountryMember" name="OtherForeignCountryMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_PcProductApplicationsMember" name="PcProductApplicationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_PerformanceStockUnitsMember" name="PerformanceStockUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_PurchaseAgreementMember" name="PurchaseAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_SeniorNotesTwoThousandTwentyFiveMember" name="SeniorNotesTwoThousandTwentyFiveMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_SeniorNotesTwoThousandTwentyFourMember" name="SeniorNotesTwoThousandTwentyFourMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_SeniorNotesTwoThousandTwentySixAndThereafterMember" name="SeniorNotesTwoThousandTwentySixAndThereafterMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_ShareBasedCompensationAwardTrancheFourMember" name="ShareBasedCompensationAwardTrancheFourMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_SouthBayDevelopmentMember" name="SouthBayDevelopmentMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_ThereafterMember" name="ThereafterMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_ThreeYearPerformanceMember" name="ThreeYearPerformanceMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_TSRPercentile50Member" name="TSRPercentile50Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_TSRPercentileAbove75Member" name="TSRPercentileAbove75Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_TSRPercentileBelow25Member" name="TSRPercentileBelow25Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_TwoThousandNineteenEquityAndIncentiveCompensationPlanMember" name="TwoThousandNineteenEquityAndIncentiveCompensationPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_TwoThousandNineteenInducementEquityPlanMember" name="TwoThousandNineteenInducementEquityPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_VideoInterfaceTechnologyMember" name="VideoInterfaceTechnologyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_WellsFargoBankMember" name="WellsFargoBankMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_WellsFargoSecuritiesLLCMember" name="WellsFargoSecuritiesLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_WirelessAndConnectivityTechnologyMember" name="WirelessAndConnectivityTechnologyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_WirelessDevelopedTechnologyMember" name="WirelessDevelopedTechnologyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_ZeroPointFiveZeroPercentConvertibleSeniorNotesDueTwoThousandTwentyTwoMember" name="ZeroPointFiveZeroPercentConvertibleSeniorNotesDueTwoThousandTwentyTwoMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_BasisOfPresentationTable" name="BasisOfPresentationTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_IncomeTaxDisclosureTable" name="IncomeTaxDisclosureTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="syna_ScheduleOfRedemptionPricesAndUnpaidInterestTableTextBlock" name="ScheduleOfRedemptionPricesAndUnpaidInterestTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_ScheduleOfSupplementalCashFlowInformationRelatedToLeasesTableTextBlock" name="ScheduleOfSupplementalCashFlowInformationRelatedToLeasesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_SaleLeaseBackTransactionsPolicyPolicyTextBlock" name="SaleLeaseBackTransactionsPolicyPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_ScheduleOfFutureMinimumRentalPaymentsForOperatingLeases1TableTextBlock" name="ScheduleOfFutureMinimumRentalPaymentsForOperatingLeases1TableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="syna_ShortTermInvestmentsPolicyTextBlock" name="ShortTermInvestmentsPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
</xsd:schema>
