SEPARATION AND GENERAL RELEASE AGREEMENT

Exhibit 10.4

SEPARATION AND GENERAL RELEASE AGREEMENT

This Separation and General Release Agreement (this “Agreement”) is entered into by and between Pedro (Pete) P. Rodriguez (“Rodriguez”) and Exar Corporation (the “Company”).

WHEREAS, Rodriguez has been employed by the Company as its Chief Executive Officer and President pursuant to the terms of a Second Amended and Restated Employment Agreement, dated March 19, 2010 (the “Employment Agreement”);

WHEREAS, Rodriguez’s employment with the Company terminated, effective November 7, 2007, due to Rodriguez’s voluntary resignation;

WHEREAS, the Company and Rodriguez agree that, subject to Rodriguez entering into this Agreement and not revoking it pursuant to Section 10(e) below, the Company will provide Rodriguez the severance benefits described in Section 4 below; and

WHEREAS, any capitalized terms that are not defined herein shall have the meaning set forth in the Employment Agreement;

NOW, THEREFORE, in consideration of the mutual promises and covenants contained herein, the Company and Rodriguez agree as follows:

1. Effective Date: This Agreement shall become effective on the eighth day after Rodriguez delivers to the Company a fully-executed version of this Agreement without modification or revocation (the “Effective Date”), provided he does not revoke this Agreement prior to such date pursuant to Section 10(e) and provided further that Rodriguez signs and returns this Agreement to the Company on or before November 26, 2011.

2. Separation from Employment and Resignation from Board of Directors: The parties acknowledge and agree that (a) Rodriguez’s employment with the Company and any of its subsidiaries or affiliates (the “Company Group”) terminated, effective November 7, 2011 (the “Severance Date”), due to his voluntary resignation; and (b) the Company reasonably relied on Rodriguez’s written notice of voluntary resignation in issuing its Form 8-K announcing Rodriguez’s voluntary resignation on or about November 9, 2011 and entering into this Agreement. As of the Severance Date, by executing this Agreement, Rodriguez acknowledges and agrees that (i) he no longer holds the title of, or performs services as, the Company’s Chief Executive Officer, President or in any other position of employment with the Company or any of its subsidiaries or affiliates; (ii) he hereby confirms his resignation effective as of the Severance Date from his position as a member of the Board and, to the extent applicable, as a member of the Company’s Board of Directors (the “Board”) or as an officer of any member of the Company Group; (iii) he no longer represents any member of the Company Group and he shall not hold himself out as having authority to represent any member of the Company Group; and (iv) he shall not communicate with third parties with which any member of the Company Group has or is negotiating business relationships or with securities analysts or similar third parties purporting to represent or be acting on behalf of any member of the Company Group or in any way that results in the communication of Company confidential information (including without limitation negotiation strategies and Company objectives).

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3. Accrued Obligations: The Company will pay to Rodriguez all Accrued Obligations in accordance with Section 5.3(a) of the Employment Agreement.

4. Severance Benefits: Provided that Rodriguez signs and does not timely revoke this Agreement, complies with the terms and conditions of this Agreement, Sections 7, 8 and 10 of the Employment Agreement and his Proprietary Information and Confidentiality Agreement with the Company (the “Confidentiality Agreement”) and Rodriguez’s spouse executes and delivers the Spousal Consent attached hereto as Exhibit D, Rodriguez shall be entitled to receive the following severance benefits (collectively, the “Severance Benefits”):

a. Severance Pay. The Company shall pay Rodriguez severance pay in the amount of $541,333.16, less standard withholdings and authorized deductions (the “Severance Pay”). The Severance Pay shall be paid in equal installments in accordance with the Company’s normal payroll practices then in effect over a period of fourteen (14) consecutive months, with the first installment payable in the month following the month in which Rodriguez’s Separation from Service occurs.

b. Health and Welfare Benefits: Rodriguez shall have the option to convert and continue health and dental insurance for himself and his eligible dependents after the Severance Date, as may be required or authorized by law under the Consolidated Omnibus Budget Reconciliation Act of 1985 (“COBRA”). Within five (5) business days following January 1, 2012, the Company shall pay to Rodriguez an amount equal to the cost of Rodriguez’s premiums charged or that will/would be charged to continue medical coverage pursuant to COBRA, at the same or reasonably equivalent medical coverage for Rodriguez (and, if applicable, Rodriguez’s eligible dependents) as in effect immediately prior to the Severance Date, for a period commencing on the Severance Date and ending on the 7-month anniversary of the Severance Date.

c. Accelerated Vesting and Extended Exercise Period: Rodriguez shall vest in any portion of each equity award held by Rodriguez as set forth in Exhibit C that is scheduled to vest on or within twelve (12) months after the Severance Date, and, with respect to any such award that is a stock option, Rodriguez shall have a period of twelve (12) months to exercise the vested portion of such stock option (including any portion that is accelerated pursuant to this provision), provided that such stock option shall remain subject to earlier termination at the end of its maximum term or in connection with the change in control of the Company or similar event as provided in the applicable option documentation. any portion of Rodriguez’s equity awards that are not vested after giving effect to the foregoing acceleration provision shall terminate on the Severance Date.

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d. Mitigation: Rodriguez will not be required to mitigate damages or the amount of any payment provided under this Agreement by seeking other employment or otherwise, nor will the amount of any payment provided for under this Agreement be reduced by any compensation earned by Rodriguez as a result of employment by another employer or otherwise.

e. Effect of Breach of Obligations. Notwithstanding the foregoing provisions of this Section 4, if Rodriguez breaches his obligations under the Confidentiality Agreement and/or this Agreement at any time, from and after the date of such breach, (x) Rodriguez will no longer be entitled to, and the Company will no longer be obligated to pay, any remaining unpaid portion of any benefits provided in this Section 4, and (y) Rodriguez will no longer be entitled to, and the Company will no longer be obligated to make available to Rodriguez or his spouse or dependents any group health, life or other similar insurance plans or any payment in respect of such plans; provided, however, that in no event shall Rodriguez be entitled to benefits pursuant to this Section 4 of less than $5,000, which amount the parties agree is good and adequate consideration, in and of itself, for Rodriguez’s release contemplated in this Agreement.

5. Termination Of Contractual Relationship: Rodriguez and the Company agree that except as arising out of this Agreement, Sections 5.7, 6-18 and 20-23 of the Employment Agreement, the Confidentiality Agreement, each equity award agreement set forth on Exhibit C hereto as amended hereby (the “Equity Agreements”), and the Indemnification Agreement (collectively, the “Ongoing Contracts”), there are no further contractual relationships between Rodriguez and any member of the Company Group following the Severance Date and Rodriguez will have no right to reinstatement with the Company or any member of the Company Group. Nothing herein shall relieve Rodriguez of his obligations not to use or disclose the Company’s trade secrets and Confidential Information, whether under the Confidentiality Agreement, the Employment Agreement or otherwise, including information learned by him as an officer and/or director of the Company or any member of the Company Group.

6. No Other Compensation or Benefits: Except as expressly set forth herein in Sections 3 and 4 of this Agreement, Rodriguez acknowledges that he will not receive, and is not entitled to receive, any additional compensation, severance or benefits after the Severance Date. Rodriguez agrees to submit any business expenses that he incurred in the scope of his employment within fifteen (15) days following the Severance Date. The Company will reimburse Rodriguez for all outstanding business expenses in accordance with the Company’s expense reimbursement policy.

7. No Admission of Liability Or Wrongdoing: This Agreement does not constitute an admission by the Company or Rodriguez of any violation of federal, state or local law, ordinance or regulation or of any violation of the Company’s policies or procedures or of any liability or wrongdoing whatsoever. Neither this Agreement nor anything in this Agreement shall be construed to be or shall be admissible in any proceeding as evidence of liability or wrongdoing by the Company or Rodriguez. This Agreement may be introduced, however, in any proceeding to enforce the Agreement.

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8. Release: Rodriguez, on his own behalf and on behalf of his descendants, dependents, heirs, executors, administrators, assigns and successors, and each of them, hereby covenants not to sue and fully releases and discharges the Company, the Company Group, and each of its and their subsidiaries, parent, or affiliated partnerships and corporations, past and present, as well as each of its and their directors, officers, trustees, shareholders, members, partners, representatives, attorneys, assignees, successors, agents and employees, past and present, and each of them (individually and collectively, “Releasees”), from and with respect to any claim, cause of action, charge, controversy, duty, agreement, wages, obligation, demand, loss, cost, debt, damages, penalties, judgment, attorneys’ fees, order, or liability, known or unknown, suspected or unsuspected (collectively, “Claims”), arising out of or in any way connected with any acts or omissions committed or omitted by Releasees prior to Rodriguez signing this Agreement, including but not limited to Rodriguez’s employment and termination of employment with the Company, membership and termination of membership on the Board of Directors of the Company, or any other relationship with, interest in or termination of relationship with any Releasees, including without limiting the generality of the foregoing, any Claim for wages, vesting, overtime, salary, severance pay, severance benefits under Section 5.3 of the Employment Agreement, director compensation, commissions, bonus or similar benefit, car allowance, sick leave, pension, retirement, vacation pay, paid time off, equity, life insurance, health or medical insurance, including coverage under the Company’s Executive Health Plan, or any other fringe benefit, or disability; any Claim for breach of the Option Agreement or Employment Agreement; any Claim pursuant to any federal, state or local law, constitution, regulation, ordinance, or common law, including, but not limited to: the federal Civil Rights Act of 1964, as amended; the federal Americans with Disabilities Act of 1990; the federal Age Discrimination in Employment Act of 1967, as amended (the “ADEA”); the California Fair Employment and Housing Act, as amended; the California Family Rights Act; the California Labor Code; the Sarbanes-Oxley Act; any tort; breach of implied, express, oral or written contract; unfair competition; wrongful discharge; discrimination; retaliation; harassment; fraud; defamation; emotional distress; breach of the implied covenant of good faith and fair dealing; or breach of any Company Executive Incentive Compensation Program, or breach of the Executive Officers’ Change in Control Severance and Benefit Plan.

Notwithstanding any provision of this Section 8, Rodriguez does not hereby release any right he may otherwise have to: (i) any obligations of the Company arising under this Agreement or the other Ongoing Contracts (as the same may be amended hereby); (ii) Rodriguez’s receipt of benefits otherwise due to terminated employees under group insurance coverage consistent with the terms of the applicable Company welfare benefit plan; (iii) Rodriguez’s rights under COBRA to continue participation in medical, dental, hospitalization and life insurance coverage; (iv) Rodriguez’s receipt of benefits otherwise due in accordance with the terms of the Company’s 401(k) plan (if any); and (v) indemnification by the Company or any member of the Company Group pursuant to applicable law or, as applicable, the certificates of incorporation or by-laws of the Company and/or any member of the Company Group, or the Indemnification Agreement.

9. Section 1542 Waiver: In executing this Agreement, and except as expressly stated in this Agreement, Rodriguez intends for it to be effective as a general release to each and every claim, demand and cause of action hereinabove specified. In furtherance of this intention,

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Rodriguez hereby expressly waives any rights and benefits conferred by SECTION 1542 OF THE CALIFORNIA CIVIL CODE, and expressly consents that this Agreement shall be given full force and effect according to each and all of its express terms and provisions, including those related to unknown and unsuspected claims, demands and causes of action, if any, as well as those relating to any other claims, demands and causes of action hereinabove specified. SECTION 1542 provides:

“A GENERAL RELEASE DOES NOT EXTEND TO CLAIMS WHICH THE CREDITOR DOES NOT KNOW OR SUSPECT TO EXIST IN HIS FAVOR AT THE TIME OF EXECUTING THE RELEASE, WHICH IF KNOWN BY HIM MUST HAVE MATERIALLY AFFECTED HIS SETTLEMENT WITH THE DEBTOR.”

Rodriguez acknowledges that he may hereafter discover claims or facts in addition to or different from those which he now knows or believes to exist against Company Releasees, respectively, with respect to the subject matter of this Agreement and which, if known or suspected at the time of executing this Agreement, may have materially affected this settlement. Nevertheless, Rodriguez hereby waives any right, claim or cause of action that might arise as a result of such different or additional claims or facts. Rodriguez acknowledges that he understands the significance and consequence of such release and such specific waiver of SECTION 1542.

10. Waiver Of Age Discrimination Claims: Rodriguez expressly acknowledges and agrees that, by entering into this Agreement, he is waiving any and all rights or claims that he may have arising under the ADEA which have arisen on or before the date of execution of this Agreement. Rodriguez also expressly acknowledges and agrees that:

a. In return for this Agreement, Rodriguez will receive consideration, i.e., something of value, beyond that to which he was already entitled before entering into this Agreement;

b. Rodriguez is hereby advised in writing by this Agreement to consult with an attorney before signing this Agreement, and has done so;

c. Rodriguez is hereby informed that he has 21 days within which to consider whether to sign and accept the terms of this Agreement and that if he wishes to execute this Agreement prior to the expiration of such 21-day period, he will execute the Acknowledgment and Waiver attached hereto as Exhibit B;

d. Nothing in this Agreement prevents or precludes Rodriguez from challenging or seeking a determination in good faith of the validity of this waiver under the ADEA, nor does it impose any condition precedent, penalties or costs from doing so, unless specifically authorized by federal law; and

e. Rodriguez is hereby informed that he has seven (7) days following the date he executes the Agreement in which to revoke it, and this Agreement will become

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null and void if Rodriguez elects revocation during that time. To be valid and effective, any revocation must be in writing and must be received by the Company during the seven-day revocation period. In the event that Rodriguez validly exercises his right of revocation, neither the Company nor Rodriguez will have any obligations under this Agreement.

11. Confidentiality Agreement. Rodriguez acknowledges that he has continuing obligations to the Company under the Confidentiality Agreement that remain in effect beyond the termination of his employment. A copy of the Confidentiality Agreement is attached hereto as Exhibit A and is expressly incorporated into this Agreement.

12. Return of Company Property and Proprietary Information:

a. Rodriguez acknowledges that, by no later than five (5) calendar days after the Severance Date, he shall return to the Company (and shall not retain any copies of) all Company Property and Confidential Information that are in his possession, custody or control unless directed otherwise by the Company. For purposes of this Agreement, the term “Company Property” shall mean all personal computers, laptop computers, cellular telephones, security cards, keys, diskettes, electronic storage devices, personal digital assistants or pda’s, and other equipment or property owned by the Company that were provided to Rodriguez or paid for by the Company during his employment with the Company (including its predecessor companies). For purposes of this Agreement, the term “Confidential Information” shall include information required to be kept confidential pursuant to the Confidentiality Agreement, and any other confidential information of any member of the Company Group. Rodriguez further agrees to make a diligent and thorough search for any Company Property and Company documents or information in his possession or control prior to the Effective Date. In addition, (i) Rodriguez will complete any forms necessary, including those of any banking institution, to remove his name from any list of Company authorized signatories, (ii) Rodriguez will execute any requested letters of resignation with respect to the Company or its subsidiaries, and (iii) Rodriguez shall otherwise assist the Company in taking all actions required to confirm that all Company Property has been returned and that full ownership of all Company Property is vested solely in the Company.

b. Exceptions. Notwithstanding the foregoing, if Rodriguez timely enters into this Agreement, the Company agrees to transfer to Rodriguez its ownership interests in the mobile phones and laptop computer provided for Rodriguez’s use in connection with Rodriguez’s employment, and Rodriguez shall be permitted to retain such mobile phone and laptop computer. The mobile phones and laptop computer shall be provided to Rodriguez in “as is” condition and without warranty or guarantee, effective as of the Severance Date, provided that, on or before five days following the Severance Date, Rodriguez must deliver such mobile phone and laptop computer to the Company so that the Company can delete in full any and all confidential or proprietary information of the Company or any member of the Company Group (other than such specific information that Rodriguez reasonably identifies as Rodriguez’s personal property). Rodriguez will be solely responsible for any and all taxes and/or costs owed as a result of the transfer of the mobile phones and laptop computer to Rodriguez.

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13. Equity: Rodriguez acknowledges that, except as set forth in Exhibit C to this Agreement (which provides, with respect to each grant of equity provided to Rodriguez by the Company, the exercise price and number of shares of the Company’s common stock and RSUs that are vested as of the Severance Date after taking into account the acceleration of vesting provided pursuant to Section 5.4(b)(iii) in the Employment Agreement), he has no further right or benefits under any agreement to receive or acquire any security or derivative security in or with respect to the Company or any member of the Company Group.

14. Non-Solicitation: Rodriguez shall comply with his continuing non-solicitation obligations under Section 8 of the Employment Agreement.

15. Non-Disparagement: Rodriguez agrees that he shall not make any disparaging remarks, or any remarks that could reasonably be construed as disparaging, whether orally or in writing, regarding the Company or any member of the Company Group, or its or their current or former officers, directors, trustees, employees, partners, owners, affiliates, or agents, in any manner that is intended to be harmful to them or their business, business reputation or personal reputation, including but not limited to statements to the media, former and present employees, consultants or customers of the Company, or existing or potential investors of the Company. The Company agrees that its officers and directors will not make any disparaging remarks, or any remarks that could reasonably be construed as disparaging, whether orally or in writing, regarding Rodriguez that is intended to be harmful to Rodriguez’s business or personal reputation. Nothing in this Section 15 is intended to prohibit Rodriguez, on the one hand, or the Company or any of its officers or directors, on the other hand, from testifying or responding truthfully in response to any court order, arbitral order, subpoena or government investigation (“Disclosure Demand”), provided that the disclosing party: (i) provides written notice to the non-disclosing party within 72 hours of receiving a Disclosure Demand and (ii) cooperates with the non-disclosing party to the extent the non-disclosing party elects to object to such Disclosure Demand.

16. Warranty of No Other Actions: Rodriguez hereby represents and warrants to the Company that he has not filed any lawsuit or administrative action against the Company or any other Company Releasee with any court, arbitration proceeding or governmental agency.

17. Assignments: Rodriguez warrants and represent that he has not assigned or transferred to any person not a party to this Agreement any released matter or any part or portion thereof and Rodriguez shall defend, indemnify and hold harmless the Company from and against any claim (including the payment of attorneys’ fees and costs actually incurred whether or not litigation is commenced) based on or in connection with or arising out of any such assignment or transfer made, purported or claimed. This Agreement shall be binding upon and inure to the benefit of the parties and their respective heirs, successors and permitted assigns. The Company may assign this Agreement, including any and all rights under this Agreement, without notice in its sole discretion. This Agreement is personal to Rodriguez and may not be assigned, in whole or in part, by Rodriguez.

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18. Waivers: No waiver of any provision or consent to any exception to the terms of this Agreement shall be effective unless in writing and signed by the party to be bound and, then, only to the specific purpose, extent and instance so provided.

19. Governing Law: This Agreement shall be governed by and construed in accordance with the laws of the State of California applicable to contracts made and performed in the State of California and without regard to conflicts of laws doctrines.

20. Arbitration: Any controversy or claim arising out of or relating to this Agreement, its enforcement, arbitrability or interpretation, or because of an alleged breach, default, or misrepresentation in connection with any of its provisions shall be resolved in accordance with Section 19 of the Employment Agreement.

21. Authority. The Company represents and warrants that all corporate action on the part of the Company necessary for the authorization, execution, delivery and performance of this Agreement have been taken.

22. Severability: If any provision of this Agreement or its application is held invalid, the invalidity shall not affect other provisions or applications of the Agreement which can be given effect without the invalid provision or application and, therefore, the provisions of this Agreement are declared to be severable.

23. Entire Agreement: With the exception of the Sections 5.7, 6-18 and 20-23 of the Employment Agreement, the Confidentiality Agreement, the Equity Agreements, and the Indemnification Agreement, this instrument constitutes and contains the entire agreement and understanding concerning Rodriguez’s employment and the other matters addressed herein. The parties intend it as a complete and exclusive statement of the terms of their agreement. It supersedes and replaces all prior negotiations and agreements, proposed or otherwise, whether written or oral, between the parties concerning the subject matters, and expressly supersedes and eliminates any rights Rodriguez may have under the Executive Health Plan and the Executive Officers’ Change in Control Severance and Benefit Plan. This is a fully integrated document. This Agreement may be modified only with a written instrument executed by both parties.

24. Voluntary Counsel: Rodriguez agrees and acknowledges that he has read and understood this Agreement prior to signing it, has entered into this Agreement freely and voluntarily and has had the opportunity to receive legal advice from counsel of his own choosing prior to entering into this Agreement.

25. Code Section 409A.

a. It is intended that any amounts payable under this Agreement shall comply with Section 409A of the Code (including the Treasury regulations and other published guidance relating thereto) (“Code Section 409A”) so as not to subject Rodriguez to payment of any interest or additional tax imposed under Code Section 409A. To the extent that any amount payable under this Agreement would trigger the additional tax imposed by Code Section 409A, the Agreement shall be construed and interpreted in a manner to avoid such additional tax yet preserve (to the nearest extent reasonably possible) the intended benefit payable to Rodriguez.

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b. Notwithstanding any provision of this Agreement to the contrary, if Rodriguez is a “specified employee” within the meaning of Treasury Regulation Section 1.409A-1(i) as of the date of the Rodriguez’s Separation from Service, Rodriguez shall not be entitled to any payment or benefit pursuant to Section 4 of this Agreement until the earlier of (i) the date which is six (6) months after Rodriguez’s Separation from Service for any reason other than death, or (ii) the date of Rodriguez’s death. Any amounts otherwise payable to Rodriguez upon or in the six (6) month period following the Rodriguez’s Separation from Service that are not so paid by reason of this Section 25(b) shall be paid (without interest) as soon as practicable (and in all events within thirty (30) days) after the date that is six (6) months after Rodriguez’s Separation from Service (or, if earlier, as soon as practicable, and in all events within thirty (30) days, after the date of the Rodriguez’s death). The provisions of this Section 25(b) shall only apply if, and to the extent, required to avoid the imputation of any tax, penalty or interest pursuant to Section 409A of the Code.

26. Notices: All notices, requests, demands and other communications required or permitted under this Agreement shall be in writing and shall be deemed to have been duly given and made if (i) delivered by hand, (ii) otherwise delivered against receipt therefor, or (iii) sent by registered or certified mail, postage prepaid, return receipt requested. Any notice shall be duly addressed to the parties as follows:

(i) if to the Company:

Exar Corporation

48720 Kato Road

Fremont, CA 94538

Attn: Legal Department

with a copy to:

Stephen Sonne, Esq.

O’Melveny & Myers LLP

2765 Sand Hill Road

Menlo Park, CA 94025

(ii) if to Rodriguez, to the address most recently on file in the payroll records of the Company.

27. Construction. Each party recognizes that this is a legally binding contract and acknowledges and agrees that they have had the opportunity to consult with legal counsel of their choice. Each party has cooperated in the drafting, negotiation and preparation of this agreement. Hence, in any construction to be made of this agreement, the same shall not be construed against

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either party on the basis of that party being the drafter of such language. Each party agrees and acknowledges that they have read and understand this agreement, is entering into it freely and voluntarily, and has been advised to seek counsel prior to entering into this agreement and has had ample opportunity to do so.

28. Section Headings: Section and other headings contained in this Agreement are for convenience of reference only and shall not affect in any way the meaning of interpretation of this Agreement.

IN WITNESS WHEREOF, the parties have executed or caused to be executed this Agreement as of the date first above written.

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EXHIBIT A

[CONFIDENTIALITY AGREEMENT]

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EXHIBIT B

[ACKNOWLEDGMENT AND WAIVER]

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EXHIBIT C

EQUITY AWARD TABLE

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EXHIBIT D

[CONSENT OF SPOUSE]

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