AGREEMENT

EXHIBIT 10.2

AGREEMENT

This Agreement is made and executed as of August 24, 2007, between Exar Corporation, a Delaware corporation (the “Company”), and Guy Adams, an individual (“Adams”), GWA Capital Partners LLC, GWA Master Fund LP and GWA Investments LLC (collectively with Adams, the “Adams Parties”).

WHEREAS, Adams has served as a member of the Board of Directors since October 27, 2005;

WHEREAS, the Company has entered into an Agreement and Plan of Merger (the “Merger Agreement”) whereby Sipex Corporation will merge with and into a wholly-owned subsidiary of the Company (the “Merger”) and, effective as of the closing of the Merger, the Board of Directors of the Company will include three new Directors who are currently serving as Directors of Sipex Corporation;

WHEREAS, the Company and Adams have mutually determined that Adams shall resign from the Company’s Board of Directors effective as of September 20, 2007;

NOW THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereby agree as follows:

1. Resignation. Adams hereby resigns as a member of the Company’s Board of Directors effective as of September 20, 2007 (the “Resignation Date”). For so long as Adams continues to serve as a member of the Company’s Board of Directors (including on any committee of the Board of Directors), he shall fulfill his responsibilities in good faith and consistent with his fiduciary duties to the Company and its stockholders. In addition, Adams agrees that, unless requested by the Company’s Board of Directors, he will not voluntarily resign from the Company’s Board of Directors or the Audit Committee of the Board of Directors prior to the Resignation Date; provided that if he shall resign from the Board of Directors upon such request, the Resignation Date shall be deemed to be the date of such resignation.

2. Cash Compensation. Adams shall be paid all applicable cash compensation for service on the Company’s Board of Directors and the Audit Committee of the Board of Directors during his service through the Resignation Date; provided that notwithstanding the termination of Adams service on the Board of Directors (and the Audit Committee) as of the Resignation Date, Adams shall be paid all cash compensation for service on the Company’s Board of Directors and the Audit Committee of the Board of Directors as if such service continued until September 30, 2007.

3. Equity. Adams shall receive any and all non-cash compensation and benefits provided to any other Director between the date hereof and the Resignation Date; provided that Adams shall not receive equity grants made solely to newly appointed or elected Directors in accordance with the Company’s Board compensation program or any equity grants made to one or more particular directors (but not all other directors) as a result of special service to the Company. On the Resignation Date, Adams shall vest in all then unvested shares of Common

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Stock subject to the option to purchase 54,000 shares of the Company’s Common Stock granted Adams upon his election to the Board of Directors on October 27, 2005 (the “Option”). In accordance with the Company’s 1996 Non-Employee Directors’ Stock Option Plan pursuant to which the Option was granted, Adams shall have 12 months from the Resignation Date to exercise the Option. In addition, in accordance with the terms of the 4,500 restricted stock units granted to Adams upon the Company’s 2006 Annual Meeting of Stockholders (the “RSUs”), Adams shall vest in all such RSUs as of the Resignation Date. Further, on the Resignation Date, the shares of Common Stock underlying the RSUs shall be distributed and issued to Adams. Except as set forth in this paragraph, Adams shall not be entitled to receive any new equity grants in connection with the Company’s 2007 Annual Meeting of Stockholders or otherwise, including any automatic grants under the Company’s 2006 Equity Incentive Plan.

4. Expenses. The Company shall pay up to $5,000 in legal expenses incurred by Adams in connection with the negotiation and execution of this Agreement. Adams (or the provider of such legal services) shall submit a reasonably detailed invoice for such legal expenses prepared by the provider of such legal services within 10 business days of the date of this Agreement, and the Company shall make such payment directly to such provider within 10 business days of the receipt of such invoice.

5. Securities Legends. After the Resignation Date, upon receipt by the Company of a representation statement in customary form executed by Adams to the effect that Adams is no longer an affiliate of the Company and such other matters as shall be reasonably requested by counsel to the Company to ensure compliance with applicable legal requirements, the Company shall use its reasonable efforts to facilitate the prompt removal of any restrictive legends on stock certificates held by Adams and to otherwise cooperate with Adams, consistent with any applicable legal requirements, to ensure that there are no contractual or other restrictions on Adams’ ability to sell shares of Common Stock currently held by him, or issued to him upon exercise of the Option or in a distribution pursuant to the RSUs.

6. No Adverse Comment; Non-Disparagement.

(a) Each of the Adams Parties covenants and agrees that during the sixteen-month period commencing on the Resignation Date, unless otherwise required by law or court process or bona fide professional obligations or consented to in writing by the Company, such Adams Party shall not, directly or indirectly (i) disclose (other than to his or its attorney) to any person or entity any Company confidential information; (ii) provide to any person (other than his or its attorney) or entity any information that concerns or relates to the negotiations or circumstances leading to the execution of this Agreement or to the terms and conditions hereof or the parties’ performance hereunder; or (iii) disparage the Company or any of its affiliates, or any of their respective officers, directors, stockholders, agents or employees in any future communications with any third-party or entity.

(b) The Company covenants and agrees that during the sixteen-month period commencing on the Resignation Date, unless otherwise required by law or court process or bona fide professional obligations or consented to in writing by Adams, neither the Company nor any of the Company’s executive officers and directors shall, directly or indirectly, (i) provide to any

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person or entity (other than the Company’s attorneys, accountants or financial advisors, or any potential investor or acquirer of the Company (including its agents or representatives)) any information that concerns or relates to the negotiations or circumstances leading to the execution of this Agreement or to the terms and conditions hereof or the parties’ performance hereunder; or (ii) disparage any Adams Party in any future communications with any third-party or entity.

(c) The parties agree that a communication shall be considered to disparage a person or entity if, considering the surrounding facts and circumstances (whether or not known to the person making the statement) and the context, it could reasonably be understood to be derogatory, pejorative, disparaging, uncomplimentary, unkind, or otherwise to reflect unfavorably upon the other party (including, without limitation, such other party’s actions, intent, performance, prospects or motivations), regardless of the truth or falsity of such information, and regardless of whether such connotation is intended.

(d) The Company shall ensure that its direct and indirect subsidiaries (as they shall exist from time to time), and their officers and directors, shall comply with the provisions of this Section 6. Each Adams Party shall ensure that its officers, directors, members, managers, general partners or any other funds under common investment management, and their officers, directors, members, managers and general partners, shall comply with the provisions of this Section 6.

7. Restrictions. Until the date that is one year after the Resignation Date, no Adams Party shall, directly or indirectly:

(a) acquire, offer or propose to acquire or agree to acquire, whether by purchase, tender or exchange offer, through the acquisition of control of another Person, by joining a partnership, limited partnership, syndicate or other Group or otherwise, Beneficial Ownership of any Voting Securities, Derivative Securities or any other securities of the Company or any rights to acquire (whether currently, upon lapse of time, following the satisfaction of any conditions, upon the occurrence of any event or any combination of the foregoing) any Voting Securities (collectively, “Subject Securities”), other than:

(i) the acquisition by Adams, any Adams Party and/or any Affiliate of Adams of such number of Subject Securities which would not, in the aggregate, increase such parties’ combined ownership percentage to greater than 10% of the then outstanding Voting Power of the Company;

(ii) the acquisition of Subject Securities as a result of any stock split, stock dividend or other distributions, recapitalizations or offerings made available by the Company to holders of a class or series of Voting Securities generally;

(iii) the acquisition of any Subject Securities pursuant to an exercise of the Option or upon distribution of the RSUs; or

(iv) an investment in any Person (other than another Adams Party or an Affiliate of Adams), fund or other investment vehicle which owns or otherwise holds Subject Securities and which beneficially owns less than 15% of the outstanding shares of capital stock

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of the Company; provided that neither Adams nor any of his Affiliates (including any Adams Party) or any other Person under Adams’ control has any discretion or control over the assets of such Person, fund or other investment vehicle.

(b) propose or take substantial steps to effect (in either case, on behalf of himself or to or with a third party) any merger, business combination, restructuring, recapitalization or similar transaction involving the Company or any of its subsidiaries or the sale or other disposition outside the ordinary course of business of any material portion of the assets of the Company or any of its subsidiaries; provided, however, that nothing set forth in this clause (b) will prohibit the activities of any Adams Party acting together with the Company or upon the Company’s recommendation or request in connection with possible acquisitions and dispositions approved by the Company’s Board of Directors from time to time;

(c) make or in any way propose or participate in any “solicitation” of “proxies” to vote (as such terms are defined in Rule 14a-l under the Exchange Act), solicit any consent or communicate with or seek to advise or influence any Person, other than the Company, with respect to the solicitation or voting of any Voting Securities of the Company in opposition to any matter that has been recommended by the Company’s Board of Directors or in favor of any matter that has not been approved by the Company’s Board of Directors;

(d) unless first approved by the Company’s Board of Directors, initiate, propose or otherwise solicit stockholders for the approval of any stockholder proposal (as described in Rule 14a-8 under the Exchange Act or otherwise) with respect to the Company;

(e) deposit any Subject Securities into a voting trust or subject any such Subject Securities to any arrangement or agreement with respect to the voting thereof;

(f) form, be a member of, join or encourage the formation of, any Group with respect to any Subject Securities or the acquisition of any assets of the Company;

(g) otherwise act, alone or in concert with others, in a manner designed or having the deliberate effect of circumventing the restrictions otherwise imposed hereunder;

(h) disclose or publicly announce any intention, plan or arrangement inconsistent with the foregoing; or

(i) finance any other Persons in connection with any of the activities prohibited by the foregoing clauses (a) through (h).

Each Adams Party shall ensure that its officers, directors, members, managers, general partners or any other funds under common investment management, and their officers, directors, members, managers and general partners, shall comply with the provisions of this Section 7.

The following terms have the meanings indicated:

“Affiliate” shall have the meaning given it in Rule 12b-2 under the Exchange Act

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“Beneficially Own” with respect to any securities means having “beneficial ownership” of such securities (as determined pursuant to Rule 13d-3 under the Exchange Act, as in effect on the date hereof). The terms “Beneficial Ownership” and “Beneficial Owner” have correlative meanings.

“Derivative Security” shall mean any subscription, option, conversion right, warrant, phantom stock right or other agreement, security or commitment of any kind obligating the Company or any of its subsidiaries to issue, grant, deliver or sell, or cause to be issued, granted, delivered or sold, (i) any Voting Securities or any other equity security of the Company, (ii) any securities convertible into, or exchangeable for, any Voting Securities or other equity security of the Company or (iii) any obligations measured by the price or value of any shares of capital stock of the Company.

“Exchange Act” shall mean the Securities Exchange Act of 1934, as amended.

“Group” shall have the meaning provided in Section 13(d)(3) of the Exchange Act.

“Person” means any natural person, corporation, partnership, limited liability company, firm, association, trust, government, governmental agency or any other entity, whether acting as an individual, fiduciary or other capacity.

“Voting Securities” means the shares of Common Stock, any other securities of the Company having the general voting power under ordinary circumstances to elect members of the Board, and any other securities which are convertible into, or exchangeable for, Voting Securities.

“Voting Power” shall mean, calculated at a particular point in time, the aggregate votes represented by all the then outstanding Common Stock and any other securities of the Company then entitled to vote generally in the election of directors of the Company.

8. Press Release. After the close of trading on The Nasdaq Global Market August 27, 2007, the Company shall issue a press release in form and substance mutually agreed to by both Adams and the Company announcing Adams’ resignation from the Board of Directors; provided that if the parties have not agreed on such press release, the Company shall issue a press release in the Company’s normal form (i.e. heading; contact information; information about the Company; etc.) with only the following additional language: “Exar Corporation (NasdaqGM: EXAR) today announced that Mr. Guy Adams has resigned from its Board of Directors, effective as of September 20, 2007.”

9. No Other Benefits. Adams acknowledges and agrees that he is not entitled to, and will not be entitled to, any benefits, compensation or other payments or remuneration (other than reimbursement of expenses incurred in accordance with the Company’s expense reimbursement policies) upon his resignation on the Resignation Date except as set forth in this Agreement. Notwithstanding the foregoing, nothing in this Agreement shall be deemed to waive or otherwise affect Adams’ rights to indemnification pursuant to the Company’s Certificate of Incorporation, Bylaws or his Indemnification Agreement with the Company dated November 2, 2005 or to the extent he is entitled thereto pursuant to Delaware law.

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10. Remedies. The parties specifically agree that legal remedies will not be adequate in the event that the other party violates the provisions of Paragraph 6 or Paragraph 7 hereof and that the aggrieved party shall be entitled, in addition to its other legal remedies, to enjoin the activity of the other which violates either such Paragraph. The foregoing provision shall not be deemed to limit either party’s right to obtain injunctive relief with respect to any breach of any other provision of this Agreement.

11. Attorneys Fees. In the event of any action or proceeding brought by either party against the other under this Agreement, the prevailing party shall be entitled to recover all costs and expenses, including without limitation, reasonable attorneys’ fees.

12. Entire Agreement; Amendment. This Agreement constitutes the entire agreement between the parties hereto with respect to the subject matter hereof, and supersedes all prior oral or written agreements, commitments or understandings with respect to the matters provided for herein. No amendment, modification or discharge of this Agreement shall be valid or binding unless set forth in writing and duly executed by the party against whom enforcement of the amendment, modification, or discharge is sought.

13. Waiver. No delay or failure on the part of any party hereto in exercising any right, power or privilege under this Agreement shall impair any such right, power or privilege or be construed as a waiver of any default or any acquiescence therein. No single or partial exercise of any such right, power or privilege shall preclude the further exercise of such right, power or privilege or the exercise of any other right, power or privilege. No waiver shall be valid against any party hereto unless made in writing and signed by the party against whom enforcement of such waiver is sought and then only to the extent expressly specified therein.

14. Governing Law. This Agreement, the rights and obligations of the parties hereto, and any claims or disputes relating thereto, shall be governed by and construed in accordance with the laws of California (excluding the choice of law rules thereof). Venue for enforcement of any action related to this Agreement shall be in the state courts located in Alameda County, California.

15. Notices. All notices, demands, requests, or other communications that may be or are required to be given, served or sent by any party to any other party pursuant to this Agreement shall be in writing and shall be hand-delivered or mailed by first-class, registered or certified mail, return receipt requested, postage prepaid, or transmitted by hand delivery, overnight express, telegram, facsimile transmission or telex, addressed as follows:

(i) If to the Company:

Exar Corporation

Attn: General Counsel

48720 Kato Road

Fremont, CA 94538

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(ii) If to any Adams Party:

c/o Guy Adams

GWA Capital LLC

55 South Lake Avenue, Suite 720

Pasadena, CA 91101

Each party may designate by notice in writing a new address to which any notice, demand, request or communication may thereafter be so given, served or sent. Each notice, demand, request, or communication that shall be hand-delivered, mailed, transmitted by overnight express or telexed in the manner described above, or that shall be delivered to a telegraph company, shall be deemed sufficiently given, served, sent, received or delivered for all purposes at such time as it is delivered to the addressee (with the return receipt, the delivery receipt, or the answer back being deemed conclusive, but not exclusive, evidence of such delivery) or at such time as delivery is refused by the addressee upon presentation.

16. Headings. Section headings contained in this Agreement are inserted for convenience of reference only, shall not be deemed to be a part of this Agreement for any purpose, and shall not in any way define or affect the meaning, construction or scope of any of the provisions hereof.

17. Execution in Counterparts. To facilitate execution, this Agreement may be executed in as many counterparts as may be required; and it shall not be necessary that the signatures of, or on behalf of, each party, or that the signatures of all persons required to bind any party, appear on each counterpart; but it shall be sufficient that all such signatures appear on one or more of the counterparts. All counterparts shall collectively constitute a single agreement. It shall not be necessary in making proof of this Agreement to produce or account for more than a number of counterparts containing the respective signatures of, or on behalf of, all of the parties hereto.

18. Limitation on Benefits. It is the explicit intention of the parties hereto that the covenants, undertakings and agreements set forth in this Agreement shall be solely for the benefit of, and shall be enforceable only by, the parties hereto or their respective successors, heirs, executors, administrators, legal representatives and assigns.

19. Binding Effect. This Agreement shall be binding upon and shall inure to the benefit of the parties hereto and their respective successors, heirs, executors, administrators, legal representatives and permitted assigns. Adams shall not assign this Agreement without the prior written consent of the Company or its successor, and any such attempted assignment shall be void.

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20. Voluntary Agreement; Opportunity to Seek Counsel. The Parties represent and agree that this Agreement is freely and voluntarily executed and that no promise, inducement, or agreement not expressed in this Agreement has been made to it. The Parties further represent that they have had the opportunity to consult with legal counsel prior to signing this Agreement.

21. Severability. If any part or any provision of this Agreement shall be determined to be invalid or unenforceable by reason of the extent, duration or geographical scope thereof, or otherwise, then the parties agree that the court making such determination may reduce such extent, duration or geographical scope, or other provisions thereof, and in its reduced form such part of provision shall then be enforceable in the manner contemplated hereby.

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

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