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                                                                    EXHIBIT 10.2

           AMENDMENT TO AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT

      WHEREAS, Volterra Semiconductor Corporation, a Delaware corporation (the
"Company"), proposes to sale and issue shares of the Company's Series E
Preferred Stock to the investors listed on Attachment A attached hereto (the
"New Investors") pursuant to the Series E Preferred Stock Purchase Agreement,
dated October 2, 2001;

      WHEREAS, the Company has entered into that certain Amended and Restated
Investor Rights Agreement, dated October 2, 2001 (the "Agreement"), with the
investors listed on Exhibit A attached thereto and the holders of Series A
Preferred Stock Warrants and Series B Preferred Stock Warrants listed on Exhibit
B attached thereto (collectively referred to herein as the "Investors") and, for
purposes of Sections 5 and 6 of the Agreement only, the founders listed on
Exhibit C attached thereto;

      WHEREAS, in order to induce the New Investors to purchase shares of the
Company's Series E Preferred Stock, the Investors and the Company wish to amend
the Agreement to include the New Investors and the sale and issuance of
additional shares of Series E Preferred Stock; and

      WHEREAS, pursuant to Section 7.5(a) of the Agreement, the Agreement may be
amended upon the written consent of the Company and the holders of at least a
majority of the Registrable Securities (as defined in the Agreement); and

      WHEREAS, the undersigned Investors collectively constitute a majority of
the Registrable Securities.

      NOW, THEREFORE, the undersigned Investor, pursuant to Section 7.5(a) of
the Agreement, hereby agrees as follows:

      1.    AMENDMENT OF SECTION 4.6(d). Section 4.6(d) of the Agreement is
hereby amended in its entirety to read as follows:

            "(d) up to six million two hundred fifty thousand (6,250,000) shares
            of Series E Preferred Stock and the Common Stock issuable upon
            conversion thereof."

      2.    AMENDMENT OF EXHIBIT A. Exhibit A of the Agreement is hereby amended
to include the New Investors.

      3.    FULL FORCE AND EFFECT. All other provisions of the Agreement shall
remain in full force and effect.

                                       1.

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      IN WITNESS WHEREOF, the undersigned have executed this Amendment as of
January 17, 2002.

                                    VOLTERRA SEMICONDUCTOR CORPORATION

                                    By:  /s/ Jeffrey Staszak
                                         ---------------------------------------
                                          Jeffrey Staszak
                                          President and Chief Executive Officer

INVESTORS:

KLEINER PERKINS CAUFIELD & BYERS VIII

By: /s/ Kevin R. Compton
    --------------------
     Kevin R. Compton
     General Partner

KLEINER PERKINS CAUFIELD & BYERS VIII
FOUNDERS FUND

By: /s/ Kevin R. Compton
    --------------------
     Kevin R. Compton
     General Partner

MORGENTHALER VENTURE PARTNERS V

BY: MORGENTHALER MANAGEMENT
    PARTNERS V, ITS GENERAL PARTNER

By: /s/ R. D. Pavey
    ---------------
     R. D. Pavey
     Member

                                       2.

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INVESTORS:

INTEGRAL CAPITAL PARTNERS IV, L.P.

BY:  INTEGRAL CAPITAL MANAGEMENT IV,
     LLC, ITS GENERAL PARTNER

By: /s/ Pamela Hagenah
    -------------------------------------
     Pamela Hagenah
     Manager

INTEGRAL CAPITAL PARTNERS IV MS SIDE
FUND, L.P.

BY: INTEGRAL CAPITAL PARTNERS NBT,
    LLC, ITS GENERAL PARTNER

By: /s/ Pamela Hagenah
    -------------------------------
     Pamela Hagenah
     Manager

      This Amendment may be executed in counterparts with the same force and
effect as if each of the signatories had executed the same document.

                                       3.