Exhibit 10.2

FIRST AMENDMENT TO LEASE AGREEMENT

THIS FIRST AMENDMENT TO THE LEASE AGREEMENT (“First Amendment”) is entered into as of the 23rd day of March, 2010, by and between ProLogis, a Maryland real estate investment trust (“Landlord”) and Volterra Semiconductor Corporation, a Delaware corporation (“Tenant”).

WITNESSETH:

WHEREAS, Landlord and Tenant entered into that certain Lease Agreement dated as of May 9, 2007, pursuant to which Landlord leased to Tenant certain premises located at 47467 Fremont Boulevard, Fremont California 94538 consisting of approximately 42,711 rentable square feet (such lease, as heretofore and hereafter modified, being herein referred to as the “Lease”).

WHEREAS, Landlord and Tenant desire to modify the term of the Lease on the terms and conditions set forth below.

NOW THEREFORE, in consideration of Ten Dollars ($10.00) and other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the Landlord and Tenant agree as follows:

1. The Lease Term is extended for Twenty-eight (28) months, such that the Lease shall terminate on the 28th day of February, 2015 (“First Extension Term”). All of the terms and conditions of the Lease shall remain in full force and effect during such extension period except as provided below.

2. The Monthly Base Rent due and payable under this Lease is hereby amended and shall be as following through the First Extension Term:

8. Right of First Offer:

(a) “Offered Space” shall mean collectively the following, as shown on Exhibit B:

(b) Provided that as of the date of the giving of Landlord’s Notice, (x) Tenant is the Tenant originally named herein or any assignee of a Permitted Transfer (as defined in the Lease), (y) Tenant and/or any transferee of a Permitted Transfer actually occupies all of the Premises originally demised under this Lease, and (z) no Event of Default under this Lease or Tenant’s lease at 47451 Fremont Boulevard, Fremont, California (the “47451 Lease”) or event which but for the passage of time in the giving of notice, or both, would constitute an Event of Default under this Lease or the 47451 Lease has occurred and is continuing, if at any time during the Lease Term any lease for any portion of the Offered Space shall expire, then Landlord, before offering such Offered Space to anyone, other than the tenant then occupying such space (or its affiliates), shall offer to Tenant the right to include the Offered Space within the Premises on the same terms and conditions upon which Landlord intends to offer the Offered Space for lease.

(c) Such offer shall be made by Landlord to Tenant in a written notice (hereinafter called the “First Offer Notice”) which offer shall designate the space being offered and shall specify the terms which Landlord intends to offer with respect to any such Offered Space. Tenant may accept the offer set forth in the First Offer Notice by delivering to Landlord an unconditional acceptance (hereinafter called “Tenant’s Notice”) of such offer within 5 business days after delivery by Landlord of the First Offer Notice to Tenant. Time shall be of the essence with respect to the giving of Tenant’s Notice. If Tenant does not accept (or fails to timely accept) an offer made by Landlord pursuant to the provisions of this Amendment or the 47451 Lease with respect to the Offered Space designated in the First Offer Notice, Landlord shall be under no further obligation with respect to such space by reason of this Amendment.

(d) Tenant must accept all Offered Space offered by Landlord at any one time if it desires to accept any of such Offered Space; provided, however, if the Offered Space includes both the 47661 Space and the 47669 Space, Tenant shall have the right and may elect to accept only one of those two spaces, either the entire 47661 Space or the entire 47669 Space, and Tenant may not exercise its right with respect to only part of such space.

(e) If Tenant at any time declines the 47661 Space, or the 47669 Space, or both, offered by Landlord pursuant to this Lease or the 47451 Lease, Tenant shall be deemed to have irrevocably waived all further rights to such specific Offered Space in that specific building, and Landlord shall be free to lease the Offered Space to third parties including on terms which may be less favorable to Landlord, but at rental rates that are at least 90% of the rental rate offered to Tenant. If Landlord desires to offer the Offered Space to the market at rental rates that are less than 90% of the rental rate previously offered to Tenant, then Landlord shall resubmit such Offered Space to Tenant in accordance with the terms of Section 9(c) above.

(f) Additionally, (i) in the event that less than all of the Offered Space is available at the time the available portion of the Offered Space is offered to Tenant in accordance with this Right of First Offer and (ii) Tenant accepts such offer set forth in the First Offer Notice, then Tenant shall have the further right to any additional Offered Space that later becomes available in that building.

(g) Notwithstanding anything contained herein to the contrary, Tenant agrees and understands that Tenant’s Right of First Offer shall not be effective and shall terminate effective immediately upon any of the following transactions taking place (each an “Terminating Event”): (a) the Building and the Offered Space are not both owned in fee by ProLogis, a Maryland real estate investment trust; or (b) any mortgage holder or lien holder has taken possession of the Building or the Offered Space as a result of a foreclosure or deed-in-lieu of foreclosure. Tenant agrees and understands that in the event of an Terminating Event, this Right of First Offer shall be automatically deemed null and void and of no further force or effect upon such event or transaction.

4. Except as modified herein, the Lease, and all of the terms and conditions thereof, shall remain in full force and effect.

5. Any obligation or liability whatsoever of ProLogis, a Maryland real estate investment trust, which may arise at any time under the Lease or this First Amendment or any obligation or liability which may be incurred by it pursuant to any other instrument, transaction or undertaking contemplated hereby, shall not be personally binding upon, nor shall resort for the enforcement thereof be had to the property of, its trustees, directors, shareholders, officers, employees, or agents regardless of whether such obligation or liability is in the nature of contract, tort or otherwise.

IN WITNESS WHEREOF, the parties hereto have signed this First Amendment to Lease Agreement as of the day and year first above written.

Exhibit A

Right of First Offer

Offered Space