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                                                                     EXHIBIT 3.2

                           SECOND AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                               PDF SOLUTIONS, INC.

        The undersigned, John Kibarian and Peter Cohn, hereby certify that:

        1. They are the duly elected and acting President and Secretary,
respectively, of PDF Solutions, Inc., a Delaware corporation.

        2. The Certificate of Incorporation of this corporation was originally
filed with the Secretary of State of Delaware on July 19, 2000 under the name of
PDF Solutions, Inc. and the First Amended and Restated Certificate of
Incorporation of this corporation was filed with the Secretary of State of
Delaware on August 4, 2000.

        3. The Certificate of Incorporation of this corporation shall be amended
and restated to read in full as follows:

                                   "ARTICLE I

        The name of this corporation is PDF Solutions, Inc. (the "Corporation").

                                   ARTICLE II

        The address of the Corporation's registered office in the State of
Delaware is 1013 Centre Road, City of Wilmington, County of New Castle. The name
of its registered agent at such address is Corporation Service Company.

                                   ARTICLE III

        The purpose of the Corporation is to engage in any lawful act or
activity for which corporations may be organized under the General Corporation
Law of Delaware.

                                   ARTICLE IV

        (A) The Corporation is authorized to issue two classes of stock to be
designated, respectively, "Common Stock" and "Preferred Stock." The total number
of shares which the Corporation is authorized to issue is 75,000,000 shares,
each with a par value of $0.0001 per share. 70,000,000 shares shall be Common
Stock and 5,000,000 shares shall be Preferred Stock.

        (B) The Preferred Stock may be issued from time to time in one or more
series. The Board of Directors is hereby authorized, by filing a certificate
pursuant to the applicable law of the state of Delaware and within the
limitations and restrictions stated in this Certificate of Incorporation, to
determine or alter the rights, preferences, privileges and restrictions granted
to or imposed upon any wholly unissued series of Preferred Stock and the number
of shares constituting any such series and the designation thereof, or any of
them; and to increase or decrease the number of shares of any series subsequent
to the issuance of shares of that series, but not below the number of shares of
such series then outstanding. In case the number of shares


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of any series shall be so decreased, the shares constituting such decrease shall
resume the status which they had prior to the adoption of the resolution
originally fixing the number of shares of such series.

                                    ARTICLE V

        The number of directors of the Corporation shall be fixed from time to
time by a bylaw or amendment thereof duly adopted by the Board of Directors.

                                   ARTICLE VI

        On or prior to the date on which the Corporation first provides notice
of an annual meeting of the stockholders, the Board of Directors of the
Corporation shall divide the directors into three classes, as nearly equal in
number as reasonably possible, designated Class I, Class II and Class III,
respectively. Directors shall be assigned to each class in accordance with a
resolution or resolutions adopted by the Board of Directors. At the first annual
meeting of stockholders or any special meeting in lieu thereof, the terms of the
Class I directors shall expire and Class I directors shall be elected for a full
term of three years. At the second annual meeting of stockholders or any special
meeting in lieu thereof, the terms of the Class II directors shall expire and
Class II directors shall be elected for a full term of three years. At the third
annual meeting of stockholders or any special meeting in lieu thereof, the terms
of the Class III directors shall expire and Class III directors shall be elected
for a full term of three years. At each succeeding annual meeting of
stockholders or special meeting in lieu thereof, directors elected to succeed
the directors of the class whose terms expire at such meeting shall be elected
for a full term of three years.

        Notwithstanding the foregoing provisions of this Article VI, each
director shall serve until his or her successor is duly elected and qualified or
until his or her death, resignation, or removal. No decrease in the number of
directors constituting the Board of Directors shall shorten the term of any
incumbent director.

        Any vacancies on the Board of Directors resulting from death,
resignation, disqualification, removal, or other causes shall be filled by
either (i) the affirmative vote of the holders of a majority of the voting power
of the then-outstanding shares of voting stock of the Corporation entitled to
vote generally in the election of directors (the "Voting Stock") voting together
as a single class; or (ii) by the affirmative vote of a majority of the
remaining directors then in office, even though less than a quorum of the Board
of Directors. Subject to the rights of any series of Preferred Stock then
outstanding, newly created directorships resulting from any increase in the
number of directors shall, unless the Board of Directors determines by
resolution that any such newly created directorship shall be filled by the
stockholders, be filled only by the affirmative vote of the directors then in
office, even though less than a quorum of the Board of Directors, or by a sole
remaining director. Any director elected in accordance with the preceding
sentence shall hold office for the remainder of the full term of the class of
directors in which the new directorship was created or the vacancy occurred and
until such director's successor shall have been elected and qualified. Any
director, or the entire Board of Directors, may be removed from office, with or
without cause, by the holders of a majority of the Voting Stock.


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                                   ARTICLE VII

        In the election of directors, each holder of shares of any class or
series of capital stock of the Corporation shall be entitled to one vote for
each share held. No stockholder will be permitted to cumulate votes at any
election of directors.

                                  ARTICLE VIII

        No action shall be taken by the stockholders of the Corporation other
than at an annual or special meeting of the stockholders, upon due notice and in
accordance with the provisions of the Bylaws of the Corporation (the "Bylaws"),
and no action shall be taken by the stockholders by written consent.

                                   ARTICLE IX

        The Corporation reserves the right to amend, alter, change or repeal any
provision contained in this Certificate of Incorporation, in the manner now or
hereafter prescribed by statute, and all rights conferred upon stockholders
herein are granted subject to this reservation.

                                    ARTICLE X

        (A) Except as otherwise provided in the Bylaws, the Bylaws may be
altered or amended or new Bylaws adopted by the affirmative vote of at least 66
2/3% of the voting power of all of the then-outstanding shares of the voting
stock of the Corporation entitled to vote. The Board of Directors of the
Corporation is expressly authorized to adopt, amend or repeal Bylaws.

        (B) The directors of the Corporation need not be elected by written
ballot unless the Bylaws so provide.

        (C) Advance notice of stockholder nominations for the election of
directors or of business to be brought by the stockholders before any meeting of
the stockholders of the Corporation shall be given in the manner provided in the
Bylaws.

                                   ARTICLE XI

        Meetings of stockholders may be held within or without the State of
Delaware, as the Bylaws may provide. The books of the Corporation may be kept
(subject to any provision contained in the statutes) outside the State of
Delaware at such place or places as may be designated from time to time by the
Board of Directors or in the bylaws of the Corporation.

                                   ARTICLE XII

        The Corporation shall have perpetual existence.

                                  ARTICLE XIII

        (A) To the fullest extent permitted by the General Corporation Law of
Delaware, as the same may be amended from time to time, a director of the
Corporation shall not be personally


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liable to the Corporation or its stockholders for monetary damages for breach of
fiduciary duty as a director. If the General Corporation Law of Delaware is
hereafter amended to authorize, with the approval of a corporation's
stockholders, further reductions in the liability of a corporation's directors
for breach of fiduciary duty, then a director of the Corporation shall not be
liable for any such breach to the fullest extent permitted by the General
Corporation Law of Delaware, as so amended.

        (B) Any repeal or modification of the foregoing provisions of this
Article XIII shall not adversely affect any right or protection of a director of
the Corporation with respect to any acts or omissions of such director occurring
prior to such repeal or modification.

                                   ARTICLE XIV

        (A) To the fullest extent permitted by applicable law, the Corporation
is also authorized to provide indemnification of (and advancement of expenses
to) such agents (and any other persons to which Delaware law permits the
Corporation to provide indemnification) through Bylaw provisions, agreements
with such agents or other persons, vote of stockholders or disinterested
directors or otherwise, in excess of the indemnification and advancement
otherwise permitted by Section 145 of the General Corporation Law of Delaware,
subject only to limits created by applicable Delaware law (statutory or
non-statutory), with respect to actions for breach of duty to a corporation, its
stockholders, and others.

        (B) Any repeal or modification of any of the foregoing provisions of
this Article XIV shall not adversely affect any right or protection of a
director, officer, agent or other person existing at the time of, or increase
the liability of any director of the Corporation with respect to any acts or
omissions of such director, officer or agent occurring prior to such repeal or
modification."

                                     * * *

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        The foregoing Amended and Restated Certificate of Incorporation has been
duly adopted by this Corporation's Board of Directors and stockholders in
accordance with the applicable provisions of Section 228, 242 and 245 of the
General Corporation Law of the State of Delaware.

        Executed at Menlo Park, on the ____ day of October, 2000.



                                            ------------------------------------
                                            John Kibarian, President


                                            ------------------------------------
                                            Peter Cohn, Secretary






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