AMENDED AND RESTATED
 
                          CERTIFICATE OF INCORPORATION
 
                                       OF
 
                                IXYS CORPORATION
 
 
          Nathan Zommer hereby certifies that:
 
          ONE:    The original name of this corporation is Paradigm Technology
Delaware Corporation and the date of filing of the original Certificate of
Incorporation of this corporation with the Secretary of State of Delaware is
April 4, 1995.
 
          TWO:    The name of this corporation changed to Paradigm Technology,
Inc. pursuant to a Certificate of Merger filed June 22, 1995.
 
          THREE:  The name of this corporation changed to IXYS Corporation
pursuant to an Certificate of Amendment to the Amended and Restated Certificate
of Incorporation filed on September 23, 1998.
 
          FOUR:   He is the duly elected and acting President of the
Corporation.
 
          FIVE:   The Restated Certificate of Incorporation, as amended, of the
Corporation is hereby amended and restated to read in its entirety as follows:
 
                                       1.
<PAGE>
 
                                  Article I.
 
                                     Name
                                     ----
 
 
     The name of this Corporation is IXYS Corporation.
 
 
 
                                  Article II.
 
                               Registered Agent
                               ----------------
 
     The registered agent and the address of the registered office in the State
of Delaware are:
 
 
                               CorpAmerica, Inc.
                               30 Old Rudnick Lane
                               County of Kent
                               Dover, Delaware 19901
 
 
                                 Article III.
 
                                    Purpose
                                    -------
 
     The purpose of this Corporation is to engage in any lawful act or activity
for which a corporation may be organized under the General Corporation Law of
Delaware.
 
 
                                  Article IV
 
                                     Stock
                                     -----
 
     (A)  This corporation is authorized to issue 85,000,000 shares of its
Capital Stock, which shall be divided into two classes known as "Common Stock"
and "Preferred Stock," respectively.
 
 
     (B)  The total number of shares of Common Stock which this Corporation is
authorized to issue is 80,000,000. The total number of shares of Preferred Stock
which this Corporation is authorized to issue is 5,000,000. All of the shares of
Common Stock and Preferred Stock shall have a par value of $.01 per share.
 
 
     (C)  This Corporation shall from time to time in accordance with the laws
of the State of Delaware increase the authorized amount of its Common Stock if
at any time the number of shares of Common Stock remaining unissued and
available for issuance shall not be sufficient to permit conversion of the
Preferred Stock in accordance with the applicable conversion provisions.
 
 
 
                                       2.
<PAGE>
 
     (D)  This Corporation shall be authorized to issue Preferred Stock in any
number of series, as determined by the Board of Directors. The Board of
Directors may by resolution fix the designation and number of shares of any such
series, and may determine, alter or revoke the rights, preferences, privileges
and restrictions granted to or imposed upon any wholly unissued series, provided
that such action by the Board of Directors be unanimously approved by the all
members of the Board of Directors whether such approval is provided via written
consent or at a meeting of the complete Board of Directors, after provision of
proper notice of the action contemplated or waiver of such notice of such
meeting, to the Board of Directors. The Board of Directors may thereafter in the
same manner, within the limits and restrictions stated in any resolution or
resolutions of the Board of Directors originally fixing the number of shares
constituting any series, increase or decrease the number of shares of any such
series (but not below the number of shares of that series then outstanding),
provided that such action by the Board of Directors be unanimously approved by
all the members of the Board of Directors whether such approval is provided via
written consent or at a meeting of the complete Board of Directors, after
provision of proper notice of the action contemplated or waiver of such notice
of such meeting, to the Board of Directors. In case the number of shares of any
series shall be 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
 
                                  Management
                                  ----------
 
 
     (A)  The business and affairs of the Corporation shall be managed by or
under the direction of the Board of Directors. In addition to the powers and
authority expressly conferred upon them by Statute or by this Certificate of
Incorporation or the Bylaws of the Corporation, the directors are hereby
empowered to exercise all such powers and do all such acts and things as may be
exercised or done by the Corporation.
 
     (B)  Election of directors need not be by written ballot unless the Bylaws
so provide.
 
     (C)  Any action required or permitted to be taken by the stockholders of
the corporation must be effected at a duly called annual or special meeting of
stockholders of the Corporation and may not be effected by any consent in
writing by such stockholders.
 
 
                                   Article VI
 
                                     Bylaws
                                     ------
 
     The Board of Directors is authorized to make, adopt, amend, alter or repeal
the Bylaws of the Corporation. The stockholders shall also have power to make,
adopt, amend, alter or repeal the Bylaws of the Corporation by an affirmative
vote of the holders of at least 66-2/3% of the voting power of all of the then
outstanding shares of the capital stock of the Corporation entitled to vote
generally in the election of directors, voting together as a single class.
 
                                       3.
<PAGE>
 
                                  Article VII
 
                            Limitation of Liability
                            -----------------------
 
     To the fullest extent permitted by the Delaware General Corporation Law, a
director of the Corporation shall not be personally liable to the Corporation or
its stockholders for monetary damages for breach of fiduciary duty as a
director, except for liability (i) for any breach of the director's duty of
loyalty to the Corporation or its stockholders, (ii) for acts or omissions not
in good faith or which involved intentional misconduct or a knowing violation of
law, (iii) under section 174 of the Delaware General Corporation Law, or (iv)
for any transaction from which the director derived an improper personal
benefit. Any repeal or modification of the foregoing provisions of this Article
VII by the stockholders of the Corporation shall not adversely affect any right
or protection of a director of the Corporation existing at the time of such
repeal or modification
 
 
                                 Article VIII
 
                                  Amendments
                                  ----------
 
     The Corporation reserves the right to amend or repeal any of the provisions
contained in this Certificate of Incorporation in any manner now or hereafter
permitted by law, and the rights of the stockholders of this Corporation are
granted subject to this reservation; provided, however, that, notwithstanding
                                     --------  -------
any other provision of this Certificate of Incorporation or any provision of law
which might otherwise permit a lesser vote or no vote, but in addition to any
vote of the holders of any class or series of the stock of this Corporation
required by law or by this Certificate of Incorporation, the affirmative vote of
the holders of at least 66-2/3% of the voting power of all of the then
outstanding shares of the capital stock of the Corporation entitled to vote
generally in the election of directors, voting together as a single class, shall
be required to amend or repeal Article V, Article VI, Article VII or this
Article VIII.
 
 
                                   *********
 
     SIX:      This Amended and Restated Certificate of Incorporation has been
duly adopted in accordance with the provisions of Sections 242 and 245 of the
DGCL by the Board of Directors and the stockholders of the Company.
 
                                      4.
<PAGE>
 
     In Witness Whereof, IXYS Corporation has caused this Certificate to be
subscribed this 23rd day of March, 2001 by the undersigned who affirms that the
statements made herein are true and correct.
 
                                               /s/ Nathan Zommer
                                               -----------------
                                               Nathan Zommer
                                               President