Exhibit 4.1


                            CERTIFICATE OF AMENDMENT

                                       OF

                      RESTATED CERTIFICATE OF INCORPORATION

                                       OF

                        ADVANCED ENERGY INDUSTRIES, INC.



     Advanced Energy Industries, Inc. (hereinafter called the "Corporation"), a
Corporation organized and existing under and by virtue of the General
Corporation Law of the State of Delaware, does hereby certify:

     1. The name of the Corporation is Advanced Energy Industries, Inc.

     2. The Restated Certificate of Incorporation of the Corporation is hereby
amended by striking out Article IV. A. thereof and by substituting in lieu of
said Article IV. A. the following new Article IV. A:

               "A. This 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 forty-one million (41,000,000) shares. Forty million
          (40,000,000) shares shall be Common Stock, par value $0.001 per share,
          and one million (1,000,000) shares shall be Preferred Stock, par value
          $0.001 per share."

     3. The amendment of the Restated Certificate of Incorporation herein
certified has been duly adopted in accordance with the provisions of Section 242
of the General Corporation Law of the State of Delaware.

Executed on this 18th day of May, 1999.
                -----

                                    /s/ Richard P. Beck
                                    ----------------------------------
                                    Richard P. Beck, Senior Vice
                                    President, Chief Financial Officer
                                    and Assistant Secretary