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                                                                    Exhibit 4.12
 
THIS WARRANT AND THE SECURITIES RECEIVABLE UPON EXERCISE HEREOF HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"),
OR ANY STATE SECURITIES LAW, AND MAY NOT BE SOLD, TRANSFERRED, PLEDGED,
HYPOTHECATED OR OTHERWISE DISPOSED OF UNLESS (i) A REGISTRATION STATEMENT UNDER
THE SECURITIES ACT AND APPLICABLE STATE SECURITIES LAWS SHALL HAVE BECOME
EFFECTIVE WITH REGARD THERETO, OR (ii) AN EXEMPTION FROM REGISTRATION UNDER THE
SECURITIES ACT AND APPLICABLE STATE SECURITIES LAWS IS AVAILABLE IN CONNECTION
WITH SUCH OFFER, SALE OR TRANSFER.

Warrant to Purchase
   "N"      SHARES
-----------        

                       WARRANT TO PURCHASE COMMON STOCK
                                      OF
                      ANCOR COMMUNICATIONS, INCORPORATED

     THIS CERTIFIES that Dunwoody Brokerage Services, Inc. or any subsequent
holder ("Holder") hereof, has the right to purchase from ANCOR COMMUNICATIONS,
INCORPORATED, a Minnesota corporation (the "Company"), not more than "N" (as
defined below) fully paid and nonassessable shares of the Company's Common
Stock, $.01 par value ("Common Stock"), at a price equal to the Exercise Price
(as defined in Section 3 below), subject to adjustment as provided herein, at
any time on or before 5:00 p.m., Atlanta, Georgia time, on March 21, 2002. For
purposes hereof, "N" shall equal 6% of the Amount Placed, divided by the Fixed
Conversion Price, where "Amount Placed" shall mean the total dollar amount of
Series B Preferred Stock issued by the Company in its offering of Series B
Preferred Stock closing on or about March 21, 1997 and "Fixed Conversion Price"
shall have the meaning ascribed to it in the Company's Certificate of
Designation of Series B Preferred Stock.

     The Holder of this Warrant agrees with the Company that this Warrant is
issued and all rights hereunder shall be held subject to all of the conditions,
limitations and provisions set forth herein.

     1.   Date of Issuance.
          -----------------

     This Warrant shall be deemed to be issued on March 21, 1997 ("Date of
Issuance").

     2.   Exercise.
          ---------

     (a)  Manner of Exercise. This Warrant may be exercised as to all or any
lesser number of full shares of Common Stock covered hereby upon surrender of
this Warrant, with the Exercise Form attached hereto as Exhibit A ("Exercise
Form") duly executed, together with the full Exercise Price (as defined in
Section 3) for each share of Common

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Stock as to which this Warrant is exercised, at the office of the Company, Ancor
Communications, Incorporated, 6130 Blue Circle Drive, Minnetonka, MN 55343,
Attention: President, Telephone No. (612) 932-4000, Facsimile No. (612) 932-
4037, or at such other office or agency as the Company may designate in writing,
by overnight mail, with an advance copy of the Exercise Form by facsimile (such
surrender and payment of the Exercise Price hereinafter called the "Exercise").

     (b)  Date of Exercise. The "Date of Exercise" of the Warrant shall be
defined as the date that the advance copy of the Exercise Form is sent by
facsimile to the Company, provided that the original Warrant, Exercise Form and
full Exercise Price are received by the Company within five (5) business days
thereafter. The original Warrant, Exercise Form and full Exercise Price must be
received within five (5) business days of the Date of Exercise, or the exercise
may, at the Company's option, be considered void. Alternatively, the Date of
Exercise shall be defined as the date the original Exercise Form is received by
the Company, if Holder has not sent advance notice by facsimile.

     (c)  Cancellation of Warrant. This Warrant shall be canceled upon its
Exercise and, as soon as practical after the Date of Exercise, the Holder hereof
shall be entitled to receive Common Stock certificates representing the number
of shares purchased upon such Exercise, and if this Warrant is not exercised in
full, the Holder shall be entitled to receive a new Warrant or Warrants
(containing terms identical to this Warrant) representing any unexercised
portion of this Warrant in addition to such Common Stock.

     (d)  Holder of Record. Each person in whose name any Warrant for shares of
Common Stock is issued shall, for all purposes, be deemed to have become the
Holder of record of such shares on the Date of Exercise of this Warrant,
irrespective of the date of delivery of such shares of Common Stock. Nothing in
this Warrant shall be construed as conferring upon the Holder hereof any rights
as a shareholder of the Company.

     3.   Payment of Warrant Exercise Price.
          ----------------------------------

     The "Exercise Price" shall equal the Fixed Conversion Price (as defined in
the Company's Certificate of Designation of Series B Preferred Stock).

     Payment of the Exercise Price may be made by either of the following, or a
combination thereof, at the election of Holder:

     (i)  Cash Exercise: cash, certified check or cashiers check or wire
transfer; or

     (ii) Cashless Exercise: surrender of this Warrant at the principal office
of the Company together with notice of cashless election, in which event the
Company shall issue Holder a number of shares of Common Stock computed using the
following formula:
 
                                 X = Y (A-B)/A

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where: X = the number of shares of Common Stock to be issued to Holder.

       Y = the number of shares of Common Stock for which this Warrant is being
exercised.

       A = the Market Price of one (1) share of Common Stock (for purposes of
this Section 3(ii), the "Market Price" shall be defined as the average closing
price of the Common Stock for the five (5) trading days prior to the Date of
Exercise of this Warrant (the "Average Closing Price"), as reported by Nasdaq or
if the Common Stock is not traded on Nasdaq, the average closing price on the
primary market for the Common Stock. If the Common Stock is/was not traded
during the five (5) trading days prior to the Date of Exercise, then the closing
price for the last publicly traded day shall be deemed to be the closing price
for any and all (if applicable) days during such five (5) trading day period.

       B = the Exercise Price.

For purposes of Rule 144 and sub-section (3)(ii) thereof, it is intended,
understood and acknowledged that the Common Stock issuable upon exercise of this
Warrant in a cashless exercise transaction shall be deemed to have been acquired
at the time this Warrant was issued to the extent permitted by applicable law.
Moreover, it is intended, understood and acknowledged that the holding period
for the Common Stock issuable upon exercise of this Warrant in a cashless
exercise transaction shall be deemed to have commenced on the date this Warrant
was issued to the extent permitted by applicable law.

     4.   Transfer and Registration.
          --------------------------

     (a)  Transfer Rights. Subject to the provisions of Section 8 of this
Warrant, this Warrant may be transferred on the books of the Company, in whole
or in part, in person or by attorney, upon surrender of this Warrant properly
endorsed. This Warrant shall be canceled upon such surrender and, as soon as
practicable thereafter, the person to whom such transfer is made shall be
entitled to receive a new Warrant or Warrants as to the portion of this Warrant
transferred, and the Holder of this Warrant shall be entitled to receive a new
Warrant or Warrants as to the portion hereof retained.

     (b)  Registrable Securities. The Common Stock issuable upon the exercise of
this Warrant constitute "Registrable Securities" under that certain Registration
Rights Agreement dated on or about March 21, 1997 by and between the Company and
Dunwoody Brokerage Services, Inc. and, accordingly, has the benefit of the
registration rights pursuant to that agreement.

     5.   Anti-Dilution Adjustments.
          --------------------------

     (a)  Stock Dividend. If the Company shall at any time declare a dividend
payable in shares of Common Stock, then the Holder hereof, upon Exercise of this

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Warrant after the record date for the determination of Holders of Common Stock
entitled to receive such dividend, shall be entitled to receive upon Exercise of
this Warrant, in addition to the number of shares of Common Stock as to which
this Warrant is Exercised, such additional shares of Common Stock as such Holder
would have received had this Warrant been Exercised immediately prior to such
record date and the Exercise Price will be proportionately adjusted.

     (b)  Recapitalization or Reclassification. If the Company shall at any time
effect a recapitalization, reclassification or other similar transaction of such
character that the shares of Common Stock shall be changed into or become
exchangeable for a larger or smaller number of shares, then upon the effective
date thereof, the number of shares of Common Stock which the Holder hereof shall
be entitled to purchase upon Exercise of this Warrant shall be increased or
decreased, as the case may be, in direct proportion to the increase or decrease
in the number of shares of Common Stock by reason of such recapitalization,
reclassification or similar transaction, and the Exercise Price shall be, in the
case of an increase in the number of shares, proportionally decreased and, in
the case of decrease in the number of shares, proportionally increased. The
Company shall give the Warrant Holder the same notice it provides to holders of
Common Stock of any transaction described in this Section 5(b).

     (c)  Distributions. If the Company shall at any time distribute to Holders
of Common Stock cash, evidences of indebtedness or other securities or assets
(other than cash dividends or distributions payable out of earned surplus or net
profits for the current or preceding year) then, in any such case, the Holder of
this Warrant shall be entitled to receive, upon exercise of this Warrant, with
respect to each share of Common Stock issuable upon such Exercise, the amount of
cash or evidences of indebtedness or other securities or assets which such
Holder would have been entitled to receive with respect to each such share of
Common Stock as a result of the happening of such event had this Warrant been
Exercised immediately prior to the record date or other date fixing shareholders
to be affected by such event (the "Determination Date") or, in lieu thereof, if
the Board of Directors of the Company should so determine at the time of such
distribution, a reduced Exercise Price determined by multiplying the Exercise
Price on the Determination Date by a fraction, the numerator of which is the
result of such Exercise Price reduced by the value of such distribution
applicable to one share of Common Stock (such value to be determined by the
Board in its discretion) and the denominator of which is such Exercise Price.

     (d)  Notice of Consolidation or Merger. In the event of a merger,
consolidation, exchange of shares, recapitalization, reorganization, or other
similar event, as a result of which shares of Common Stock of the Company shall
be changed into the same or a different number of shares of the same or another
class or classes of stock or securities or other assets of the Company or
another entity or there is a sale of all or substantially all the Company's
assets (a "Corporate Change"), then this Warrant shall be assumed by the
acquiring entity or any affiliate thereof and thereafter this Warrant shall be
exerciseable into such class and type of securities or other assets as the
Holder would have received had the Holder exercised this Warrant immediately
prior to such Corporate

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Change; provided, however, that Company may not affect any Corporate Change
unless it first shall have given thirty (30) business days notice to the Holder
hereof of any Corporate Change.

     (e)  Exercise Price Adjusted. As used in this Warrant, the term "Exercise
Price" shall mean the Exercise Price per share specified in the first paragraph
of this Warrant, until the occurrence of an event stated in subsection (a), (b)
or (c) of this Section 5 and thereafter shall mean said price as adjusted from
time to time in accordance with the provisions of said subsections. No such
adjustment under this Section 5 shall be made unless such adjustment would
change the Exercise Price at the time by $.01 or more; provided, however, that
all adjustments not so made shall be deferred and made when the aggregate
thereof would change the Exercise Price at the time by $.01 or more. No
adjustment made pursuant to any provision of this Section 5 shall have the
effect of increasing the total consideration payable upon Exercise of this
Warrant in respect of all the Common Stock as to which this Warrant may be
exercised. Notwithstanding anything to the contrary contained herein, the
Exercise Price shall not be reduced to an amount below the par value of the
Common Stock.

     (f)  Adjustments: Additional Shares, Securities or Assets. In the event
that at any time, as a result of an adjustment made pursuant to this Section 5,
the Holder of this Warrant shall, upon Exercise of this Warrant, become entitled
to receive shares and/or other securities or assets (other than Common Stock)
then, wherever appropriate, all references herein to shares of Common Stock
shall be deemed to refer to and include such shares and/or other securities or
assets; and thereafter the number of such shares and/or other securities or
assets shall be subject to adjustment from time to time in a manner and upon
terms as nearly equivalent as practicable to the provisions of this Section 5.

     6.   Fractional Interests.
          ---------------------
 
     No fractional shares or scrip representing fractional shares shall be
issuable upon the Exercise of this Warrant, but on Exercise of this Warrant, the
Holder hereof may purchase only a whole number of shares of Common Stock. If, on
Exercise of this Warrant, the Holder hereof would be entitled to a fractional
share of Common Stock or a right to acquire a fractional share of Common Stock,
such fractional share shall be disregarded and the number of shares of Common
Stock issuable upon conversion shall be the next higher number of shares.

     7.   Reservation of Shares.
          ----------------------

          The Company shall at all times reserve for issuance such number of
authorized and unissued shares of Common Stock (or other securities substituted
therefore as herein above provided) as shall be sufficient for Exercise of this
Warrant. The Company covenants and agrees that upon Exercise of this Warrant,
all shares of Common Stock issuable upon such Exercise shall be duly and validly
issued, fully paid, nonassessable and not subject to preemptive rights, rights
of first refusal or similar rights of any person or entity.

                                       5
<PAGE>
 
     8.   Restrictions on Transfer.
          -------------------------

          (a)  Registration or Exemption Required.  This Warrant and the Common
Stock issuable on Exercise hereof have not been registered under the Securities
Act of 1933, as amended, and may not be sold, transferred, pledged, hypothecated
or otherwise disposed of in the absence of registration or the availability of
an exemption from registration under said Act. All shares of Common Stock issued
upon Exercise of this Warrant shall bear an appropriate legend to such effect,
if applicable.

          (b)  Assignment. Assuming the conditions of (a) above regarding
registration or exemption have been satisfied, the Holder may sell, transfer,
assign, pledge or otherwise dispose of this Warrant, in whole or in part. Holder
shall deliver a written notice to Company, substantially in the form of the
Assignment attached hereto as Exhibit B, indicating the person or persons to
whom the Warrant shall be assigned and the respective number of warrants to be
assigned to each assignee. The Company shall effect the assignment within ten
days, and shall deliver to the assignee(s) designated by Holder a Warrant or
Warrants of like tenor and terms for the appropriate number of shares.

          (c)  Investment Intent. The Warrant and Common Stock issuable upon
conversion are intended to be held for investment purposes and not with an
intent to distribution, as defined in the Act.

     9.   Benefits of this Warrant.
          -------------------------

          Nothing in this Warrant shall be construed to confer upon any person
other than the Company and the Holder of this Warrant any legal or equitable
right, remedy or claim under this Warrant and this Warrant shall be for the sole
and exclusive benefit of the Company and the Holder of this Warrant.
 
     10.  Applicable Law.
          ---------------

          This Warrant is issued under and shall for all purposes be governed by
and construed in accordance with the laws of the state of Minnesota, without
giving effect to conflict of law provisions thereof.
 
     11.  Loss of Warrant.
          ----------------

          Upon receipt by the Company of evidence of the loss, theft,
destruction or mutilation of this Warrant, and (in the case of loss, theft or
destruction) of indemnity or security reasonably satisfactory to the Company,
and upon surrender and cancellation of this Warrant, if mutilated, the Company
shall execute and deliver a new Warrant of like tenor and date.

                                       6
<PAGE>
 
     12.  Notice or Demands.
          ------------------

          Notices or demands pursuant to this Warrant to be given or made by the
Holder of this Warrant to or on the Company shall be sufficiently given or made
if sent by certified or registered mail, return receipt requested, postage
prepaid, and addressed, until another address is designated in writing by the
Company, Ancor Communications, Incorporated, 6130 Blue Circle Drive, Minnetonka,
MN 55343, Attention: President, Telephone No. (612) 932-4059, Facsimile No.
(612) 932-4037. Notices or demands pursuant to this Warrant to be given or made
by the Company to or on the Holder of this Warrant shall be sufficiently given
or made if sent by certified or registered mail, return receipt requested,
postage prepaid, and addressed, Attn: Holder, address: c/o Dunwoody Brokerages
Services, Inc., 8309 Dunwoody Place, Atlanta, Georgia 30350, until another
address is designated in writing by Holder.



     IN WITNESS WHEREOF, the undersigned has executed this Warrant as of the
_____ day of ___________________, 1997.

                                    ANCOR COMMUNICATIONS,
                                INCORPORATED

                                            By:
                                               ---------------------------------
                                                                               
                                                                     Print Name:
                                                                               
                                               ---------------------------------

                                         Title:
                                               ---------------------------------

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<PAGE>
 
                                   EXHIBIT A

                                 EXERCISE FORM

                           TO:  ___________________.

     The undersigned hereby irrevocably exercises the right to purchase
____________ of the shares of Common Stock of ANCOR COMMUNICATIONS,
INCORPORATED, a Minnesota corporation, evidenced by the attached Warrant, and
herewith makes payment of the Exercise Price with respect to such shares in
full, all in accordance with the conditions and provisions of said Warrant.

     The undersigned agrees not to offer, sell, transfer or otherwise dispose of
any of such Common Stock, except in accordance with the provisions of Section 8
of the Warrant, and consents that the following legend may be affixed to the
stock certificates for the Common Stock hereby subscribed for, if such legend is
applicable:

     "The securities represented hereby have not been registered under the
     Securities Act of 1933, as amended (the "Securities Act"), or any
     provincial or state securities law, and may not be sold, transferred,
     pledged, hypothecated or otherwise disposed of until either (i) a
     registration statement under the Securities Act and applicable provincial
     or state securities laws shall have become effective with regard thereto,
     or (ii) an exemption from registration under the Securities Act or
     applicable provincial or state securities laws is available in connection
     with such offer, sale or transfer."

     The undersigned requests that stock certificates for such shares be issued,
and a warrant representing any unexercised portion hereof be issued, pursuant to
the Warrant in the name of the Registered Holder and delivered to the
undersigned at the address set forth below:


Dated:

________________________________________________________________________________
                        Signature of Registered Holder

________________________________________________________________________________
                       Name of Registered Holder (Print)


________________________________________________________________________________
                                    Address

________________________________________________________________________________

________________________________________________________________________________

                                       8
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                                   EXHIBIT B

                                  ASSIGNMENT

                   (To be executed by the registered Holder
                       desiring to transfer the Warrant)

FOR VALUE RECEIVED, the undersigned Holder of the attached Warrant hereby sells,
assigns and transfers unto the person or persons below named the right to
purchase _______ shares of the Common Stock of ANCOR COMMUNICATIONS,
INCORPORATED evidenced by the attached Warrant and does hereby irrevocably
constitute and appoint _______________________ attorney to transfer the said
Warrant on the books of the Company, with full power of substitution in the
premises.

Dated:                                  ______________________________
                                                   Signature


Fill in for new Registration of Warrant:

___________________________________
             Name

___________________________________
            Address

_________________________________________
Please print name and address of assignee
(including zip code number)

________________________________________________________________________________

NOTICE

The signature to the foregoing Exercise Form or Assignment must correspond to
the name as written upon the face of the attached Warrant in every particular,
without alteration or enlargement or any change whatsoever.

________________________________________________________________________________

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