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                                                                     EXHIBIT 4.2

                          CERTIFICATE OF DESIGNATION OF
                     SERIES B CONVERTIBLE PREFERRED STOCK OF
                       ILLINOIS SUPERCONDUCTOR CORPORATION



         The undersigned, Ora E. Smith and Stephen G. Wasko, hereby certify
that:

         I. They are the duly elected and acting President and Secretary,
respectively, of Illinois Superconductor Corporation, a Delaware corporation
(the "Company").

         II. The Certificate of Incorporation of the Company authorizes 100,000
shares of preferred stock, par value $.001 per share, none of which are
currently issued and outstanding.

         III. The following is a true and correct copy of resolutions duly
adopted by the Board of Directors of the Company (the "Board of Directors") at a
meeting duly held on June 4, 1997, which constituted all requisite action on the
part of the Company for adoption of such resolutions.

                                   RESOLUTIONS

         WHEREAS, the Board of Directors is authorized to provide for the
issuance of the shares of preferred stock in series, and by filing a certificate
pursuant to the applicable law of the State of Delaware, to establish from time
to time the number of shares to be included in each such series, and to fix the
designations, relative rights, qualifications, limitations or restrictions of
the shares of each such series.

         WHEREAS, the Board of Directors desires, pursuant to its authority as
aforesaid, to designate a new series of preferred stock, set the number of
shares constituting such series and fix the rights, preferences, privileges and
restrictions of such series.

         NOW, THEREFORE, BE IT RESOLVED, that the Board of Directors hereby
designates a new series of preferred stock and the number of shares constituting
such series and fixes the rights, preferences, privileges and restrictions
relating to such series as follows:

         Section 1. Designation, Amount and Par Value. The series of preferred
stock shall be designated as the Series B Convertible Preferred Stock (the
"Preferred Stock"), and the number of shares so designated shall be 600 (which
shall not be subject to increase without the consent of the holders of a
majority of the then outstanding Preferred Stock hereof). Each share



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of Preferred Stock shall have a par value of $.001 per share and a stated value
of $5,000 per share (the "Stated Value").

         Section 2.        Dividends.

         (a) Holders of Preferred Stock shall be entitled to receive, when and
as declared by the Board of Directors out of funds legally available therefor,
and the Company shall pay, cumulative dividends at the rate per share (as a
percentage of the Stated Value per share) equal to 5% per annum, payable, in
cash or shares of Common Stock (as defined in Section 7) at the option of the
Company, quarterly in arrears, but in no event later than the Conversion Date
(as hereinafter defined) applicable to such share of Preferred Stock in
accordance with the delivery terms hereof. Dividends on the Preferred Stock
shall be calculated on the basis of a 360-day year, shall accrue daily
commencing the Original Issue Date (as defined in Section 7), and shall be
deemed to accrue on such date whether or not earned or declared and whether or
not there are profits, surplus or other funds of the Company legally available
for the payment of dividends. The party that holds the Preferred Stock of record
on an applicable record date for any dividend payment will be entitled to
receive such dividend payment and any other accrued and unpaid dividends which
accrued prior to such dividend payment date, without regard to any sale or
disposition of such Preferred Stock subsequent to the applicable record date but
prior to the applicable dividend payment date. Except as otherwise provided
herein, if at any time the Company pays less than the total amount of dividends
then accrued on account of the Preferred Stock, such payment shall be
distributed ratably among the holders of the Preferred Stock based upon the
number of shares held by each holder. Payment of dividends on the Preferred
Stock is further subject to the provisions of Section 5(c)(i). Notwithstanding
anything to the contrary contained herein, the Company may not, without the
written consent of the holders of a majority of the then outstanding Preferred
Stock, pay dividends in cash on the Preferred Stock unless both the payment
thereof and the retention of such paid cash by the holders is consented to in
writing free of any subordination prior thereto by all lenders and debt holders
0of the Company or by all holders of any class of securities of the Company who
by agreement have the right to consent to or force the subordination of such
payment.

         (b) Notwithstanding anything to the contrary contained herein, the
Company may not issue shares of Common Stock in payment of dividends (and must
deliver cash in respect thereof) on the Preferred Stock if:

              (i) the number of shares of Common Stock at the time authorized,
unissued and unreserved for all purposes, or held as treasury stock, is
insufficient to issue such dividends to be paid in shares of Common Stock;

              (ii) such shares are not registered for resale pursuant to an
effective registration statement that names the recipient of such dividend as a
selling stockholder thereunder and may not be sold without volume restrictions
pursuant to Rule 144 promulgated under the Securities Act of 1933, as amended
(the "Securities Act"), as determined by counsel


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to the Company pursuant to a written opinion letter, addressed to the Company's
transfer agent, in the form and substance reasonably acceptable to the holder;

              (iii) such shares are not listed on The Nasdaq National Market,
The Nasdaq SmallCap Market, The New York Stock Exchange, the American Stock
Exchange and any other exchange or quotation system on which the Common Stock is
then listed for trading; or

              (iv) the issuance of such shares would result in the recipient
thereof beneficially owning, in accordance with Rule 13d-3 promulgated under the
Securities Exchange Act of 1934, as amended, more than 4.999% of the issued and
outstanding shares of Common Stock.

                  (c) So long as any Preferred Stock shall remain outstanding,
neither the Company nor any subsidiary thereof shall redeem, purchase or
otherwise acquire directly or indirectly any Junior Securities (as defined in
Section 7), nor shall the Company directly or indirectly pay or declare any
dividend or make any distribution (other than a dividend or distribution
described in Section 5) in excess, of in the aggregate, $250,000 upon, nor shall
any distribution be made in respect of, any Junior Securities, nor shall any
monies in excess, of in the aggregate, $1,000,000 be set aside for or applied to
the purchase or redemption (through a sinking fund or otherwise) of any Junior
Securities.

                  Section 3. Voting Rights. Except as otherwise provided herein
and as otherwise required by law, the Preferred Stock shall have no voting
rights. However, so long as any shares of Preferred Stock are outstanding, the
Company shall not, without the affirmative vote of the holders of a majority of
the shares of the Preferred Stock then outstanding, (a) alter or change
adversely the powers, preferences or rights given to the Preferred Stock, (b)
alter or amend this Certificate of Designation or (c) authorize or create any
class of stock ranking as to dividends or distribution of assets upon a
Liquidation (as defined in Section 4) senior to, prior to or pari passu with the
Preferred Stock, except for any other series of Preferred Stock issued and sold
in accordance with the Purchase Agreement.

                  Section 4. Liquidation. Upon any liquidation, dissolution or
winding-up of the Company, whether voluntary or involuntary (a "Liquidation"),
the holders of Preferred Stock shall be entitled to receive out of the assets of
the Company, whether such assets are capital or surplus, for each share of
Preferred Stock an amount equal to the Stated Value plus all accrued but unpaid
dividends per share, whether declared or not, before any distribution or payment
shall be made to the holders of any Junior Securities, and if the assets of the
Company shall be insufficient to pay in full such amounts, then the entire
assets to be distributed to the holders of Preferred Stock shall be distributed
among the holders of Preferred Stock ratably in accordance with the respective
amounts that would be payable on such shares if all amounts payable thereon were
paid in full. A sale, conveyance or disposition of all or substantially all of
the assets of the Company or the effectuation by the Company of a transaction or
series of related transactions in which more than 50% of the voting power of the
Company is disposed of, or a consolidation

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or merger of the Company with or into any other company or companies shall not
be treated as a Liquidation, but instead shall be subject to the provisions of
Section 5. The Company shall mail written notice of any such Liquidation, not
less than 45 days prior to the payment date stated therein, to each record
holder of Preferred Stock.

         Section 5.      Conversion.

         (a)(i) Each share of Preferred Stock shall be convertible into shares
of Common Stock (subject to reduction pursuant to Section 5(a)(ii) and Section
5(a)(iii) below and Section 3.8 of the Purchase Agreement (as defined in Section
7)) at the Conversion Ratio (as defined in Section 7) at the option of the
holder in whole or in part at any time after the Original Issue Date. The holder
shall effect conversions by surrendering the certificate or certificates
representing the shares of Preferred Stock to be converted to the Company,
together with a fully executed notice of conversion in the form of conversion
notice attached hereto as Exhibit A (the "Conversion Notice"). Each Conversion
Notice shall specify the number of shares of Preferred Stock to be converted and
the date on which such conversion is to be effected, which date may not be prior
to the date such Conversion Notice is delivered hereunder (the "Conversion
Date"). If no Conversion Date is specified in a Conversion Notice, the
Conversion Date shall be the date that the Conversion Notice is deemed delivered
pursuant to Section 5(i). Subject to Sections 5(b), 5(a)(ii) hereof and Section
3.8 of the Purchase Agreement, each Conversion Notice, once given, shall be
irrevocable. If the holder is converting less than all shares of Preferred Stock
represented by the certificate or certificates tendered by the holder with the
Conversion Notice, or if a conversion hereunder cannot be effected in full for
any reason, the Company shall promptly deliver to such holder (in the manner and
within the time set forth in Section 5(b)) a certificate for such number of
shares as have not been converted.

         (ii) Certain Regulatory Approval. If on the Conversion Date applicable
to any conversion under this Section 5(a), (A) the Common Stock is then listed
for trading on the Nasdaq National Market or if the rules of The Nasdaq Stock
Market, Inc. are hereafter amended to extend Rule 4460(i) promulgated thereby
(or any successor or replacement provision thereof) to The Nasdaq SmallCap
Market or the American Stock Exchange and the Company's Common Stock is then
listed for trading on such market or exchange, (B) the Conversion Price then in
effect is such that the aggregate number of shares of Common Stock that would
then be issuable upon conversion of all outstanding shares of Preferred Stock,
together with any shares of Common Stock previously issued upon conversion of
Preferred Stock and in respect of payment of dividends hereunder, would equal or
exceed 20% of the number of shares of Common Stock outstanding on the Original
Issue Date (the "Issuable Maximum"), and (C) the Company has not previously
obtained Shareholder Approval (as defined below), then the Company shall issue
to the holder so requesting conversion of Preferred Stock an amount of shares of
Common Stock equal to the Issuable Maximum and, with respect to any shares of
Common Stock that otherwise would have been issuable to such holder in respect
of the Conversion Notice at issue or in respect of payment of dividends
hereunder in excess of the Issuable Maximum, the holder shall have the option to
require the Company to either (1) as promptly as possible, but in no event later
than 60 days after such Conversion Date, convene


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a meeting of the holders of the Common Stock and use its best efforts to obtain
the Stockholder Approval or (2) redeem, from funds legally available therefor at
the time of such redemption, the balance of the Preferred Stock subject to such
Conversion Notice at a price per share equal to the product of (i) the average
Per Share Market Value for the five (5) Trading Days immediately preceding (1)
the Conversion Date or (2) the date of payment in full by the Company of such
redemption price, whichever is greater, and (ii) the Conversion Ratio calculated
on the Conversion Date; provided, however, that if the holder has requested that
the Company obtain Stockholder Approval under paragraph (1) above and the
Company fails for any reason to obtain such Stockholder Approval within the time
period set forth in (1) above, the Company shall be obligated to redeem the
Preferred Stock not converted as a result of the provisions of this Section in
accordance with the provisions of paragraph (2) above, and in such case the
interest contemplated by the immediately succeeding sentence shall be deemed to
accrue from the Conversion Date. If the holder has requested that the Company
redeem shares of Preferred Stock pursuant to this Section and the Company fails
for any reason to pay the redemption price under (2) above within seven days
after the Conversion Date, the Company will pay interest on such redemption
price at a rate of 15% per annum to the converting holder of Preferred Stock,
accruing from the Conversion Date until the redemption price plus any accrued
interest thereon is paid in full. The entire redemption price, including
interest thereon, shall be paid in cash. "Stockholder Approval" means the
approval by a majority of the total votes cast on the proposal, in person or by
proxy, at a meeting of the shareholders of the Company held in accordance with
the Company's Certificate of Incorporation and by-laws, of the issuance by the
Company of shares of Common Stock exceeding the Issuable Maximum as a
consequence of the conversion of Preferred Stock into Common Stock at a price
less than the greater of the book or market value on the Original Issue Date as
and to the extent required pursuant to Rule 4460(i) of The Nasdaq Stock Market,
Inc. or Rule 713 of the American Stock Exchange (or any successor or replacement
provision thereof), as applicable.

              (iii) If on any Conversion Date applicable to a conversion under
Section 5(a) or a redemption pursuant to Section 6, the average Per Share Market
Value for the five Trading Days immediately preceding such Conversion Date
exceeds the Initial Conversion Price (defined in Section 5(c(i)) by more than
50%, the Conversion Price otherwise applicable to such conversion or repayment
shall be increased by an amount equal to 50% of the difference between (A) the
average Per Share Market Value for the five Trading Days immediately preceding
such Conversion Date, and (B) 150% of the Initial Conversion Price.

              (b) Not later than three Trading Days after the Conversion Date,
the Company will deliver to the holder (i) a certificate or certificates which
shall be free of restrictive legends and trading restrictions (other than those
required by Section 3.1(b) of the Purchase Agreement) representing the number of
shares of Common Stock being acquired upon the conversion of shares of Preferred
Stock (subject to reduction pursuant to Sections 5(a)(ii), 5(a)(iii) and Section
3.8 of the Purchase Agreement) and (ii) one or more certificates representing
the number of shares of Preferred Stock not converted, if any, and (iii) a check
drawn on the account of the Company and payable to the holder in an amount equal
to any accrued but unpaid dividends, if the Company elects to pay such dividends
in cash; provided, however, that the Company shall

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not be obligated to issue certificates evidencing the shares of Common Stock
issuable upon conversion of any shares of Preferred Stock until certificates
evidencing such shares of Preferred Stock are either delivered for conversion to
the Company for the Preferred Stock or Common Stock, or the holder of such
Preferred Stock notifies the Company that such certificates have been lost,
stolen or destroyed and provides a bond (or other adequate security reasonably
acceptable to the Company) reasonably satisfactory to the Company to indemnify
the Company from any loss incurred by it in connection therewith. The Company
shall, upon request of the holder, use its best efforts to deliver any
certificate or certificates required to be delivered by the Company under this
Section electronically through the Depository Trust Corporation or another
established clearing corporation performing similar functions. If in the case of
any Conversion Notice such certificate or certificates, including for purposes
hereof, any shares of Common Stock to be issued on the Conversion Date on
account of accrued but unpaid dividends hereunder, are not delivered to or as
directed by the applicable holder by the third Trading Day after the Conversion
Date, the holder shall be entitled by written notice to the Company at any time
on or before its receipt of such certificate or certificates thereafter, to
rescind such conversion, in which event the Company shall immediately return the
certificates representing the shares of Preferred Stock tendered for conversion.
If the Company fails to deliver to the holder such certificate or certificates
pursuant to this Section, including for purposes hereof, any shares of Common
Stock to be issued on the Conversion Date on account of accrued but unpaid
dividends hereunder, prior to the fifth Trading Day after the Conversion Date,
the Company shall pay to such holder, in cash, as liquidated damages and not as
a penalty, $1,500 for each Trading Day after such fifth Trading Day until such
certificates are delivered. If the Company fails to deliver to the holder such
certificate or certificates pursuant to this Section prior to the 20th day after
the Conversion Date, the Company shall, at the holder's option (i) redeem, from
funds legally available therefor at the time of such redemption, such number of
shares of Preferred Stock then held by such holder, as requested by such holder,
and (ii) pay all accrued but unpaid dividends on account of the Preferred Stock
for which the Company shall have failed to issue Common Stock certificates
hereunder, in cash. The redemption price per share shall be equal to the sum of
(i) the product of (A) the average Per Share Market Value for the five (5)
Trading Days immediately preceding (1) the Conversion Date or (2) the date of
payment in full by the Company of such redemption price, whichever is greater,
and (B) the Conversion Ratio calculated on the Conversion Date and (ii) the
aggregate of all accrued and unpaid dividends and other amounts payable in
respect of such shares. If the holder has requested that the Company redeem
shares of Preferred Stock pursuant to this Section and the Company fails for any
reason to pay the redemption price above within seven days after such notice is
deemed delivered pursuant to Section 5(i), the Company will pay interest on the
redemption price at a rate of 15% per annum, in cash to such holder, accruing
from such seventh day until the redemption price and any accrued interest
thereon is paid in full.

              (c) (i) The conversion price ("Conversion Price") applicable to
conversions of Preferred Stock into Common Stock hereunder shall be determined
in accordance with this Section. Subject to adjustment as provided in this
paragraph (c)(i), for any conversions that occur prior to the earlier of (1) the
date the Securities and Exchange Commission (the "Commission") declares
effective an Underlying Shares Registration Statement (as defined


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below) or (ii) the 89th day after the Original Issue Date (such period, the
"Pre-Effective Period"), the Conversion Price for each share of Preferred Stock
shall equal the average Per Share Market Value for the five (5) Trading Days
immediately preceding the Original Issue Date (the "Initial Conversion Price").
For all conversions occurring after the Pre-Effective Period, subject to the
immediately preceding sentence, the Conversion Price shall be the lesser of (a)
the Initial Conversion Price or (b) 101% of the average of the lowest Per Share
Market Value for the five (5) consecutive Trading Days during the 60 Trading
Days immediately preceding such Conversion Date (which may not include the date
that any Conversion Notice is deemed delivered pursuant to Section 5(i) below);
provided, however, that in no event shall the Conversion Price be calculated
based on the Per Share Market Value for any five (5) consecutive Trading Day
period for which the Purchaser's or any of its Affiliates' volume of trading in
the Common Stock exceeds 20% of the trading volume in the Common Stock
(excluding any de minimis amount by which the Purchaser or any of its
Affiliates' inadvertently exceeds such 20% limitation) during such five (5)
consecutive Trading Day period as reported by the Nasdaq National Market, The
Nasdaq SmallCap Market, the New York Stock Exchange, the American Stock Exchange
or such other market or exchange on which the Common Stock is traded (for
example, if the Purchaser's or any of its Affiliates' volume in the Common Stock
exceeds such 20% level during Trading Days 10-14, but does not exceed such level
for Trading Days 11-15, then the Conversion Price may be calculated based upon
the Per Share Market Value for Trading Days 11-15 but not for Trading Days
10-14). Notwithstanding the foregoing, (a) if the registration statement
contemplated by the Registration Rights Agreement, which among other things,
requires the Company to register the resale of the shares of Common Stock
issuable upon conversion of the Preferred Stock (the "Underlying Shares
Registration Statement") is not filed on or prior to the 30th day after the
Original Issue Date, or (b) the Company fails to file with the Commission a
request for acceleration in accordance with Rule 12d1-2 promulgated under the
Securities Exchange Act of 1934, as amended, within five (5) days of the date
that the Company is notified (orally or in writing, whichever is earlier) by the
Commission that an Underlying Shares Registration Statement will not be
"reviewed" or is advised that such Registration Statement is not subject to
further review or comment, or (c) if the Underlying Shares Registration
Statement is not declared effective by the Commission on or prior to the 90th
day after the Original Issue Date, or (d) if such Underlying Shares Registration
Statement is filed with and declared effective by the Commission but thereafter
ceases to be effective as to all Registrable Securities (as such term is defined
in the Registration Rights Agreement) at any time prior to the expiration of the
"Effectiveness Period" (as such term as defined in the Registration Rights
Agreement), without being succeeded within 10 Business Days by a subsequent
Underlying Shares Registration Statement filed with and declared effective by
the Commission, or (e) if trading in the Common Stock shall be suspended for any
reason for more than three consecutive Trading Days or five Trading Days in the
aggregate, or (f) if the conversion rights of the holders of Preferred Stock
hereunder are suspended for any reason, or (g) the Company postpones or suspends
the filing or effectiveness of any Registration Statement in excess of 20
consecutive days or 60 days in the aggregate during any twelve month period (any
such failure being referred to as an "Event," and for purposes of clauses (a),
(c) and (f) the date on which such Event occurs, or for purposes of clause (b)
the date on which such five (5) day period is exceeded, or for purposes of
clause (d) the date which such 10 Business Day-period is exceeded,

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or for purposes of clause (e) the date on which such three Trading Day period is
exceeded, or for purposes of clause (g) the date on which such 20 consecutive
day or 60 aggregate day period is exceeded, being referred to as "Event Date"),
the Conversion Price shall be decreased by 2.5% on each monthly anniversary of
an Event Date until the earlier to occur of the second month anniversary after
the Event Date and such time as the applicable Event is cured. Commencing the
second month anniversary after the Event Date, at the option of each holder for
each applicable monthly period either (a) the Company shall pay to the holders
of the Preferred Stock 2.5% of the product of the number of outstanding shares
of Preferred Stock and the Stated Value (each holder being entitled to receive
such portion of such amount as equals its pro rata portion of the Preferred
Stock then outstanding), in cash or (b) the Conversion Price shall be decreased
by 2.5% for each additional such month (to be effective in full on the monthly
applicable Event Date) as liquidated damages, and not as a penalty on the first
day of each monthly anniversary of the Event Date in either case until such time
as the applicable Event, is cured. Any decrease in the Conversion Price pursuant
to this Section shall continue notwithstanding the fact that the Event causing
such decrease has been subsequently cured. The provisions of this Section are
not exclusive and shall in no way limit the Company's obligations under the
Registration Rights Agreement. Notwithstanding anything to the contrary set
forth herein, the Company may not, without the prior written consent of the
holders, pay liquidated damages hereunder in cash unless it shall have received
the prior written consent of all lenders, debt holders or holders of any class
of securities of the Company or its Affiliates that have the right to require
such consent or to subordinate any such cash payment, which consent shall
provide that the payment by the Company of any such liquidated damages hereunder
(and the retention of such sum by the receiving holder) is not subject to any
applicable subordination rights of such lender or holders of such class of
securities.

              (ii) If the Company, at any time while any shares of Preferred
Stock are outstanding, (a) shall pay a stock dividend or otherwise make a
distribution or distributions on shares of its Junior Securities payable in
shares of Common Stock, (b) subdivide outstanding shares of Common Stock into a
larger number of shares, (c) combine outstanding shares of Common Stock into a
smaller number of shares, or (d) issue by reclassification of shares of Common
Stock any shares of capital stock of the Company, the Initial Conversion Price
shall be multiplied by a fraction of which the numerator shall be the number of
shares of Common Stock (excluding treasury shares, if any) outstanding before
such event and of which the denominator shall be the number of shares of Common
Stock outstanding after such event. Any adjustment made pursuant to this Section
5(c)(ii) shall become effective immediately after the record date for the
determination of stockholders entitled to receive such dividend or distribution
and shall become effective immediately after the effective date in the case of a
subdivision, combination or re-classification.

              (iii) If the Company, at any time while any shares of Preferred
Stock are outstanding, shall issue rights or warrants to all holders of Common
Stock entitling them to subscribe for or purchase shares of Common Stock at a
price per share less than the Per Share Market Value of Common Stock at the
record date mentioned below, the Initial Conversion Price shall be multiplied by
a fraction, of which the denominator shall be the number of shares


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of Common Stock (excluding treasury shares, if any) outstanding on the date of
issuance of such rights or warrants plus the number of additional shares of
Common Stock offered for subscription or purchase, and of which the numerator
shall be the number of shares of Common Stock (excluding treasury shares, if
any) outstanding on the date of issuance of such rights or warrants plus the
number of shares which the aggregate offering price of the total number of
shares so offered would purchase at such Per Share Market Value. Such adjustment
shall be made whenever such rights or warrants are issued, and shall become
effective immediately after the record date for the determination of
stockholders entitled to receive such rights or warrants. However, upon the
expiration of any right or warrant to purchase Common Stock the issuance of
which resulted in an adjustment in the Initial Conversion Price pursuant to this
Section 5(c)(iii), if any such right or warrant shall expire and shall not have
been exercised, the Initial Conversion Price shall immediately upon such
expiration be recomputed and effective immediately upon such expiration be
increased to the price which it would have been (but reflecting any other
adjustments in the Initial Conversion Price made pursuant to the provisions of
this Section 5 after the issuance of such rights or warrants) had the adjustment
of the Initial Conversion Price made upon the issuance of such rights or
warrants been made on the basis of offering for subscription or purchase only
that number of shares of Common Stock actually purchased upon the exercise of
such rights or warrants actually exercised.

              (iv) If the Company, at any time while shares of Preferred Stock
are outstanding, shall distribute to all holders of Common Stock (and not to
holders of Preferred Stock) evidences of its indebtedness or assets or rights or
warrants to subscribe for or purchase any security (excluding those referred to
in Sections 5(c)(ii) and (iii) above), then in each such case the Initial
Conversion Price at which each share of Preferred Stock shall thereafter be
convertible shall be determined by multiplying the Initial Conversion Price in
effect immediately prior to the record date fixed for determination of
stockholders entitled to receive such distribution by a fraction of which the
denominator shall be the Per Share Market Value of Common Stock determined as of
the record date mentioned above, and of which the numerator shall be such Per
Share Market Value of the Common Stock on such record date less the then fair
market value at such record date of the portion of such assets or evidence of
indebtedness so distributed applicable to one outstanding share of Common Stock
as determined by the Board of Directors in good faith; provided, however, that
if the holders of a majority in interest of the shares of Preferred Stock
dispute such amount, such holders may select a nationally recognized or major
regional investment banking firm or firm of independent certified public
accountants of recognized standing (an "Appraiser") paid for by the holders of a
majority in interest of the shares of Preferred Stock then outstanding, in which
case the fair market value shall be equal to the average of the determinations
by the Board of Directors and such Appraiser. In either case the adjustments
shall be described in a statement provided to the holders of Preferred Stock of
the portion of assets or evidences of indebtedness so distributed or such
subscription rights applicable to one share of Common Stock. Such adjustment
shall be made whenever any such distribution is made and shall become effective
immediately after the record date mentioned above.


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              (v) All calculations under this Section 5 shall be made to the
nearest cent or the nearest 1/100th of a share, as the case may be.

              (vi) Whenever the Initial Conversion Price is adjusted pursuant to
Section 5(c)(ii),(iii) or (iv), the Company shall promptly mail to each holder
of Preferred Stock, a notice setting forth the Initial Conversion Price after
such adjustment and setting forth a brief statement of the facts requiring such
adjustment.

              (vii) In case of any reclassification of the Common Stock, any
consolidation or merger of the Company with or into another previously
unaffiliated person, the sale or transfer of all or substantially all of the
assets of the Company or any compulsory share exchange pursuant to which the
Common Stock is converted into other securities, cash or property (each, a
"Business Combination"), the holders of the Preferred Stock then outstanding
shall have the right thereafter to, at their option, (A) convert such shares
only into the shares of stock and other securities, cash and property receivable
upon or deemed to be held by holders of Common Stock following such Business
Combination, and the holders of the Preferred Stock shall be entitled upon such
event to receive such amount of securities, cash or property as the shares of
the Common Stock of the Company into which such shares of Preferred Stock could
have been converted immediately prior to such Business Combination would have
been entitled or (B) require the Company to redeem, from funds legally available
therefor at the time of such redemption, its shares of Preferred Stock then
outstanding at a price per share equal to the sum of (x) the product of (i) the
average Per Share Market Value for the five (5) Trading Days immediately
preceding (1) the effective date or the date of the closing, as the case may be,
of the Business Combination, or the triggering of such redemption right or (2)
the date of payment in full by the Company of the redemption price hereunder,
whichever is greater, and (ii) the Conversion Ratio calculated on the date of
the closing or the effective date, as the case may be, of the Business
Combination triggering such redemption right, as the case may be and (y) the
aggregate of all accrued and unpaid dividends and other amounts payable in
respect of such shares. The entire redemption price shall be paid in cash, and
the terms of payment of such redemption price shall be subject to the provisions
set forth in Section 6(b). The terms of any such Business Combination shall
include such terms so as to continue to give to the holder of Preferred Stock
the right to receive the securities, cash or property set forth in this Section
5(c)(vii) upon any conversion or redemption following such Business Combination.
This provision shall similarly apply to successive reclassifications,
consolidations, mergers, sales, transfers or share exchanges.

              (viii) If:

                     A.     the Company shall declare a dividend (or any other
                            distribution) on its Common Stock; or

                     B.     the Company shall declare a special nonrecurring
                            cash dividend on or a redemption of its Common
                            Stock; or


                                      -10-

   11



                     C.     the Company shall authorize the granting to all
                            holders of the Common Stock rights or warrants to
                            subscribe for or purchase any shares of capital
                            stock of any class or of any rights; or

                     D.     the approval of any stockholders of the Company
                            shall be required in connection with any
                            reclassification of the Common Stock of the Company,
                            any consolidation or merger to which the Company is
                            a party, any sale or transfer of all or
                            substantially all of the assets of the Company, of
                            any compulsory share of exchange whereby the Common
                            Stock is converted into other securities, cash or
                            property; or

                     E.     the Company shall authorize the voluntary or
                            involuntary dissolution, liquidation or winding up
                            of the affairs of the Company;

then the Company shall cause to be filed at each office or agency maintained for
the purpose of conversion of Preferred Stock, and shall cause to be mailed to
the holders of Preferred Stock at their last addresses as they shall appear upon
the stock books of the Company, at least 30 calendar days prior to the
applicable record or effective date hereinafter specified, a notice stating (x)
the date on which a record is to be taken for the purpose of such dividend,
distribution, redemption, rights or warrants, or if a record is not to be taken,
the date as of which the holders of Common Stock of record to be entitled to
such dividend, distributions, redemption, rights or warrants are to be
determined or (y) the date on which such reclassification, consolidation,
merger, sale, transfer or share exchange is expected to become effective or
close, and the date as of which it is expected that holders of Common Stock of
record shall be entitled to exchange their shares of Common Stock for
securities, cash or other property deliverable upon such reclassification,
consolidation, merger, sale, transfer or share exchange; provided, however, that
the failure to mail such notice or any defect therein or in the mailing thereof
shall not affect the validity of the corporate action required to be specified
in such notice. Holders are entitled to convert shares of Preferred Stock during
the 30-day period commencing the date of such notice to the effective date of
the event triggering such notice.

       (d) The Company covenants that it will at all times reserve and keep
available out of its authorized and unissued Common Stock solely for the purpose
of issuance upon conversion of Preferred Stock and payment of dividends on
Preferred Stock, each as herein provided, free from preemptive rights or any
other actual contingent purchase rights of persons other than the holders of
Preferred Stock, not less than such number of shares of Common Stock as shall
(subject to any additional requirements of the Company as to reservation of such
shares set forth in the Purchase Agreement) be issuable (taking into account the
adjustments and restrictions of Section 5(c)) upon the conversion of all
outstanding shares of Preferred Stock and payment of dividends hereunder. The
Company covenants that all shares of Common Stock that

                                      -11-

   12



shall be so issuable shall, upon issue, be duly and validly authorized, issued
and fully paid, nonassessable and freely tradeable.

       (e) Upon a conversion hereunder the Company shall not be required to
issue stock certificates representing fractions of shares of Common Stock, but
may if otherwise permitted, make a cash payment in respect of any final fraction
of a share based on the Per Share Market Value at such time. If the Company
elects not, or is unable, to make such a cash payment, the holder of a share of
Preferred Stock shall be entitled to receive, in lieu of the final fraction of a
share, one whole share of Common Stock.

       (f) The issuance of certificates for shares of Common Stock on conversion
of Preferred Stock shall be made without charge to the holders thereof for any
documentary stamp or similar taxes that may be payable in respect of the issue
or delivery of such certificate, provided that the Company shall not be required
to pay any tax that may be payable in respect of any transfer involved in the
issuance and delivery of any such certificate upon conversion in a name other
than that of the holder of such shares of Preferred Stock so converted and the
Company shall not be required to issue or deliver such certificates unless or
until the person or persons requesting the issuance thereof shall have paid to
the Company the amount of such tax or shall have established to the satisfaction
of the Company that such tax has been paid.

       (g) Shares of Preferred Stock converted into Common Stock shall be
canceled and shall have the status of authorized but unissued shares of
preferred stock.

       (h) Any and all notices or other communications or deliveries to be
provided by the holders of the Preferred Stock hereunder, including, without
limitation, any Conversion Notice, shall be in writing and delivered personally,
by facsimile, sent by a nationally recognized overnight courier service or sent
by certified or registered mail, postage prepaid, addressed to the attention of
the Chief Financial Officer of the Company at the facsimile telephone number or
address of the principal place of business of the Company as set forth in the
Purchase Agreement. Any and all notices or other communications or deliveries to
be provided by the Company hereunder shall be in writing and delivered
personally, by facsimile, sent by a nationally recognized overnight courier
service or sent by certified or registered mail, postage prepaid, addressed to
each holder of Preferred Stock at the facsimile telephone number or address of
such holder appearing on the books of the Company, or if no such facsimile
telephone number or address appears, at the principal place of business of the
holder. Any notice or other communication or deliveries hereunder shall be
deemed given and effective on the earliest of (i) the date of transmission, if
such notice or communication is delivered via facsimile at the facsimile
telephone number specified in this Section prior to 4:30 p.m. (Eastern Time),
(ii) the date after the date of transmission, if such notice or communication is
delivered via facsimile at the facsimile telephone number specified in this
Section later than 4:30 p.m. (Eastern Time) on any date and earlier than 11:59
p.m. (Eastern Time) on such date, (iii) four days after deposit in the United
States mails, (iv) the Business Day following the date of mailing, if sent by
nationally recognized overnight courier service, or (v) upon actual receipt by
the party to whom such notice is required to be given.


                                      -12-

   13




       Section 6. Redemption. (a) The Company shall have the right, exercisable
at any time upon 5 Trading Days notice to the holders of the Preferred Stock
given at any time on or after the third anniversary of the Original Issue Date
to redeem, from funds legally available therefor at the time of such redemption,
all or any portion of the shares of Preferred Stock which have not previously
been converted or redeemed, at a price per share equal to the sum of (x) the
product of (i) the average Per Share Market Value for the five (5) Trading Days
immediately preceding (1) the date of the redemption notice referenced above or
(2) the date of payment in full by the Company of the redemption price
hereunder, whichever is greater, and (ii) the Conversion Ratio calculated on the
date of such redemption notice and (y) the aggregate of all accrued but unpaid
dividends and other amounts payable in respect of such shares. The entire
redemption price shall be paid in cash. Holders of Preferred Stock may convert
any shares of Preferred Stock, including shares subject to a redemption notice
given under this Section, during the period from the date of such redemption
notice through the 4th Trading Day thereafter and the Company shall honor all
properly tendered Conversion Notices during such period. Any redemption notice
under this section shall indicate the number of shares of Preferred Stock to be
redeemed and the date (subject to the terms hereof) on which such redemption is
to occur. The holders of the Preferred Stock to be redeemed shall tender by
overnight mail, shares of Preferred Stock subject to such redemption on the date
prior to the redemption date. If the Company intends to redeem less than all of
the then outstanding Preferred Stock, it shall do so on a pro rata basis among
such holders in accordance with this Section. If any portion of the applicable
redemption price under this Section 6 shall not be paid by the Company within
seven (7) calendar days after the date due, interest shall accrue thereon at the
rate of 15% per annum until the redemption price plus all such interest is paid
in full (which amount shall be paid as liquidated damages and not as a penalty).
In addition, if any portion of such redemption price remains unpaid for more
than 7 calendar days after the date due, the holder of the Preferred Stock
subject to such redemption may elect, by written notice to the Company given
within 30 days after the date due, to either (i) demand conversion in accordance
with the formula and the time frame therefor set forth in Section 5 of all of
the shares of Preferred Stock for which such redemption price, plus accrued
liquidated damages thereof, has not been paid in full (the "Unpaid Redemption
Shares"), in which event the Per Share Market Price for such shares shall be the
lower of the Per Share Market Price calculated on the date such redemption price
was originally due and the Per Share Market Price as of the holder's written
demand for conversion, or (ii) invalidate ab initio such redemption,
notwithstanding anything herein contained to the contrary. If the holder elects
option (i) above, the Company shall within three (3) Trading Days of its receipt
of such election deliver to the holder the shares of Common Stock issuable upon
conversion of the Unpaid Redemption Shares subject to such holder conversion
demand and otherwise perform its obligations hereunder with respect thereto; or,
if the Holder elects option (ii) above, the Company shall promptly, and in any
event not later than three (3) Trading Days from receipt of holder's notice of
such election, return to the holder all of the Unpaid Redemption Shares.
Notwithstanding anything to the contrary contained herein, the Company may not,
without the written consent of the holders of a majority in interest of the then
outstanding Preferred Stock, redeem shares of Preferred Stock unless both the
payment thereof and the retention of such paid cash by the holder is consented
to in writing free of any subordination prior thereto by all lenders or holders
of any class of

                                      -13-

   14



securities of the Company who by agreement have the right to consent to or force
the subordination of such payment.

       (b) The Company shall have the right, exercisable within 20 days after
the issuance of a press release disclosing the execution by the Company of a
definitive agreement for a Business Combination, to provide a notice of
redemption to the holders of the Preferred Stock as to all, but not less than
all, of the then outstanding shares of Preferred Stock. The aggregate redemption
price shall be paid in cash on the closing date for such Business Combination.
The redemption price per share shall equal the sum of (x) the product of (i) the
average Per Share Market Value for the five (5) Trading Days immediately
preceding the closing date for the Business Combination triggering such
redemption and (ii) the Conversion Ratio calculated on the date of such
redemption notice (provided, however, the Conversion Price for these purposes
shall not be based upon the Pre-Effective Period) and (y) the aggregate of all
accrued but unpaid dividends and other amounts payable in respect of such
shares. The definitive merger or purchase agreement for such Business
Combination shall include a provision by which the Company covenants to pay the
redemption price under this Section on the closing date therefor.

       Section 7. Definitions. For the purposes hereof, the following terms
shall have the following meanings:

       "Business Day" means any day except Saturday, Sunday and any day which
shall be a legal holiday or a day on which banking institutions in the State of
New York are authorized or required by law or other government action to close.

       "Common Stock" means the common stock, $.001 par value per share, of the
Company and stock of any other class into which such shares may hereafter be
reclassified or changed.

       "Conversion Ratio" means, at any time, a fraction, of which the numerator
is Stated Value plus accrued but unpaid dividends (including any accrued but
unpaid interest thereon) but only to the extent to be paid in shares of Common
Stock in accordance with the terms hereof, and of which the denominator is the
Conversion Price at such time.

       "Junior Securities" means the Common Stock and all other equity
securities of the Company which are junior in rights and liquidation preference
to the Preferred Stock.

       "Original Issue Date" shall mean the date of the first issuance of any
shares of the Preferred Stock regardless of the number of transfers of any
particular shares of Preferred Stock and regardless of the number of
certificates which may be issued to evidence such Preferred Stock.

       "Per Share Market Value" means on any particular date (a) the closing bid
price per share of the Common Stock on such date on The Nasdaq National Market,
Inc. or other

                                      -14-

   15



stock exchange or quotation system on which the Common Stock is then listed or
if there is no such price on such date, then the closing bid price on such
exchange or quotation system on the date nearest preceding such date, or (b) if
the Common Stock is not listed then on The Nasdaq National Market, Inc. or any
stock exchange or quotation system, the closing bid price for a share of Common
Stock in the over-the-counter market, as reported by the Nasdaq Stock Market or
in the National Quotation Bureau Incorporated or similar organization or agency
succeeding to its functions of reporting prices) at the close of business on
such date, or (c) if the Common Stock is not then reported by the National
Quotation Bureau Incorporated (or similar organization or agency succeeding to
its functions of reporting prices), then the average of the "Pink Sheet" quotes
for the relevant conversion period, as determined in good faith by the holder,
or (d) if the Common Stock is not then publicly traded the fair market value of
a share of Common Stock as determined by an Appraiser selected in good faith and
paid for by the holders of a majority in interest of the shares of Preferred
Stock; provided, however, that the Company, after receipt of the determination
by such appraiser, shall have the right to select an additional Appraiser (which
may be the firm of independent accountants that regularly reviews the Company's
financial statements), in which case, the fair market value shall be equal to
the average of the determinations by each such Appraiser.

       "Person" means a corporation, an association, a partnership,
organization, a business, an individual, a government or political subdivision
thereof or a governmental agency.

       "Purchase Agreement" means the Convertible Preferred Stock Purchase
Agreement, dated as of June 6, 1997, between the Company and the original holder
of the Preferred Stock.

       "Registration Rights Agreement" means the Registration Rights Agreement,
dated as of June 6, 1997, between the Company and the original holder of
Preferred Stock.

       "Trading Day" means (a) a day on which the Common Stock is traded on The
Nasdaq National Market, Inc. or other stock exchange or market on which the
Common Stock has been listed, or (b) if the Common Stock is not listed on The
Nasdaq National Market, Inc. or any stock exchange or market, a day on which the
Common Stock is traded in the over-the-counter market, as reported by the OTC
Bulletin Board, or (c) if the Common Stock is not quoted on the OTC Bulletin
Board, a day on which the Common Stock is quoted in the over-the-counter market
as reported by the National Quotation Bureau Incorporated (or any similar
organization or agency succeeding its functions of reporting prices).

                  "Underlying Shares" means the number of shares of Common Stock
into which the shares of Preferred Stock are convertible in accordance with the
terms hereof and the Purchase Agreement.


                                      -15-

   16




                  RESOLVED FURTHER, that the President and Secretary of the
Company be, and they hereby are, authorized and directed to prepare, execute,
verify, and file with the Secretary of State of Delaware, a Certificate of
Designation in accordance with these resolutions and as required by law.

                  IN WITNESS WHEREOF, Illinois Superconductor Corporation has
caused its corporate seal to be hereunto affixed and this certificate to be
signed by Ora E. Smith, its President, and attested by Stephen G. Wasko, its
Secretary, this 6th day of June, 1997.


                                        ILLINOIS SUPERCONDUCTOR CORPORATION


                                        By: /s/ ORA E. SMITH 
                                           --------------------------------
                                           Name: Ora E. Smith
                                           Title: President

Attest:

By: /s/ STEPHEN G. WASKO
   --------------------------
   Name: Stephen G. Wasko
   Title: Secretary


                                       -16-
   17

                                    EXHIBIT A

                              NOTICE OF CONVERSION


(To be Executed by the Registered Holder in order to Convert shares of Preferred
Stock)

The undersigned hereby elects to convert the number of shares of Series B
Convertible Preferred Stock (the "Preferred Stock") indicated below, into shares
of Common Stock, par value $.001 per share (the "Common Stock"), of Illinois
Superconductor Corporation (the "Company") according to the conditions hereof,
as of the date written below. If shares are to be issued in the name of a person
other than undersigned, the undersigned will pay all transfer taxes payable with
respect thereto and is delivering herewith such certificates and opinions as
reasonably requested by the Company in accordance therewith. No fee will be
charged to the holder for any conversion, except for such transfer taxes, if
any.

Conversion calculations:      -------------------------------
                              Date to Effect Conversion

                              ------------------------------------------------  
                              Number of shares of Preferred Stock to be
                              Converted

                              ------------------------------------------------  
                              Number of shares of Common Stock to be Issued
                              (without taking into account any accrued but 
                              unpaid dividends issuable upon this conversion, 
                              if any)

                              ------------------------------------------------  
                              Applicable Conversion Price

                              ------------------------------------------------  
                              Signature

                              ------------------------------------------------  
                              Name

                              ------------------------------------------------  
                              Address



The Company undertakes to promptly upon its receipt of this conversion notice
(and, in any case prior to the time it effects the conversion requested hereby),
notify the converting holder by facsimile of the number of shares of Common
Stock which would be issuable to the holder if the conversion requested in this
conversion notice were effected in full, whereupon, if the converting holder
determines that such conversion would result in it owning in excess of 4.999% of
the outstanding shares of Common Stock on such date, such holder will so notify
the Company and the Company shall convert up to an amount equal to 4.999% of the
outstanding shares of Common Stock and issue to the holder one or more
certificates representing shares of Preferred Stock which have not been
converted as a result of this provision.