<PAGE>

                                                                    Exhibit 99.1
                                                                    ------------

                                MICROTUNE, INC.

                   SERIES E PREFERRED STOCK OPTION AGREEMENT


I.        NOTICE OF STOCK OPTION GRANT
          ----------------------------

     Barry Koch

     c/o Temic Telefunken

     Hochfrequenztechnik GmbH

     Marie Curie Str. 1

     85055 Ingolstadt, Germany

     You have been granted a Nonstatutory Stock Option to purchase Series E
Preferred Stock of the Company, subject to the terms and conditions of this
Agreement, as follows:

     Grant Number                       204

     Date of Grant                      January 11, 2000

     Vesting Commencement Date          January 1, 2000

     Exercise Price per Share           $16.00

     Total Number of Shares Granted     130,000

     Total Exercise Price               $2,080,000.00 (U.S. Dollars)

     Type of Option                     Non-Qualified Stock Option

     Term/Expiration Date:              January 11, 2010


I.   Exercise Schedule:
     -----------------

     This Option may be exercised, in whole or in part, in accordance with the
following schedule:
<PAGE>

         a.   For the first one hundred and twenty (120) days after the Vesting
Commencement Date (the "Initial Exercise Period"), the Shares shall be
exercisable, in whole or in part.

         b.   After the Initial Exercise Period the portion of the Shares not
exercised in the Initial Exercise Period (the "Unexercised Portion") shall be
exercisable: (i) twenty percent (20%) of the Unexercised Portion of the total
Shares shall be exercisable twelve (12) months after the Vesting Commencement
Date, and (ii) one sixtieth (1/60th) of the Unexercised Portion of the total
Shares shall be exercisable each month thereafter.

         2. Vesting Schedule:
            ----------------

         This Option shall vest and may be exercised, in whole or in part, in
accordance with the following schedule:

         Twenty percent (20%) of the total Shares shall be come exercisable and
vest twelve (12) months after the Vesting Commencement Date, and one sixtieth
(1/60/th/) of the total Shares shall become exercisable and vest each month
thereafter.

         3. Consideration for Exercising Shares:
            -----------------------------------

         a.   For Shares exercised under the Initial Exercise Period, the
Optionee shall purchase immediately the exercised portion of the Shares in the
Company at the Exercise Price. The Company will accept in consideration for the
Optionee's purchase price (1) a promissory note in the amount of $12.80 (U.S.
Dollars) per share, payable at the lowest allowed applicable federal IRS
interest rate (AFR) and due forty-eight (48) months after the Exercise
Commencement Date and (2) consideration for the remaining $3.20 (U.S. Dollars)
per share shall be paid according to section 5 of the Option Agreement.

         b.   For Shares exercised after the Initial Exercise Period, the
Optionee agrees to purchase shares in the Company at the Exercise Price stated
above. Consideration shall be paid according to section 5 of the Option
Agreement.

         4. Repurchase Option:
            -----------------

         a.   In the event of the voluntary or involuntary termination of your
employment with or services to the Company (including death or disability)
before all of the Shares are vested according to the Vesting Schedule above ,
the Company shall, upon the date of such termination (as reasonably fixed and
determined by the Company) have an irrevocable, exclusive option for a period of
ninety (90) days from such date to repurchase all or any portion of the unvested
portion of the Shares at the original purchase price per share. Said repurchase
option shall be exercised by the Company by written notice to the Optionee or
his executor and, at the Company's option, (i) by delivery to Optionee or his
executor with such notice of a check in the amount of the repurchase price for
the Shares being repurchased, or (ii) by cancellation by the Company of an
amount of Optionee's indebtedness to the Company equal to the repurchase price
for the Shares being repurchased, or (iii) by a combination of (i) and (ii) so
that the combined payment and cancellation of indebtedness equals such
repurchase price. Upon delivery of such notice and the payment of the repurchase
price in any of the ways described above, the Company shall become the legal and
beneficial owner of the Shares being repurchased and all rights and interests
therein or relating thereto, and the Company shall have the right to retain and
transfer to its own name the number of shares of the Shares being repurchased by
the Company.

         b.   Whenever the Company shall have the right to repurchase shares of
the Shares hereunder, the Company may designate and assign one or more
employees, officers, directors or shareholders of the Company or other persons
or organizations to exercise all or a part of the Company's repurchase rights
under

                                      -2-
<PAGE>

this Agreement and purchase all or a part of such Shares.

     5. Termination Period
        ------------------
     This Option may be exercised for two (2) months after Optionee ceases to be
a Service Provider in accordance with Section 8 of this Agreement. Upon the
death or Disability of the Optionee, this Option may be exercised for twelve
(12) months after the Optionee ceases to be a Service Provider in accordance
with Sections 9 and 10 of this Agreement. In no event shall this Option be
exercised later that the Term/Expiration Date provided.

II.  AGREEMENT

          1.   Definitions. As used herein, the following definitions shall
               -----------
apply:

                   (a) "Agreement" means this stock option agreement between the
                        ---------
Company and Optionee evidencing the terms and conditions of this Option.

                   (b) "Applicable Laws" means the requirements relating to the
                        ---------------
administration of stock options under U.S. state corporate laws, U.S. federal
and state securities laws, the Code, any stock exchange or quotation system on
which the Common Stock is listed or quoted and the applicable laws of any
foreign country or jurisdiction that may apply to this Option.

                   (c) "Board" means the Board of Directors of the Company or
                        -----
any committee of the Board that has been designated by the Board to administer
this Agreement.

                   (d) "Code" means the U.S. Internal Revenue Code of 1986, as
                        ----
amended.

                   (e) "Common Stock" means the common stock of the Company.
                        ------------

                   (f) "Company" means MicroTune, Inc., a Texas corporation.
                        -------

                   (g) "Consultant" means any person, including an advisor,
                        ----------
engaged by the Company or a Parent or Subsidiary to render services to such
entity.

                   (h) "Director" means a member of the Board.
                        --------

                   (i) "Disability" means total and permanent disability as
                        ----------
defined in Section 22(e)(3) of the Code.

                   (j) "Employee" means any person, including Officers and
                        --------
Directors, employed by the Company or any Parent or Subsidiary of the Company. A
Service Provider shall not cease to be an Employee in the case of (i) any leave
of absence approved by the Company or (ii) transfers between locations of the
Company or between the Company, its Parent, any Subsidiary, or any successor.
Neither service as a Director nor payment of a director's fee by the Company
shall be sufficient to constitute "employment" by the Company.

                   (k) "Exchange Rate" means the Securities Exchange Act of
                        -------------
1934, as amended.
                   (l) "Fair Market Value" means, as of any date, with respect
                        -----------------
to the Series E Preferred Stock, the Fair Market Value of the Common Stock
issuable upon conversion of such Series E Preferred Stock, and, with respect to
the Common Stock, the value of Common Stock determined as follows:

                                      -3-
<PAGE>

                   (1) If the Common Stock is listed on any established stock
exchange or a national market system, including without limitation the Nasdaq
National Market or The Nasdaq SmallCap Market of The Nasdaq Stock Market, its
Fair Market Value shall be the closing sales price for such stock (or the
closing bid, if no sales were reported) as quoted on such exchange or system for
the last market trading day prior to the time of determination, as reported in
The Wall Street Journal or such other source as the Administrator deems
reliable;

                   (2) If the Common Stock is regularly quoted by a recognized
securities dealer but selling prices are not reported, its Fair Market Value
shall be the mean between the high bid and low asked prices for the Common Stock
on the last market trading day prior to the day of determination; or

                   (3) In the absence of an established market for the Common
Stock, the Fair Market Value thereof shall be determined in good faith by the
Board .

               (m) "Nonstatutory Stock Option" means an Option not intended to
                    -------------------------
qualify as an incentive stock option within the meaning of Section 422 of the
Code and the regulations promulgated thereunder.

               (n) "Notice of Grant" means a written notice, in Part I of this
                    ---------------
Agreement, evidencing certain the terms and conditions of this Option grant. The
Notice of Grant is part of the Option Agreement.

               (o) "Officer" means a person who is an officer of the Company
                    -------
within the meaning of Section 16 of the Exchange Act and the rules and
regulations promulgated thereunder.

               (p) "Option"  means this stock option.
                    ------

               (q) "Optioned Stock" means the Series E Preferred Stock or the
                    --------------
Common Stock, as the case may be, subject to this Option.

               (r) "Optionee" means the person named in the Notice of Grant or
                    --------
such person's successor.

               (s) "Parent" means a "parent corporation," whether now or
                    ------
hereafter existing, as defined in Section 424(e) of the Code.


               (t) "Series E Preferred Stock" means the Series E Preferred Stock
                    ------------------------
of the Company.

               (u) "Service Provider" means an Employee, Director or Consultant.
                    ----------------

               (v) "Share" means a share of the Series E Preferred Stock, as
                    -----
adjusted in accordance with Section 11 of this Agreement; provided, that in the
event that the Series E Preferred Stock is converted into Common Stock, "Shares"
shall refer to the shares of Common Stock of the Company issued upon conversion
of each share of Series E Preferred Stock, as such Common Stock may be adjusted
in accordance with Section 11 of this Agreement.

               (w) "Subsidiary" means a "subsidiary corporation", whether now or
                    ----------
hereafter existing, as defined in Section 424(f) of the Code.

                                      -4-
<PAGE>

          2. Grant of Option. The Board hereby grants to the Optionee named in
             ---------------
the Notice of Grant attached as Part I of this Agreement the Option to purchase
the number of Shares, as set forth in the Notice of Grant, at the exercise price
per share set forth in the Notice of Grant (the "Exercise Price"), subject to
the terms and conditions of this Agreement.

          3. Exercise of Option.
             ------------------

               (a) Right to Exercise. This Option is exercisable during its term
                   -----------------
in accordance with the Vesting Schedule set out in the Notice of Grant and the
applicable provisions of this Agreement.

               (b) Method of Exercise. This Option is exercisable by delivery of
                   ------------------
an exercise notice, in the form attached as Exhibit A (the "Exercise Notice"),
                                            ---------
which shall state the election to exercise the Option, the number of Shares in
respect of which the Option is being exercised (the "Exercised Shares"), and
such other representations and agreements as may be required by the Company. The
Exercise Notice shall be completed by the Optionee and delivered to Secretary of
the Company. The Exercise Notice shall be accompanied by payment of the
aggregate Exercise Price as to all Exercised Shares. This Option shall be deemed
to be exercised upon receipt by the Company of such fully executed Exercise
Notice accompanied by such aggregate Exercise Price.

               (c) Legal Compliance. No Shares shall be issued pursuant to the
                   ----------------
exercise of this Option unless such issuance and exercise complies with
Applicable Laws. Assuming such compliance, for income tax purposes the Exercised
Shares shall be considered transferred to the Optionee on the date the Option is
exercised with respect to such Exercised Shares.

               (d) Buyout Provisions. The Board may at any time offer to buy out
                   -----------------
for a payment in cash or Shares an Option previously granted based on such terms
and conditions as the Board shall establish and communicate to the Optionee at
the time that such offer is made.

          4. Optionee's Representations. In the event the Shares have not been
             --------------------------
registered under the Securities Act of 1933, as amended, at the time this
Option is exercised, the Optionee shall, if required by the Company,
concurrently with the exercise of all or any portion of this Option, deliver to
the Company his or her Investment Representation Statement in the form attached
hereto as Exhibit B.
          ---------

          5. Method of Payment. Payment of the aggregate Exercise Price shall be
             -----------------
by any of the following, or a combination thereof, at the election of the
Optionee:

               (a) cash or check;

               (b) consideration received by the Company under a cashless
exercise program implemented by the Company; or

               (c) surrender of other shares of Series E Preferred Stock and/or
Common Stock which (i) in the case of shares acquired upon exercise of an
option, have been owned by the Optionee for more than six (6) months on the date
of surrender, and (ii) have a Fair Market Value on the date of surrender equal
to the aggregate Exercise Price of the Exercised Shares.

          6. Non-Transferability of Option. This Option may not be transferred
             -----------------------------
in any manner otherwise than by will or by the laws of descent or distribution
and may be exercised during the lifetime of Optionee only by the Optionee. The
terms of this Agreement shall be binding upon the executors, administrators,
heirs, successors and assigns of the Optionee.

                                      -5-
<PAGE>

          7.  Term of Option. This Option may be exercised only within the term
              --------------
set out in the Notice of Grant, and may be exercised during such term only in
accordance with the terms of this Agreement.

          8.  Termination of Relationship as a Service Provider. If the Optionee
              -------------------------------------------------
ceases to be a Service Provider (other than for death or Disability), this
Option may be exercised for a period of two (2) months after the date of such
termination (but in no event later than the expiration date of this Option as
set forth in the Notice of Grant) to the extent that the Option is vested on the
date of such termination. To the extent that the Optionee does not exercise this
Option within the time specified herein, the Option shall terminate.

          9.  Disability of Optionee. If the Optionee ceases to be a Service
              ----------------------
Provider as a result of the Optionee's Disability, this Option may be exercised
for a period of twelve (12) months after the date of such termination (but in no
event later than the expiration date of this Option as set forth in the Notice
of Grant) to the extent that the Option is vested on the date of such
termination. To the extent that Optionee does not exercise this Option within
the time specified herein, the Option shall terminate.

          10. Death of Optionee. If the Optionee dies while a Service Provider,
              -----------------
the Option may be exercised at any time within twelve (12) months following the
date of death (but in no event later than the expiration date of this Option as
set forth in the Notice of Grant), by the Optionee's estate or by a person who
acquired the right to exercise the Option by bequest or inheritance, but only to
the extent that the Optionee was entitled to exercise the Option at the date of
death. If, after death, the Optionee's estate or a person who acquired the right
to exercise the Option by bequest or inheritance does not exercise the Option
within the time specified herein, the Option shall terminate.

          11. Adjustments Upon Changes in Capitalization, Dissolution, Merger or
              ------------------------------------------------------------------
Asset Sale.
----------

               (a) Changes in Capitalization. Upon the conversation of all of
                   -------------------------
the Series E Preferred Stock into Common Stock, this Option shall automatically
become exercisable for shares of Common Stock in accordance with the conversion
provisions of the Company's Articles of Incorporation, as then amended and
restated. In addition, subject to any required action by the stockholders of the
Company, the number of Shares covered by this Option, as well as the price per
Share covered by this Option, shall be proportionately adjusted for any increase
or decrease in the number of issued shares of Series E Preferred Stock or Common
Stock, as the case may be, resulting from a stock split, reverse stock split,
stock dividend, combination or reclassification of the Series E Preferred Stock
or Common Stock, as the case may be, or any other increase or decrease in the
number of issued shares of Series E Preferred Stock or Common Stock, as the case
may be, effected without receipt of consideration by the Company; provided,
however, that conversion of any convertible securities of the Company (including
the Series E Preferred Stock) shall not be deemed to have been "effected without
receipt of consideration." Such adjustment shall be made by the Board, whose
determination in that respect shall be final, binding and conclusive. Except as
expressly provided herein, no issuance by the Company of shares of stock of any
class, or securities convertible into shares of stock of any class, shall
affect, and no adjustment by reason thereof shall be made with respect to, the
number or price of shares of Series E Preferred Stock or Common Stock, as the
case may be, subject to this Option.

               (b) Dissolution or Liquidation. In the event of the proposed
                   --------------------------
dissolution or liquidation of the Company, the Board shall notify Optionee as
soon as practicable prior to the effective date of such proposed transaction.
The Board in its discretion may provide for the Optionee to have the right to
exercise his or her Option until fifteen (15) days prior to such transaction as
to all of the Optioned Stock covered thereby, including Shares as to which the
Option would not otherwise be exercisable. To the extent it has not been
previously exercised, the Option will terminate immediately prior to the
consummation of such proposed action.

                                      -6-
<PAGE>

               (c) Merger or Asset Sale. In the event of a merger of the Company
                   --------------------
with or into another corporation, or the sale of substantially all of the assets
of the Company, the Option shall be assumed or an equivalent option substituted
by the successor corporation or a Parent or Subsidiary of the successor
corporation. In the event that the successor corporation refuses to assume or
substitute for the Option, the Optionee shall fully vest in and have the right
to exercise the Option as to all of the Optioned Stock, including Shares as to
which it would not otherwise be vested or exercisable. If the Option becomes
fully vested and exercisable in lieu of assumption or substitution in the event
of a merger or sale of assets, the Board shall notify the e Optionee in writing
or electronically that the Option shall be fully exercisable for a period of
fifteen (15) days from the date of such notice, and the Option shall terminate
upon the expiration of such period. For the purposes of this paragraph, the
Option shall be considered assumed if, following the merger or sale of assets,
the option confers the right to purchase or receive, for each Share of Optioned
Stock subject to the Option immediately prior to the merger or sale of assets,
the consideration (whether stock, cash, or other securities or property)
received in the merger or sale of assets by holders of Series E Preferred Stock
or Common Stock, as the case may be, for each Share held on the effective date
of the transaction (and if holders were offered a choice of consideration, the
type of consideration chosen by the holders of a majority of the outstanding
Shares); provided, however, that if such consideration received in the merger or
sale of assets is not solely common stock of the successor corporation or its
Parent, the Administrator may, with the consent of the successor corporation,
provide for the consideration to be received upon the exercise of the Option,
for each Share of Optioned Stock subject to the Option, to be solely common
stock of the successor corporation or its Parent equal in fair market value to
the per share consideration received by holders of Series E Preferred Stock or
Common Stock, as the case may be, in the merger or sale of assets.

               12. Lock-Up Period. Optionee hereby agrees that, if so requested
                   --------------
by the Company or any representative of the underwriters (the "Managing
Underwriter") in connection with any registration of the offering of any
securities of the Company under the Securities Act, Optionee shall not sell or
otherwise transfer any Shares or other securities of the Company during the 180-
day period (or such other period as may be requested in writing by the Managing
Underwriter and agreed to in writing by the Company) (the "Market Standoff
Period") following the effective date of a registration statement of the Company
filed under the Securities Act. Such restriction shall apply only to the first
registration statement of the Company to become effective under the Securities
Act that includes securities to be sold on behalf of the Company to the public
in an underwritten public offering under the Securities Act. The Company may
impose stop-transfer instructions with respect to securities subject to the
foregoing restrictions until the end of such Market Standoff Period.

               13. Notices. Any notice to be given to the Company hereunder
                   -------
shall be in writing and shall be addressed to the Company. at its then current
principal executive office or to such other address as the Company may hereafter
designate to the Optionee by notice as provided in this Section. Any notice to
be given to the Optionee hereunder shall be addressed to the Optionee at the
address set forth beneath his signature hereto, or at such other address as the
Optionee may hereafter designate to the Company by notice as provided herein. A
notice shall be deemed to have been duly given when personally delivered or
mailed by registered or certified mail to the party entitled to receive it.

               14. Tax Consequences. Some of the U.S. federal tax consequences
                   ----------------
relating to this Option, as of the date of this Option, are set forth below.
THIS SUMMARY IS NECESSARILY INCOMPLETE, AND THE TAX LAWS AND REGULATIONS ARE
SUBJECT TO CHANGE. THE OPTIONEE SHOULD CONSULT A TAX ADVISER BEFORE EXERCISING
THIS OPTION OR DISPOSING OF THE SHARES.

                    (a) Exercising the Option. The Optionee may incur regular
                        ---------------------
U.S. federal income tax liability upon exercise of a Nonstatutory Stock Option
(an "NSO"). The Optionee will be treated as having received compensation income
(taxable at ordinary income tax rates) equal to the excess, if any, of the

                                      -7-
<PAGE>

Fair Market Value of the Exercised Shares on the date of exercise over their
aggregate Exercise Price. If the Optionee is an Employee or a former Employee,
the Company will be required to withhold from his or her compensation or collect
from Optionee and pay to the applicable taxing authorities an amount in cash
equal to a percentage of this compensation income at the time of exercise, and
may refuse to honor the exercise and refuse to deliver Shares if such
withholding amounts are not delivered at the time of exercise.

               (b) Disposition of Shares. If the Optionee holds NSO Shares for
                   ---------------------
at least one year, any gain realized on disposition of the Shares will be
treated as long-term capital gain for U.S. federal income tax purposes.

          15. Entire Agreement; Governing Law. This Agreement constitute the
              -------------------------------
entire agreement of the parties with respect to the subject matter hereof and
supersede in their entirety all prior undertakings and agreements of the Company
and Optionee with respect to the subject matter hereof, and may not be modified
adversely to the Optionee's interest except by means of a writing signed by the
Company and Optionee. This agreement is governed by the internal substantive
laws, but not the choice of law rules, of Texas.

          16. NO GUARANTEE OF CONTINUED SERVICE. OPTIONEE ACKNOWLEDGES AND
              ---------------------------------
AGREES THAT THE VESTING OF SHARES PURSUANT TO THE VESTING SCHEDULE HEREOF IS
EARNED ONLY BY CONTINUING AS A SERVICE PROVIDER AT THE WILL OF THE COMPANY (AND
NOT THROUGH THE ACT OF BEING HIRED, BEING GRANTED AN OPTION OR PURCHASING SHARES
HEREUNDER). OPTIONEE FURTHER ACKNOWLEDGES AND AGREES THAT THIS AGREEMENT, THE
TRANSACTIONS CONTEMPLATED HEREUNDER AND THE VESTING SCHEDULE SET FORTH HEREIN DO
NOT CONSTITUTE AN EXPRESS OR IMPLIED PROMISE OF CONTINUES ENGAGEMENT AS A
SERVICE PROVIDER FOR THE VESTING PERIOD, FOR ANY PERIOD, OR AT ALL, AND SHALL
NOT INTERFERE WITH OPTIONEE'S RIGHT OR THE COMPANY'S RIGHT TO TERMINATE
OPTIONEE'S RELATIONSHIP AS A SERVICE PROVIDER AT ANY TIME, WITH OR WITHOUT
CAUSE.

                                      -8-
<PAGE>

       By your signature and the signature of the Company's representative
below, you and the Company agree that this Option is granted under and governed
by the terms and conditions of this Agreement. Optionee has reviewed this
Agreement in its entirety, has had an opportunity to obtain the advice of
counsel prior to executing this Agreement and fully understands all provisions
of this Agreement. Optionee hereby agrees to accept as binding, conclusive and
final all decisions or interpretations of the Board upon any questions relating
to this Agreement. Optionee further agrees to notify the Company upon any change
in the residence address indicated below.

OPTIONEE                                 MICROTUNE, INC.

                                         /S/ Douglas J. Bartek
______________________________           ------------------------------
Sign                                     Douglas J. Bartek

/S/ Barry F. Koch
------------------------------           ______________________________
Barry Koch                               Chairman and CEO


______________________________
Residence Address

Peisserstr. 58
------------------------------

D-85053 Ingolstadt
------------------------------

                                      -9-
<PAGE>

                                                                    Exhibit 99.1
                                                                    ------------

                               CONSENT OF SPOUSE

       The undersigned spouse of Optionee has read and hereby approves the terms
and conditions of this Agreement. In consideration of the Company's granting his
or her spouse the right to purchase Shares as set forth in this Agreement, the
undersigned hereby agrees to be irrevocably bound by the terms and conditions of
this Agreement and further agrees that any community property interest shall be
similarly bound. The undersigned hereby appoints the undersigned's spouse as
attorney-in-fact for the undersigned with respect to any amendment or exercise
of rights under this Agreement.

                                               /S/ Claudia Koch
                                               -------------------------------
                                               Spouse of Optionee

                                      -10-
<PAGE>

                                   EXHIBIT A
                                   ---------

                                MICROTUNE, INC.

                                EXERCISE NOTICE

MicroTune, Inc.
2540 East Plano Parkway, Suite 188
Plano, Texas  75074

Attention:

          1. Exercise of Option. Effective as of today, ________________, 199__,
             ------------------
the undersigned ("Purchaser") hereby elects to purchase ______________ shares
(the "Shares") of the [Series E Preferred Stock] [Common Stock] of MicroTune,
Inc. (the "Company") under and pursuant to the Stock Option Agreement dated
January 10, 2000 (the "Option Agreement"). The purchase price for the Shares
shall be $____________, as required by the Option Agreement.

          2. Delivery of Payment. Purchaser herewith delivers to the Company the
             -------------------
full purchase price for the Shares.

          3. Representations of Purchaser. Purchaser acknowledges that Purchaser
             ----------------------------
has received, read and understood the Option Agreement and agrees to abide by
and be bound by their terms and conditions.

          4. Rights as Shareholder. Until the issuance (as evidenced by the
             ---------------------
appropriate entry on the books of the Company or of a duly authorized transfer
agent of the Company) of the Shares, no right to vote or receive dividends or
any other rights as a stockholder shall exist with respect to the Optioned
Stock, notwithstanding the exercise of the Option. The Shares so acquired shall
be issued to the Optionee as soon as practicable after exercise of the Option.
No adjustment will be made for a dividend or other right for which the record
date is prior to the date of issuance, except as provided in Section 11 of the
Option Agreement.

          5. Company's Right of First Refusal. Before any Shares held by
             --------------------------------
Optionee or any transferee (either being sometimes referred to herein as the
"Holder") may be sold or otherwise transferred (including transfer by gift or
operation of law), the Company or its assignee(s) shall have a right of first
refusal to purchase the Shares on the terms and conditions set forth in this
Section (the "Right of First Refusal").

               (a) Notice of Proposed Transfer. The Holder of the Shares shall
                   ---------------------------
deliver to the Company a written notice (the "Notice") stating: (i) the Holder's
bona fide intention to sell or otherwise transfer such Shares; (ii) the name of
each proposed purchaser or other transferee ("Proposed Transferee"); (iii) the
number of Shares to be transferred to each Proposed Transferee; and (iv) the
bona fide cash price or other consideration for which the Holder proposes to
transfer the

                                      -11-
<PAGE>

Shares (the "Offered Price"), and the Holder shall offer the Shares at the
Offered Price to the Company or its assignee(s).

               (b) Exercise of Right of First Refusal. At any time within thirty
                   ----------------------------------
(30) days after receipt of the Notice, the Company and/or its assignee(s) may,
by giving written notice to the Holder, elect to purchase all, but not less than
all, of the Shares proposed to be transferred to any one or more of the Proposed
Transferees, at the purchase price determined in accordance with subsection (c)
below.
               (c) Purchase Price. The purchase price ("Purchase Price") for the
                   --------------
Shares purchased by the Company or its assignee(s) under this Section shall be
the Offered Price. If the Offered Price includes consideration other than cash,
the cash equivalent value of the non-cash consideration shall be determined by
the Board in good faith.

               (d) Payment. Payment of the Purchase Price shall be made, at the
                   -------
option of the Company or its assignee(s), in cash (by check), by cancellation of
all or a portion of any outstanding indebtedness of the Holder to the Company
(or, in the case of repurchase by an assignee, to the assignee), or by any
combination thereof within 30 days after receipt of the Notice or in the manner
and at the times set forth in the Notice.

               (e) Holder's Right to Transfer. If all of the Shares proposed in
                   --------------------------
the Notice to be transferred to a given Proposed Transferee are not purchased by
the Company and/or its assignee(s) as provided in this Section, then the Holder
may sell or otherwise transfer such Shares to that Proposed Transferee at the
Offered Price or at a higher price, provided that such sale or other transfer is
consummated within 120 days after the date of the Notice, that any such sale or
other transfer is effected in accordance with any applicable securities laws and
that the Proposed Transferee agrees in writing that the provisions of this
Section shall continue to apply to the Shares in the hands of such Proposed
Transferee. If the Shares described in the Notice are not transferred to the
Proposed Transferee within such period, a new Notice shall be given to the
Company, and the Company and/or its assignees shall again be offered the Right
of First Refusal before any Shares held by the Holder may be sold or otherwise
transferred.

               (f) Exception for Certain Family Transfers. Anything to the
                   --------------------------------------
contrary contained in this Section notwithstanding, the transfer of any or all
of the Shares during the Optionee's lifetime or on the Optionee's death by will
or intestacy to the Optionee's immediate family or a trust for the benefit of
the Optionee's immediate family shall be exempt from the provisions of this
Section. "Immediate Family" as used herein shall mean spouse, lineal descendant
or antecedent, father, mother, brother or sister. In such case, the transferee
or other recipient shall receive and hold the Shares so transferred subject to
the provisions of this Section, and there shall be no further transfer of such
Shares except in accordance with the terms of this Section.

               (g) Termination of Right of First Refusal. The Right of First
                   -------------------------------------
Refusal shall terminate as to any Shares upon the first sale of Common Stock of
the Company to the general public pursuant to a registration statement filed
with and declared effective by the Securities and Exchange Commission under the
Securities Act of 1933, as amended.

                                      -12-
<PAGE>

          6. Tax Consultation. Purchaser understands that Purchaser may suffer
             ----------------
adverse tax consequences as a result of Purchaser's purchase or disposition of
the Shares. Purchaser represents that Purchaser has consulted with any tax
consultants Purchaser deems advisable in connection with the purchase or
disposition of the Shares and that Purchaser is not relying on the Company for
any tax advice.

          7. Restrictive Legends and Stop-Transfer Orders.
             --------------------------------------------

             (h) Legends. Optionee understands and agrees that the Company shall
                 -------
cause the legends set forth below or legends substantially equivalent thereto,
to be placed upon any certificate(s) evidencing ownership of the Shares together
with any other legends that may be required by the Company or by state or U.S.
federal or other countries' securities laws:

          THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE
          SECURITIES ACT OF 1933 (THE "ACT") AND MAY NOT BE OFFERED, SOLD OR
          OTHERWISE TRANSFERRED, PLEDGED OR HYPOTHECATED UNLESS AND UNTIL
          REGISTERED UNDER THE ACT OR, IN THE OPINION OF COMPANY COUNSEL
          SATISFACTORY TO THE ISSUER OF THESE SECURITIES, SUCH OFFER, SALE OR
          TRANSFER, PLEDGE OR HYPOTHECATION IS IN COMPLIANCE THEREWITH.

          THE SHARES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO CERTAIN
          RESTRICTIONS ON TRANSFER AND A RIGHT OF FIRST REFUSAL HELD BY THE
          ISSUER OR ITS ASSIGNEE(S) AS SET FORTH IN THE EXERCISE NOTICE BETWEEN
          THE ISSUER AND THE ORIGINAL HOLDER OF THESE SHARES, A COPY OF WHICH
          MAY BE OBTAINED AT THE PRINCIPAL OFFICE OF THE ISSUER. SUCH TRANSFER
          RESTRICTIONS AND RIGHT OF FIRST REFUSAL ARE BINDING ON TRANSFEREES OF
          THESE SHARES.

             (i) Stop-Transfer Notices. Optionee agrees that, in order to ensure
                 ---------------------
compliance with the restrictions referred to herein, the Company may issue
appropriate "stop transfer" instructions to its transfer agent, if any, and
that, if the Company transfers its own securities, it may make appropriate
notations to the same effect in its own records.

             (j) Refusal to Transfer. The Company shall not be required (i) to
                 -------------------
transfer on its books any Shares that have been sold or otherwise transferred in
violation of any of the provisions of this Exercise Notice or (ii) to treat as
owner of such Shares or to accord the right to vote or pay dividends to any
purchaser or other transferee to whom such Shares shall have been so
transferred.

          8. Successors and Assigns. The Company may assign any of its rights
             ----------------------
under this Exercise Notice to single or multiple assignees, and this Exercise
Notice shall inure to the benefit of the successors and assigns of the Company.
Subject to the restrictions on transfer herein set forth, this Exercise Notice
shall be binding upon Optionee and his or her heirs, executors, administrators,
successors and assigns.

                                      -13-
<PAGE>

          9.  Interpretation. Any dispute regarding the interpretation of this
              --------------
Exercise Notice shall be submitted by Optionee or by the Company forthwith to
the Administrator which shall review such dispute at its next regular meeting.
The resolution of such a dispute by the Administrator shall be final and binding
on all parties.

          10. Entire Agreement; Governing Law. The Option Agreement is
              -------------------------------
incorporated herein by reference. This Agreement, and the Option Agreement
constitute the entire agreement of the parties with respect to the subject
matter hereof and supersede in their entirety all prior undertakings and
agreements of the Company and Purchaser with respect to the subject matter
hereof, and may not be modified adversely to the Purchaser's interest except by
means of a writing signed by the Company and Purchaser. This agreement is
governed by the internal substantive laws, but not the choice of law rules, of
Texas.

Submitted by:                           Accepted by:

OPTIONEE                                MICROTUNE, INC.

_______________________________         By:____________________________
Signature

_______________________________         Title:_________________________
Print Name


_______________________________         _______________________________
Address                                 Address


_______________________________         _______________________________

_______________________________         _______________________________


                                        Date Received:_____________

                                      -14-
<PAGE>

                                   EXHIBIT B
                                   ---------

                      INVESTMENT REPRESENTATION STATEMENT

OPTIONEE: Barry Koch

COMPANY:  MICROTUNE, INC.

SECURITY: SERIES E PREFERRED STOCK and the COMMON STOCK issued or issuable upon
          conversation thereof

AMOUNT:   $2,080,000.00 (U.S. Dollars)

DATE:     January 11, 2000


     In connection with the purchase of the above-listed Securities, the
undersigned Optionee represents to the Company the following:

          (a) Optionee is aware of the Company's business affairs and financial
condition and has acquired sufficient information about the Company to reach an
informed and knowledgeable decision to acquire the Securities. Optionee is
acquiring these Securities for investment for Optionee's own account only and
not with a view to, or for resale in connection with, any "distribution" thereof
within the meaning of the Securities Act of 1933, as amended (the "Securities
Act").

          (b) Optionee acknowledges and understands that the Securities
constitute "restricted securities" under the Securities Act and have not been
registered under the Securities Act in reliance upon a specific exemption
therefrom, which exemption depends upon, among other things, the bona fide
nature of Optionee's investment intent as expressed herein. In this connection,
Optionee understands that, in the view of the Securities and Exchange
Commission, the statutory basis for such exemption may be unavailable if
Optionee's representation was predicated solely upon a present intention to hold
these Securities for the minimum capital gains period specified under tax
statutes, for a deferred sale, for or until an increase or decrease in the
market price of the Securities, or for a period of one year or any other fixed
period in the future. Optionee further understands that the Securities must be
held indefinitely unless they are subsequently registered under the Securities
Act or an exemption from such registration is available. Optionee further
acknowledges and understands that the Company is under no obligation to register
the Securities. Optionee understands that the certificate evidencing the
Securities will be imprinted with a legend which prohibits the transfer of the
Securities unless they are registered or such registration is not required in
the opinion of counsel satisfactory to the Company, and any other legend
required under applicable state securities laws.

          (c) Optionee is familiar with the provisions of Rule 701 and Rule 144,
each promulgated under the Securities Act, which, in substance, permit limited
public resale of "restricted securities" acquired, directly or indirectly from
the issuer thereof, in a non-public offering subject to the satisfaction of
certain conditions. Rule 701 provides that if the issuer qualifies under Rule
701 at the time of the grant of the Option to the Optionee, the exercise will be
exempt from registration under the Securities Act.

                                     -15-
<PAGE>

In the event the Company becomes subject to the reporting requirements of
Section 13 or 15(d) of the Securities Exchange Act of 1934, ninety (90) days
thereafter (or such longer period as any market stand-off agreement may require)
the Securities exempt under Rule 701 may be resold, subject to the satisfaction
of certain of the conditions specified by Rule 144, including: (1) the resale
being made through a broker in an unsolicited "broker's transaction" or in
transactions directly with a market maker (as said term is defined under the
Securities Exchange Act of 1934); and, in the case of an affiliate, (2) the
availability of certain public information about the Company, (3) the amount of
Securities being sold during any three month period not exceeding the
limitations specified in Rule 144(e), and (4) the timely filing of a Form 144,
if applicable.

          In the event that the Company does not qualify under Rule 701 at the
time of grant of the Option, then the Securities may be resold in certain
limited circumstances subject to the provisions of Rule 144, which requires the
resale to occur not less than one year after the later of the date the
Securities were sold by the Company or the date the Securities were sold by an
affiliate of the Company, within the meaning of Rule 144; and, in the case of
acquisition of the Securities by an affiliate, or by a non-affiliate who
subsequently holds the Securities less than two years, the satisfaction of the
conditions set forth in sections (1), (2), (3) and (4) of the paragraph
immediately above.

          (d) Optionee further understands that in the event all of the
applicable requirements of Rule 701 or 144 are not satisfied, registration under
the Securities Act, compliance with Regulation A, or some other registration
exemption will be required; and that, notwithstanding the fact that Rules 144
and 701 are not exclusive, the Staff of the Securities and Exchange Commission
has expressed its opinion that persons proposing to sell private placement
securities other than in a registered offering and otherwise than pursuant to
Rules 144 or 701 will have a substantial burden of proof in establishing that an
exemption from registration is available for such offers or sales, and that such
persons and their respective brokers who participate in such transactions do so
at their own risk. Optionee understands that no assurances can be given that any
such other registration exemption will be available in such event.

                                         Signature of Optionee:

                                         _______________________________________


                                         Date:
                                              __________________________________

                                      -16-