<PAGE>   1
                                                                   EXHIBIT 10.13

                             SYNAPTICS INCORPORATED

                             1996 STOCK OPTION PLAN

                          NOTICE OF STOCK OPTION GRANT

Federico Faggin


      You have been granted an option to purchase Common Stock "Common Stock" of
Synaptics Incorporated (the "Company") as follows:

      Date of  Grant:              ((GrantDate))

      Vesting Commencement Date:   ((VestingCommenceDate))

      Exercise Price per Share:    $((ExercisePrice))

      Total Number of Shares
      Granted:                     ((NoofShares))

      Total Exercise Price:        $((TotalExercisePrice))

      Type of Option:              ((ISO)) Incentive Stock Option

                                   ((NSO)) Nonstatutory Stock Option

      Term/Expiration Date:        ((ExpirDate))

      Vesting Schedule:            This Option may be exercised, in whole or in
                                   part, in accordance with the following
                                   schedule: 25% of the Shares subject to the
                                   Option shall vest on the twelve (12) month
                                   anniversary of the Vesting Commencement Date
                                   and 1/48th of the total number of Shares
                                   subject to the Option shall vest on the 1st
                                   of each month thereafter. In the event of a
                                   change in control, such shares shall
                                   immediately vest 50% of the unvested options
                                   granted.

      Termination Period:          This Option may be exercised for 90 days
                                   after termination of employment or consulting
                                   relationship except as set out in Sections 6
                                   and 7 of the Stock Option Agreement (but in
                                   no event later than the Expiration Date).
<PAGE>   2
      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 the 1996 Stock Option Plan and the Stock Option
Agreement, both of which are attached and made a part of this document.


FEDERICO FAGGIN:                      SYNAPTICS INCORPORATED

                                      By:
------------------------------           -------------------------------
Signature

                                         Francis Lee, President
------------------------------           -------------------------------
Print Name                               (Print Name and Title)


                                      -2-
<PAGE>   3
                              SYNAPTIC INCORPORATED

                             1996 STOCK OPTION PLAN

                             STOCK OPTION AGREEMENT


      1.    GRANT OF OPTION. Synaptics Incorporated, a California corporation
(the "Company"), hereby grants to Federico Faggin ("Optionee"), an option (the
"Option") to purchase a total number of shares of Common Stock (the "Shares")
set forth in the Notice of Stock Option Grant, at the exercise price per share
set forth in the Notice of Stock Option Grant (the "Exercise Price") subject to
the terms, definitions and provisions of the Synaptics Incorporated 1996 Stock
Option Plan (the "Plan") adopted by the Company, which is incorporated herein by
reference. Unless otherwise defined herein, the terms defined in the Plan shall
have the same defined meanings in this Option.

      If designated an Incentive Stock Option, this Option is intended to
qualify as an Incentive Stock Option as defined in Section 422 of the Code.

      2.    EXERCISE OF OPTION. This Option shall be exercisable during its Term
in accordance with the Vesting Schedule set out in the Notice of Stock Option
Grant and with the provisions of Section 9 of the Plan as follows:

            (a)   RIGHT TO EXERCISE.

                  (i)   This Option may not be exercised for a fraction of a
share.

                  (ii)  In the event of Optionee's death, disability or other
termination of employment, the exercisability of the Option is governed by
Sections 5, 6 and 7 below, subject to the limitation contained in Section
2(a)(i).

                  (iii) In no event may this Option be exercised after the
Expiration Date of this Option as set forth in the Notice of Stock Option Grant.

            (b)   METHOD OF EXERCISE. This Option shall be exercisable by
execution and delivery of the Exercise Notice and Restricted Stock Purchase
Agreement attached hereto as Exhibit A (the "Exercise Agreement") or of any
other form of written notice approved for such purpose by the Company which
shall state the election to exercise the Option, the number of Shares in respect
of which the Option is being exercised, and such other representations and
agreements as to the holder's investment intent with respect to such shares of
Common Stock as may be required by the Company pursuant to the provisions of the
Plan. Such written notice shall be signed by Optionee and shall be delivered in
person or by certified mail to the Secretary of the Company. The written notice
shall be accompanied by payment of the Exercise Price. This Option shall be
deemed to be exercised upon receipt by the Company of such written notice
accompanied by the Exercise Price.
<PAGE>   4
      No Shares will be issued pursuant to the exercise of an Option unless such
issuance and such exercise shall comply with all relevant provisions of
applicable law and the requirements of any stock exchange upon which the Shares
may then be listed. Assuming such compliance, for income tax purposes the Shares
shall be considered transferred to Optionee on the date on which the Option is
exercised with respect to such Shares.

      3.    METHOD OF PAYMENT.  Payment of the Exercise Price shall be by any of
the following, or a combination thereof, at the election of Optionee:

            (a)   cash;

            (b)   check;

            (c)   surrender of other shares of Common Stock of the Company which
(i) in the case of Shares acquired pursuant to the exercise of a Company option,
have been owned by Optionee for more than six months on the date of surrender,
and (ii) have a Fair Market Value on the date of surrender equal to the Exercise
Price of the Shares as to which the Option is being exercised;

            (d)   if there is a public market for the Shares and they are
registered under the Exchange Act, delivery of a properly executed exercise
notice together with irrevocable instructions to a broker to deliver promptly to
the Company the amount of sale or loan proceeds required to pay the Exercise
Price; or

            (e)   a promissory note.

      4.    RESTRICTIONS ON EXERCISE. This Option may not be exercised until
such time as the Plan has been approved by the shareholders of the Company, or
if the issuance of such Shares upon such exercise or the method of payment of
consideration for such shares would constitute a violation of any applicable
federal or state securities or other law or regulation, including any rule under
Part 207 of Title 12 of the Code of Federal Regulations as promulgated by the
Federal Reserve Board. As a condition to the exercise of this Option, the
Company may require Optionee to make any representation and warranty to the
Company as may be required by any applicable law or regulation.

      5.    TERMINATION OF RELATIONSHIP. In the event of termination of
Optionee's Continuous Status as an Employee or Consultant, Optionee may, to the
extent otherwise so entitled at the date of such termination (the "Termination
Date"), exercise this Option during the Termination Period set forth in the
Notice of Stock Option Grant. To the extent that Optionee was not entitled to
exercise this Option at such Termination Date, or if Optionee does not exercise
this Option within the Termination Period, the Option shall terminate.

      6.    DISABILITY OF OPTIONEE.

            (a)   Notwithstanding the provisions of Section 5 above, in the
event of termination of Optionee's Continuous Status as an Employee or
Consultant as a result of


                                      -2-
<PAGE>   5
Optionee's total and permanent disability (as defined in Section 22(e)(3) of the
Code), Optionee may, but only within twelve months from the Termination Date
(but in no event later than the Expiration Date set forth in the Notice of Stock
Option Grant), exercise this Option to the extent Optionee was entitled to
exercise it as of such Termination Date. To the extent that Optionee was not
entitled to exercise the Option as of the Termination Date, or if Optionee does
not exercise such Option (to the extent so entitled) within the time specified
in this Section 6(a), the Option shall terminate.

            (b)   Notwithstanding the provisions of Section 5 above, in the
event of termination of Optionee's consulting relationship or Continuous Status
as an Employee as a result of disability not constituting a total and permanent
disability (as set forth in Section 22(e)(3) of the Code), Optionee may, but
only within six months from the Termination Date (but in no event later than the
Expiration Date set forth in the Notice of Stock Option Grant), exercise the
Option to the extent Optionee was entitled to exercise it as of such Termination
Date; provided, however, that if this is an Incentive Stock Option and Optionee
fails to exercise this Incentive Stock Option within three months from the
Termination Date, this Option will cease to qualify as an Incentive Stock Option
(as defined in Section 422 of the Code) and Optionee will be treated for federal
income tax purposes as having received ordinary income at the time of such
exercise in an amount generally measured by the difference between the Exercise
Price for the Shares and the Fair Market Value of the Shares on the date of
exercise. To the extent that Optionee was not entitled to exercise the Option at
the Termination Date, or if Optionee does not exercise such Option to the extent
so entitled within the time specified in this Section 6(b), the Option shall
terminate.

      7.    DEATH OF OPTIONEE. In the event of the death of Optionee (a) during
the Term of this Option and while an Employee or Consultant of the Company and
having been in Continuous Status as an Employee or Consultant since the date of
grant of the Option, or (b) within 30 days after Optionee's Termination Date,
the Option may be exercised at any time within six months following the date of
death (but in no event later than the Expiration Date set forth in the Notice of
Stock Option Grant), by Optionee's estate or by a person who acquired the right
to exercise the Option by bequest or inheritance, but only to the extent of the
right to exercise that had accrued at the Termination Date.

      8.    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 him or her. The terms
of this Option shall be binding upon the executors, administrators, heirs,
successors and assigns of Optionee.

      9.    TERM OF OPTION. This Option may be exercised only within the Term
set forth in the Notice of Stock Option Grant, subject to the limitations set
forth in Section 7 of the Plan.

      10.   TAX CONSEQUENCES. Set forth below is a brief summary as of the date
of this Option of certain of the federal and California tax consequences of
exercise of this Option and disposition of the Shares under the laws in effect
as of the Date of Grant. THIS SUMMARY IS NECESSARILY INCOMPLETE, AND THE TAX
LAWS AND REGULATIONS ARE


                                      -3-
<PAGE>   6
SUBJECT TO CHANGE. OPTIONEE SHOULD CONSULT A TAX ADVISER BEFORE EXERCISING THIS
OPTION OR DISPOSING OF THE SHARES.

            (a)   EXERCISE OF INCENTIVE STOCK OPTION. If this Option qualifies
as an Incentive Stock Option, there will be no regular federal or California
income tax liability upon the exercise of the Option, although the excess, if
any, of the Fair Market Value of the Shares on the date of exercise over the
Exercise Price will be treated as an adjustment to the alternative minimum tax
for federal tax purposes and may subject Optionee to the alternative minimum tax
in the year of exercise.

            (b)   EXERCISE OF NONSTATUTORY STOCK OPTION. If this Option does not
qualify as an Incentive Stock Option, there may be a regular federal income tax
liability and a California income tax liability upon the exercise of the Option.
Optionee will be treated as having received compensation income (taxable at
ordinary income tax rates) equal to the excess, if any, of the Fair Market Value
of the Shares on the date of exercise over the Exercise Price. If Optionee is an
employee, the Company will be required to withhold from Optionee's compensation
or collect from Optionee and pay to the applicable taxing authorities an amount
equal to a percentage of this compensation income at the time of exercise.

            (c)   DISPOSITION OF SHARES. In the case of a Nonstatutory Stock
Option, if Shares are held for at least one year, any gain realized on
disposition of the Shares will be treated as long-term capital gain for federal
and California income tax purposes. In the case of an Incentive Stock Option, if
Shares transferred pursuant to the Option are held for at least one year after
exercise and are disposed of at least two years after the Date of Grant, any
gain realized on disposition of the Shares will also be treated as long-term
capital gain for federal and California income tax purposes. In either case, the
long-term capital gain will be taxed for federal income tax and alternative
minimum tax purposes at a maximum rate of 28% if the Shares are held more than
one year but less than 18 months after exercise and at 20% if the Shares are
held more than 18 months after exercise. If Shares purchased under an Incentive
Stock Option are disposed of within one year after exercise or within two years
after the Date of Grant, any gain realized on such disposition will be treated
as compensation income (taxable at ordinary income rates) to the extent of the
difference between the Exercise Price and the lesser of (i) the Fair Market
Value of the Shares on the date of exercise, or (ii) the sale price of the
Shares.

            (d)   NOTICE OF DISQUALIFYING DISPOSITION OF INCENTIVE STOCK OPTION
SHARES. If the Option granted to Optionee herein is an Incentive Stock Option,
and if Optionee sells or otherwise disposes of any of the Shares acquired
pursuant to the Incentive Stock Option on or before the later of (i) the date
two years after the Date of Grant, or (ii) the date one year after the date of
exercise, Optionee shall immediately notify the Company in writing of such
disposition. Optionee acknowledges and agrees that he or she may be subject to
income tax withholding by the Company on the compensation income recognized by
Optionee from the early disposition by payment in cash or out of the current
earnings paid to Optionee.

      11.   WITHHOLDING TAX OBLIGATIONS. Optionee understands that, upon
exercising a Nonstatutory Stock Option, he or she will recognize income for tax
purposes in an amount equal


                                      -4-
<PAGE>   7
to the excess of the then Fair Market Value of the Shares over the Exercise
Price. However, the timing of this income recognition may be deferred for up to
six months if Optionee is subject to Section 16 of the Exchange Act. If Optionee
is an employee, the Company will be required to withhold from Optionee's
compensation, or collect from Optionee and pay to the applicable taxing
authorities an amount equal to a percentage of this compensation income.
Additionally, Optionee may at some point be required to satisfy tax withholding
obligations with respect to the disqualifying disposition of an Incentive Stock
Option. Optionee shall satisfy his or her tax withholding obligation arising
upon the exercise of this Option by one or some combination of the following
methods: (a) by cash payment, (b) out of Optionee's current compensation, (c) if
permitted by the Administrator, in its discretion, by surrendering to the
Company Shares which (i) in the case of Shares previously acquired from the
Company, have been owned by Optionee for more than six months on the date of
surrender, and (ii) have a Fair Market Value on the date of surrender equal to
or greater than Optionee's marginal tax rate times the ordinary income
recognized, or (d) by electing to have the Company withhold from the Shares to
be issued upon exercise of the Option that number of Shares having a Fair Market
Value equal to the amount required to be withheld. For this purpose, the Fair
Market Value of the Shares to be withheld shall be determined on the date that
the amount of tax to be withheld is to be determined (the "Tax Date").

      If Optionee is subject to Section 16 of the Exchange Act (an "Insider"),
any surrender of previously owned Shares to satisfy tax withholding obligations
arising upon exercise of this Option must comply with the applicable provisions
of Rule 16b-3 promulgated under the Exchange Act ("Rule 16b-3").

      All elections by Optionee to have Shares withheld to satisfy tax
withholding obligations shall be made in writing in a form acceptable to the
Administrator and shall be subject to the following restrictions:

            (a)   the election must be made on or prior to the applicable Tax
Date;

            (b)   once made, the election shall be irrevocable as to the
particular Shares of the Option as to which the election is made; and

            (c)   all elections shall be subject to the consent or disapproval
of the Administrator.

      12.   MARKET STANDOFF AGREEMENT. In connection with the initial public
offering of the Company's securities and upon request of the Company or the
underwriters managing such underwritten offering of the Company's securities,
Optionee agrees not to sell, make any short sale of, loan, grant any option for
the purchase of, or otherwise dispose of any securities of the Company (other
than those included in the registration) without the prior written consent of
the Company or such underwriters, as the case may be, for such period of time
(not to exceed 180 days) from the effective date of such registration as may be
requested by the Company or such managing underwriters and to execute an
agreement reflecting the foregoing as may be requested by the underwriters at
the time of the Company's initial public offering.


                                      -5-
<PAGE>   8
                            [Signature Page Follows]


                                      -6-
<PAGE>   9
      This Agreement may be executed in two or more counterparts, each of which
shall be deemed an original and all of which together shall constitute one
document.

                                    SYNAPTICS INCORPORATED


                                    By:
                                       ---------------------------------

                                       Francis Lee, President
                                    ------------------------------------
                                       (Print name and title)

      OPTIONEE ACKNOWLEDGES AND AGREES THAT THE VESTING OF SHARES PURSUANT TO
THE OPTION HEREOF IS EARNED ONLY BY CONTINUING EMPLOYMENT OR CONSULTANCY AT THE
WILL OF THE COMPANY (NOT THROUGH THE ACT OF BEING HIRED, BEING GRANTED THIS
OPTION OR ACQUIRING SHARES HEREUNDER). OPTIONEE FURTHER ACKNOWLEDGES AND AGREES
THAT NOTHING IN THIS AGREEMENT, NOR IN THE COMPANY'S STOCK OPTION PLAN WHICH IS
INCORPORATED HEREIN BY REFERENCE, SHALL CONFER UPON OPTIONEE ANY RIGHT WITH
RESPECT TO CONTINUATION OF EMPLOYMENT OR CONSULTANCY BY THE COMPANY, NOR SHALL
IT INTERFERE IN ANY WAY WITH OPTIONEE'S RIGHT OR THE COMPANY'S RIGHT TO
TERMINATE OPTIONEE'S EMPLOYMENT OR CONSULTANCY AT ANY TIME, WITH OR WITHOUT
CAUSE.

      Optionee acknowledges receipt of a copy of the Plan and represents that he
or she is familiar with the terms and provisions thereof, and hereby accepts
this Option subject to all of the terms and provisions thereof. Optionee has
reviewed the Plan and this Option in their entirety, has had an opportunity to
obtain the advice of counsel prior to executing this Option and fully
understands all provisions of the Option. Optionee hereby agrees to accept as
binding, conclusive and final all decisions or interpretations of the
Administrator upon any questions arising under the Plan or this Option.



Dated:
      ------------------------------            ------------------------------
                                                Federico Faggin


                                      -7-