LM4908 LM4908 10kV ESD Rated, Dual 120 mW Headphone Amplifier Literature Number: SNAS218B LM4908 10kV ESD Rated, Dual 120 mW Headphone Amplifier General Description The LM4908 is a dual audio power amplifier capable of delivering 120mW per channel of continuous average power into a 16 load with 0.1% (THD+N) from a 5V power supply. Boomer audio power amplifiers were designed specifically to provide high quality output power with a minimal amount of external components using surface mount packaging. Since the LM4908 does not require bootstrap capacitors or snubber networks, it is optimally suited for low-power portable systems. The unity-gain stable LM4908 can be configured by external gain-setting resistors. j Output power at 0.1% THD+N at 1kHz into 32 75mW (typ) Features n n n n n n Up to 10kV ESD protection on all pins MSOP, SOP, and LLP surface mount packaging Switch on/off click suppression Excellent power supply ripple rejection Unity-gain stable Minimum external components Applications Key Specifications j THD+N at 1kHz at 120mW continuous average output power into 16 n Headphone Amplifier n Personal Computers n Portable electronic devices 0.1% (typ) j THD+N at 1kHz at 75mW continuous average output power into 32 0.1% (typ) Typical Application 20075201 *Refer to the Application Information Section for information concerning proper selection of the input and output coupling capacitors. FIGURE 1. Typical Audio Amplifier Application Circuit Boomer (R) is a registered trademark of National Semiconductor Corporation. (c) 2004 National Semiconductor Corporation DS200752 www.national.com 10kV ESD Rated, Dual 120 mW Headphone Amplifier February 2004 LM4908 Connection Diagrams SOP (MA) and MSOP (MM) Package 20075202 Top View Order Number LM4908MA, LM4908MM See NS Package Number M08A, MUA08A LLP (LQ) Package 200752A2 Top View Order Number LM4908LQ See NS Package Number LQB08A www.national.com 2 JC (MSOP) 56C/W If Military/Aerospace specified devices are required, please contact the National Semiconductor Sales Office/ Distributors for availability and specifications. JA (MSOP) 210C/W JC (SOP) 35C/W JA (SOP) 170C/W JC (LLP) 15C/W Supply Voltage 6.0V Storage Temperature Input Voltage -65C to +150C JA (LLP) 117C/W (Note 9) -0.3V to VDD + 0.3V JA (LLP) 150C/W (Note 10) Power Dissipation (Note 4) Internally limited ESD Susceptibility (Note 5) 10.0kV ESD Susceptibility (Note 6) 500V Junction Temperature Operating Ratings Temperature Range 150C TMIN TA TMAX Soldering Information (Note 1) -40C T Small Outline Package Vapor Phase (60 seconds) 215C Infrared (15 seconds) 220C A 85C 2.0V VDD 5.5V Supply Voltage Note 1: See AN-450 "Surface Mounting and their Effects on Product Reliability" for other methods of soldering surface mount devices. Thermal Resistance Electrical Characteristics (Notes 2, 3) The following specifications apply for VDD = 5V unless otherwise specified, limits apply to TA = 25C. Symbol Parameter Conditions LM4908 Typ (Note 7) VDD Supply Voltage Limit (Note 8) Units (Limits) 2.0 V (min) 5.5 V (max) IDD Supply Current VIN = 0V, IO = 0A 1.6 3.0 mA (max) Ptot Total Power Dissipation VIN = 0V, IO = 0A 8 16.5 mW (max) VOS Input Offset Voltage VIN = 0V 5 50 mV (max) Ibias Input Bias Current VCM Common Mode Voltage GV Open-Loop Voltage Gain RL = 5k Io Max Output Current THD+N < 0.1 % RO Output Resistance VO Output Swing 10 pA 0 V 4.3 V 67 dB 70 mA 0.1 RL = 32, 0.1% THD+N, Min .3 RL = 32, 0.1% THD+N, Max 4.7 V PSRR Power Supply Rejection Ratio Cb = 1.0F, Vripple = 100mVPP, f = 40Hz 90 dB Crosstalk Channel Separation RL = 32, f = 1kHz 82 dB THD+N Total Harmonic Distortion + Noise f = 1 kHz RL = 16, VO =3.5VPP (at 0 dB) 0.05 % 66 dB RL = 32, VO =3.5VPP (at 0 dB) 0.05 % 66 dB SNR Signal-to-Noise Ratio VO = 3.5Vpp (at 0 dB) 100 dB fG Unity Gain Frequency Open Loop, RL = 5k 25 MHz Po Output Power THD+N = 0.1%, f = 1 kHz RL = 16 120 RL = 32 75 mW 60 mW THD+N = 10%, f = 1 kHz CI RL = 16 157 mW RL = 32 99 mW 3 pF Input Capacitance 3 www.national.com LM4908 Absolute Maximum Ratings (Note 3) LM4908 Electrical Characteristics (Notes 2, 3) (Continued) The following specifications apply for VDD = 5V unless otherwise specified, limits apply to TA = 25C. Symbol Parameter Conditions LM4908 Typ (Note 7) CL Load Capacitance SR Slew Rate Limit (Note 8) 200 Unity Gain Inverting 3 Units (Limits) pF V/s Electrical Characteristics (Notes 2, 3) The following specifications apply for VDD = 3.3V unless otherwise specified, limits apply to TA = 25C. Symbol Parameter Conditions Conditions Typ (Note 7) IDD Supply Current VIN = 0V, IO = 0A VOS Input Offset Voltage VIN = 0V Po Output Power THD+N = 0.1%, f = 1 kHz Limit (Note 8) Units (Limits) 1.4 mA (max) 5 mV (max) RL = 16 43 mW RL = 32 30 mW RL = 16 61 mW RL = 32 41 mW THD+N = 10%, f = 1 kHz Electrical Characteristics (Notes 2, 3) The following specifications apply for VDD = 2.6V unless otherwise specified, limits apply to TA = 25C. Symbol Parameter Conditions Conditions Typ (Note 7) IDD Supply Current VIN = 0V, IO = 0A VOS Input Offset Voltage VIN = 0V Po Output Power THD+N = 0.1%, f = 1 kHz Limit (Note 8) Units (Limits) 1.3 mA (max) 5 mV (max) RL = 16 20 mW RL = 32 16 mW RL = 16 34 mW RL = 32 24 mW THD+N = 10%, f = 1 kHz Note 2: All voltages are measured with respect to the ground pin, unless otherwise specified. Note 3: Absolute Maximum Ratings indicate limits beyond which damage to the device may occur. Operating Ratings indicate conditions for which the device is functional, but do not guarantee specific performance limits. Electrical Characteristics state DC and AC electrical specifications under particular test conditions which guarantee specific performance limits. This assumes that the device is within the Operating Ratings. Specifications are not guaranteed for parameters where no limit is given, however, the typical value is a good indication of device performance. Note 4: The maximum power dissipation must be derated at elevated temperatures and is dictated by TJMAX, JA, and the ambient temperature TA. The maximum allowable power dissipation is PDMAX = (TJMAX - TA) / JA. For the LM4908, TJMAX = 150C, and the typical junction-to-ambient thermal resistance, when board mounted, is 210C/W for package MUA08A and 170C/W for package M08A. Note 5: Human body model, 100pF discharged through a 1.5k resistor. Note 6: Machine Model, 220pF-240pF discharged through all pins. Note 7: Typicals are measured at 25C and represent the parametric norm. Note 8: Tested limits are guaranteed to National's AOQL (Average Outgoing Quality Level). Datasheet min/max specification limits are guaranteed by design, test, or statistical analysis. Note 9: The given JA is for an LM4908 packaged in an LQB08A with the Exposed-DAP soldered to a printed circuit board copper pad with an area equivalent to that of the Exposed-DAP itself. Note 10: The given JA is for an LM4908 packaged in an LQB08A with the Exposed-DAP not soldered to any printed circuit board copper. www.national.com 4 LM4908 External Components Description (Figure 1) Components Functional Description 1. Ri The inverting input resistance, along with Rf, set the closed-loop gain. Ri, along with Ci, form a high pass filter with fc = 1/(2RiCi). 2. Ci The input coupling capacitor blocks DC voltage at the amplifier's input terminals. Ci, along with Ri, create a highpass filter with fC = 1/(2RiCi). Refer to the section, Selecting Proper External Components, for an explanation of determining the value of Ci. 3. Rf The feedback resistance, along with Ri, set closed-loop gain. 4. CS This is the supply bypass capacitor. It provides power supply filtering. Refer to the Application Information section for proper placement and selection of the supply bypass capacitor. 5. CB This is the half-supply bypass pin capacitor. It provides half-supply filtering. Refer to the section, Selecting Proper External Components, for information concerning proper placement and selection of CB. 6. CO This is the output coupling capacitor. It blocks the DC voltage at the amplifier's output and forms a high pass filter with RL at fO = 1/(2RLCO) 7. RB This is the resistor which forms a voltage divider that provides 1/2 VDD to the non-inverting input of the amplifier. Typical Performance Characteristics THD+N vs Frequency VDD = 2.6V, PWR = 15mW, RL = 16 THD+N vs Frequency VDD = 2.6V, PWR = 15mW, RL = 8 20075267 20075268 5 www.national.com LM4908 Typical Performance Characteristics (Continued) THD+N vs Frequency VDD = 2.6V, PWR = 15mW, RL = 32 THD+N vs Frequency VDD = 3.3V, PWR = 25mW, RL = 8 20075269 20075270 THD+N vs Frequency VDD = 3.3V, PWR = 25mW, RL = 32 THD+N vs Frequency VDD = 3.3V, PWR = 25mW, RL = 16 20075271 20075272 THD+N vs Frequency VDD = 5V, PWR = 50mW, RL = 16 THD+N vs Frequency VDD = 5V, PWR = 50mW, RL = 8 20075273 www.national.com 20075274 6 LM4908 Typical Performance Characteristics (Continued) THD+N vs Frequency VDD = 5V, PWR = 50mW, RL = 32 THD+N vs Frequency VDD = 5V, VOUT = 3.5Vpp, RL = 5k 20075275 20075276 THD+N vs Output Power VDD = 2.6V, RL = 16, f = 1kHz THD+N vs Output Power VDD = 2.6V, RL = 8, f = 1kHz 20075277 20075278 THD+N vs Output Power VDD = 3.3V, RL = 8, f = 1kHz THD+N vs Output Power VDD = 2.6V, RL = 32, f = 1kHz 20075279 20075280 7 www.national.com LM4908 Typical Performance Characteristics (Continued) THD+N vs Output Power VDD = 3.3V, RL = 16, f = 1kHz THD+N vs Output Power VDD = 3.3V, RL = 32, f = 1kHz 20075281 20075282 THD+N vs Output Power VDD = 5V, RL = 16, f = 1kHz THD+N vs Output Power VDD = 5V, RL = 8, f = 1kHz 20075283 20075284 Output Power vs Load Resistance VDD = 2.6V, f = 1kHz THD+N vs Output Power VDD = 5V, RL = 32, f = 1kHz 20075286 20075285 www.national.com 8 LM4908 Typical Performance Characteristics (Continued) Output Power vs Load Resistance VDD = 3.3V, f = 1kHz Output Power vs Load Resistance VDD = 5V, f = 1kHz 20075287 20075288 Output Power vs Supply Voltage RL = 16, f = 1kHz Output Power vs Supply Voltage RL = 8, f = 1kHz 20075289 20075290 Clipping Voltage vs Supply Voltage Output Power vs Supply Voltage RL = 32, f = 1kHz 20075292 20075291 9 www.national.com LM4908 Typical Performance Characteristics (Continued) Power Dissipation vs Output Power Power Dissipation vs Output Power 20075229 20075230 Power Dissipation vs Output Power Crosstalk vs Frequency VDD = 5V, RL = 8 20075231 20075293 Output Noise vs Frequency VDD = 5V, RL = 32 Crosstalk vs Frequency VDD = 5V, RL = 32 20075294 20075295 www.national.com 10 (Continued) PSRR vs Frequency VDD = 5V, RL = 32, VRIPPLE = 100mVpp Inputs Terminated PSRR vs Frequency VDD = 5V, RL = 32, VRIPPLE = 100mVpp Pins 3 and 5 directly driven, Inputs Floating 20075297 20075296 Open Loop Frequency Response VDD = 5V, RL = 32 Open Loop Frequency Response VDD = 5V, RL = 8 20075298 20075299 Supply Current vs Supply Voltage (no Load) Open Loop Frequency Response VDD = 5V, RL = 5k 200752A0 200752A1 11 www.national.com LM4908 Typical Performance Characteristics LM4908 Typical Performance Characteristics (Continued) Frequency Response vs Output Capacitor Size Frequency Response vs Output Capacitor Size 20075245 20075246 Frequency Response vs Output Capacitor Size Typical Application Frequency Response 20075247 20075248 Typical Application Frequency Response 20075249 www.national.com 12 As with any power amplifier, proper supply bypassing is critical for low noise performance and high power supply rejection. Applications that employ a 5V regulator typically use a 10F in parallel with a 0.1F filter capacitors to stabilize the regulator's output, reduce noise on the supply line, and improve the supply's transient response. However, their presence does not eliminate the need for a local 0.1F supply bypass capacitor, CS, connected between the LM4908's supply pins and ground. Keep the length of leads and traces that connect capacitors between the LM4908's power supply pin and ground as short as possible. Connecting a 1.0F capacitor, CB, between the IN A(+) / IN B(+) node and ground improves the internal bias voltage's stability and improves the amplifier's PSRR. The PSRR improvements increase as the bypass pin capacitor value increases. Too large, however, increases the amplifier's turn-on time. The selection of bypass capacitor values, especially CB, depends on desired PSRR requirements, click and pop performance (as explained in the section, Selecting Proper External Components), system cost, and size constraints. EXPOSED-DAP PACKAGE PCB MOUNTING CONSIDERATION The LM4908's exposed-dap (die attach paddle) package (LQ) provides a low thermal resistance between the die and the PCB to which the part is mounted and soldered. This allows rapid heat transfer from the die to the surrounding PCB copper traces, ground plane, and surrounding air. The LQ package should have its DAP soldered to a copper pad on the PCB. The DAP's PCB copper pad may be connected to a large plane of continuous unbroken copper. This plane forms a thermal mass, heat sink, and radiation area. However, since the LM4908 is designed for headphone applications, connecting a copper plane to the DAP's PCB copper pad is not required. The LM4908's Power Dissipation vs Output Power Curve in the Typical Performance Characteristics shows that the maximum power dissipated is just 45mW per amplifier with a 5V power supply and a 32 load. Further detailed and specific information concerning PCB layout, fabrication, and mounting an LQ (LLP) package is available from National Semiconductor's Package Engineering Group under application note AN1187. SELECTING PROPER EXTERNAL COMPONENTS Optimizing the LM4908's performance requires properly selecting external components. Though the LM4908 operates well when using external components with wide tolerances, best performance is achieved by optimizing component values. The LM4908 is unity-gain stable, giving a designer maximum design flexibility. The gain should be set to no more than a given application requires. This allows the amplifier to achieve minimum THD+N and maximum signal-to-noise ratio. These parameters are compromised as the closed-loop gain increases. However, low gain demands input signals with greater voltage swings to achieve maximum output power. Fortunately, many signal sources such as audio CODECs have outputs of 1VRMS (2.83VP-P). Please refer to the Audio Power Amplifier Design section for more information on selecting the proper gain. POWER DISSIPATION Power dissipation is a major concern when using any power amplifier and must be thoroughly understood to ensure a successful design. Equation 1 states the maximum power dissipation point for a single-ended amplifier operating at a given supply voltage and driving a specified output load. PDMAX = (VDD) 2 / (22RL) (1) Since the LM4908 has two operational amplifiers in one package, the maximum internal power dissipation point is twice that of the number which results from Equation 1. Even with the large internal power dissipation, the LM4908 does not require heat sinking over a large range of ambient temperature. From Equation 1, assuming a 5V power supply and a 32 load, the maximum power dissipation point is 40mW per amplifier. Thus the maximum package dissipation point is 80mW. The maximum power dissipation point obtained must not be greater than the power dissipation that results from Equation 2: PDMAX = (TJMAX - TA) / JA Input and Output Capacitor Value Selection Amplifying the lowest audio frequencies requires high value input and output coupling capacitors (CI and CO in Figure 1). A high value capacitor can be expensive and may compromise space efficiency in portable designs. In many cases, however, the speakers used in portable systems, whether internal or external, have little ability to reproduce signals below 150Hz. Applications using speakers with this limited frequency response reap little improvement by using high value input and output capacitors. Besides affecting system cost and size, Ci has an effect on the LM4908's click and pop performance. The magnitude of the pop is directly proportional to the input capacitor's size. Thus, pops can be minimized by selecting an input capacitor value that is no higher than necessary to meet the desired -3dB frequency. As shown in Figure 1, the input resistor, RI and the input capacitor, CI, produce a -3dB high pass filter cutoff frequency that is found using Equation (3). In addition, the output load RL, and the output capacitor CO, produce a -3db high pass filter cutoff frequency defined by Equation (4). (2) For package MUA08A, JA = 210C/W. TJMAX = 150C for the LM4908. Depending on the ambient temperature, TA, of the system surroundings, Equation 2 can be used to find the maximum internal power dissipation supported by the IC packaging. If the result of Equation 1 is greater than that of Equation 2, then either the supply voltage must be decreased, the load impedance increased or TA reduced. For the typical application of a 5V power supply, with a 32 load, the maximum ambient temperature possible without violating the maximum junction temperature is approximately 133.2C provided that device operation is around the maximum power dissipation point. Power dissipation is a function of output power and thus, if typical operation is not around the maximum power dissipation point, the ambient temperature may be increased accordingly. Refer to the Typical Performance Characteristics curves for power dissipation information for lower output powers. 13 fI-3db=1/2RICI (3) fO-3db=1/2RLCO (4) www.national.com LM4908 POWER SUPPLY BYPASSING Application Information LM4908 Application Information package. Once the power dissipation equations have been addressed, the required gain can be determined from Equation (7). (Continued) Also, careful consideration must be taken in selecting a certain type of capacitor to be used in the system. Different types of capacitors (tantalum, electrolytic, ceramic) have unique performance characteristics and may affect overall system performance. (7) Thus, a minimum gain of 1.497 allows the LM4908 to reach full output swing and maintain low noise and THD+N perfromance. For this example, let AV = 1.5. The amplifiers overall gain is set using the input (Ri ) and feedback (Rf ) resistors. With the desired input impedance set at 20k, the feedback resistor is found using Equation (8). Bypass Capacitor Value Besides minimizing the input capacitor size, careful consideration should be paid to the value of the bypass capacitor, CB. Since CB determines how fast the LM4908 settles to quiescent operation, its value is critical when minimizing turn-on pops. The slower the LM4908's outputs ramp to their quiescent DC voltage (nominally 1/2 VDD), the smaller the turn-on pop. Choosing CB equal to 1.0F or larger, will minimize turn-on pops. As discussed above, choosing Ci no larger than necessary for the desired bandwith helps minimize clicks and pops. AV = Rf/Ri (8) The value of Rf is 30k. AUDIO POWER AMPLIFIER DESIGN The last step in this design is setting the amplifier's -3db frequency bandwidth. To achieve the desired 0.25dB pass band magnitude variation limit, the low frequency response must extend to at lease one-fifth the lower bandwidth limit and the high frequency response must extend to at least five times the upper bandwidth limit. The gain variation for both response limits is 0.17dB, well within the 0.25dB desired limit. The results are an Design a Dual 70mW/32 Audio Amplifier Given: Power Output 70mW Load Impedance Input Level 32 1Vrms (max) Input Impedance 20k Bandwidth 100Hz-20kHz 0.50dB The design begins by specifying the minimum supply voltage necessary to obtain the specified output power. One way to find the minimum supply voltage is to use the Output Power vs Supply Voltage curve in the Typical Performance Characteristics section. Another way, using Equation (5), is to calculate the peak output voltage necessary to achieve the desired output power for a given load impedance. To account for the amplifier's dropout voltage, two additional voltages, based on the Dropout Voltage vs Supply Voltage in the Typical Performance Characteristics curves, must be added to the result obtained by Equation (5). For a singleended application, the result is Equation (6). fH = 20kHz*5 = 100kHz (10) As stated in the External Components section, both Ri in conjunction with Ci, and Co with RL, create first order highpass filters. Thus to obtain the desired low frequency response of 100Hz within 0.5dB, both poles must be taken into consideration. The combination of two single order filters at the same frequency forms a second order response. This results in a signal which is down 0.34dB at five times away from the single order filter -3dB point. Thus, a frequency of 20Hz is used in the following equations to ensure that the response is better than 0.5dB down at 100Hz. (6) Ci 1 / (2 * 20 k * 20 Hz) = 0.397F; use 0.39F. The Output Power vs Supply Voltage graph for a 32 load indicates a minimum supply voltage of 4.8V. This is easily met by the commonly used 5V supply voltage. The additional voltage creates the benefit of headroom, allowing the LM4908 to produce peak output power in excess of 70mW without clipping or other audible distortion. The choice of supply voltage must also not create a situation that violates maximum power dissipation as explained above in the Power Dissipation section. Remember that the maximum power dissipation point from Equation (1) must be multiplied by two since there are two independent amplifiers inside the www.national.com (9) and a (5) VDD (2VOPEAK + (VODTOP + VODBOT)) fL = 100Hz/5 = 20Hz Co 1 / (2 * 32 * 20 Hz) = 249F; use 330F. The high frequency pole is determined by the product of the desired high frequency pole, fH, and the closed-loop gain, AV. With a closed-loop gain of 1.5 and fH = 100kHz, the resulting GBWP = 150kHz which is much smaller than the LM4908's GBWP of 3MHz. This figure displays that if a designer has a need to design an amplifier with a higher gain, the LM4908 can still be used without running into bandwidth limitations. 14 LM4908 Demonstration Board Layout 20075264 Recommended MSOP Board Layout: Top Overlay 20075265 Recommended MSOP Board Layout: Top Layer 20075266 Recommended MSOP Board Layout: Bottom Layer 15 www.national.com LM4908 Demonstration Board Layout (Continued) 200752B1 Recommended LQ Board Layout: Top Overlay 200752B0 Recommended LQ Board Layout: Top Layer 200752A9 Recommended LQ Board Layout: Bottom Layer www.national.com 16 LM4908 Demonstration Board Layout (Continued) 200752B4 Recommended MA Board Layout: Top Overlay 200752B3 Recommended MA Board Layout: Top Layer 200752B2 Recommended MA Board Layout: Bottom Layer 17 www.national.com LM4908 LM4908 MDC MWC Dual 120MW Headphone Amplifier 20075263 Die Layout (A - Step) DIE/WAFER CHARACTERISTICS Fabrication Attributes General Die Information Physical Die Identification LM4908A Bond Pad Opening Size (min) 70m x 70m Die Step A Bond Pad Metalization ALUMINUM Passivation NITRIDE Wafer Diameter 150mm Back Side Metal BARE BACK Dise Size (Drawn) 889m x 622m 35.0mils x 24.5mils Back Side Connection Floating Thickness 216m Nominal Min Pitch 216m Nominal Physical Attributes Special Assembly Requirements: Note: Actual die size is rounded to the nearest micron. Die Bond Pad Coordinate Locations (A - Step) (Referenced to die center, coordinates in m) NC = No Connection, N.U. = Not Used SIGNAL NAME INPUT B+ PAD# NUMBER 1 X/Y COORDINATES PAD SIZE X Y X -367 232 70 x 70 Y INPUT B- 2 -367 15 70 x 70 OUTPUT B 3 -367 -232 70 x 70 VDD 4 35 -232 155 x 70 OUTPUT A 5 367 -232 70 x 70 INPUT A- 6 367 15 70 x 70 INPUT A+ 7 367 232 70 x 70 GND 8 68 232 155 x 70 www.national.com 18 LM4908 LM4908 MDC MWC Dual 120MW Headphone Amplifier (Continued) IN U.S.A Tel #: 1 877 Dial Die 1 877 342 5343 Fax: 1 207 541 6140 IN EUROPE Tel: 49 (0) 8141 351492 / 1495 Fax: 49 (0) 8141 351470 IN ASIA PACIFIC Tel: (852) 27371701 IN JAPAN Tel: 81 043 299 2308 19 www.national.com LM4908 Physical Dimensions inches (millimeters) unless otherwise noted Order Number LM4908LQ NS Package Number LQB08A Order Number LM4908MA NS Package Number M08A www.national.com 20 10kV ESD Rated, Dual 120 mW Headphone Amplifier Physical Dimensions inches (millimeters) unless otherwise noted (Continued) Order Number LM4908MM NS Package Number MUA08A LIFE SUPPORT POLICY NATIONAL'S PRODUCTS ARE NOT AUTHORIZED FOR USE AS CRITICAL COMPONENTS IN LIFE SUPPORT DEVICES OR SYSTEMS WITHOUT THE EXPRESS WRITTEN APPROVAL OF THE PRESIDENT AND GENERAL COUNSEL OF NATIONAL SEMICONDUCTOR CORPORATION. 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