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1.5A 280kHz BOOST REGULATOR Power Management GM3255 products


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GM3255
1.5A 280kHz BOOST REGULATOR
Power Management
GM3255 products switching regulators with high efficiency, integrated switch. These parts operate over wide input voltage range, from flexibility design allows chips operate most power supply configurations, including boost, flyback, forward, inverting, SEPIC. utilize current mode architecture, which allows excellent load line regulation, well practical means limiting current. Combining high frequency operation with highly integrated regulator circuit results extremely compact power supply solution. circuit design includes provisions features such frequency synchronization, shutdown, feedback controls either positive negative voltage regulation.
Features
Integrated Power Switch: Guaranteed Wide Input Range: High Frequency Allows Small Components Minimum External Components Easy External Synchronization Built Overcurrent Protection Frequency Foldback Reduces Component Stress During Overcurrent Condition Thermal Shutdown with Hysteresis Regulates Either Positive Negative Output Voltages Shut Down Current: Maximum Wide Temperature Range Commercial Grade 70°C
Application
Boost Regulators CCFL Backlight Driver
Multiple Output Flyback Supplies Inverting Supplies Bias Supplies
Laptop Computer Supplies
TYPICAL APPLICATION CIRCUITS
3.72K
GM3255
PGND 22µH 22µF
MBRS120T3
VOUT
0.01µF 3.3V
Test AGND
22µF
1.28k
www.gammamicro.com
PRELIMINARY
GM3255
Revision Jun. 2004
GM3255 MARKING INFORMATION CONFIGURATIONS (TOP VIEW)
SOP-8 (SO-8)
PGND AGND
GM3255 AYWW
Test
Assembly Location Year Work Week
Ordering Number
GM3255S8T GM3255S8R
Package
Shipping
Units Tube 2,500 Units Tape Reel
detail Ordering Number identification, please last page.
DESCRIPTION
NUMBER
SYMBOL
FUNCTION
Loop compensation pin. output error amplifier used loop compensation, current limit start. Loop compensation implemented simple network shown application diagram page Positive regulator feedback pin. This senses positive output voltage referenced 1.276V. When voltage this falls below chip switching frequency reduces nominal frequency. These pins connected internal test logic should either left floating tied ground. Connection voltage between 9.5V shuts down internal oscillator leaves power switch running. Synchronization shutdown pin. This used synchronize part nearly twice base frequency. shut part down into current mode. synchronization used, this should either tied high left floating normal operation. Input power supply pin. This supplies power part should have bypass capacitor connected AGND. Analog ground. This provides clean ground controller circuitry should path large currents. output voltage sensing resistors should connected substrate. Power ground. This ground connection emitter power switching transistor. Connection good ground plane essential. High current switch pin. This connects internally collector power switch. open voltage across power switch high 40V. minimize radiation, trace short practical.
Test
AGND
PGND
ABSOLUTE MAXIMUM RATINGS
PARAMETER VALUE
+150 +150
UNITS
GM3255
Package Thermal Resistance Junction-to-Case, RqJC junction-to-Ambient, RqJC Junction Temperature Range, Storage Temperature Range, TSTG Lead Temperature (Peak) (reflow soldering sec. maximum above 183°C) ESD, Human Body Model
maximum package power dissipation must observed.
GM3255 MAXIMUM RATINGS:
NAME
Power Input Shutdown Sync Loop Compensation Voltage Feedback Input Test Power Ground Analog Ground Switch Input
SYMBOL
Test PGND AGND
VMAX
VMIN
-0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3
ISOURCE
ISINK
BLOCK DIAGRAM
Shutdown Delay Timer Sync 2.0V Regulator
Thermal Shutdown Oscillator Frequency Shift Slope Compensation Latch Driver Switch
63mW Ramp Summer
Test Comparator PGND
Detector 1.276 Positive Error
AGND
GM3255
GM3255
ELECTRICAL CHARACTERISTICS
(2.7 Industrial Grade: 70°C; Commercial Grade: 125°C; unless otherwise noted)
CHARACTERISTICS
Error Amplifier Section
Reference Voltage Input Current Reference Voltage Line Regulation Error Transconductance Error Gain Negative Error Gain Source Current Sink Current High Clamp Voltage Clamp Voltage Threshold
TEST CONDITIONS
UNIT
tied measure VREF (Note (Note 1.0V, =1.25V 1.5V, 1.25V 1.0V; sources 25µA 1.5V, sinks 25µA Reduce from 1.5V until switching stops
1.246 -1.0 0.25 0.75
1.276 0.01 0.50 1.05
1.300 0.03 1500 0.65 1.30
µMho
Oscillator Section
Base Operating Frequency Reduced Operating Frequency Maximum Duty Cycle Frequency Shift Threshold
1.0V Frequency drops reduced operating frequency
0.36
0.40
0.44
Sync/ Shutdown Section
Sync Range Sync Pulse Transition Threshold Bias Current Shutdown Threshold Shutdown Delay
Rise time 20ns 3.0V
-3.0 0.85
GM3255
(Note maximum package power dissipation must observed. (Note Guaranteed design, 100% tested production.
GM3255
ELECTRICAL CHARACTERISTICS
(2.7 Industrial Grade: 70°C; Commercial Grade: 125°C; unless otherwise noted)
CHARACTERISTICS
Power Switch Section
TEST CONDITIONS
UNIT
ISWITCH 1.5A, (Note Switch Saturation Voltage ISWITCH 1.0A, 85°C
1.0A
0.55 0.75 0.09
1.00 1.30 0.45
ISWITCH=1.0A, -40°C 0°C(Note ISWITCH 10mA Switch Current Limit Minimum Pulse Width duty cycle(Note duty cycle(Note =4.0A(Note DVSW 12V, 10mA
30V, 10mA 1.0A 12V, 10mA 1.5A (Note 30V, 10mA 1.5A (Note
Switch Leakage General Section Operating Current Shutdown Mode Current Minimum Operation Input Voltage Thermal Shutdown Thermal Hysteresis
0.8V, 2.7V 0.8V,
2.45
2.70
switching, maximum 10mA (Note2) (Note2)
(Note Guaranteed design, 100% tested production.
GM3255
GM3255
TYPICAL PERFORMANCE CHARACTERISTICS
Current (mA)
Temperature (°C) 2.7V
Temperature (°C)
Figure Switching) Temperature
2.50
fosc (kHz) Current
Figure Minimum Input Voltage Temperature
2.60
2.40
2.7V
2.30
Temperature (°C)
2.20
Temperature (°C)
Figure Switching Frequency Temperature (GM3255 only)
Figure Current Limit Temperature
Duty Cycle
22.7V
GM3255
Temperature (°C)
Figure Maximum Duty Cycle Temperature
GM3255
APPLICATION INFORMATION
Current Mode Control
Oscillator
Shown Figure power switch turned output Comparator.
Power Switch
Comparator
SUMMER Slope Compensation
RLOAD
Driver
TTL-compatible sync input capable syncing times base oscillator frequency. shown Figure order sync higher frequency, positive transition turns power switch before output oscillator goes high, thereby resetting oscillator. sync operation allows multiple power supplies operate same frequency. sustained logic will shut down reduce supply current. additional feature includes frequency shift nominal frequency when either pins trigger threshold. During power overload, short circuit conditions, minimum switch on-time limited comparator minimum pulse width. Extra switch off-time reduces minimum duty cycle protect external components itself. Previously mentioned, this block also produces ramp slope compensation improve regulator stability. Error Amplifier
Figure Current Mode Control Scheme
GM3255 family incorporates current mode control scheme, which ramp signal derived from power switch current. This ramp signal compared output error amplifier control on-time power switch. oscillator used fixed-frequency clock ensure constant operational frequency. resulting control scheme features several advantages over conventional voltage mode control. First, derived directly from inductor, ramp signal responds immediately line voltage changes. This eliminates delay caused output filter error amplifier, which commonly found voltage mode controllers. second benefit comes from inherent pulse-by pulse current limiting merely clamping peak switching current. Finally, since current mode commands output current rather than voltage, filter offers only single pole feedback loop. This allows both simpler compensation higher gain-bandwidth over comparable voltage mode circuit. Without discrediting apparent merits, current mode control comes with peculiar problems, mainly, subharmonic oscillation duty cycles over 50%. GM3255 family solves this problem adopting slope compensation scheme which fixed ramp generated oscillator added current ramp. proper slope rate provided improve circuit stability without sacrificing advantages current mode control. Oscillator Shutdown
1.276 CM3255 120pF
Voltage Clamp
0.01µF
positive error-amp
Figure Error Amplifier Equivalent Circuit
Sync Current Ramp
Figure Timing Diagram sync shutdown
oscillator trimmed guarantee frequency accuracy. output oscillator turns power switch frequency 280kHz,
external shunt connected between ground reduce clamp voltage.
GM3255
directly connected inverting input positive error amplifier, whose nonincerting input 1.276V reference. amplifier transconductance amplifier with high output impedance approximately 1MW, shown Figure connected output error amplifiers internally clamped between 0.5V 1.7V typical connection includes capacitor series with resistor ground, forming pole zero loop compensation.
GM3255
Consequently, current limit internal power transistor current reduced from nominal value.
Switch Driver Power Switch
switch driver receives control signal from logic section drive output power switch. switch grounded through emitter resistors (63mW total) PGND pin. PGND connected substrate that switching noise isolated from analog ground. peak switching current clamped internal circuit. clamp current guaranteed greater than 1.5A varies with duty cycle slope compensation. power switch withstand maximum voltage collector(VSW pin). saturation voltage switch typically less than minimize power dissipation. Short Circuit Condition When short circuit condition happens boost circuit, inductor current will increase during whole switching cycle, causing excessive current drawn from input power supply. Since control don's have means limit load current, external current limit circuit(such fuse relay) implemented protect load, power supply ICs. other topologies, frequency shift built into prevents damage chip external components. This feature reduces minimum duty cycle allows transformer secondary absorb excess energy before switch turns back GM3255 activated either connecting voltage source enabling pin. When voltage below minimum supply voltage, high impedance. Therefore, current conduces directly from input power source output through inductor diode. Once reaches approximately 1.5V, internal power switch briefly turns This part GM3255's normal operation. turn-on power switch accounts initial current swing. When voltage rises above threshold, internal power switch starts switch voltage pulse seen pin. Detecting output voltage pin, built-in frequency shift feature reduces switching frequency fraction nominal value, reducing minimum duty cycle, which otherwise limited minimum on-time switch. peak current during this phase clamped internal current limit.
When voltage rises above 0.4V, frequency increases nominal value, peak current begins decrease output approaches regulation voltage. overshoot output voltage prevented active pull-on, which sink current error amplifier increased once overvoltage condition detected. overvoltage condition defined when voltage 50mV greater than reference voltage. COMPONENT SELECTION Frequency Compensation goal frequency compensation achieve desirable transient response regulation while ensuring stability system. typical compensation network, shown Figure provides frequency response poles zero. This frequency response further illustrated Bode plot shown Figure
GM3255
Figure Typical Compensation Network
high gain Figure desirable achieving accuracy over ling load variations. gain transconductance error amplifier calculated follows:
GainDC
Where: error amplifier transconductance; error amplifier output resistance frequency pole, fp1, determined error amplifier output resistance
2pC1R
GM3255
first zero generated
2pC1R1
GM3255
phase lead provided this zero ensures that loop least 45°C phase margin crossover frequency. Therefore, this zero should placed close pole generated power stage which identified frequency:
where:
2pCORLOAD
equivalent output capacitance error amplifier 120pF; RLOAD load resistance. high frequency pole, fP2, placed output filter's zero half switching frequency. Placing pole this frequency will down switching noise. frequency this pole determined value
2pC1R1
When power switch turns off, there exists voltage spike superimposed steady-state voltage. Usually this voltage spike caused transformer leakage inductance charging stray capacitance between PGND pins. precent voltage from exceeding maximum rating, transient voltage suppressor series with diode paralleled with primary windings. Another method clamping switch voltage connect transient voltage suppressor between ground. Magnetic Component Selection When choosing magnetic component, must consider factors such peak current, core ferrite material, output voltage ripple, EMI, temperature range, physical size cost. boost circuits, average inductor current product output current voltage gain (VOUT VCC), assuming 100% energy transfer efficiency. continuous conduction mode, inductor ripple current
IRIPPLE VCC(VOUT VCC) )(VOUT)
simple method ensure adequate phase margin design frequency response with decade slope, until unity-gain crossover. crossover frequency should selected midpoint between where phase margin maximized.
Gain (dB) Gain
Frequency(LOG)
Figure Bode Plot Compensation Network Shown Figure
Voltage Limit boost topology, maximum voltage maximum output voltage plus output diode forward voltage. diode forward voltage typically 0.5V Schottky diodes 0.8V ultrafast diodes
VSW(MAX) VOUT(MAX)
where: 280kHz. peak inductor current equal average current plus half ripple current, which should cause inductor saturation. above equation also referenced when selecting value inductor based tolerance ripple current circuits. Small ripple current provides benefits small input capacitors greater output current capability. core geometry like barrel prone generating high magnetic field radiation, relatively cheap small. Other core geometries, such toroids, provide closed magnetic loop prevent EMI. Input Capacitor Selection boost circuits, inductor becomes part input filter, shown Figure continuous mode, input current waveform triangular does contain large pulsed current, During continuous conduction mode, peak peak inductor ripple current given previous section. most applications, input capacitors range 10µF 100µF with less than 0.3W work well full 1.5A switch current.
Where:
output diode forward voltage. flyback topology, peak voltage governed VSW(MAX) VCC(MAX) (VOUT
Where:
transformer turns ratio, primary over secondary
GM3255
GM3255
Reducing Current Limit some applications, designer prefer lower limit switch current than 1.5A. external shunt connected between ground reduce clamp voltage. Consequently, current limit internal power transistor current reduced from nominal value. voltage evaluated with equation
ISWREAV
RESR
Figure Boost Circuit Effective Input Filter
situation different flyback circuit. input current discontinuous significant pulse current input capacitors. Therefore, there requirements capacitors flyback regulator: energy storage filtering. maintain stable voltage supply chip, storage capacitor larger than 20µF with required. reduce noise generated inductor, insert 1.0µF ceramic capacitor between ground close simple diode clamp, shown Figure12, clamps possible chip. voltage diode drop above voltage reWhen power switch turned shunted sistor Unfortunately, such simple circuit generally acceptable loosely regulated. ground IOUT discharges output capacitor. When ripple small enough, treated constant equal input current IIN, Summing output voltage peak-peak ripple calculated
(IIN IOUT) VOUT(RIPPLE) (COUT)(f) IOUTD (COUT)(f)
where: 0.063W, value internal emitter resistor; gain current sense amplifier. Since cannot changed user, only available method limiting switch current below 1.5A clamp lower voltage. maximum switch inductor current substituted into equation above, desired clamp voltage will result.
equation expressed more conveniently terms VCC, VOUT IOUT design purposes follows:
VOUT(RIPPLE) IOUT(VOUT VCC) (COUT)(f) (COUT)(f)
(IOUT)(VOUT)(ESR)
Figure Current Limiting using Diode Clamp
capacitor ripple current
GM3255
IRIPPLE (IIN IOUT) (IOUT) IOUT VOUT
Although above equations apply only boost circuits, similar equations derived flyback circuits.
GM3255
Another solution current limiting problem externally measure current through switch using sense resistor. Such circuit illustrated Figure
some cases, rear ugly head despite presence onboard slope compensation. simple cure this problem more slope compensation avoid unwanted oscillation. that case, external circuit, shown Figure added increase amount slope compensation used. This circuit requires only components "tacked compensation network.
PGND AGND
RSENSE Output Ground
Figure 13.Current Limiting using Current Sense Resistor
switch current limited
VBE(Q1) ISWITCH(PEAK)
ESENSE
Where: VBE(Q1) base emitter voltage drop typically 0.65V. improved circuit does require require regulated voltage operate properly. Unfortunately, price must paid this convenience overall efficiency circuit. designer should note that input output grounds longer common. Also, addition current sense resistor, RSENSE, results considerable power loss which increase with duty cycle. Resistor capacitor form pass filter remove noise. Subharmonic Oscillation Subharmonic oscillation (SHM) problem found Current-mode control systems, where instability results when duty cycle exceeds 50%. only occurs switching regulators with continuous inductor current. This instability harmful converter usually does affect output voltage regulation. will increase radiated noise from converter cause, under certain circumstances, inductor emit high frequency audile noise. easily remedied problem. rising slope inductor current supplemented with internal "slope compensation" prevent duty cycle instability from carrying through next switching cycle. GM3255, slope compensation added during entire switch on-time, typically amount mA/µs.
Figure Technique Increasing Slope Compensation
dashed contains normal compensation circuitry limit bandwidth error amplifier. Resistors form voltage divider pin. normal operation looks similar square wave, dependent converter topology. Formulas calculating boost flyback topologies given section "VSW Voltage Limit." voltage charges capacitor when switch off, causing voltage shift upwards. When switch turns discharges through producing negative slope pin. negative slope provides slope compensation. amount slope compensation added this circuit
R3C3fSW
GM3255
GM3255
Where:
amount slope compensation added (A/s); voltage switch node when transistor turned (V); switching frequency, typically 280kHz (GM3255) 560kHz duty cycle; 0.063W, value internal emitter resistor; 5V/V, gain current sense amplifier.
Resistor capacitors form compensation network. turn voltage starts come charging capacitor through Schottky diode clamping voltage such that switching begins when reaches threshold, typically 1.05V (refer graphs detail over temperature). VF(D2) Therefore, slows startup circuit limiting voltage pin. soft- start time increases with size Diode discharges when low. shutdown function used with this part, cathode should connected VIN. Calculating Junction Temperature ensure safe operation GM3255, designer must calculate on-chip power dissipation determine expected junction temperature. Internal thermal protection circuitry will turn part once junction temperature exceeds 180°C 30°C. However, repeated operation such high temperatures will ensure reduced operating life. Calculation junction temperature imprecise simple task. First, power losses must quantified. There three major sources power loss GM3255: Biasing internal control circuitry, PBIAS Switch driver, PDRIVER Switch saturation, PSAT internal control circuitry, including oscillator linear regulator, requires small amount power even when switch turned off. specifications section this datasheet reveals that typical operating current this circuitry Additional guidance found graph operating current temperature. This graph shows that strongly dependent input voltage, VIN, temperature. Then PBIAS VINIQ Since onboard switch transistor, base drive current must factored well. This current drawn from pin, addition control circuitry current. base drive current listed specifications DICC/DISW, switch transconductance. before designer will find additional guidance graphs. With that information, designer calculate PDRIVER VINISW DISW
selecting appropriate values slope compensation network, designer advised choose convenient capacitor, then select values such that amount slope compensation added 100mA /µs. Then increased decreased necessary. course, series combination should large enough avoid drawing excessive current from VSW. Additionally, ensure that control loop stability improved, time constant formed additional components should chosen such that
Finally, worth mentioning that added slope compensation trade-off between duty cycle stability transient response. more slope compensation designer adds, slower transient response will external circuitry interfering with proper operation error amplifier. Soft Start Through addition external circuit, soft-start function added GM3255 components. Soft-start circuitry prevents from slamming high during startup, thereby inhibiting inductor current from rising high slope. This circuit, shown Figure requires minimum number components allows soft-start circuitry activate time used restart converter.
Test
GM3255
Test
Figure Soft Start
GM3255
approaches 150°C, designer should conWhere current through switch; sider possible means reducing junction temperature. Perhaps another converter topology could duty cycle percentage switch on-time. dependent type converter. selected reduce switch current. Increasing airflow across surface chip might consida boost convert, ered reduce
ISW(AVG) ILOAD Efficiency VOUT -VIN VOUT
flyback converter,
ISW(AVG) VOUTILOAD Efficiency VOUT VOUT
Output Setting GM3255 develops 1.276 reference (VREF) from ground. Output voltage connecting output resistor divider (Figure 16). bias current represents small error usually ignored values suggested value 6.19k.
VOUT VREF Figure Output Resistor Divider VOUT VREF
switch saturation voltage, V(CE)SAT, last major source on-chip power loss. V(CE)SAT collector-emitter voltage internal transistor when driven into saturation base drive current. value V(CE)SAT obtained from specifications from graphs, "Switch Saturation Voltage." Thus,
PSAT V(CE)SATISW
1.276
Finally, total on-chip power losses
PBIAS PDRIVER PSAT
Power dissipation semiconductor device results generation heat junctions surface chip. This heat transferred surface package, thermal gradient exists resistive properties package molding compound. magnitude thermal gradient expressed manufacturers' data sheets QJA, junction-to- ambient thermal resistance. on-chip junction temperature calculated QJA, temperature near surface on-chip power dissipation known.
(PDQJA)
Circuit Layout Guidelines switching power supply, circuit layout very important proper operation. Rapidly switching currents combined with trace inductance generates voltage transitions that cause problems. Therefore following guidelines should followed layout. boost circuits, high current circulates within loop composed diode, output capacitor, on-chip power transistor. length associated traces leads should kept short possible. flyback circuit, high current loops exist both sides transformer. primary side, loop consists input capacitor, transformer, on-chip power transistor, while transformer, rectifier diodes, output capacitors form another loop secondary side. Just boost circuit, traces leads containing large current should kept short.
where: junction temperature (°C); Separate current signal grounds from ambient temperature (°C); power grounds. single point grounding ground plane construction best results. power dissipated part question(W); junction-to ambient thermal resistance Locate voltage feedback near possible keep sensitive feedback wiring short. GM3255, 165°C Once Connect feedback resistors current analog signer calculated question whether ground. GM3255 used application settled. exceeds 150°C, absolute maximum allowable junction temperature, GM3255 suitable that application.
GM3255
GM3255
PGND AGND GM3255 MBRS120T3
Figure Additional Application Diagram, Input, 400mA Output Boost Converter
4.87 0.01µF 1.27
Test GM3255 PGND AGND
VOUT
22µF
MBRS120T3
22µF
22µH MBRS120T3
22µF
Figure Additional Application Diagram, 5.0V -12V/ 75mA Inverting Converter
MBRS140T3
P6KE-15A 1N4148
47µF
PGND AGND GM3255
MBRS140T3 1.28 10.72
GM3255
Figure Additional Application Diagram, Input, Output Flyback Converter
GM3255
0.01µF AGND PGND GM3255
-5.0 VOUT
Figure Additional Application Diagram, -9.0 Input, -5.0 V/700 Output Inverted Buck Converter
PGND AGND GM3255 0.01µF 12.76k
37.24
Figure Additional Application Diagram, Input, Output SEPIC Converter
1.245 99.755k 0.1µ 0.1µ 0.1µ
1N4148 1N4148 1N4148 1N4148 1N4148 1N4148 1N4148
GM3255 0.01µ 0.1µ Test PGND AGND
0.1µ 0.1µ
0.1µ
0.1µ
0.1µ
Figure Additional Application Diagram, Input, Output Boost Converter with Output Voltage Multiplier
GM3255
GM3255
0.01 GM3255 Test +5.0 1.28 10.72 PGND AGND
Figure Additional Application Diagram, Input, Output Dual Boost Converter
2.7V
GM3255
P6KE-15A 1N4148
2.49k 2.49k
MBRS130LT3
0.047
0.0047
Figure Positive Negative Converter with Direct Feedback
1.21k 2.7V MBRS140T3 P6KE-20A VOUT
1N4148
GM3255
-15V 12.1k 2.49k
GM3255
0.047
MBRS140T3
0.0047
Figure Dual Output Flyback Converter with Over Voltage Protetion
GM3255
GM3255
250mA
27pF 4.5V
LAMP
1N4148
0.047µF 4.99k 47µF 2.7V 5.5V
1N5818
1N4148
0.0047µF
DIMMING
GM3255
1N4148
Figure Ripple "Cuk" Converter
OPTIONAL REMOTE DIMMING
Figure CCFL Supply
GM3255
MBRS130LT3
18.7k 6.19k
0.047µF
0.0047µF
Figure Lion Cell SEPIC Converter
GM3255
GM3255
SOP-8(SO-8) PACKAGE OUTLINE DIMENSIONS
0.008 +0.0018 -0.0005
0.028
+0.022 -0.013 +0.56 -0.33
(0.20
+0.05 -0.01
(0.71
Layout
0.060 1.52
(5.99
+0.21 -0.20
0.236 0.008
0.275
0.155
0.154
+0.003 -0.004
INDENT
(3.91 0.1)
0.024
0.050 1.270
Inches
0.191
+0.004 -0.002 +0.10 -0.05
(4.85
0.063 0.005 (1.60 0.13)
0.057 (1.45)
Inches
0.0025 0.0015 (0.175 0.075)
0.050 (1.270)
0.016
+0.004 -0.003 +0.10 -0.08
(0.41
ORDERING NUMBER
3255
Gamma Micro. Circuit Type Shipping Tape Reel
GM3255
Package SO-8

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