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  aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 1 switchreg ? general description the aat1231/1231-1 are high frequency, high effi- ciency constant current boost converters capable of 24v maximum output voltage. both devices are ideal power solutions for backlight applications with up to six white leds in series or up to twelve white leds in a parallel/series configuration. the input voltage is 2.7v to 5.5v for single-cell lithium- ion/polymer (li-ion) based portable devices. the led current is digitally controlled across a 6x operating range using analogictech?s simple serial control? (s 2 cwire?) interface. programmability across 26 discrete current steps provides high reso- lution, low noise, flicker-free, constant led outputs. in programming aat1231 operation, led brightness increases based on the data received at the en/set pin. in programming aat1231-1 operation, led brightness decreases based on the data received at the en/set pin. the sel logic pin changes the feed- back voltage between two programmable ranges. the aat1231 and the aat1231-1 feature high current limit and fast, stable transitions for stepped or pulsed current applications. the high switching frequency (up to 2mhz) provides fast response and allows the use of ultra-small external components, including chip inductors and capacitors. fully integrated control cir- cuitry simplifies design and reduces total solution size. the aat1231 and the aat1231-1 offer a true load disconnect feature which isolates the load from the power source while in the off or disabled state. this eliminates leakage current, making the devices ideal- ly suited for battery-powered applications. the aat1231 and the aat1231-1 are available in pb- free, thermally-enhanced 12-pin tsopjw packages. features ? input voltage range: 2.7v to 5.5v ? maximum continuous output 24v @ 50ma ? drives 6 leds in series, 12 leds in parallel/ series configuration ? constant led current with 6% accuracy ? digital control with s 2 cwire single wire interface ? 26 discrete steps ? no pwm control required ? no additional circuitry ? up to 82% efficiency ? up to 2mhz switching frequency allows small external chip inductor and capacitors ? hysteretic control ? no external compensation components ? excellent load transient response ? high efficiency at light loads ? integrated soft start with no external capacitor ? true load disconnect guarantees <1.0a shutdown current ? selectable feedback voltage ranges for high resolution control of load current ? short-circuit, over-voltage, and over- temperature protection ? 12-pin tsopjw package ? -40c to +85c temperature range applications ? digital still cameras (dscs) ? mobile handsets ? mp3 players ? pdas and notebook pcs ? white led drivers typical application lin c 2 2.2f r 2 226k r 3 12k r 1 (r ballast ) 30.1 c 1 2.2f l = 2.2h ds1 capable of driving six leds in series (see applications section) osram lw m678 en/set pgnd pvin aat1231/ 1231-1 sw fb sel up to 24v/ 50ma max vin agnd ovp li-ion: v in = 2.7v to 4.2v enable/set select
pin descriptions pin configuration tsopjw-12 (top view) pin # symbol function 1 pvin input power pin; connected to the source of the p-channel mosfet. connect to the input capacitor(s). 2 en/set ic enable pin and s 2 cwire input control to set output current. 3 sel fb voltage range select. for the aat1231, a logic low sets the fb voltage range from 0.1v to 0.4v; a logic high sets the fb voltage range from 0.3v to 0.6v. for the aat1231-1, a logic low sets the fb voltage range from 0.4v to 0.1v; a logic high sets the fb voltage range from 0.6v to 0.3v. 4 vin input voltage for the converter. connect directly to the pvin pin. 5 n/c no connection. 6, 7 sw boost converter switching node. connect the power inductor between this pin and lin. 8 pgnd power ground for the boost converter. 9 agnd ground pin. 10 fb feedback pin. connect a resistor to ground to set the maximum led current. 11 ovp feedback pin for over-voltage protection sense. 12 lin switched power input. connect the power inductor between this pin and sw. aat1231/1231-1 step-up dc/dc converters for white led backlight applications 2 1231.2007.01.1.2 1 2 3 4 5 6 12 11 10 9 8 7 pvin en/set sel vin n/c sw lin ovp fb agnd pgnd sw
part number descriptions absolute maximum ratings 1 t a = 25c unless otherwise noted. thermal information symbol description value units ja thermal resistance 160 c/w p d maximum power dissipation 625 mw symbol description value units pvin, vin input voltage -0.3 to 6.0 v sw switching node 28 v lin, en/set, maximum rating v in + 0.3 v sel, fb t j operating temperature range -40 to 150 c t s storage temperature range -65 to 150 c t lead maximum soldering temperature (at leads, 10 sec) 300 c sel polarity s 2 c feedback part number high low voltage programming aat1231itp 0.3v v fb 0.6v 0.1v v fb 0.4v see table 2 aat1231itp-1 0.6v v fb 0.3v 0.4v v fb 0.1v see table 3 aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 3 1. stresses above those listed in absolute maximum ratings may cause permanent damage to the device. functional operation at c ondi- tions other than the operating conditions specified is not implied. only one absolute maximum rating should be applied at any one time.
electrical characteristics 1 t a = -40c to +85c unless otherwise noted. typical values are at 25c, v in = 3.6v. symbol description conditions min typ max units power supply pv in , v in input voltage range 2.7 5.5 v v out(max) maximum output voltage 24 v i q operating current sel = gnd, fb = 0.1v 40 70 a i shdn shutdown current en/set = gnd 1.0 a i out maximum continuous output 2.7v < v in < 5.5v, v out = 24v 50 ma current 2 v linereg(fb) / line regulation v in = 2.7v to 5.5v, v fb = 0.6v 0.7 %/v v in r ds(on) l low side switch on resistance 80 m r ds(on) in input disconnect switch 180 m on resistance t ss soft-start time from enable to output regulation; 300 s v fb = 300mv v ovp over-voltage protection threshold v out rising 1.1 1.2 1.3 v over-voltage hysteresis v out falling 100 mv i limit n-channel current limit 2.5 a t sd t j thermal shutdown threshold 140 c t hys t j thermal shutdown hysteresis 15 c sel, en/set v sel(l) sel threshold low 0.4 v v sel(h) sel threshold high 1.4 v v en/set(l) enable threshold low 0.4 v v en/set(h) enable threshold high 1.4 v t en/set (lo) en/set low time v en/set < 0.6v 0.3 75 s t en/set(hi) en/set high time v en/set > 1.4v 75 s t off en/set off timeout v en/set < 0.6v 500 s t lat en/set latch timeout v en/set > 1.4v 500 s i en/set en/set input leakage v en/set = 5v v in = 5v -1 1 a aat1231 v in = 2.7v to 5.5v, sel = gnd, 0.09 0.1 0.11 fb fb pin regulation en/set = high v v in = 2.7v to 5.5v, sel = high, 0.564 0.6 0.636 en/set = data16 aat1231-1 v in = 2.7v to 5.5v, sel = gnd, 0.09 0.1 0.11 fb fb pin regulation en/set = data16 v v in = 2.7v to 5.5v, sel = high, 0.564 0.6 0.636 en/set = high aat1231/1231-1 step-up dc/dc converters for white led backlight applications 4 1231.2007.01.1.2 1. specification over the -40c to +85c operating temperature range is assured by design, characterization, and correlation wi th statis- tical process controls. 2. maximum continuous output current increases with reduced output voltage, but may vary depending on operating efficiency and ther- mal limitations.
typical characteristics aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 5 feedback voltage vs. temperature (r ballast = 30.1 ) temperature ( 0 100 200 300 400 500 600 700 -40 -15 10 35 60 85 shutdown current vs. input voltage (en = gnd) input voltage (v) shutdown current (a) 0.0 0.2 0.4 0.6 0.8 1.0 2.7 3.1 3.5 3.9 4.3 4.7 5.1 5.5 -40 c 85 c 25 c efficiency vs. led current (12 white leds; r ballast = 30.1 ) led current (ma) efficiency (%) 74 75 76 77 78 79 80 81 82 83 84 2 4 6 8 10 12 14 16 18 20 v in = 3.6v v in = 4.2v v in = 5v efficiency vs. led current (6 white leds; r ballast = 30.1 ) led current (ma) efficiency (%) 73 74 75 76 77 78 79 80 81 2 4 6 8 10 12 14 16 18 20 v in = 3.6v v in = 4.2v v in = 5v efficiency vs. led current (5 white leds; r ballast = 30.1 ) led current (ma) efficiency (%) 75 76 77 78 79 80 81 82 83 2 4 6 8 10 12 14 16 18 20 v in = 3.6v v in = 4.2v v in = 5v efficiency vs. led current (4 white leds; r ballast = 30.1 ) led current (ma) efficiency (%) 77 78 79 80 81 82 83 84 85 2 4 6 8 10 12 14 16 18 20 v in = 3.6v v in = 4.2v v in = 5v
typical characteristics aat1231/1231-1 step-up dc/dc converters for white led backlight applications 6 1231.2007.01.1.2 output ripple (6 white leds; i led = 20ma) time (200ns/div) v out (dc offset 20.7v) (20mv/div) v lx (v) i l (a) 0 0.5 0 20 output ripple (6 white leds; i led = 13ma) time (400ns/div) v out (dc offset 19.8v) (50mv/div) v lx (v) i l (a) 0 0.5 0 20 shutdown (v fb = 0.6v; i led = 20ma) enable voltage (v) (top) feedback voltage (v) (middle) inductor current (a) (bottom) time (50s/div) 0 0.2 0.4 0.6 0.0 0.5 2.5v 0v line transient (6 white leds; r ballast = 30.1 ) input voltage (top) (v) output voltage (middle) (v) feedback voltage (bottom) (v) time (50s/div) 20.2 20.4 20.6 20.8 0.4 0.6 0.8 3.6v 4.2v accuracy i led vs. input voltage (v fb = 0.6v; r ballast = 30.1 ) input voltage (v) accuracy i led (%) -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.7 3.2 3.7 4.2 4.7 5.2 5.7 -40 c 25 c 85 c accuracy i led vs. temperature (v fb = 0.6v; r ballast = 30.1 ) temperature ( -1.0 -0.8 -0.5 -0.3 0.0 0.3 0.5 0.8 1.0 -40 -15 10 35 60 85
typical characteristics aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 7 aat1231 soft start (6 white leds; v fb = 0.3v) enable voltage (top) (v) feedback voltage (middle) (v) inductor current (bottom) (a) time (50s/div) 0 0.2 0 1 2 0v 2.5v aat1231 soft start with s 2 cwire (6 white leds; v fb = 0.6v) time (100s/div) 0 0.2 0.4 0 1 2 0v 2.5v enable voltage (top) (v) feedback voltage (middle) (v) inductor current (bottom) (a) transition of led current (6 white leds; sel = low; i led = 3.3ma to 13.3ma) output voltage (top) (v) feedback voltage (bottom) (v) time (20s/div) 18 20 22 0.0 0.1 0.2 0.3 0.4 transition of led current (6 white leds; sel = low; i led = 13.3ma to 6.6ma) output voltage (top) (v) feedback voltage (bottom) (v) time (20s/div) 18 20 22 0.0 0.1 0.2 0.3 0.4 aat1231-1 soft start (6 white leds; v fb = 0.6v) enable voltage (top) (v) feedback voltage (middle) (v) inductor current (bottom) (a) time (50s/div) 0 0.2 0.4 0.6 0 1 0v 2.5v aat1231-1 soft start with s 2 cwire (6 white leds; v fb = 0.3v) enable voltage (top) (v) feedback voltage (middle) (v) inductor current (bottom) (a) time (100s/div) 0 0.2 0.4 0.6 0 1 0v 2.5v
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 8 1231.2007.01.1.2 typical characteristics input disconnect switch resistance vs. input voltage input voltage (v) r ds(on)in (m ) 140 160 180 200 220 240 260 280 300 2.5 3 3.5 4 4.5 5 5.5 6 120 c 100 c 25 c 85 c low side switch on resistance vs. input voltage input voltage (v) r ds(on)l (m ) 40 60 80 100 120 140 160 2.5 3 3.5 4 4.5 5 5.5 6 120 c 100 c 25 c 85 c en/set high threshold vs. input voltage input voltage (v) v ih (v) 0.6 0.5 0.4 0.7 0.8 0.9 1.0 1.1 1.2 2.7 3.1 3.5 3.9 4.3 4.7 5.1 5.5 25 c85 c -40 c en/set low threshold vs. input voltage input voltage (v) v il (v) 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 2.7 3.1 3.5 3.9 4.3 4.7 5.1 5.5 -40 c 25 c 85 c en/set off timeout vs. input voltage input voltage (v) en/set off timeout (s) 50 100 150 200 250 300 2.7 3.1 3.5 3.9 4.3 4.7 5.1 5.5 25c 85c -40c en/set latch timeout vs. input voltage input voltage (v) en/set latch timeout (s) 100 150 200 250 300 350 2.7 3.1 3.5 3.9 4.3 4.7 5.1 5.5 85 c -40 c 25 c
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 9 functional block diagram functional description the aat1231 and the aat1231-1 consist of a dc/dc boost controller, an integrated slew rate controlled input disconnect mosfet switch, and a high voltage mosfet power switch. a high voltage rectifier, power inductor, output capacitor, and sense resistors are required to implement a dc/dc constant current boost converter. the input discon- nect switch is activated when a valid input voltage is present and the en/set pin is pulled high. the slew rate control on the p-channel mosfet ensures minimal inrush current as the output volt- age is charged to the input voltage, prior to the switching of the n-channel power mosfet. monotonic turn-on is guaranteed by the integrated soft-start circuitry. soft-start eliminates output volt- age overshoot across the full input voltage range and all loading conditions. the maximum current through the led string is set by the ballast resistor and the feedback voltage of the ic. the output current may be programmed by adjusting the level of the feedback reference volt- age which is programmed through the s 2 cwire interface. the sel pin selects one of two feedback voltage ranges. for the aat1231 and with a low logic level applied to the sel pin, the fb pin volt- age can be programmed from 0.1v to 0.4v. with a logic high applied to the sel pin, the fb pin volt- age can be programmed from 0.3v to 0.6v. in the aat1231-1, the sel function is inverted in that the fb pin voltage can be programmed from 0.4v to 0.1v with a logic low applied to the sel pin and 0.6v to 0.3v with a logic high applied to the sel control reference output select fb sel en/set pvin lin sw agnd pgnd ovp vin
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 10 1231.2007.01.1.2 pin. regardless of which device is chosen, the feedback voltage can be set to any one of 16 cur- rent levels within each fb range, providing high- resolution control of the led current, using the sin- gle-wire s 2 cwire control. for torch and flash applications where a short duration, pulsed load is desired, applying a low- to-high transition on the aat1231's sel pin pro- duces a 1.5x to 3.0x led current step. in the aat1231-1 on the other hand, the led current step for a low-to-high transition on the sel pin can be programmed from 3.0x to 1.5x. in both products, the step size is determined by the pro- grammed voltage at the fb pin where the internal default setting is 3.0x in the aat1231 and 1.5x in the aat1231-1. control loop the aat1231/1231-1 provide the benefits of cur- rent mode control with a simple hysteretic output current loop providing exceptional stability and fast response with minimal design effort. the device maintains exceptional constant current regulation, transient response, and cycle-by-cycle current limit without additional compensation components. the aat1231/1231-1 modulate the power mos- fet switching current to maintain the pro- grammed fb voltage. this allows the fb voltage loop to directly program the required inductor cur- rent in order to maintain the desired led current. the switching cycle initiates when the n-channel mosfet is turned on and current ramps up in the inductor. the on interval is terminated when the inductor current reaches the programmed peak current level. during the off interval, the input current decays until the lower threshold, or zero inductor current, is reached. the lower cur- rent is equal to the peak current minus a preset hysteresis threshold, which determines the induc- tor ripple current. the peak current is adjusted by the controller until the led output current require- ment is met. the magnitude of the feedback error signal deter- mines the average input current. therefore, the aat1231/1231-1 controller implements a pro- grammed current source connected to the output capacitor, parallel with the led string and ballast resistor. there is no right-half plane zero, and loop stability is achieved with no additional com- pensation components. an increase in the feedback voltage (v fb ) results in an increased error signal sensed across the ballast resistor (r1). the controller responds by increasing the peak inductor current, resulting in higher average current in the inductor and led string(s). alternatively, when the v fb is reduced, the controller responds by decreasing the peak inductor current, resulting in lower average cur- rent in the inductor and led string(s). under light load conditions, the inductor off inter- val current goes below zero and the boost convert- er enters discontinuous mode operation. further reduction in the load current results in a correspon- ding reduction in the switching frequency. the aat1231/1231-1 provide pulsed frequency opera- tion which reduces switching losses and maintains high efficiency under light load conditions. operating frequency varies with changes in the input voltage, output voltage, and inductor size. once the boost converter has reached continuous mode, further increases in the led current will not significantly change the operating frequency. a small 2.2h (20%) inductor is selected to main- tain high frequency switching (up to 2mhz) and high efficiency operation for outputs up to 24v. soft start / enable the input disconnect switch is activated when a valid input voltage is present and the en/set pin is pulled high. the slew rate control on the p- channel mosfet ensures minimal inrush current as the output voltage is charged to the input volt- age, prior to switching of the n-channel power mosfet. monotonic turn-on is guaranteed by the built-in soft-start circuitry. soft start eliminates output current overshoot across the full input volt- age range and all loading conditions. after the soft start sequence has terminated, the initial led current is determined by the internal, default fb voltage across the external ballast resis- tor at the fb pin. additionally, the aat1231 and the
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 11 aat1231-1 have been designed to offer the sys- tem designer two choices for the default fb voltage based on the state of the sel pin. changing the led current from its initial default setting is easy by using the s 2 cwire single wire serial interface; the fb voltage can be increased (as in the aat1231; see table 2) or decreased (as in the aat1231-1; see table 3) relative to the default fb voltage. current limit and over-temperature protection the switching of the n-channel mosfet termi- nates when a current limit of 2.5a (typical) is exceeded. this minimizes power dissipation and component stresses under overload and short-cir- cuit conditions. switching resumes when the cur- rent decays below the current limit. thermal protection disables the aat1231/1231-1 when internal dissipation becomes excessive. thermal protection disables both mosfets. the junction over-temperature threshold is 140c with 15c of temperature hysteresis. the output voltage automatically recovers when the over-temperature fault condition is removed. over-voltage protection over-voltage protection prevents damage to the aat1231/1231-1 during open-circuit or high output voltage conditions. an over-voltage event is defined as a condition where the voltage on the ovp pin exceeds the over-voltage threshold limit (v ovp = 1.2v typical). when the voltage on the ovp pin has reached the threshold limit, the con- verter stops switching and the output voltage decays. switching resumes when the voltage on the ovp pin drops below the lower hysteresis limit, maintaining an average output voltage between the upper and lower ovp thresholds multiplied by the resistor divider scaling factor. under-voltage lockout internal bias of all circuits is controlled via the vin input. under-voltage lockout (uvlo) guarantees sufficient v in bias and proper operation of all inter- nal circuitry prior to soft start. application information over-voltage protection ovp protection with open circuit failure the ovp protection circuit consists of a resistor network tied from the output voltage to the ovp pin (see figure 1). to protect the device from open cir- cuit failure, the resistor divider can be selected such that the over-voltage threshold occurs prior to the output reaching 24v (v out(max) ). the value of r3 should be selected from 10k to 20k to mini- mize losses without degrading noise immunity. figure 1: over-voltage protection circuit. figure 2: over-voltage protection open circuit response (no led). over voltage protection pin (top) (v) inductor current (bottom (a) output voltage (middle) (v) time (5ms/div) 0 1 2 22 24 26 1.168v 1.224v r2 r3 c out vout aat1231/1231-1 ovp gnd r 2 = r 3 - 1 v out(max) v ovp ?? ??
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 12 1231.2007.01.1.2 assume r3 = 12k and v out(max) = 24v. selecting 1% resistor for high accuracy, this results in r2 = 226k (rounded to the nearest standard value). the minimum ovp threshold can be calculated: to avoid ovp detection and subsequent reduction in the programmed output current (see following section), the maximum operating voltage should not exceed the minimum ovp set point. in some cases, this may disallow configurations with high led forward voltage (v fled ) and/or greater than five series white leds. v fled unit-to- unit tolerance can be as high as +15% of nominal for white led devices. ovp constant voltage operation under closed loop constant current conditions, the output voltage is determined by the operating cur- rent, led forward voltage characteristics (v fled ), quantity of series connected leds (n), and the feedback pin voltage (v fb ). when the rising ovp threshold is exceeded, switching is stopped and the output voltage decays. switching automatically restarts when the output drops below the lower ovp hysteresis volt- age (100mv typical) and, as a result, the output voltage increases. the cycle repeats, maintaining an average dc output voltage proportional to the average of the rising and falling ovp levels (multi- plied by the resistor divider scaling factor). high operating frequency and small output voltage ripple ensure dc current and negligible flicker in the led string(s). the waveform in figure 3 shows the output voltage and led current at cold temperature with a six series white led string and v ovp = 19.4v. as shown, the output voltage rises as a result of the increased v fled which triggers the ovp constant voltage operation. self heating of the leds trig- gers a smooth transition back to constant current control. figure 3: over-voltage protection constant voltage operation (6 white leds; i led = 13ma; r 2 = 182k ; r 3 = 12k ). while ovp is active, the maximum led current programming error ( i led ) is proportional to voltage error across an individual led ( v fled ). to minimize the i led error, the minimum ovp volt- age (v out(ovp_min) ) may be increased, yielding a corresponding increase in the maximum ovp volt- age (v out(ovp_max) ). measurements should confirm that the maximum switching node voltage (v sw(max) ) is less than 28v under worst-case oper- ating conditions. (n v fled(max) - v out(ovp _ min) - v fb ) n v fled = ovp constant voltage operation i led (10ma/div) v out (5v/div) i led cold temperature applied self-recovery time (1s/div) v out = v fb + n v fled v out(max) < v out(ovp_min) ?? + 1 ?? v out(ovp_min) = v ovp(min) = 21.8v r 2 r 3
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 13 v f = schottky diode ds1 forward voltage at turn- off v ring = voltage ring occurring at turn-off led selection and current setting the aat1231/1231-1 are well suited for driving white leds with constant current. applications include main and sub-lcd display backlighting, and color leds. the led current is controlled by the fb voltage and the ballast resistor. for maximum accuracy, a 1% tolerance resistor is recommended. the ballast resistor (r ballast ) value can be cal- culated as follows: where: v fb(max) = 0.4v when sel = low v fb(max) = 0.6v when sel = high i.e., for a maximum led current of 20ma (sel = high): table 1: maximum led current and r ballast resistor values (1% resistor tolerance). typical white leds are driven at maximum con- tinuous currents of 15ma to 20ma. for maximum output, two parallel strings of six series leds are used. a total output current of 30ma or 40ma is required (15ma to 20ma in each string). the maximum quantity of series connected leds is determined by the minimum ovp voltage of the boost converter (v out(ovp_min) ), minus the maxi- mum feedback voltage (v fb(max) ) divided by the maximum led forward voltage (v fled(max) ). v fled(max) can be estimated from the manufactur- ers? datasheet at the maximum led operating current. figure 4 shows the schematic of using six leds in series. assume v fled @ 20ma = 3.5v (typical) from lw m673 (osram) datasheet. therefore, under typical operating conditions, six leds can be used in series. maximum i led r ballast ( ) current (ma) sel = high sel = low 50 12.1 8.06 40 15.0 10.0 35 16.9 11.3 30 20.0 13.3 25 24.3 16.2 20 30.1 20.0 15 40.2 26.7 10 60.4 40.2 5 121.0 80.6 ?? + 1 + v f + v ring ?? v sw(max) = v ovp(max) r 3 r 2 21.82v - 0.6v 3.5v n = 6.1 ?? + 1 ?? v out(ovp_min) = 1.1v = 21.82v 226k 12k (v out(ovp_min) - v fb(max) ) v fled(max) n = ?? + 1 ?? v out(ovp_min) = v ovp(min) r 2 r 3 v fb i led(max) 0.6 0.020 r ballast = = = 30 30.1 v fb(max) i led(max) r ballast =
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 14 1231.2007.01.1.2 led brightness control the aat1231 and the aat1231-1 use s 2 cwire pro- gramming to control led brightness and does not require pwm (pulse width modulation) or addition- al control circuitry. this feature greatly reduces the burden on a microcontroller or system ic to man- age led or display brightness, allowing the user to "set it and forget it." with its high-speed serial inter- face (1mhz data rate), the output current of the aat1231 and the aat1231-1 can be changed suc- cessively to brighten or dim the leds in smooth transitions (i.e., to fade out) or in abrupt steps, giv- ing the user complete programmability and real- time control of led brightness. figure 5: programming aat1231 led current with r ballast = 30.1 . figure 4: aat1231/1231-1 white led boost converter schematic. 0 5 10 15 20 25 147101316 led current (ma) s 2 cwire data register sel = high sel = low (default) v in = 2.7v to 5.5v c1 2.2f c2 2.2f 2.2h l1 226k r2 12k r3 r1 30.1 v out = 24v/20m a 1 2 3 enable jp1 r4 10k 1 2 3 select jp2 ds1 n/c 5 vin 1 sw 6 pgnd 8 en 2 sel 3 sw 7 vp 4 gnd 9 fb 10 ovp 11 lin 12 tsop12jw u1 aat1231/1231-1 tsopjw-12 l1 2.2h sd3814-2r2 c1 2.2f 10v 0603 c2 2.2f 25v 0805 d1-d6 lw m673 white led ds1 30v 0.2a bat42w sod-123 r1 30.1 0603 r2 226k 0603 r3 12k 0603 r4 10k 0603 u1 aat1231/1231-1 d4 led d3 led d2 led d1 led led d5 led d6
figure 6: programming aat1231-1 led current with r ballast = 30.1 . alternatively, toggling the sel logic pin from low to high implements stepped or pulsed led currents by increasing the fb pin voltage. figures 7 and 8 illus- trate the select pin scaling factor, defined as the led current with sel=high divided by the led current with sel=low. for the aat1231, scaling factors from 1.5x to 3.0x are possible, depending on the s 2 cwire data register (default = 3.0x). in the aat1231-1, the possible scaling factors are 3.0x to 1.5x with the internal default setting of 1.5x. figure 7: aat1231 sel pin scaling factor: i led (sel = high) divided by i led (sel = low). figure 8: aat1231-1 sel pin scaling factor: i led (sel = high) divided by i led (sel = low). s 2 cwire serial interface analogictech's s 2 cwire single wire serial interface is a proprietary high-speed single-wire interface available only from analogictech. the s 2 cwire interface records rising edges of the en/set input and decodes them into 16 individual states. each state corresponds to a reference feedback voltage setting on the fb pin, as shown in table 2. s 2 cwire serial interface timing the s 2 cwire single wire serial interface data can be clocked-in at speeds up to 1mhz. after data has been submitted, en/set is held high to latch the data for a period t lat . the fb pin voltage is subse- quently changed to the level as defined by the state of the sel logic pin. when en/set is set low for a time greater than t off , the aat1231/1231-1 is dis- abled. when either the aat1231 or the aat1231-1 is disabled, the register is reset to its default value. in the aat1231, the default register value sets the fb pin voltage to 0.6v if the en/set pin is subse- quently pulled high. in the aat1231-1, the fb pin voltage is set to 0.3v under the same condition. aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 15 s 2 cwire data register select pin scaling factor (low to high) (default) 1. 0 1. 5 2. 0 2. 5 3. 0 3. 5 14 7101316 1.0 1.5 2.0 2.5 3.0 3.5 14 7101316 s 2 cwire data register select pin scaling factor (high to low) (default) s 2 cwire data register led current (ma) 0 5 10 15 20 25 147101316 sel=low sel=high (default)
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 16 1231.2007.01.1.2 figure 9: aat1231/1231-1 s 2 cwire timing diagram to program the output voltage. table 2: aat1231 s 2 cwire reference feedback voltage control settings with r ballast = 30.1 (assume nominal values). rising clock sel = low sel = high edges/data reference led current (ma); reference led current (ma); register voltage (v) r ballast = 30.1 voltage (v) r ballast = 30.1 1 0.1 (default) 3.32 0.3 (default) 9.97 2 0.12 3.99 0.32 10.63 3 0.14 4.65 0.34 11.30 4 0.16 5.32 0.36 11.96 5 0.18 5.98 0.38 12.62 6 0.20 6.64 0.40 13.29 7 0.22 7.31 0.42 13.95 8 0.24 7.97 0.44 14.62 9 0.26 8.64 0.46 15.28 10 0.28 9.30 0.48 15.95 11 0.30 9.97 0.50 16.61 12 0.32 10.63 0.52 17.28 13 0.34 11.30 0.54 17.94 14 0.36 11.96 0.56 18.60 15 0.38 12.62 0.58 19.27 16 0.40 13.29 0.60 19.93 s 2 cwire feedback voltage programming the fb pin voltage is set to the default level at ini- tial powerup. the aat1231 and the aat1231-1 are programmed through the s 2 cwire interface. table 2 illustrates fb pin voltage programming for the aat1231 and table 3 illustrates fb pin voltage pro- gramming for the aat1231-1. the rising clock edges applied at the en/set pin determine the fb pin voltage. if a logic low is applied at the sel pin, the default feedback voltage range for the aat1231 is 0.1v to 0.4v; for a logic high condition at the sel pin, the default feedback voltage range is 0.3v to 0.6v. conversely, if a logic low is applied at the sel pin of the aat1231-1, the default feedback voltage range becomes 0.4v to 0.1v and 0.6v to 0.3v for a logic high condition at the sel pin. 1 en/set 2 n-1 n 16 data reg 0n-1 0 t hi t lo t lat t off
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 17 table 3: aat1231-1 s 2 cwire reference feedback voltage control settings with r ballast = 30.1 (assumes nominal values). rising clock sel = low sel = high edges/data reference led current (ma); reference led current (ma); register voltage (v) r ballast = 30.1 voltage (v) r ballast = 30.1 1 0.4 (default) 13.29 0.6 (default) 19.93 2 0.38 12.62 0.58 19.27 3 0.36 11.96 0.56 18.60 4 0.34 11.30 0.54 17.94 5 0.32 10.63 0.52 17.28 6 0.30 9.97 0.50 16.61 7 0.28 9.30 0.48 15.95 8 0.26 8.64 0.46 15.28 9 0.24 7.97 0.44 14.62 10 0.22 7.31 0.42 13.95 11 0.20 6.64 0.40 13.29 12 0.18 5.98 0.38 12.62 13 0.16 5.32 0.36 11.96 14 0.14 4.65 0.34 11.30 15 0.12 3.99 0.32 10.63 16 0.10 3.32 0.30 9.97 selecting the schottky diode to ensure minimum forward voltage drop and no recovery, high voltage schottky diodes are consid- ered the best choice for the aat1231/1231-1 boost converters. the output diode is sized to maintain acceptable efficiency and reasonable operating junction temperature under full load operating con- ditions. forward voltage (v f ) and package thermal resistance ( ja ) are the dominant factors to consid- er in selecting a diode. the diode non-repetitive peak forward surge current rating (i fsm ) should be considered for high pulsed load applications, such as camera flash. i fsm rating drops with increasing conduction period. manufacturers? datasheets should be consulted to verify reliability under peak loading conditions. the diode's published current rating may not reflect actual operating conditions and should be used only as a comparative meas- ure between similarly rated devices. 20v rated schottky diodes are recommended for out- puts less than 15v, while 30v rated schottky diodes are recommended for outputs greater than 15v. the switching period is divided between on and off time intervals. during the on time, the n-channel power mosfet is conducting and storing energy in the boost induc- tor. during the off time, the n-channel power mosfet is not conducting. stored energy is trans- ferred from the input battery and boost inductor to the output load through the output diode. = t on + t off 1 f s
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 18 1231.2007.01.1.2 duty cycle is defined as the on time divided by the total switching interval. the maximum duty cycle can be estimated from the relationship for a continuous mode boost con- verter. maximum duty cycle (d max ) is the duty cycle at minimum input voltage (v in(min) ). the average diode current during the off time can be estimated. the following curves show the v f characteristics for different schottky diodes (100c case). the v f of the schottky diode can be estimated from the average current during the off time. the average diode current is equal to the output current. the average output current multiplied by the for- ward diode voltage determines the loss of the out- put diode. for continuous led currents, the diode junction temperature can be estimated. table 4: typical surface mount schottky rectifiers for various output levels. rated non-repetitive thermal part forward peak surge rated resistance manufacturer number current (a) current (a) voltage (v) ( ja , c/w) case diodes, inc. b340la 3 70.0 40 25 sma diodes, inc. bat42w 0.2 4.0 30 500 sod-123 on semi mbr0530t 0.5 5.5 30 206 sod-123 zetex zhcs350 0.35 4.2 40 330 sod-523 central semi cmdsh2-3 0.2 1.0 30 500 sod-323 t j(diode) = t amb + ja p loss(diode) p loss(diode) = i avg(tot) v f = i out v f i avg(tot) = i out forward voltage (v) forward current (ma) 10 100 1000 10000 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 b340la mbr0530t zhcs350 bat42w i out 1 - d max i avg(off) = v out - v in(min) v out d max = t on t on + t off d = = t on ? f s
output diode junction temperature should be main- tained below 110oc, but may vary depending on application and/or system guidelines. the diode ja can be minimized with additional pcb area on the cathode. pcb heat-sinking the anode may degrade emi performance. the reverse leakage current of the rectifier must be considered to main- tain low quiescent (input) current and high efficien- cy under light load. the rectifier reverse current increases dramatically at elevated temperatures. selecting the boost inductor the aat1231 and the aat1231-1 controllers utilize hysteretic control and the switching frequency varies with output load and input voltage. the value of the inductor determines the maximum switching frequency of the boost converter. increased output inductance decreases the switch- ing frequency, resulting in higher peak currents and increased output voltage ripple. to maintain 2mhz maximum switching frequency and stable opera- tion, an output inductor sized from 1.5h to 2.7h is recommended. a better estimate of d max is possible once v f is known. where v f is the schottky diode forward voltage. if not known, it can be estimated at 0.5v. manufacturer?s specifications list both the inductor dc current rating, which is a thermal limitation, and peak inductor current rating, which is determined by the saturation characteristics. measurements at full load and high ambient temperature should be completed to ensure that the inductor does not sat- urate or exhibit excessive temperature rise. the output inductor (l) is selected to avoid satura- tion at minimum input voltage, maximum output load conditions. peak current may be estimated using the following equation, assuming continuous con- duction mode. worst-case peak current occurs at minimum input voltage (maximum duty cycle) and maximum load. switching frequency (f s ) can be estimated from the curves and assumes a 2.2h inductor. at light load and low output voltage, the controller reduces the operating frequency to maintain maxi- mum operating efficiency. as a result, further reduction in output load does not reduce the peak current. minimum peak current can be estimated from 0.5a to 0.75a. at high load and high output voltages, the switch- ing frequency is somewhat diminished, resulting in higher i peak . bench measurements are recom- mended to confirm actual i peak and ensure that the inductor does not saturate at maximum led cur- rent and minimum input voltage. the rms current flowing through the boost induc- tor is equal to the dc plus ac ripple components. under worst-case rms conditions, the current waveform is critically continuous. the resulting rms calculation yields worst-case inductor loss. the rms current value should be compared against the manufacturer's temperature rise, or thermal derating, guidelines. aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 19 i out (1 - d max ) d max v in(min) (2 f s l) i peak = + output current (ma) switching frequency (mhz) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 40 50 60 70 80 90 100 v in = 3.6v v out = 10v v in = 3.6v v out = 12v v in = 2.7v v out = 12v v in = 2.7v v out = 10v v in = 3.0v v out = 10v v in = 3.0v v out = 12v output current (ma) switching frequency (mhz) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 40 50 60 70 80 90 100 v in = 2.7v v out = 15v v in = 2.7v v out = 18v v in = 3.0v v out = 15v v in = 3.0v v out = 18v v in = 3.6v v out = 15v v in = 3.6v v out = 18v (v out + v f - v in(min) ) (v out + v f ) d max =
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 20 1231.2007.01.1.2 table 5: recommended inductors for various output levels (select i peak < i sat ). maximum part inductance dc i sat dcr size (mm) manufacturer number (h) current (ma) (m ) lxwxh type sumida cdrh2d11-2r2 2.2 780 78 3.2x3.2x1.2 shielded www.sumida.com cooper electronics sd3814-2r2 2.2 1900 77 4.0x4.0x1.4 shielded www.cooperet.com sd3110-2r2 2.2 910 161 3.1x3.1x1.0 shielded murata lqh2mcn2r2m02l 2.2 455 440 2.0x1.6x0.7 shielded www.murata.com nr3010t-2r2m 2.2 1100 95 3.0x3.0x1.0 shielded taiyo yuden cbc2016t2r2m 2.2 750 200 2.0x1.6x1.6 chip www.t-yuden.com non-shielded cbc2518t2r2m 2.2 510 90 2.5x1.8x1.8 shielded for a given inductor type, smaller inductor size leads to an increase in dcr winding resistance and, in most cases, increased thermal impedance. winding resistance degrades boost converter efficiency and increases the inductor?s operating temperature. to ensure high reliability, the inductor case temper- ature should not exceed 100oc. in some cases, pcb heatsinking applied to the lin node (non- switching) can improve the inductor's thermal capability. pcb heatsinking may degrade emi per- formance when applied to the sw node (switching) of the aat1231/1231-1. shielded inductors provide decreased emi and may be required in noise sensitive applications. unshielded chip inductors provide significant space savings at a reduced cost compared to shielded (wound and gapped) inductors. in general, chip- type inductors have increased winding resistance (dcr) when compared to shielded, wound varieties. inductor efficiency considerations the efficiency for different inductors is shown in figure 7 for six white leds in series. smaller inductors yield increased dcr and reduced oper- ating efficiency. figure 10: aat1231/1231-1 efficiency for different inductor types (v in = 3.6v; six white leds in series). 65 68 71 74 77 80 25811141720 led current (ma) efficiency (%) cooper sd3814-2r2 (77m ) cooper sd3110-2r2 (161m ) murata lqh2mcn2r2m02l (440m ) p loss(inductor) = i rms 2 dcr i peak i rms = 3
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 21 selecting the boost capacitors the high output ripple inherent in the boost con- verter necessitates low impedance output filtering. multi-layer ceramic (mlc) capacitors provide small size and adequate capacitance, low parasitic equivalent series resistance (esr) and equivalent series inductance (esl), and are well suited for use with the aat1231/1231-1 boost regulator. mlc capacitors of type x7r or x5r are recommended to ensure good capacitance stability over the full operating temperature range. the output capacitor is sized to maintain the output load without significant voltage droop ( v out ) dur- ing the power switch on interval, when the output diode is not conducting. a ceramic output capacitor from 2.2f to 4.7f is recommended (see table 5). typically, 25v rated capacitors are required for the 24v maximum boost output. ceramic capacitors sized as small as 0805 are available which meet these requirements. mlc capacitors exhibit significant capacitance reduction with applied voltage. output ripple meas- urements should confirm that output voltage droop and operating stability are acceptable. voltage derat- ing can minimize this factor, but results may vary with package size and among specific manufacturers. output capacitor size can be estimated at a switch- ing frequency (f s ) of 500khz (worst case). to maintain stable operation at full load, the output capacitor should be sized to maintain v out between 100mv and 200mv. the boost converter input current flows during both on and off switching intervals. the input ripple current is less than the output ripple and, as a result, less input capacitance is required. pcb layout guidelines boost converter performance can be adversely affected by poor layout. possible impact includes high input and output voltage ripple, poor emi per- formance, and reduced operating efficiency. every attempt should be made to optimize the layout in order to minimize parasitic pcb effects (stray resist- ance, capacitance, and inductance) and emi cou- pling from the high frequency sw node. a suggest- ed pcb layout for the aat1231/1231-1 boost con- verter is shown in figures 10 and 11. the following pcb layout guidelines should be considered: 1. minimize the distance from capacitor c1 and c2 negative terminal to the pgnd pins. this is especially true with output capacitor c2, which conducts high ripple current from the output diode back to the pgnd pins. 2. minimize the distance between l1 to ds1 and switching pin sw; minimize the size of the pcb area connected to the sw pin. 3. maintain a ground plane and connect to the ic pgnd pin(s) as well as the gnd terminals of c1 and c2. 4. consider additional pcb area on ds1 cathode to maximize heatsinking capability. this may be necessary when using a diode with a high v f and/or thermal resistance. table 6: recommended ceramic capacitors. manufacturer part number value (f) voltage rating temp co case size murata grm188r60j225ke19 2.2 6.3 x5r 0603 murata grm188r61a225ke34 2.2 10 x5r 0603 murata grm219r61e225ka12 2.2 25 x5r 0805 murata grm21br71e225ka73l 2.2 25 x7r 0805 murata grm21br61e475ka12 4.7 25 x5r 0805 i out d max f s v out c out =
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 22 1231.2007.01.1.2 figure 11: aat1231/1231-1 evaluation figure 12: aat1231/1231-1 evaluation board top side layout (with six leds board bottom side layout (with six leds and microcontroller). and microcontroller). aat1231/1231-1 white led driver s 2 cwire microcontroller
figure 13: aat1231 /1231-1 evaluation board schematic (with six leds and microcontroller). aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 23 c1 2.2f 2.2h l1 r2 226k r3 12k 30.1 r1 vout c2 2.2f schottky ds1 n/c 5 vin 1 sw 6 pgnd 8 en 2 sel 3 sw 7 vp 4 gnd 9 fb 10 ovp 11 lin 12 aat1231/1231-1 u1 d1 led d2 led d3 led d4 led led d5 led d6 vdd 1 gp5 2 gp4 3 gp3 4 gp2 5 gp1 6 gp0 7 vss 8 pic12f675 u2 c3 1f r5 1k vcc 10k r4 r6 1k r7 1k up down select r8 330 d7 red 1 2 3 4 5 0 sw1 1 2 3 4 5 0 sw2 1 2 3 4 5 0 sw3 d8 green (select indicator) s 2 cwire microcontroller aat1231/1231-1 white led driver r9 330 1 2 3 j1 jp1 dc- dc+ vcc j2 j3 u1 analogictech aat1231/1231-1 tsopjw-12 package u2 pic12f675 c1 grm188r60j225ke01 c2 grm21br71e225ka73 c3 grm216r61a105ka01 r1 30.1 , 1%, 1/4w; 0603 r2 226k , 1%, 1/4w; 0603 r3 12.1k , 1%, 1/4w; 0603 r4 10k , 5%, 1/4w; 0603 r5, r6, r7 1k , 5%, 1/4w; 0805 r8, r9 330 , 5%, 1/4w; 0805 jp1 0 , 5%; 0805 ds1 bat42w l1 cooper electronics 2.2h sd3814-2r2 d1-d6 white hyper-bright led lw m673 d7 red led 1206 d8 green lec 1206 sw1 - sw3 spst, 5mm j1, j2, j3 conn. header, 2mm
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 24 1231.2007.01.1.2 additional applications figure 14: four leds in series configuration. figure 15: five leds in series configuration. efficiency vs. led current (5 white leds; r ballast = 30.1 ) led current (ma) efficiency (%) 75 76 77 78 79 80 81 82 83 2 4 6 8 10 12 14 16 18 20 v in = 3.6v v in = 4.2v v in = 5v lin l = 2.2h ds1 c 2 2.2f c 1 2.2f r 2 196k r 3 12k 30.1 20ma enset pgnd pvin aat1231/ 1231-1 sw fb sel up to 24v/ 50ma max vin agnd ovp li-ion v in = 2.7v to 5.5v efficiency vs. led current (4 white leds; r ballast = 30.1 ) led current (ma) efficiency (%) 77 78 79 80 81 82 83 84 85 2 4 6 8 10 12 14 16 18 20 v in = 3.6v v in = 4.2v v in = 5v lin l = 2.2h ds1 c 2 2.2f c 1 2.2f r 2 187k r 3 12k 30.1 20ma enset pgnd pvin aat1231/ 1231-1 sw fb sel up to 24v/ 50ma max vin agnd ovp li-ion v in = 2.7v to 5.5v
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 25 figure 16: six leds in series configuration. figure 17: twelve leds in series/parallel configuration. lin en/set pgnd pvin c 2 2.2f c 1 2.2f r 2 226k r 3 12k 30.1 20ma l = 2.2h ds1 aat1231/ 1231-1 sw fb sel up to 24v/ 50ma max vin agnd ovp li-ion v in = 2.7v to 5.5v efficiency vs. led current (12 white leds; r ballast = 30.1 ) led current (ma) efficiency (%) 74 75 76 77 78 79 80 81 82 83 84 2 4 6 8 10 12 14 16 18 20 v in = 3.6v v in = 4.2v v in = 5v lin en/set pgnd pvin c 2 2.2f c 1 2.2f r 2 226k r 3 12k 30.1 20ma 30.1 20m a l = 2.2h ds1 aat1231/ 1231-1 sw fb sel up to 24v/ 50ma max vin agnd ovp li-ion v in = 2.7v to 5.5v efficiency vs. led current (6 white leds; r ballast = 30.1 ) led current (ma) efficiency (%) 73 74 75 76 77 78 79 80 81 2 4 6 8 10 12 14 16 18 20 v in = 3.6v v in = 4.2v v in = 5v
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 26 1231.2007.01.1.2 ordering information package information tsopjw-12 all dimensions in millimeters. package marking 1 part number (tape and reel) 2 tsopjw-12 sdxyy aat1231itp-t1 tsopjw-12 tuxyy AAT1231ITP-1-T1 1. xyy = assembly and date code. 2. sample stock is generally held on part numbers listed in bold . 0.20 + 0.10 - 0.05 0.055 0.045 0.45 0.15 7 nom 4 4 3.00 0.10 2.40 0.10 2.85 0.20 0.50 bsc 0.50 bsc 0.50 bsc 0.50 bsc 0.50 bsc 0.15 0.05 0.9625 0.0375 1.00 + 0.10 - 0.065 0.04 ref 0.010 2.75 0.25 all analogictech products are offered in pb-free packaging. the term ?pb-free? means semiconductor products that are in compliance with current rohs standards, including the requirement that lead not exceed 0.1% by weight in homogeneous materials. for more information, please visit our website at http://www.analogictech.com/pbfree.
aat1231/1231-1 step-up dc/dc converters for white led backlight applications 1231.2007.01.1.2 27 advanced analogic technologies, inc. 830 e. arques avenue, sunnyvale, ca 94085 phone (408) 737- 4600 fax (408) 737- 4611 ? advanced analogic technologies, inc. analogictech cannot assume responsibility for use of any circuitry other than circuitry entirely embodied in an analogictech pr oduct. no circuit patent licenses, copyrights, mask work rights, or other intellectual property rights are implied. analogictech reserves the right to make changes to their products or specifi cations or to discontinue any product or service without notice. customers are advised to obtain the latest version of relevant information to verify, before placing orders, that information b eing relied on is current and complete. all products are sold sub- ject to the terms and conditions of sale supplied at the time of order acknowledgement, including those pertaining to warranty, patent infringement, and limitation of liability. analogictech warrants performance of its semiconductor products to the specifications applicable at the time of sale in accordance with anal ogictech?s standard warranty. testing and other quality con- trol techniques are utilized to the extent analogictech deems necessary to support this warranty. specific testing of all param eters of each device is not necessarily performed. analogictech and the analogictech logo are trademarks of advanced analogic technologies incorporated. all other brand and produ ct names appearing in this document are regis- tered trademarks or trademarks of their respective holders.


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