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august 2009 doc id 15015 rev 1 1/33 AN2823 application note current source for led driving based on the l5973ad introduction leds are devices where the light intensity (b rightness), measured in millicandelas or in lumens, is proportional to the forward current flowing through them. two main classes can be identified given the typical forward current of the final application: low current leds, from 15 ma to 50 ma, mainly used in the portable market for backlighting and signaling applications high current leds, with forward current between 350 ma to 1000 ma, typically used in lighting applications the typical voltage drop across the leds when forward-biased depends on the color of the emitted light, and the spread is high even when considering leds from the same production lot, as shown in figure 1 . figure 1. v-i characteristic of 8 white leds of the same type the spread of the forward voltage and the exponential trend of the i-v characteristic makes current mode driving more convenient than voltage driving. as a consequence, the current source regulates the led current and the output voltage is fixed by the forward voltage across each led. !-v )led;!= 6fw;6= www.st.com
contents AN2823 2/33 doc id 15015 rev 1 contents 1 basic principles of led driving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 the l5973ad in led driving appli cations . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 designing a high efficiency current source (topology 1) . . . . . . . . . . . . . . . 7 2.1.1 dc gain design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 the dimming operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.3 frequency compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.4 led current accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 designing a high efficiency current source (topology 2) . . . . . . . . . . . . . . 18 2.2.1 dc gain design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 the dimming operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.3 frequency compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2.4 led current accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3 revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
AN2823 list of figures doc id 15015 rev 1 3/33 list of figures figure 1. v-i characteristic of 8 white leds of the same type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 figure 2. basic schematic of series-driven leds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 figure 3. basic schematic of parallel-driven leds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 figure 4. basic schematic of a dc-dc converter driving leds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 figure 5. improved schematic of the current generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 figure 6. block diagram of l5973ad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 figure 7. schematic of the dimmable current source using l5973ad . . . . . . . . . . . . . . . . . . . . . . . . 10 figure 8. voltage mode architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 figure 9. q1 disables the switching activity clamping the comp signal . . . . . . . . . . . . . . . . . . . . . . 11 figure 10. time delay in the led current leading edge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 figure 11. dimming signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 figure 12. load equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 figure 13. aled(s) plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 figure 14. power stage equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 figure 15. ota equivalent circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 figure 16. module plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 figure 17. phase plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 figure 18. basic schematic of the current source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 figure 19. schematic of the dimmable current source using l5973ad . . . . . . . . . . . . . . . . . . . . . . . . 20 figure 20. q1 disables the switching activity by clamping the comp signal. . . . . . . . . . . . . . . . . . . . 22 figure 21. time delay in the led current leading edge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 figure 22. dimming signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 figure 23. aled(s) plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 figure 24. equivalent circuit of block k(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 figure 25. module plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 figure 26. phase plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 figure 27. maximum efficiency vs. voltage drop (i led =350 ma) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 figure 28. power losses across the sense resistor (i led =350 ma) . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 figure 29. spread of the led current vs. voltage drop (i led =350 ma) . . . . . . . . . . . . . . . . . . . . . . . . 29 figure 30. power losses across the sense resistor (i led =350 ma) . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 figure 31. maximum efficiency vs. voltage drop (i led =700 ma) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 figure 32. power losses across the sense resistor (i led =700 ma) . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 figure 33. spread of the led current vs. voltage drop (i led =700 ma) . . . . . . . . . . . . . . . . . . . . . . . . 31
basic principles of led driving AN2823 4/33 doc id 15015 rev 1 1 basic principles of led driving this paragraph deals with different ways to arrange a set of leds to generate the required lumen output. advantages and disadvantages for each topology are also provided. the easiest and cheapest way to drive leds is to connect them in series, as shown in figure 2 . however, this implies that the led driver must provide an output voltage that is the sum of the forward voltage of the leds. figure 2. basic schematic of series-driven leds therefore, in other cases the preferred solution is to drive leds in parallel, matching the different current sources ( figure 3 ). figure 3. basic schematic of parallel-driven leds an easy and cost-effective way to design a constant current source to drive leds is to use a dc-dc converter, as shown in figure 4 . since the voltage control loop of the device regulates the voltage at the fb pin, a constant current source can be obtained by simply connecting a resistor between this pin and gnd. application note an1891 from stmicroelectronics provides helpful information for designing a similar application using monolithic dc-dc converters. !-v !-v
AN2823 basic principles of led driving doc id 15015 rev 1 5/33 figure 4. basic schematic of a dc-dc converter driving leds the main drawback of the circuit shown in figure 4 is the amount of wasted power on the sense resistor. this can affect the efficiency of the overall application, especially in cases where the voltage reference of the embedded error amplifier is not negligible compared to the voltage drop across the leds, or when high current devices are used. the main objective of this document is to implement a more efficient current source by converting the voltage loop of a monolithic dc-dc converter into a current loop. am01 3 54v1
the l5973ad in led driving applications AN2823 6/33 doc id 15015 rev 1 2 the l5973ad in led driving applications a good candidate within st?s monolithic dc-dc port folio is the l5973ad. the device is an asynchronous buck regulator and belongs to the l597x family. the reference for the embedded error amplifier of the devices listed in ta b l e 1 is 1.235 v, so the topology proposed in figure 4 can be improved by increasing the efficiency of the conversion in accordance with application requirements. in addition to the high efficiency conversion requirement, more and more often customers look for smaller application size and lower cost and count of external components. the purpose of this document is the implementation of an efficient and dimmable current source for led driving developed with the l5973ad. in section 2.1 , two resistors are used to implement a simple, helpful trick for decreasing the voltage drop across the sense resistor. in section 2.2 , a general-purpose external operational amplifier is used to further increase the overall efficiency of the conversion. the ts321 selected (in a small sot23-5 package) is one of the two embedded amplifiers composing the lm158 market standard. in both cases the compensation network is designed for device operation without the output capacitor filter, to reduce the cost and the count of external components. the main consequence is a load current unfiltered from the ripple current: the high natural switching frequency (500 khz) of the l5973ad helps keep the ripple current negligible in all operating conditions even compared to the minimum load current (350 ma) given an inductor value of 100 h. the maximum accuracy of the load current is finally provided considering the spread of the involved parameters at the end of each section. table 1. main monolithic devices within the l597x family device v in range f sw i out dc v out features package l5970d 4 v to 36 v 250 khz 1 a 1.235 v to v in v ref , synch, inh so-8 l5970ad 4 v to 36 v 500 khz 1 a 1.235 v to v in v ref , synch, inh so-8 l5973d 4 v to 36 v 250 khz 2 a 1.235 v to v in v ref , synch, inh hsop8 l5973ad 4 v to 36 v 500 khz 1.5 a 1.235 v to v in v ref , synch, inh hsop8
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 7/33 2.1 designing a high efficiency current source (topology 1) the reference of the embedded error amplifier of the l597x family is 1.235 v. the sense resistor value when the circuit proposed in figure 4 is used to implement a 350 ma current source is: equation 1 and the power losses across it are: equation 2 so if the current generator is powering a string composed of 1 w leds, the total efficiency of the conversion is affected by the sense resistor at a percentage of 43%. obviously this circuit could be rendered acceptable by increasing the number of leds composing the string, but is, in any case, limited when the load is a single 3 w led. 2.1.1 dc gain design figure 5 shows the guiding principle to implement an improved current generator using the l5973ad and two additional resistors. figure 5. improved schematic of the current generator r1 and r6 resistors are used to decrease the magnitude of the regulated voltage across the sense resistor. applying the superimposition of the effects, the equation of the fb voltage can be written as: equation 3 r sense v fb i led ----------- 1.235 0.35 -------------- - 3.52 = = = p losses r sense i led 2 430mw ? ? = !-v v fb v ref r 6 r 1 r 6 + -------------------- v s r 1 r 1 r 6 + -------------------- ? + ? =
the l5973ad in led driving applications AN2823 8/33 doc id 15015 rev 1 so the regulated v sense is: equation 4 the accuracy of the regulated current is mainly affected by the tolerance of the resistors r6, r1 and r s . if the selected sense resistor value is equal to r s =1.5 , the required voltage drop on the sense resistor to set 350 ma flowing through the led string is 525 mv. the required resistor ratio is: equation 5 given r6 = 6.8 k and r1 = 20 k , the nominal led current is 355 ma. the power wasted on the sense resistor is so decreased from 430 mw to: equation 6 improving the efficiency of the conversion. 2.1.2 the dimming operation the best way to dim an led device is by pwm dimming performed on the current flowing through it. the device is powered with a constant current for minimal color shift, even when the amount of emitted light is decreased. this requirement must be converted in the specifications for the dimmable current source. devices specifically tailored for the led market (see the led7706 and led7707 as examples) implement additional circuitry to me et these specifications and offer exceptional dimming performance. the implementation of the dimming feature in a constant current generator developed with standard switching regulators can be tricky, as no dedicated circuitry is embedded in the device to provide this operation. as a consequence, the design of the compensation network must be a trade-off between the response to the small signal necessary for system stability and the large signal du ring the dimming operation. the lc filter of the output stage filters the output voltage but the output capacitor value affects the dimming performance. in fact, even if the pwm input signal disables the current generator, the current flowing through the led string drops to zero only when the voltage across the capacitor does not guarantee the minimum forward voltage across each led. the l5973ad is an asynchronous device: the rectification of the inductor current is given by the external diode. the device is not capable of sinking current and so it can not quickly discharge the output capacitor to power off the emitting diodes. as a consequence, a large output capacitor value better filters the current flowing in the led from the current ripple, but significantly limits the dimming performance as it introduces additional delay in the falling edge of the led current. v s v fb r 6 r 1 ------ - v ref v fb ? () 1.235 r 6 r 1 ------ - 2.065 ? ? = ? ? = r 1 r 6 ------ - 2.9 = p losses r sense i led 2 184mw ? ? =
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 9/33 the current source schematic in figure 7 shows a negligible value for the output capacitor to achieve better performance in the dimming operation. the high switching frequency of the l5973ad helps to keep the unfiltered current ripple in the led negligible compared to the dc current, so the color shift of the emitted light in all operating conditions can be considered negligible. the l5973ad is based on a voltage mode control loop. therefore, the duty ratio of the internal switch is obtained through a comparison between a sawtooth waveform (generated by an oscillator) and the output voltage of the error amplifier (see figure 6 ). the embedded error amplifier is a transconductance type so its output stage delivers current to the compensation network. figure 6. block diagram of l5973ad in figure 7 , the output of the embedded transconductance error amplifier is clamped by switch q1, in accordan ce with the pwm signal. when switch q1 is on, the comp pin is low (see figure 9 ). regardless of the fb input there is no intersection between the internal sawtooth waveform and the output of the error amplifier. the internal switch is thus disabled and the inductor current starts decreasing down to zero. when the pwm signal disables the q1 switch (see figure 10 ), no current flows in the sense resistor rs, so the error amplifier is highly unbalanced and free to charge the compensation network composed of c4, c5 and r5. when the voltage of the comp pin crosses the internal sawtooth ramp, the embedded switch is enabled: the current source starts charging the inductor and the rising edge phase of the led begins. the minimum voltage of the internal sawtooth waveform is about 1 v (see the voltage mode architecture in figure 8 ) so there is a time delay between the disabling of the q1 switch and the first pulse of the internal mosfet. the delay is due to the time necessary to charge the compensation network to the minimum voltage to cross the internal ramp. this provides a shift between the duty cycle of the input pwm signal and the real pwm dimming performed on the load current. figure 9 and figure 10 show the dimming operation monitoring the input dimming signal and the led current. am01 3 57v1
the l5973ad in led driving applications AN2823 10/33 doc id 15015 rev 1 figure 7. schematic of the dimmable current source using l5973ad !-v n23232 n23232 n22427 n22427 vled+ vled- vin sync inh vref m! dimming gnd gnd d_dimm1 dnm c4 68nf c4 68nf jp4 jp4 r18 r18 r16 dnm r16 dnm gnd gnd d_dimm1 d_dimm1 r3 dnm r3 dnm rs1 1.5 1% rs1 1.5 1% 1 2 3 4 5 6 12 11 10 9 8 7 j1 j1 r17 dnm r17 dnm ds1 stps 2l40u ds1 stps 2l40u jp6 jp6 c1 10uf c1 10uf r15 dnm r15 dnm r11 dnm r11 dnm vin vin r2 dnm r2 dnm vout 1 vcc 8 vref 6 gnd 9 inh 3 comp 4 gnd 7 fb 5 sync 2 u1 l5973ad u1 l5973ad c7 dnm c7 dnm q1 2n7002 q1 2n7002 vled- vled- jp5 jp5 r4 dnm r4 dnm r12 dnm r12 dnm c2 100nf c2 100nf r13 dnm r13 dnm sync sync vref vref jp1 jp1 c5 33pf c5 33pf c6 dnm c6 dnm dimming dimming r7 dnm r7 dnm c10 c10 r14 dnm r14 dnm jp3 jp3 r8 dnm r8 dnm c9 dnm c9 dnm l1 100uh l1 100uh inh inh r1 20k r1 20k r6 6k8 r6 6k8 c8 100nf c8 100nf q2 dnm q2 dnm c3 100nf c3 100nf r10 10k- 5% r10 10k- 5% vled+ vled+ d1 dnm d1 dnm r9 10- 5% r9 10- 5% jp2 jp2 3 4 1 5 2 - + u2 dnm - + u2 dnm gnd. gnd. r5 330-1% r5 330-1% d2 dnm d2 dnm
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 11/33 the dimming performance of the circuit depends on the input voltage and number n of the led composing the row. the higher the voltage applied on the inductor (vin-n*v led_fw ), the higher the rising time of the led current given the inductor value. figure 8. voltage mode architecture figure 9. q1 disables the switching activity clamping the comp signal !-v to drive rs v ramp v out_ea to drive rs v ramp v out_ea v out + - + - v ref e/a pwm oscillator ramp to drive rs v ramp v out_ea to drive rs v ramp v out_ea to drive rs v ramp v out_ea to drive rs v ramp v out_ea v out + - + - v ref e/a pwm oscillator ramp + - + - v ref e/a pwm oscillator ramp !-v
the l5973ad in led driving applications AN2823 12/33 doc id 15015 rev 1 figure 10. time delay in the led current leading edge the minimum dimming duty cycle is determined based on the specification of the rising / falling time of the led current referred to the dimming time and on the dimming frequency. figure 11. dimming signal from figure 9 and 10 (vin = 18 v, string composed of two leds) the following data can be inferred: equation 7 considering a dimming frequency of 250 hz, the minimum duty cycle of the pwm dimming satisfies the equation: equation 8 so the minimum d is about 5%. am01 3 60v1 !-v t rise 40 s = t fall 6 s = ? ? ? t rise t fall + 0.2 t min_pulse ? 0.2 d min t dimming ?? ==
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 13/33 relaxing the edge requirements or increasing the transient performance of the circuit, which depend on vin and the number of leds composing the string and inductor value, a lower d can achieved. 2.1.3 frequency compensation the loop transfer function can be written as the product of meaningful terms. equation 9 where g pwm (fsw) is a specific parameter of the l5973ad and represents the gain of the pwm stage, aota(s) is the transfer function of the error amplifier block, gpwr(s) represents the power stage and led(nled) is the partition of the output voltage directly applied to the fb pin. the gain of the pwm stage g pwm (fsw) is: equation 10 so it is 26.3 at a switching frequency of 500 khz. when the system has reached working conditions, the leds composing the row are biased and their equivalent circuit can be consider ed as a resistor for frequency << 1 mhz. typically, the manufacturer provides the typical equivalent dynamic resistance of the led biased with different dc current. this parameter is useful to study the behavior of the system in small signal analysis. the equivalent dynamic resistance of the luxeon iii star from lumiled measured with different bias current level is reported below: equation 11 figure 12. load equivalent circuit g loop s () g pwm f sw () a ota s () g pwr s () led n led () ? ? ? = g pwm f sw () 1 0.076 -------------- - f sw khz () 250 ------------------------- - ? = r led 1.3 i led 350ma = 0.9 i led 700ma = ? ? ? !-v
the l5973ad in led driving applications AN2823 14/33 doc id 15015 rev 1 as a consequence, the term led (s) can be calculated as: equation 12 and considering r sense << (r1+r6) the equation can be simplified as follows: equation 13 the term is plotted as a function of the led composing the row and the biasing current, as shown in figure 13 . figure 13. led(s) plot the power components, their stray contributions and the load constitute the equivalent circuit of the power stage shown in figure 14 . led n led () r sense n led r led r sense // r 1 r 6 + () + ? --------------------------------------------------------------------------------------- r 1 r sense r 1 r 6 ++ ------------------------------------------------ ? = led n led () r sense n led r led r sense + ? --------------------------------------------------------- - r 1 r 1 r 6 + -------------------- ? !-v
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 15/33 figure 14. power stage equivalent circuit the main contribution is given by the lc filter of the output stage which introduces a double pole in the transfer function of the control loop. the overall contribution to the small signal model can be written as: equation 14 considering l=100 h and cout=100 nf (see figure 19 ) the frequency of the double pole can be approximated to 50 khz. the equivalent circuit of the embedded transconductance error amplifier including the external compensation network is provided in figure 15 . the embedded error amplifier is used to compensate the double pole contribution within the system bandwidth introducing a zero before its frequency; an additional pole outside the bandwidth is also introduced but typically its contribution to the phase margin can be ignored. the transfer function of the equivalent circuit can be calculated as: equation 15 !-v l sw1 dc sw2 cout rled1 rled2 rledn rsens e dcr es r g pwr s () 1 1 esr 1 sc out ? ---------------------- + ----------------------------------------- - 1 n_led rled_eq r sense + ? --------------------------------------------------------------- - + ---------------------------------------------------------------------------------------------------------------- - dcr s l 1 1 esr 1 sc out ? ---------------------- + ----------------------------------------- - 1 n_led rled_eq r sense + ? --------------------------------------------------------------- - + ---------------------------------------------------------------------------------------------------------------- - + ? + ------------------------------------------------------------------------------------------------------------------------------- ----------------------- = a ota s () g m 1 1 r 0 ------ - sc ea c 5 + () 1 r 5 1 sc 4 ? -------------- + --------------------------- - + ? + ------------------------------------------------------------------------------------- ? =
the l5973ad in led driving applications AN2823 16/33 doc id 15015 rev 1 figure 15. ota equivalent circuit so the frequencies of the singularities are: equation 16 equation 17 where the values of the components related to the embedded error amplifier are: cea=3 pf, gm=2.3 ms, r o =0.8 m . the plots of magnitude and phase of the overall gain transfer loop of the system are provided in figure 16 and 17 . figure 16. module plot !-v gm*v d r o c ea r5 c4 c5 v+ v- v d f zero 1 2 r 5 c 4 ?? ? --------------------------------- - 7khz = = f pole_lf 1 2 r o c 4 ?? ? ----------------------------------- 2.9hz = = f pole_hf 1 2 r 5 c ea c 5 + () ?? ? -------------------------------------------------------- 13mhz = = am01 3 66v1
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 17/33 figure 17. phase plot the cutoff frequency and the phase margin are: equation 18 2.1.4 led current accuracy the purpose of this paragraph is to estimate each contribution which affects the accuracy of the dc current flowing through the load (r 6 =6.8 k , r1=20 k , r s =1.5 w, p losses = 184 mw). the current flowing in the led satisfies the equation: equation 19 the accuracy l597x of the reference and feedback voltage of the embedded error amplifier is 1.2% (see the l5973ad device datasheet). the two parameters are based on the internal bandgap cell of the device, so the relative spread is minimized (they are in tracking). the spread of the current flowing in the led is expressed as: equation 20 am01 3 67v1 f c 36khz = m 84 o = i led r sense v s v fb r 6 r 1 ------ - v ref v fb ? () ? ? = = ? i led v fb 1 l597x () ? r 6 1 r 6 () ? r 1 1 r 1 () ? --------------------------------- - v ref v fb ? () 1 l597x () ?? ? r sense 1 r sense () ? ------------------------------------------------------------------------------------------------------------------------------- --------------------------------- =
the l5973ad in led driving applications AN2823 18/33 doc id 15015 rev 1 which can be written as: equation 21 the accuracy of the selected components rs, r8 and r1 is 1%, so the overall positive and negative contributions in the worst case are estimated below: equation 22 equation 23 and so the percentage shift is: equation 24 equation 25 so the overall spread of the led current is: equation 26 2.2 designing a high efficiency current source (topology 2) the purpose of this section is to improve the topology presented in section 2.1 , reducing the power losses on the sense resistor to obtain better efficiency of the conversion. this is achieved with the use of a few external components to implement a gain block placed between the sense resistor and the inverting input of the embedded error amplifier in order to amplify the dc drop across the sense resistor. i led v fb r 6 1 r 6 () ? r 1 1 r 1 () ? --------------------------------- - v ref v fb ? () ? ? ?? ?? ?? 1 l597x () ? r sense 1 r sense () ? ------------------------------------------------------------------------------------------------------------------------------- ---- = i + v fb r 6 1 r 6 ? () ? r 1 1 r 1 + () ? ---------------------------------- v ref v fb ? () ? ? ?? ?? ?? 1 l597x + () ? r sense 1 r sense ? () ? ------------------------------------------------------------------------------------------------------------------------------- ---- = 1.235 6.8 20 ------- - 0.99 1.01 ----------- 2.065 ?? ? ?? ?? 1.01 ? 1.5 0.99 ? -------------------------------------------------------------------------------------- - 0.371a ?? i - v fb r 6 1 r 6 + () ? r 1 1 r 1 ? () ? ---------------------------------- v ref v fb ? () ? ? ?? ?? ?? 1 l597x ? () ? r sense 1 r sense + () ? ------------------------------------------------------------------------------------------------------------------------------- --- - = 1.235 6.8 20 ------- - 1.01 0.99 ----------- 2.065 ?? ? ?? ?? 0.99 ? 1.5 1.01 ? -------------------------------------------------------------------------------------- - 0.338a ?? i + % () i + i led ? i led ------------------------ 100 0.371a 0.355a ? 0.355a -------------------------------------------- 100 +4.5% ? ? ? ? = i - % () i - i led ? i led ----------------------- 100 0.338a 0.355a ? 0.355a -------------------------------------------- 100 -4.78% ? ? ? ? = i spread % () i + % () i - % () ? = 9.28% =
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 19/33 a general-purpose external operational amplifier in non inverting topology implements the dc gain block. the selected ts321 (small sot23-5 package) is one of the two embedded amplifiers composing the lm158 market standard. the compensation network is designed for device operation without an output capacitor filter to reduce the count and cost of external components. the main consequence is a load current unfiltered from the ripple current: the high natural switching frequency (500 khz) of the l5973ad helps keep the ripple current negligible in all operating conditions even when compared to the minimum load current (350 ma), given an inductor value of 100 h. the maximum accuracy of the load current is finally provided considering the spread of the involved parameters. 2.2.1 dc gain design the basic schematic of the enhanced dimmable current generator is shown in figure 18 . figure 18. basic schematic of the current source !-v ,!$ +s 2 3%.3% &" ,!$ +s +s 2 3%.3% &"
the l5973ad in led driving applications AN2823 20/33 doc id 15015 rev 1 figure 19. schematic of the dimmable current source using l5973ad !-v . . . . 2 + 2 + 2 2 *0 *0 # n& # n& $3 3403,5 $3 3403,5 2 $.- 2 $.- * * 23 23 2 $.- 2 $.- $?$)-- $?$)-- '.$ '.$ # u& # u& 2 $.- 2 $.- 6). 6). 2 + 2 + 6/54 6## 62%& '.$ ).( #/-0 '.$ &" 39.# 5 ,!$ 5 ,!$ 2 $.- 2 $.- # p& # p& 2 $.- 2 $.- 2 $.- 2 $.- *0 *0 6,%$ 6,%$ 1 . 1 . 2 + 2 + # n& # n& 62%& 62%& 39.# 39.# *0 *0 # $.- # $.- # p& # p& 2 + 2 + # # 2 + 2 + $)--).' $)--).' *0 *0 # n& # n& 2 $.- 2 $.- 2 $.- 2 $.- ).( ).( , u( , u( # n& # n& 2 + 2 + *0 *0 6,%$ 6,%$ 2 + 2 + # n& # n& 1 $.- 1 $.- $ $.- $ $.- 2 2 '.$ '.$ 5 43 5 43 *0 *0 2 2 $ $.- $ $.-
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 21/33 the gain block k(s) amplifies the voltage sensed on the resistor and thus decreases the power lost across it. its frequency behavior can also be useful to compensate the loop function, introducing a pole or a zero if needed (see figure 19 ). the k(s) is implemented through an operational amplifier working in a non inverting configuration. in the schematic shown in figure 19 , the gain is equation 27 so leaving jp4 and jp5 open k(0) 10.01, otherwise closing both jumper k(0) 5.7. considering the r sense =0.33 , the regulated current is: equation 28 and the power lost across r sense is: equation 29 it can be considered negligible when compared to the amount of power delivered to the load. 2.2.2 the dimming operation the dimming operation is implemen ted as previously described in section 2.1.2 : switch q1 clamps the output of the error amplifier to disable the switching activity. figure 20 and 21 show the dimming operation of the schematic in figure 19 , monitoring the input dimming signal and the led current. ks () 1 r15//r16//r11//r13 r14//r12 ------------------------------------------------------- + ?? ?? = i led1 v fb k jp4 open, jp5 open 0 () r sense ? -------------------------------------------------------------------------------------- 1.235 10.01 0.33 ? ------------------------------ - 375 ma ? ? = i led2 v fb k jp4 close, jp5 close 0 () r sense ? ------------------------------------------------------------------------------------------- - 1.235 5.3 0.33 ? ------------------------ 706 ma ?? = ? ? ? ? ? ? ? p loss 1 r sense i led () 2 46.4 mw ? ? = p loss 2 r sense i led () 2 142 mw ? ? = ? ? ? ? ?
the l5973ad in led driving applications AN2823 22/33 doc id 15015 rev 1 figure 20. q1 disables the switching activity by clamping the comp signal figure 21. time delay in the led current leading edge the dimming performance of the circuit depends on the input voltage and number n of the led composing the row. the higher the voltage applied on the inductor (vin-n*v led_fw ) the higher the rising time of the led current given the inductor value. the minimum dimming duty cycle is determined based on the specification of the rising / falling time of the led current referred to the dimming time and on the dimming frequency. !-v am01 3 71v1
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 23/33 figure 22. dimming signal from figure 20 and 21 (vin = 18 v, string composed of two leds) the following data can be inferred: equation 30 considering a dimming frequency of 250 hz, the minimum duty cycle of the pwm dimming satisfies the equation: equation 31 so the minimum d is about 5%. by relaxing the edge requirements or increasing the transient performance of the circuit, which depend on vin and the number of led composing the string and inductor value, a lower d can be achieved. 2.2.3 frequency compensation most of the theory explained in section 2.1.3 on page 13 is still valid for the circuit in figure 19 . the equation of the loop transfer function is: equation 32 where the terms g pwm , a ota and g pwm are already known. here, the term led(s) is slightly different and can be calculated as: equation 33 !-v 2 t rise 40 s = t fall 6 s = ? ? ? t rise t fall + 0.2 t min_pulse ? 0.2 d min t dimming ?? == g loop s () g pwm f sw () ks () a ota s () g pwr s () led n led () ? ? ? ? = led n led () r sense n led r led r sense + ? --------------------------------------------------------- - =
the l5973ad in led driving applications AN2823 24/33 doc id 15015 rev 1 and it is plotted in figure 24 . figure 23. led(s) plot k(s) represents the transfer function of the block implemented through the external amplifier (see figure 24 ). the external error amplifier bandwidth is 0.8 mhz, so the correction term of the ideal gain is introduced into the calculations to obtain a better analytical description of the real transfer function of the block. equation 34 figure 24. equivalent circuit of block k(s) !-v ks () 1 z 2 s () z 1 s () -------------- + 1 1 g loop_ea s () ------------------------------ ? --------------------------------------- - 1 z 2 s () z 1 s () -------------- + 1 z 1 s () z 2 s () + a ea s () ----------------------------------- 1 z 1 s () -------------- ? ?? ?? ? --------------------------------------------------------------------- - == am01 3 74v1 led1 led2 ledn rsense z2 z1 r7 to l5973ad pin 5
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 25/33 where: equation 35 considering l=100 h and c out =100 nf (see figure 19 ), the frequency of the double pole can be approximated to 50 khz. figure 25. module plot the cutoff frequency and the phase margin are: equation 36 figure 26. phase plot z 1 s () 1 sc 6 ? 1 r 14 --------- + ------------------------------ - = z 2 s () 1 sc 7 ? 1 r 16 --------- + ------------------------------ - = am01 3 75v1 f c 73khz = m 35 o = am01 3 76v1
the l5973ad in led driving applications AN2823 26/33 doc id 15015 rev 1 2.2.4 led current accuracy the reference of the embedded error amplifier is 1.235 v 1.2% (see the l5973ad device datasheet). the current flowing through the led satisfies the equation: equation 37 so considering r 14 =1.1 k , r 16 =10 k , r sense =330 mw (p losses =46.4 mw) the nominal regulated current is: equation 38 the designed dc gain of the k(s) clock equal to: equation 39 makes negligible the contribution to the overall led accuracy introduced by the voltage offset of the embedded ota compared to the one introduced by the external error amplifier. the datasheet of the ts321 reports a maximum input voltage offset of 5 mv (typical value is 0.5 mv) and a maximum bias current of 50 na. the resistor r 8 =1.1 k compensates the contribution of r14//r15 1.1 k , thus minimizing the error introduced by the bias current, which can be disregarded. the maximum voltage offset in relation to the nominal drop across the sense resistor is: equation 40 the typical loop gain of the ts321 is 85 db, so its magnitude allows the disregard of the error e given in the dc gain set with the resistor r 14 , r 16 . finally, the spread of the value of the external component affect the led current. the accuracy of the selected components rs1, r 14 , r 16 is 1%, so the overall positive and negative contributions in the worst case are estimated below: equation 41 i led r sense 1 r 16 r 14 --------- + ?? ?? v fb = ?? i led v fb r sense 1 r 16 r 14 --------- + ?? ?? ? --------------------------------------------------- = 1.235 330m 1 10 1.1 ------- - + ?? ?? ? ------------------------------------------------ 0.375a ? = r sense 1 r 16 r 14 --------- + ?? ?? 3.3033 ? i offset % () v offset r sense i led ? ------------------------------------- - = 100 ? 5mv 330m 375ma ? -------------------------------------------- 100 4% = ? = i + v fb 1 fb_ota + () ? r sense 1 sense ? () 1 r 16 1 16 ? () ? r 14 1 14 + () ? ------------------------------------ + ?? ?? ?? --------------------------------------------------------------------------------------------------------------------- = 1.25 326.7m 9.9108 ? ----------------------------------------------- - 0.386a ??
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 27/33 equation 42 and so the percentage shift is: equation 43 equation 44 finally, considering the contribution given by the offset of the lm351: equation 45 equation 46 so the overall spread of the led current is: equation 47 2.3 conclusions this paragraph highlights the benefits and limitations of the two circuit topologies in terms of spread of the regulated leds in different operating conditions. given the voltage drop on the sense resistor, the efficiency of the conversion depends on the number of leds as the output power increases. equation 48 figure 27 shows the efficiency of an ideal current generator considering only the loss across the sense resistor. it can be inferred that, when the objective of the design is to reach a certain minimum efficiency of the conversion, higher losses on the sense resistor could be accepted by increasing the number of the leds in the string. i - v fb 1 fb_ota ? () ? r sense 1 sense + () 1 r 16 1 16 + () ? r 14 1 14 ? () ? ------------------------------------ + ?? ?? ?? --------------------------------------------------------------------------------------------------------------------- = 1.22 333.3m 10.27 ? -------------------------------------------- 0.356a ?? i + % () i + i led ? i led ------------------------ 100 0.386a 0.375a ? 0.375a -------------------------------------------- 100 +2.93% ? ? ? ? = i - % () i - i led ? i led ----------------------- 100 0.356a 0.375a ? 0.375a -------------------------------------------- 100 -5.06% ? ? ? ? = i - led % () i - % () i offset ? % () = -9.06% ? i - led % () i - % () i offset ? % () = -9.06% ? i spread % () i + % () i - % () ? = 15.99% = p led p led r sense i led () 2 ? + ----------------------------------------------------------------- - =
the l5973ad in led driving applications AN2823 28/33 doc id 15015 rev 1 figure 27. maximum efficiency vs. voltage drop (i led =350 ma) figure 28 shows the power losses across the resistor: equation 49 figure 28. power losses across the sense resistor (i led =350 ma) figure 29 compares the spread of the led current when implementing the different topologies described in the section 2.1 and 2.2 as a function of the voltage across rs and using the same calculations provided in section 2.1.4 and 2.1.4 . am01 3 77v1 p losses r sense i led () 2 ? = !-v
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 29/33 figure 29. spread of the led current vs. voltage drop (i led =350 ma) figure 27 and 28 are useful to choose the required voltage sense to satisfy the efficiency specification. from figure 29 , it follows that the circuit topology using the external operational amplifier becomes attractive in terms of parameter spread when the sense voltage is lower than 650 mv (led current is 350 ma). the trade-off between required current accuracy and efficiency determines the circuit topology to be used in the design. as discussed in section 2.1.4 (topology 2), the accuracy of the current is mainly affected by the voltage offset of the external error amplifier: better results can be achieved by selecting an error amplifier with a limited offset (i.e. trimmed). figure 29 shows the same data provided in figure 28 , but considering a maximum voltage offset of 0.5 mv (which is also the typical offset of the ts321 device): the spread of the load current drops from 10.7% ( figure 29 ) to 7.7% ( figure 28 ), when v sense =300 mv. as a consequence, selecting an external error amplifier with a better offset voltage decreases the intersection point of the two traces in figure 29 , making topology ii more convenient than topology i, in terms of current accuracy, for a wider v sense range. am01 3 79v1
the l5973ad in led driving applications AN2823 30/33 doc id 15015 rev 1 figure 30. power losses across the sense resistor (i led =350 ma) figure 31 , 32 and 33 give the same data when driving 700 ma leds. figure 31. maximum efficiency vs. voltage drop (i led =700 ma) am01 38 0v1 am01 38 1v1
AN2823 the l5973ad in led driving applications doc id 15015 rev 1 31/33 figure 32. power losses across the sense resistor (i led =700 ma) figure 33. spread of the led current vs. voltage drop (i led =700 ma) am01 38 2v1 am01 38 2v1
revision history AN2823 32/33 doc id 15015 rev 1 3 revision history table 2. document revision history date revision changes 11-aug-2009 1 initial release
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