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The TL431 in the Control of Switching Power Supplies Agenda

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The TL431 in the Control of Switching Power Supplies Agenda The TL431 in the Control of Switching Power Supplies Agenda Feedback generalities The TL431 in a compensator Small-signal analysis of the return chain A type 1 implementation with the TL431 A type 2 implementation with the TL431 A type 3 implementation with the TL431 Design examples Conclusion Agenda Feedback generalities The TL431 in a compensator Small-signal analysis of the return chain A type 1 implementation with the TL431 A type 2 implementation with the TL431 A type 3 implementation with the TL431 Design examples Conclusion What is a Regulated Power Supply? Vout is permanently compared to a reference voltage Vref. The reference voltage Vref is precise and stable over temperature. The error,ε =−VVrefα out, is amplified and sent to the control input. The power stage reacts to reduce ε as much as it can. Power stage - H Vout Control d variable Error amplifier - G Rupper + - Vin - - α + + Vp Modulator - G V PWM ref Rlower How is Regulation Performed? Text books only describe op amps in compensators… Vout Verr The market reality is different: the TL431 rules! V I’m the out law! Verr TL431 optocoupler How do we Stabilize a Converter? We need a high gain at dc for a low static error We want a sufficiently high crossover frequency for response speed ¾ Shape the compensator G(s) to build phase and gain margins! Ts( ) fc = 6.5 kHz 0° -0 dB ∠Ts( ) -88° GM = 67 dB ϕm = 92° -180° Ts( ) =−67 dB 10 100 1k 10k 100k 1Meg How Much Phase Margin to Chose? a Q factor of 0.5 (critical response) implies a ϕm of 76° a 45° ϕm corresponds to a Q of 1.2: oscillatory response! 10 Q < 0.5 over damping 1.80 Q = 5 Q = 0.5 critical damping Q = 1 Q > 0.5 under damping 7.5 Q 1.40 Q = 0.707 Asymptotically stable 1.00 5 ϕm 600m Q = 0.5 Fast response 2.5 76° and no overshoot! 200m Q = 0.5 Q = 0.1 0 5.00u 15.0u 25.0u 35.0u 45.0u 0 255075100 phase margin depends on the needed response: fast, no overshoot… good practice is to shoot for 60° and make sure ϕm always > 45° Which Crossover Frequency to Select? crossover frequency selection depends on several factors: switching frequency: theoretical limit is Fsw 2 ¾ in practice, stay below 1/5 of Fsw for noise concerns output ripple: if ripple pollutes feedback, «tail chasing» can occur. ¾ crossover frequency rolloff is mandatory, e.g. in PFC circuits presence of a Right-Half Plane Zero (RHPZ): ¾ you cannot cross over beyond 30% of the lowest RHPZ position output undershoot specification: ¾ select crossover frequency based on undershoot specs ΔIout Vp ≈ 2π fcC out Vout(t) What Compensator Types do we Need? There are basically 3 compensator types: ¾ type 1, 1 pole at the origin, no phase boost ¾ type 2, 1 pole at the origin, 1 zero, 1 pole. Phase boost up to 90° ¾ type 3, 1 pole at the origin, 1 zero pair, 1 pole pair. Boost up to 180° Gs() Gs( ) Gs( ) boost boost −270° ∠=−°Gs() 270 −270° ∠Gs( ) ∠Gs( ) 1 2 5 10 20 50 100 200 500 1k 10 100 1k 10k 100k 10 100 1k 10k 100k Type 1 Type 2 Type 3 Agenda Feedback generalities The TL431 in a compensator Small-signal analysis of the return chain A type 1 implementation with the TL431 A type 2 implementation with the TL431 A type 3 implementation with the TL431 Design examples Conclusion The TL431 Programmable Zener The TL431 is the most popular choice in nowadays designs It associates an open-collector op amp and a reference voltage The internal circuitry is self-supplied from the cathode current When the R node exceeds 2.5 V, it sinks current from its cathode K R K TL431A R A 2.5V R A K A The TL431 is a shunt regulator The TL431 Programmable Zener The TL431 lends itself very well to optocoupler control Fast lane Slow lane Vdd Vout Vout RLED Rpullup RLED R1 I1 VFB 1V ILED Ibias = Rbias Rbias Rbias VVf ≈1 I C2 C1 1 TL431 Rlower VVmin = 2.5 dc representation RLED must leave enough headroom over the TL431: upper limit! The TL431 Programmable Zener This LED resistor is a design limiting factor in low output voltages: VVVout− f− TL431,min RRLED,max≤ pullupCTR min VVdd−+ CE,min sat I biasCTR R pullup When the capacitor C1 is a short-circuit, RLED fixes the fast lane gain Vsout ( ) R LED R1 Vdd VsFB()= −⋅ CTR R pullup ⋅ I1 I1 Vs() R out pullup I1 = 0 V RLED in ac Ic Vs FB () Vs() R FB =−CTR pullup Rlower Vsout() R LED This resistor plays a role in dc too! The TL431 – the Static Gain Limit Let us assume the following design: 512.5− − VV= 5 RLED,max ≤××20k 0.3 out 4.8−+×× 0.3 1mk 0.3 20 VVf = 1 VVTL431,min = 2.5 VVdd = 4.8 VmVCE, sat = 300 RLED,max ≤Ω857 ImAbias = 1 CTRmin = 0.3 Rkpullup =Ω20 Rpullup 20 GordB0 >>>≈CTR 0.3 7 17 RLED 0.857 In designs where RLED fixes the gain, G0 cannot be below 17 dB You cannot “amplify” by less than 17 dB The TL431 – the Static Gain Limit You must identify the areas where compensation is possible dB ° 40.0 180 Not ok Requires f > 500 Hz less c 20.0 90.0 Hs ( ) than 17 dB of gain 0 0 -17 dB -20.0 -90.0 arg H (s) Requires 17 dB -40.0 -180 ok or more 10 100500 1k 10k 100k TL431 – Injecting Bias Current A TL431 must be biased above 1 mA to guaranty its parameters If not, its open-loop suffers – a 10-dB difference can be observed! > 10-dB difference I Easy bias Ibias = 1.3 mA solution Rbias Ibias = 300 µA 1 R = =Ω1 k bias 1m Agenda Feedback generalities The TL431 in a compensator Small-signal analysis of the return chain A type 1 implementation with the TL431 A type 2 implementation with the TL431 A type 3 implementation with the TL431 Design examples Conclusion TL431 – Small-Signal Analysis The TL431 is an open-collector op amp with a reference voltage Neglecting the LED dynamic resistance, we have: Vs VsVsout()− op ( ) out ( ) Is()= 1 R LED 1 RLED R1 sC1 1 Vsop()=− V out () s =− V out () s RuppersR upper C1 C1 I1 11⎡ ⎤ Is1 ()=+ Vout () s ⎢1 ⎥ ≈ 0 RLED⎣⎢ sR upper C1 ⎦⎥ We know that: VsFB()= −⋅ CTR R pullup ⋅ I1 Rlower Vsop () Vs( ) RpullupCTR⎡ 1+ sR upper C1 ⎤ FB =− ⎢ ⎥ Vsout() R LED⎣⎢ sRC upper 1 ⎦⎥ TL431 – Small-Signal Analysis In the previous equation we have: Rpullup 9 a static gain G0 =CTR RLED 1 9 a 0-dB origin pole frequency ωpo = CR1 upper 1 9 a zero ω = z1 RupperC1 We are missing a pole for the type 2! Vdd Type 2 transfer function R pullup Add a cap. from Vs collector to ground FB () ⎡ ⎤ Vs() RsRCpullupCTR 1+ upper 1 FB =− ⎢ ⎥ C2 Vs R sR C1+ sR C out() LED ⎣⎢ upper12() pullup ⎦⎥ TL431 – Small-Signal Analysis The optocoupler also features a parasitic capacitor ¾ it comes in parallel with C2 and must be accounted for Vout(s) Vdd Rpullup V (s) FB FB c C Copto CCC2 = || opto e optocoupler TL431 – Small-Signal Analysis The optocoupler must be characterized to know where its pole is Cdc Rled Ic 10uF 20k 2 5 Rpullup ∠Os( ) 20k Rbias VFB 1 3 Vdd 5 X1 4 6 SFH615A-4 Os() Vbias Vac IF -3 dB 4 k Adjust Vbias to have VFB at 2-3 V to be in linear region, then ac sweep The pole in this example is found at 4 kHz 11 Another design CnF== ≈2 opto constraint! 26.28204π Rfpullup pole ×× kk Agenda Feedback generalities The TL431 in a compensator Small-signal analysis of the return chain A type 1 implementation with the TL431 A type 2 implementation with the TL431 A type 3 implementation with the TL431 Design examples Conclusion The TL431 in a Type 1 Compensator To make a type 1 (origin pole only) neutralize the zero and the pole ⎡ ⎤ Vs() RsRCpullupCTR 1+ upper 1 FB =− ⎢ ⎥ Vs R sR C1+ sR C out() LED ⎣⎢ upper12() pullup ⎦⎥ R substitute 1 pullup ω = sRCsRCupper12= pullup CC12= po RRupper LED Rupper C1 CTR CTR RpullupCTR ω = C = po CR 2 2 LED 2π fRpo LED Once neutralized, you are left with an integrator 1 f po CTR Gs()= ||Gf()= f = Gf C2 = s c pofcc 2πGfR fc fc cLED ω po TL431 Type 1 Design Example We want a 5-dB gain at 5 kHz to stabilize the 5-V converter VVout = 5 VVf = 1 Apply 15% VVTL431,min = 2.5 margin VVdd = 4.8 RLED,max ≤ 857 Ω RLED = 728 Ω VmVCE, sat = 300 ImAbias = 1 CTRmin = 0.3 Rkpullup =Ω20 5 20 G fc ==10 1.77 CTR 0.3 CnF2 == ≈7.4 fkHz10 2πGfR 6.28××× 1.77 5 k 728 c = fcLEDc Copto = 2 nF Rpullup CnnnF= 7.4−= 2 5.4 CCnF12=≈14.7 Rupper TL431 Type 1 Design Example SPICE can simulate the design – automate elements calculations… parameters Vout=5 Vf=1 Vref=2.5 VCEsat=300m Vdd=4.8 E1 Ibias=1m Vdd -1k L1 A=Vout-Vf-Vref {Vdd} 4.99V 1k 4.99V 4.99V B=Vdd-VCEsat+Ibias*CTR*Rpullup 4.80V err Rmax=(A/B)*Rpullup*CTR 6 5 7 Rupper=(Vout-2.5)/250u Rpullup RLED R2 R5 2.50V fc=5k {Rpullup} {RLED} {Rupper} 100m 9 Gfc=-5 2.50V 2.50V 4.99V 3.97V 2 10 G=10^(-Gfc/20) VFB 4 3 C3 B1 pi=3.14159 Voltage R6 1k V2 Fpo=G*fc 0V V(err)<0 ? 2.5 1k 0 : V(err) C1 Rpullup=20k {C1} V3 Cpole 2.96V AC = 1 RLED=Rmax*0.85 {Cpole} 1 C1=Cpole1*Rpullup/Rupper X2 Cpole1=CTR/(2*pi*Fpo*RLED)Optocoupler R3 Cpole=Cpole1-Copto Cpole = Copto X1 Automatic bias CTR = CTR 10k Fopto=4k TL431_G Copto=1/(2*pi*Fopto*Rpullup) point selection CTR = 0.3 TL431 Type 1 Design Example We have a type 1 but 1.3 dB of gain is missing? Hu? dB 20.0 Gs() 10.0 3.7 dB 0 -10.0 -20.0 ° 270 argGs( ) 180 90.0 0 -90.0 100 200 500 1k 2k 5k 10k 20k 50k 100k TL431 Type 1 Design Example The 1-kΩ resistor in parallel with the LED is an easy bias However, as it appears in the loop, does it affect the gain? Vout(s) VIRIRFB= c pullup= L pullupCTR R RLED II= bias L 1 RR+ ac representation bias d I1 VRout bias IL = VFB(s) I I L b RLED++RRRR bias|| d bias d I R c d R bias R CTR VFB pullup Rbias s=0 = Rpullup VRRRRR++|| Vf out LED bias d bias d CTR Both bias and dynamic resistances have a role in the gain expression TL431 Type 1 Design Example A low operating current increases the dynamic resistor SFH615A-2 -FORWARD CHARACTERISTICS 0.002000 Rpullup =
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