Feedback Control Design of Off-line Flyback Converter

Transcription

1 Application Note Edwin Wang AN7 Jun 24 Feedback Control Deign of Off-line Flyback Converter Abtract Controlling the feedback of off-line flyback converter ha often perplexed power engineer becaue it involve the continuou conduction mode (CCM) and dicontinuou conduction mode (DCM) mall ignal model. Due to the unique feedback compenation mode of the TL43 along with the optocoupler, tuning the feedback parameter till relie on trial and error. Thi application note provide comprehenive deign guideline, from illutrating power circuit tranfer function to deigning the circuitry for the TL43 and the optocoupler, to aiting ytem deigner to gain a good phae margin o a to meet the requirement of tranient tability. In thi note, theoretical computation are done by Mathcad oftware and verified by Simpli. Thi method will be applicable to all application with RT773x erie off-line flyback controller. Content. Scope of Application: Secondary-Side Flyback Converter Power Circuit Small-Signal Model Feedback Compenation Circuit Deign... 7 AN7 24 Richtek Technology Corporation

2 Feedback Control Deign of Off-line Flyback Converter. Scope of Application: Secondary-Side Flyback Converter Mot flyback converter ue econdary-ide peak current-mode control of the econdary-ide converter to adjut feedback for the output voltage a in Figure. The econdary-ide output voltage i fed back through the TL43 and the optocoupler to the primary-ide. The output of the optocoupler, V COMP, i compared with the primary-ide peak current. Thi reult erve a the negative feedback to the loop and then determine the duty cycle of the witching component Q. R S i the reitor for the primary-tage current detection. CTR i the current tranfer ratio of the optocoupler. G FB i the mall-ignal gain. (Note: It i deigned to be about /3 of gain internally for all the RT773x IC.) S e i added externally a the lope compenation to eliminate ub-harmonic ocillation. Some baic aumption are made to facilitate the following derivation and explanation a below:. Switching component, Q, and the diode in the econdary-ide, D, are ideal. 2. The tranformer i ideal. 3. The open-loop gain of the TL43 i infinity. (It nominal open-loop gain i about 5 ~ 6 db.) 4. The current tranfer ratio, CTR, of the optocoupler i a contant. In reality, the current tranfer ratio i a relatively nonlinear value, varying with the operating point (which i the current through the diode in the optocoupler). However, to implify the derivation, we aume it i a contant value over the current through it. In practical application, current through the optocoupler diode are fairly low, a low a ma, which caue a current tranfer ratio le than 2%. Other term and ymbol are defined a below: D : duty cycle f : witching frequency M nv V o : voltage tranfer ratio in Np n : tranformer coil ratio N 2Lp f τl : time contant 2 n R S V in n R : the voltage lope when the primary-ide current i detected on R S (unit: V/ec) Lp S e : the externally added voltage (unit: V/ec) G FB vˆ vˆ RS FB : the mall-ignal gain AN7 24 Richtek Technology Corporation 2

3 Feedback Control Deign of Off-line Flyback Converter n : V O V IN L P L S D C o R R S Q R C S n V REG S e R c3 R d V COMP CTR G FB R a C a C b PC87 TL43 R b Figure. The chematic of the flyback converter with the TL43 and the optocoupler. 2. Power Circuit Small-Signal Model Variou mall-ignal model of flyback converter can be found in many reference [-3]. Thee model are all derived baed on the method of tate averaging. There are ome minor difference among them, which probably reult from the different aumption being made. In thi note, the mall-ignal model of Chritophe Bao [] i adapted for our feedback compenation deign. However, with other mall-ignal model, imilar reult can alo be achieved. The tranfer function of the continuou conduction mode (CCM) ( ) ( ) vˆ o() z z2 G vˆ comp() ( ) p () where, nr G G R FB 2 ( D) p z ( D) τl R C c o τ L 3 e ( 2 ) D RC o S S n S Sn e 2 2 M (ESR Zero, LHP) z2 2 2 ( D) n R DL p (RHP Zero) AN7 24 Richtek Technology Corporation 3

4 Feedback Control Deign of Off-line Flyback Converter Thi i a pole 2 zero ytem, a hown in Figure 2. The pole i determined by the circuit parameter and the ize of the load. The firt zero i fixed becaue it depend on the output capacitance and the equivalent erie reitance (ESR). The other zero i on the right half -plane, o called RHP zero. The location of RHP zero i determined by the input voltage, and the load current. Uually, in a well-deigned ytem, the cro-over frequency i et far below the RHP zero frequency o the ytem can have ufficient phae margin. Baed on thi fact, thi RHP zero i regarded a negligible when deigning the compenation circuit. f p - + f z f z2 Figure 2. The tranfer function of CCM P2Z. The tranfer function of the dicontinuou conduction mode (DCM) ( ) ( ) vˆ o() z z2 G vˆ comp() ( ) ( ) p p2 (2) where, G V G in FB Lp Sn Se p 2 R C o p2 2 f f R 2 ( ) D ( ) M 2 z z2 R C c o 2 n R M ( M) L p (ESR Zero, LHP) (RHP Zero) AN7 24 Richtek Technology Corporation 4

5 Load Current (A) Feedback Control Deign of Off-line Flyback Converter The tranfer function of Equation (2) i hown in Figure 3. In mall-ignal model of dicontinuou conduction mode, DCM, the power circuit ha two pole and two zero. One of the pole, p2, i extremely high (far above the target cro-over frequency). Therefore, deigning the compenation, thi pole can be neglected. A a reult, with the mall-ignal model of either CCM or DCM, their tranfer function can be conidered a pole 2 zero. Therefore, the election of the feedback network become much eaier. From the tranfer function of Equation () and (2), ome pole and zero are fixed, uch a the zero from the output capacitance and the equivalent erie reitance ESR. However, mot pole and zero are influenced by the operating point, which decribe the operating condition of the circuit and i pecified by the input voltage and the load current condition. Next, the change of the pole and zero with the operating point will be illutrated with the circuit parameter plugged in. f p - + f p2 f z f z2 Figure 3. The tranfer function of DCM P2Z. Operating Point and Variation of Pole and Zero With a flyback converter a an example, given input voltage: 9V to 36V, load current: -3A, and output voltage a 2V. The circuit parameter are a below: L P =.mh, N P/N S = n = 7.7, C O = 36μF, R ESR = 3 mω, R S =.56Ω, f S = 65kHz, S e = 3.46 x 4 V/ec, G FB =.3333, where S e and G FB are provided by the controller IC According to the operating principle of flyback converter, in a typical deign, high input voltage with light load alway caue converter to operate in continuou conduction mode; on the contrary, low input voltage with heavy load in the dicontinuou conduction mode. A boundary exit between CCM and DCM, a hown in Figure 4 and it equation i a Equation (3) Input Voltage (V) Figure 4. The boundary of CCM and DCM. AN7 24 Richtek Technology Corporation 5

6 Feedback Control Deign of Off-line Flyback Converter n V V Io 2 ( ) 2 2 o IN 2 LP fs VIN nvo (3) The Variation of Pole and Zero at Different Operating Point Table how the DC gain and the location of pole and zero. Figure 5 how the Bode plot for the different input voltage and load current. From the plot, it i clear that the gain i higher with high line and light load. Thi help in chooing the operating point a the criteria for feedback network deign. It i better to deign the feedback network under low line and heavy load condition. Adequate phae margin under uch condition, can achieve an even better phae margin at different operating condition. Table. The DC gain and the location of pole and zero at different operating point V IN (V) I O (A) Mode CCM CCM CCM DCM CCM CCM DCM DCM DCM DCM G (db) f P (Hz) f P2 (Hz) NA NA NA 2.7k NA NA 25k 2.7k 32.6k 65k f Z (Hz) 3.9k 3.9k 3.9k 3.9k 3.9k 3.9k 3.9k 3.9k 3.9k 3.9k f Z2 (Hz) 6.5k 44.2k 75k 6k 6.5k 24.7k 49.5k 6k 6k 39k CCM DCM f p High Line f p High Line Low Line Low Line f z f z2 f z f p2 CCM DCM f p Light Load f p Light Load Heavy Load Heavy Load f z f z2 f z f p2 Figure 5. The variation of the gain v. frequency with different operating condition. AN7 24 Richtek Technology Corporation 6

7 Feedback Control Deign of Off-line Flyback Converter 3. Feedback Compenation Circuit Deign From the previou analyi, pole and zero vary with operating point a do low-frequency DC gain. There are many way to deign compenation circuit. Typically, a Type-II compenator (with one zero frequency pole, one low-frequency zero, and one pole) i mot uitable in thi cae. Making a low-frequency zero to compenate the low-frequency pole and alo making a high-frequency pole to compenate the ESR zero can achieve a better phae margin. A pecific mid-band gain i choen to get the proper cro-over frequency, and the ytem will therefore be tabilized. One of the practical way i etting a good target loop gain a loop gain = k (4) Such loop gain i jut a traight line with the lope of -2dB/dec on the Bode plot a een in Figure 6. At the low frequency or DC region, the gain i extremely high (equivalent to the open-loop gain of the compenator), o the theoretical adjutment rate of the DC regulating voltage can be et a zero. It cro-over frequency, f C, i k fc (5) 2π Since it lope i about -2dB/dec, it phae margin i about 9 near the cro-over frequency. For an off-line flyback converter, it i bet to et the cro-over frequency between 8Hz and 3kHz under the condition of low line and full load (where witching frequency i 65kHz). 2π f c f c Figure 6. The tranfer function of the power circuit (in red) and it target loop gain (in blue). AN7 24 Richtek Technology Corporation 7

8 Feedback Control Deign of Off-line Flyback Converter Deign Procedure A dicued above, any compenation method will work. The deign procedure are lited below:. Deign the compenation network under the condition of low line (input voltage) and full load. It uually will give a very good phae margin even at variou condition. 2. Set the cro-over frequency f C, and it loop gain a -2dB/dec in the Bode plot. Higher cro-over frequency mean fater tranient repone. However, it i impoible to compenate RHP zero by the pole. Therefore, the cro-over frequency mut be far below from RHP zero. Practically, the cro-over frequency i et below 3kHz. 3. Define a 2-pole-and--zero compenation circuit and et the zero a the low-frequency pole of the power circuit. Set the high-frequency pole a the ESR zero of the power circuit. Implement the deign by a Type II compenator. It tranfer function can be the target loop gain. 4. Calculate mid-band gain according to power circuit gain at f C. 5. Etimate phae margin. 6. The tranfer function of the compenation network i determined. ( ) cz Gcomp() A ( ) cp (6) In other word, A cp and cz in Equation (6) can be found. Implementation of Compenator. Thi note illutrate the deign method with a typical Type II circuit, a widely ued circuit block of TL43 and the optocoupler, a hown in Figure 7. V reg V o V c R d R c3 R a C b Opto C a TL43 R b Figure 7. The chematic of the typical compenation circuit. AN7 24 Richtek Technology Corporation 8

9 Feedback Control Deign of Off-line Flyback Converter 2. The mall-ignal tranfer function of the circuit in Figure 7 i a hown below [5]: vˆ o( ) Rd ( CaRa ) Gcomp() CTR vˆ ( ) R C R ( C R ) c c3 a a b d (7) Figure 8 i it Bode plot. f cz f cp Figure 8. The Bode plot of the Type II compenation circuit 3. From Equation (7), there are 7 parameter, R a R b R c3 R d C a C b and CTR to be decided, and only three of them are known. R CTR R C R d A (8) c3 a a cz CR (9) a a cp CR () b d 4. Firt, chooe R d. Mot new controller IC have et the R d value, which can be obtained from vendor. 5. Next, the reference voltage V REF can alo be obtained from vendor, typically 2.5V. To make TL43 function properly, the current through R b (I vd) mut be at leat 25μA. I vd i uually pecified a 25μA with ome margin. Therefore, the value of R a and R b can be determined. R V REF b () Ivd R ( V V ) I (2) a o REF vd AN7 24 Richtek Technology Corporation 9

10 Feedback Control Deign of Off-line Flyback Converter 6. The current tranfer ratio of the optocoupler (CTR) can be etimated according to the information provided by vendor. CTR i a nonlinear value, varying with the current through the optocoupler diode. Uually the current i on the order of hundred μa with CTR around. to.5. The exact value can be found through the meaurement. Here CTR i aumed to be Now, four of the even parameter are decided. The ret three can be calculated by Equation (8), (9) and (). 8. R C3 acquired from Equation (8) mut be evaluated. From how the TL43 work, the cathode voltage mut be higher than 2.5V and the current through the cathode (I cathode) hould be greater than ma to get a correct regulating voltage. Uually, a kω reitor will be added in hunt with the optocoupler diode to provide ufficient cathode current. Thi hunt reitor will not change the mall ignal model. Therefore, we can derive the following: Vcathode VO Icathode RC3 VF 2.5V (3) I cathode Iopto _ tranitor F V ma CTR R parallel (4) where V F i forwarded biaed voltage drop of the optocoupler, around.v. The maximum value of R C3 can then be etimated. R V V 2.5 o F c3 (5) Icathode Aume I cathode i.5ma, and R C3 hould be le than 5.6kΩ. Exceice R C3 will lower the mid-band gain. If R C3 i greater than the maximum value, the cro-over frequency will be et lower or another compenation method will be ued. 9. There exit an equivalent capacitance, around 2nF to 5nF, in hunt with the phototranitor of the optocoupler. The total C b value i thi paraitic capacitance, which can be meaured, and the external added capacitor. If the paraitic capacitance i dominant, then no external capacitance i needed. Since ESR zero cannot be compenated completely, the phae margin will become wore. Deign Tool and Simulation Verification Two Mathcad computation procedure, Flyback CCM Type II Compenation and Flyback Loop Gain Analyi have been ued to facilitate the calculation and analyi of the feedback network deign. Simpli imulation are ued to compare error of the imulation model. Figure 9 i the chematic of Simpli imulation circuit. Figure to Figure 2 how the comparion of Mathcad analyi and Simpli imulation. Figure and Figure are the Bode plot of the tranfer function of the power circuit and the compenation network, repectively. Figure 2 i the Bode plot of the cloed-loop gain, (a) magnitude and (b) phae. Red line indicate the reult from Mathcad calculation and blue line from Simpli. AN7 24 Richtek Technology Corporation

11 Power Stage (db) Power Stage (deg) Feedback Control Deign of Off-line Flyback Converter From the low frequency to cro-over frequency, the mall ignal model match very well. The model tart to how a large mimatch at the high frequency region. However, ince the loop gain i much le than, the mimatch can be neglected. Figure 3 how the tep repone of the output voltage for the load current from A to 3A with 9V input voltage by Simpli imulation. Fairly mall overhoot and ettling time are hown. DIODE VOUT VOUT X IDEAL 3m 9 VIN P S RC.36m CO 4 RL U4 TX GND GATE SW VAC FB VDD AC VA IN OUT =OUT/IN VOUT PRO CS RT7736_Simplified VFB 56m RCS.2k Rc VA VFB IN OUT =OUT/IN VOUT U3 k Rf 38k Ra VA IN OUT =OUT/IN VFB 24p Cb U2 TL43 68n Ca k Rb Figure 9. The chematic of the Simpli imulation circuit Figure. The Bode plot of the tranfer function of the power circuit (a) magnitude, (b) phae. AN7 24 Richtek Technology Corporation

12 Loop Loop Gain (deg) Compenator (db) Compenator (deg) Feedback Control Deign of Off-line Flyback Converter Figure. The Bode plot of the tranfer function of the compenation network (a) magnitude, (b) phae f c ɸ m Figure 2. The Bode plot of the loop gain (a) magnitude, (b) phae. Figure 3. The repone to a large tep load current. AN7 24 Richtek Technology Corporation 2

13 Feedback Control Deign of Off-line Flyback Converter Reference [] Chritophe P. Bao, Switch-Mode Power Supplie Spice Simulation and Practical Deign, McGraw_Hill, 28. [2] W. Kleebchampee and C. Bunlakananuorn, Modeling and Control Deign of a Current-Mode Controlled Flyback Converter with Optocoupler Feedback, IEEE PEDS 25. [3] Yuri Panov and Milan M. Jovanovic, Small-Signal Analyi and Control Deign of Iolated Power Supplie with Optocoupler Feedback, IEEE TRANSACTIONS ON POWER ELECTRONICS, JULY 25. [4] 王信雄, 定频返驰式转换器设计指南, RTAD22TC, 立锜科技设计指南, 22. [5] John Schönberger, Deign of a TL43-Baed Controller for a Flyback Converter, Plexim GmbH. Related Part RT7736 SmartJitter PWM Flyback Controller Dataheet Dataheet Next Step Richtek Newletter Download Application Subcribe Richtek Newletter Download PDF Flyback Controller Richtek Technology Corporation 4F, No. 8, Tai Yuen t Street, Chupei City Hinchu, Taiwan, R.O.C. Tel: Richtek product are old by decription only. Richtek reerve the right to change the circuitry and/or pecification without notice at any time. Cutomer hould obtain the latet relevant information and data heet before placing order and hould verify that uch information i current and complete. Richtek cannot aume reponibility for ue of any circuitry other than circuitry entirely embodied in a Richtek product. Information furnihed by Richtek i believed to be accurate and reliable. However, no reponibility i aumed by Richtek or it ubidiarie for it ue; nor for any infringement of patent or other right of third partie which may reult from it ue. No licene i granted by implication or otherwie under any patent or patent right of Richtek or it ubidiarie. AN7 24 Richtek Technology Corporation 3