www.fairchildsemi.com AN-6086 Design Consideration for Interleaved Boundary Conduction Mode PFC Using FAN9611/12 1. Introduction This application note presents practical step-by-step design considerations for an interleaved Boundary-ConductionMode (BCM) Power-Factor-Correction (PFC) converter employing Fairchild PFC controllers FAN9611 and FAN9612. It includes designing the inductor and ZeroCurrent-Detection (ZCD) circuit, selecting the components, and closing the control loop. The design procedure is verified through an experimental 400W prototype converter. The FAN9611/12 interleaved dual BCM PFC controller operates two parallel-connected boost power trains 180º out of phase, extending the maximum practical power level of this control technique from 200-300W to greater than 800W. Unlike the Continuous Conduction Mode (CCM) technique often used at this power level, BCM offers inherent zero-current switching of the boost diodes (no reverse-recovery losses), which permits the use of less expensive diodes without sacrificing efficiency. Furthermore, the input and output filters can be made smaller due to ripple cancellation between the power stages and the effective doubling of the switching frequency. The advanced line feed-forward with peak detection circuit minimizes the output voltage variation during line transients. To guarantee stable operation with less switching loss at light load, the maximum switching frequency is clamped at 525kHz. Interleaved synchronization is maintained under all operating conditions. Protection functions include output overvoltage, over-current, open-feedback, under-voltage lockout, brownout protection, and secondary latching over-voltage protection. Figure 1. Typical Application Circuit of FAN9611 or FAN9612 © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com AN-6086 boost converter in BCM operation an ideal candidate for power factor correction. 2. Operation Principle of BCM Boost PFC Converter A by-product of the BCM is that the boost converter runs with variable switching frequency that depends primarily on the selected output voltage, the instantaneous value of the input voltage, the boost inductor value, and the output power delivered to the load. The operating frequency changes as the input current follows the sinusoidal input voltage waveform, as shown in Figure 3. The lowest frequency occurs at the peak of sinusoidal line voltage. The most widely used operation modes for the boost converter are the continuous conduction mode (CCM) and the boundary conduction mode (BCM). These two descriptive names refer to the current flowing through the energy storage inductor of the boost converter, as depicted in Figure 2. As the names indicate, the inductor current in CCM is continuous; while in BCM, the new switching period is initiated when the inductor current returns to zero, which is at the boundary of continuous conduction and discontinuous conduction operations. Even though the BCM operation has higher RMS current in the inductor and switching devices, it allows better switching condition for the MOSFET and the diode. As shown in Figure 2, the diode reverse recovery is eliminated and a fast recovery diode is not needed. MOSFET is also turned on with zero current, which reduces the switching loss. Figure 3. Operation Waveforms of BCM PFC The voltage-second balance equation for the inductor is: VIN (t ) ⋅ tON = (VOUT − VIN (t )) ⋅ tOFF (1) where VIN(t) is the rectified line voltage. The switching frequency of BCM boost PFC converter is obtained as: f SW = = 1 1 VOUT − VIN (t ) = ⋅ tON + tOFF tON VOUT 1 VOUT − VIN , PK ⋅ | sin(2π f LINE t ) | (2) ⋅ tON VOUT where VIN,PK is the amplitude of the line voltage and fLINE is the line frequency. Figure 2. CCM vs. BCM Control Figure 4 shows how the MOSFET on time and switching frequency changes as output power decreases. When the load decreases, as shown in the right side of Figure 4, the peak inductor current diminishes with reduced MOSFET on time and, therefore, the switching frequency increases. Since this can cause severe switching losses at light load condition, the maximum switching frequency of FAN9611/12 is limited to 525kHz. The fundamental idea of BCM PFC is that the inductor current starts from zero in each switching period, as shown in Figure 3. When the power transistor of the boost converter is turned on for a fixed time, the peak inductor current is proportional to the input voltage. Furthermore, since the current waveform is triangular, the average value in each switching period is also proportional to the input voltage. In the case of a sinusoidal input voltage, the input current of the converter follows the input voltage waveform with a very high accuracy and draws a sinusoidal input current from the source. This behavior makes the © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 2 AN-6086 3. Interleaving of BCM Boost PFC One important characteristic of a BCM boost converter is the high ripple current of the boost inductor, which goes from zero to a controlled peak value in every switching period. Accordingly, the power switch is also stressed with high peak currents. In addition, the high ripple current must be filtered by an EMI filter to meet high-frequency noise regulations enforced for equipment connected to the mains. These effects usually limit the practical output power level of the converter below 300W. However, operating two parallel-connected boost power stages 180º out of phase, as shown in Figure 6; the high peak current and over-sized EMI filter problems are solved, extending the maximum practical power level of this control technique to greater than 800W. This technique is called interleaving. Figure 4. Frequency Variation of BCM PFC Since the design of filter and inductor for a BCM PFC converter with variable switching frequency should be done at minimum frequency condition, it is worthwhile to examine how the minimum frequency of BCM PFC converter changes with operating conditions. Figure 5 shows the minimum switching frequency, which occurs at the peak of line voltage, as a function of the RMS line voltage for three output voltage settings. It is interesting to note that, depending on where the output voltage is set, the minimum switching frequency may occur at the minimum or at the maximum line voltage. When the output voltage is approximately 405V, the minimum switching frequency is the same for both low line (85VAC) and high line (265VAC). Figure 6. Interleaving Operation of BCM Boost PFC Interleaving operation provides many advantages over the single BCM PFC operation. The losses are distributed in the switching devices, which also spreads the dissipated power and eases the thermal management of the power stage design. Interleaving also yields great benefits on EMI filter size reduction since the effective switching frequency seen at the input side of the converter is doubled, while the combined ripple current is minimized due to the ripple current cancellation, as shown in the waveforms of Figure 6. Figure 5. Minimum Switching Frequency vs. RMS Line Voltage (L = 390µH, POUT = 200W) © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 3 AN-6086 4. Design Considerations In this section, a design procedure is presented using the schematic in Figure 7 as a reference. A 400W PFC application with universal input range is selected as a design example. The design specifications are as follows: - - Line voltage range: 85~265VAC (universal input), 50Hz - Nominal output voltage and current: 400V/1A (400W) - Holdup time requirement: Output voltage should not drop below 330V during one line cycle Output voltage ripple: less than 8Vp-p Minimum switching frequency: higher than 50kHz Control Bandwidth: 5~10Hz Brownout protection line voltage: 70VAC The design is for two identical converters, which deliver half of the total output power (200W), respectively. VDD is assumed to be supplied from auxiliary power supply. Figure 7. Reference Circuit for Design Example of Interleaving BCM Boost PFC [STEP-1] Boost Inductor Design The MOSFET conduction time with a given line voltage at a nominal output power is given as: The boost inductor value is determined by the output power and the minimum switching frequency. From Equation 2, the minimum frequency with a given line voltage and MOSFET on time is obtained as: f SW , MIN 1 VOUT − 2VLINE = ⋅ tON VOUT tON = (4) η ⋅ VLINE 2 where: η is the efficiency; L is the boost inductance; and POUT,CH is the nominal output power per channel (3) where: VLINE is RMS line voltage; tON is the MOSFET conduction time; and VOUT is the output voltage. © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 2 ⋅ POUT ,CH ⋅ L Using Equation 4, the minimum switching frequency of Equation 3 can be expressed as: f SW , MIN = η ⋅ VLINE 2 2 ⋅ POUT ,CH VOUT − 2VLINE ⋅L VOUT ⋅ (5) www.fairchildsemi.com 4 AN-6086 Therefore, once the output voltage and minimum switching frequency are set, the inductor value is given as: η ⋅VLINE , MINF 2 VOUT − 2VLINE , MINF (6) L= ⋅ 2 ⋅ POUT ,CH ⋅ f SW , MIN VOUT (Design Example) Since the output voltage is 400V, the minimum frequency occurs at high-line (265VAC) and full-load condition. Assuming the efficiency is 95% and selecting the minimum frequency as 52kHz, the inductor value is obtained as: η ⋅VLINE , MINF 2 VOUT − 2VLINE , MINF L= ⋅ 2 ⋅ POUT ,CH ⋅ f SW , MIN VOUT where VLINE,MINF is the RMS line voltage that results in minimum switching frequency. For universal input range, VLINE,MINF is the maximum line voltage (265VAC) when VOUT is set at lower than 405V; while VLINE,MINF is minimum line voltage (85VAC) when VOUT is set at higher than 405V. = The maximum peak inductor current at nominal output power is calculated as: As the minimum frequency decreases, the switching loss is reduced, while the inductor size and line filter size increase. Thus, the minimum switching frequency should be determined by the trade-off between efficiency and the size of magnetic components. The minimum switching frequency must be above the minimum frequency of FAN9611/12, which is set at 16.5kHz to prevent audible noise. I L , PK = 2 2 ⋅ POUT ,CH η ⋅ VLINE , MIN Ae ⋅ ΔB = 2 2 ⋅ 200 = 7A 0.95 ⋅ 85 I L , PK ⋅ L Ae ⋅ ΔB = 7 ⋅ 202 × 10−6 = 29 turns 161× 10−6 ⋅ 0.3 Thus, the number of turns (NBOOST) of boost inductor is determined as 30 turns. (7) [STEP-2] Inductor Auxiliary Winding Design Figure 9 shows the inductor current and voltage waveforms of a BCM boost converter. FAN9611/12 indirectly detects the inductor zero current point using an auxiliary winding of the boost inductor. Since the zero current detection (ZCD) circuit in FAN9611/12 is designed to turn on the MOSFET when the slope of auxiliary winding voltage becomes zero, no special consideration for timing delay is required for the auxiliary winding design. The number of turns of boost inductor should be determined considering the core saturation. The minimum number is given as: I L , PK ⋅ L η ⋅ VLINE , MIN N BOOST ≥ where VLINE,MIN is the minimum line voltage. N BOOST ≥ 2 2 ⋅ POUT ,CH Assuming PQ3230 core (PC45, Ae=161mm2) is used and setting ΔB as 0.3T, the primary winding should be: Once the inductance value is decided, the maximum peak inductor current at the nominal output power is obtained as: I L. PK = 0.95 ⋅ 2652 400 − 2 ⋅ 265 ⋅ = 202 μ H 400 2 ⋅ 200 ⋅ 52 × 103 (8) where is Ae is the cross-sectional area of core and ΔB is the maximum flux swing of the core in Tesla. ΔB should be set below the saturation flux density. Figure 8 shows the typical B-H characteristics of ferrite core from TDK (PC45). Since the saturation flux density (ΔB) decreases as the temperature increases, the high temperature characteristics should be considered. N AUX (VOUT − VIN ) N BOOST N AUX VIN N BOOST Figure 9. ZCD Detection Waveforms The voltage of the ZCD pin is clamped near zero and the resistor RZCD limits the current of the ZCD pin below 1mA as: Figure 8. Typical B-H Curves of Ferrite Core © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 5 AN-6086 RZCD > VOUT N AUX ⋅ 1mA N BOOST The startup resistor also should be determined by considering the minimum startup time, which is given as: (9) ( N BOOST VOUT ≅ N AUX 2VZ 2 2VLINE , MIN π RSTART (12) − 100 μ A) where VON is UVLO start voltage for VDD and CDD is the total capacitance of capacitors connected to the VDD pin. When supplying VDD using the auxiliary winding, the turns ratio should be determined as: N= VON CDD t START = For low-power applications, such as adaptors, the supply voltage (VDD) for FAN9611/12 is supplied by auxiliary winding of inductor, as shown in Figure 10. Since the auxiliary winding voltage varies extensively within half of line cycle, DC blocking capacitor (CB) is used to guarantee stable VDD voltage. Typically 20~50μF of electrolytic capacitor (CVDD2) is used together with 2~4μF of bypass capacitor (CVDD1). (10) The power consumption in the startup resistor is obtained as: PLOSS = where VZ is the Zener diode voltage for VDD. The reason for setting the turns ratio such that peak-to-peak voltage of auxiliary winding is around twice of VZ is to guarantee stable VDD supply without under-voltage lockout (UVLO) during startup. VLINE , MAX 2 (13) RSTART (Design Example) Selecting the turns ratio of the inductor (NBOOST/NAUX) as 10, NAUX is obtained as 3 and the value of RZCD is given as: RZCD > VOUT N AUX 400 3 ⋅ = ⋅ = 40k Ω 1mA N BOOST 1mA 30 RZCD is selected as 47kΩ. Assuming that VDD is supplied from auxiliary power supply, VDD supply circuit using the auxiliary winding is not included in this example. (VOUT − VIN (t )) −VIN (t ) VOUT N AUX N BOOST [STEP-3] Design VIN Sense Circuit Since the RMS value of AC line voltage is directly proportional to the peak of the line voltage, FAN9611/12 detects the peak value of input voltage to sense the RMS value of the line voltage, which permits a simple voltage divider for line voltage sensing, as shown in Figure 11. The detected line voltage information is used for line undervoltage lockout (UVLO), and line feed-forward for PWM control. N AUX N BOOST N AUX N BOOST When the peak of VIN pin voltage drops below 0.95V, the line UVLO (brownout protection) is triggered and FAN9611/12 stops operating. The RMS value of the line voltage that causes line UVLO is given as: Figure 10. VDD Supply Circuit using Auxiliary Winding VLINE .UVLO = The average current through the startup resistor should be larger than the startup current (100μA), determined as: I START = 2 2VLINE , MIN π RSTART > 100 μ A RIN 1 + RIN 2 RIN 2 2 ⋅ 0.95 (14) (VAC ) The internal switched current source allows UVLO hysteresis on line voltage as: (11) RIN 1 + RIN , HYS ( VLINE , HYS = 2 RIN 1 + 1) RIN 2 ⋅ 2μ A (VAC ) (15) From Equation 15, RIN,HYS with a given hysteresis of line voltage is obtained as: RIN , HYS = ( © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 2VLINE . HYS RIN 2 − RIN 1 ) ⋅ 2μ A RIN 1 + RIN 2 (16) www.fairchildsemi.com 6 AN-6086 (Design Example) Setting the brown-out protection threshold at 70VAC and selecting RIN1=2MΩ, RIN2 is obtained as: RIN 1 RIN 2 = ( 2VLINE ,UVLO / 0.925 − 1) = 2 × 106 2 ⋅ 70 / 0.925 − 1 = 18.9k Ω Assuming the hysteresis for brownout protection is 3VAC, RIN,HYS is obtained as: RIN , HYS = ( =( Figure 11. Input Voltage Sensing The line peak detection circuit is saturated when VIN exceeds 3.7V, as depicted in Figure 11. Therefore, line feedforward does not work for VIN higher than 3.7V, as illustrated in Figure 12. The minimum brownout protection trip point that allows proper line feedforward operation for universal line range is 66VAC (265VAC×0.925/3.7). When the brownout protection threshold is lower than 68VAC for universal range input, line feedforward can be lost for high line and, therefore, the limited output power increases as line voltage increases: V (17) POUT MAX . NO. FF = POUT MAX ⋅ ( IN ) 2 3.7 2VLINE .HYS RIN 2 − RIN 1 ) ⋅ 2μ A RIN 1 + RIN 2 2 ⋅3 18.9 × 103 − 2 × 106 ) ⋅ = 1.1k Ω −6 2 × 10 2 × 106 + 18.9 × 103 RIN.HYS can be omitted since the hysteresis of 2.8VAC is obtained without RIN,HYS from Equation 15. CINF is selected as 10nF, which results in RC time constant as: τ = ( RIN 2 + RIN .HYS ) ⋅ CINF = 18.9 × 103 ⋅10 × 10−9 = 189 μ s [STEP-4] Determine MOT Pin Resistor The on time of the gate drive signal is proportional to the compensation voltage as shown in Figure 13. The compensation voltage is internally clamped at 4.3V where the maximum on time is obtained. The Maximum On Time (MOT) of the gate drive signal of each channel is programmed by the resistor on the MOT pin as: Another effect of VIN sensing saturation is that the phase management threshold as a percentage of nominal output power increases as peak of VIN increases above 3.7V because the line feedforward does not work above 3.7V. tON , MAX = RMOT ⋅ 230 × 10−12 ( Since FAN9611/12 uses peak detection for the line voltage sensing, it is typical to use a small capacitor (CINF) to bypass switching noise. To minimize the effect of sensing delay, the RC time constant between RIN2 and CINF should be smaller than 5% of AC line period. RIN 1 + RIN 2 RIN 2 2VLINE )2 (18) As can be observed in Equation 18, the maximum on time is inversely proportional to the square of line voltage due to the line feed-forward operation. The MOT resistor should be determined by considering the output power since the maximum on time limits the maximum output power during overload condition as: PMAX ,CH = K MAX ⋅ POUT ,CH = VLINE 2 ⋅η tON , MAX 2L (19) where PMAX,CH is the limited maximum output power per channel and KMAX is maximum power limiting factor, which is a ratio between the limited maximum output power and nominal output power. Considering the tolerances of inductor, resistor, and controller variation; it is typical to set the limited maximum power as 20~30% higher than the nominal output power (KMAX = 1.2~1.3). Figure 12. VIN Feedforward Range © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 7 AN-6086 When the resulting maximum power limit to obtain the desired phase management threshold is too high compared to the nominal output power, the maximum power limit level can be reduced using clamping circuit on COMP pin, as shown in Figure 15. The COMP pin voltage is clamped at 3.3V and the resulting maximum power limit level is reduced from 170% to 130% of nominal output power. POUT T ON POUTMAX TONMAX 18% of POUTMAX (TONMAX) 13% of POUTMAX (TONMAX) VCOMP 0.2 0.73 4.3 0.93 Figure 13. VCOMP vs. On Time of Gate Drive Signal FAN9611/12 determines the phase management according to the COMP pin voltage (0.73V and 0.93V). Since the COMP pin voltage is proportional to the output power, the power levels for phase shedding and adding are given as percentages of limited maximum power, as shown in Figure 13. Thus, the maximum power limiting factor affects the actual phase management thresholds as percentages of nominal output power, as shown in Figure 14, which shows an example where the maximum power limit is 170% of the nominal output power. In that case, the actual phase management thresholds are 22% and 31% of nominal output power, which can maximize the efficiency at 20% of nominal load for 80-plus efficiency requirement. In this way, the phase management thresholds can be adjusted upward by adjusting the maximum on time (through RMOT). Figure 15. COMP Voltage Clamping Circuit and Phase Management Threshold After determining the limited maximum output power, the boost inductor maximum flux density should be examined to make sure that the inductor is not saturated during overload condition. The maximum flux density of boost inductor during overload condition is given by: # of phase operating 2 Bmax = 1 13% 18% 50% 100% I L , PK ⋅ K MAX ⋅ L Ae ⋅ N BOOST (20) Output Power Normalized to POMAX # of phase operating 2 POMAX=1.7 PONOMINAL 1 22% 31% 50% 100% Output Power Normalized to PONOMINAL 170% Figure 14. Phase Management Threshold © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 8 AN-6086 [STEP-7] Determine current sensing resistor (Design Example) Setting the limited output power as 120% of nominal output power, the maximum on time is given as: tON , MAX = PMAX , CH ⋅ 2 L VLINE , MIN 2 ⋅η = ( K MAX ⋅ POUT , CH ) ⋅ 2 L I CS , LIM ≥ 2 2 ⋅ VLINE , MIN 2 ⋅η (1.2 ⋅ 200) ⋅ 2 ⋅ 202 × 10 852 ⋅ 0.95 = It is typical to set the pulse-by-current limit level a little higher than the maximum inductor current at maximum power limit condition as: −6 = 14.1μ s RMOT = 230 × 10−12 ( RIN2 2VLINE , MIN RIN1 + RIN2 RCS = )2 I CS , LIM ≥ 2 2 ⋅ The maximum flux density during overload condition is obtained as: I L, PK ⋅ K MAX ⋅ L = Ae ⋅ N BOOST RCS = = 0.35 tesla [STEP-5] Design Feedback Circuit (21) COUT > obtained as: RFB1 FAN9611/12 has two levels of over-voltage protection (OVP) for the output. Non-latching OVP is combined with the feedback (FB) pin and trips when the output voltage exceeds 108% of its nominal value. The latching OVP uses dedicated pin and trips when the OVP pin voltage exceeds an independent threshold of 3.5V, expressed as: COUT > (22) (25) 2 POUT ⋅ t HOLD VOUT 2 − VOUT , MIN 2 (26) where: POUT is total nominal output power of two boost PFC stage (2POUT,CH); tHOLD is the required holdup time; and VOUT,MIN is the allowable minimum output voltage during the holdup time. (Design Example) Selecting OVP level as 472V and ROV1 as 2MΩ, ROV2 is obtained as: VOUT , LATCH −1 3.5 I OUT 2π ⋅ f LINE ⋅ VOUT , RIPPLE The holdup time also should be considered when determining the output capacitor as: When the latching OVP is combined with FB pin, it trips at 115% of the nominal output voltage. = 0.2 0.2 = = 0.022Ω I CS .LIM 9.1 Since too large ripple on the output voltage may cause premature OVP during normal operation, the peak-to-peak ripple specification should be smaller than 15% of the nominal output voltage. [STEP-6] Design OVP Circuit ROV 1 200 ⋅1.2 = 8.4 A 85 ⋅ 0.95 where IOUT is total nominal output current of two boost PFC stage and VOUT,RIPPLE is the peak-to-peak output voltage ripple specification. 1× 106 = = = 7.56k Ω VOUT 400 −1 −1 3 3 ROV 2 = =2 2⋅ The output voltage ripple should be considered when selecting the output capacitor. Figure 16 shows the twice line frequency ripple on the output voltage. With a given specification of output ripple, the condition for the output capacitor is obtained as: (Design Example) Selecting RFB1 as 1MΩ, RFB2 is RFB 2 ⋅ VOUT , LATCH = 3.5V RFB1 + RFB 2 PMAX ,CH VLINE , MIN ⋅η [STEP-8] Output Capacitor Selection To regulate the output voltage to a desired value, the voltage divider for feedback should be designed to result in 3V to the feedback (FB) pin, expressed as: RFB 2 (24) Choosing ICS.LIM as 9.1A (10% margin on 8.4A), the sensing resistor is selected as: 7 ⋅1.2 ⋅ 202 × 10−6 161× 10−6 ⋅ 30 RFB 2 ⋅VOUT = 3V RFB1 + RFB 2 0.2 I CS .LIM (Design Example) 14.1×10−6 18.9 ⋅ 2 ⋅ 85 2 = ( ) = 78k Ω 230 ×10−12 18.9 + 2000 Bmax = (23) VLINE , MIN ⋅η Then, the sensing resistor is selected as: Then, the resistor on MOT pin is obtained as: tON , MAX PMAX ,CH 2 × 106 = 14.9k Ω 472 −1 3.5 © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 9 AN-6086 ID I D , AVG I D , AVG = I OUT (1 − cos(4π ⋅ f LINE ⋅ t )) I OUT VOUT , RIPPLE = I OUT 2π f LINE COUT VOUT Figure 17. Small Signal Modeling of the Power Stage Figure 16. Output Voltage Ripple (Design Example) With the ripple specification of 8Vp-p, the capacitor should be: COUT > I OUT 1 = = 398μ F 2π ⋅ f LINE ⋅ VOUT , RIPPLE 2π ⋅ 50 ⋅ 8 Since minimum allowable output voltage during one cycle line (20ms) drop-outs is 330V, the capacitor should be: COUT > 2 POUT ⋅ t HOLD VOUT 2 − VOUT , MIN 2 = 2 ⋅ 400 ⋅ 20 × 10−3 4002 − 3302 = 313μ F By averaging the diode current during the half line cycle, the low frequency behavior of the voltage controlled current source of Figure 17 is obtained as: I D , LF = I OUT ⋅ K MAX ⋅ Then, the low-frequency, small-signal, control-to-output transfer function is obtained as: vˆOUT I ⋅K R 1 = OUT MAX ⋅ L ⋅ vˆCOMP 4.1 2 1+ s 2π f P where f P = [STEP-9] Design Compensation Network (28) 2 and 2π ⋅ RL COUT RL is the output load resistance in a given load condition. Figure 18 shows the variation of the control-to-output transfer function for different loads. As can be seen, the characteristics at frequencies above the pole are unchanged while the pole moves as load changes. Since the low frequency gain increases as load decreases, the light load condition is the worst condition for feedback loop compensation. Assuming the load resistance is infinite, the control-to-output transfer function at light load condition is obtained from Equation 28 as: vˆOUT I ⋅K 1 |@ LIGHT , LOAD ≅ OUT MAX ⋅ 4.1 vˆCOMP sCOUT © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 (27) where IOUT is total nominal output current corresponding to POUT, VCOMP is compensation pin voltage, 0.2V is PWM offset voltage and 4.1 is error amplifier control range (refer to Figure 13). Thus, two 220μF capacitors in parallel are selected for the output capacitor. The boost PFC power stage can be modeled as shown in Figure 17. Since FAN9611/12 employs line feed-forward, the power stage transfer function becomes independent of the line voltage. Then, the power stage can be modeled as a voltage-controlled current source supplying RC network. (VCOMP − 0.2) 4.1 (29) www.fairchildsemi.com 10 AN-6086 The procedure to design the feedback loop is as follows: (a) Determine the crossover frequency (fC) around 1/10~1/5 of line frequency. Since the control-to-output transfer function of power stage has -20dB/dec slope and -90o phase at the crossover frequency, as shown in Figure 20; it is required to place the zero of the compensation network (fCZ) around the crossover frequency so that 45° phase margin is obtained. Then, the capacitor CCOMP,LF is determined as: CCOMP , LF = 80 μ A / V ⋅ I OUT ⋅ K MAX 3 ⋅ 4.1 ⋅ COUT ⋅ (2π fC ) 2 VOUT (31) To place the compensation zero at the crossover frequency, the compensation resistor is obtained as: Figure 18. Control-to-Output Transfer Function Proportional and integration (PI) control with high frequency pole is typically used for compensation, as shown in Figure 19. The compensation zero (fCZ) introduces phase boost, while the high frequency compensation pole (fCP) attenuates the switching ripple. The transfer function of the compensation network is obtained as: s 1+ vˆCOMP 2π f I 2π fCZ = ⋅ vˆOUT s 1+ s 2π fCP fI = RCOMP = 1 2π ⋅ f C ⋅ CCOMP , LF (32) (b) Place compensator high-frequency pole (fCP) at least a decade higher than fC to ensure that it does not interfere with the phase margin of the voltage regulation loop at its crossover frequency. It should also be sufficiently lower than the switching frequency of the converter so noise can be effectively attenuated. Then, the capacitor CCOMP,HF is determined as: (30) CCOMP , HF = 1 2π ⋅ fCP ⋅ RCOMP (33) 3 80μ A / V ⋅ , VOUT 2π ⋅ CCOMP , LF where f = CZ fCP = 1 , 2π ⋅ RCOMP ⋅ CCOMP , LF 1 2π ⋅ RCOMP ⋅ CCOMP , HF Figure 20. Compensation Network Design V RFB 2 = SS , REF RFB1 + RFB 2 VOUT ^ v COMP ^ vOUT f CZ = 10CCOMP , HF ≤ CCOMP , LF 1 2π ⋅ RCOMP CCOMP , LF f CP = 1 2π ⋅ RCOMP CCOMP , HF Figure 19. Compensation Network © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 11 AN-6086 (Design Example) Choosing the crossover frequency (control bandwidth) at 5Hz, CCOMP,LF is obtained as: CCOMP , LF = = 80μ A / V ⋅ I OUT ⋅ K MAX 3 ⋅ 4.1 ⋅ COUT ⋅ (2π fC ) 2 VOUT 10−4 ⋅1 ⋅ 1.2 3 ⋅ = 405nF 2 −6 4.1 ⋅ 440 × 10 ⋅ (2π ⋅ 5) 400 0.3 ⋅ 5μ A ⋅ COUT ⋅ VOUT 5μ A ⋅ COUT ⋅ VOUT (35) < CSS < 0.6 ⋅ I OUT ⋅ K MAX ⋅ VSS , REF 0.3 ⋅ I OUT ⋅ K MAX ⋅ VSS , REF (Design Example) Since two 220μF capacitors in parallel are selected for the output capacitor: 1 1 = = = 82k Ω 2π ⋅ f C ⋅ CCOMP , LF 2π ⋅ 5 ⋅ 390 ×10−9 5μ A ⋅ COUT ⋅ VOUT 5μ A ⋅ COUT ⋅ VOUT < CSS < 0.6 ⋅ I OUT ⋅ K MAX ⋅ VSS , REF 0.3 ⋅ I OUT ⋅ K MAX ⋅VSS , REF Selecting the high-frequency pole as 120Hz, CCOMP,HF is obtained as: CCOMP , HF = 406nF < CSS < 813nF 1 1 = = 16.3nF 2π fCP ⋅ RCOMP 2π ⋅120 ⋅ 82 ×103 Actual COMP,HF is determined as 15nF since it is the closest value among the off-the-shelf capacitors. These components result in a control loop with a bandwidth of 6Hz and phase margin of 45° as below. The actual bandwidth is a little larger than the asymptotic design (34) where VSS,REF is the final value of soft-start capacitor voltage. Then, the condition for the soft-start capacitor is given as: Actual CCOMP,LF is determined as 390nF since it is the closest value among the off-the-shelf capacitors. Then, RCOMP is obtained as: RCOMP I OUT ⋅ K MAX I ⋅K 5μ A < < 0.6 ⋅ OUT MAX COUT ⋅ VOUT CSS ⋅ VSS , REF COUT ⋅ VOUT Thus, a 470nF capacitor is selected for the soft-start capacitor. [STEP-11] Line Filter Capacitor Selection It is typical to use small bypass capacitors across bridge rectifier output stage to filter the switching current ripple, as shown in Figure 21. Since the impedance of the line filter inductor at line frequency is negligible compared to the impedance of the capacitors, the line frequency behavior of the line filter stage can be simply modeled, as shown in Figure 21. Even though the bypass capacitors absorb switching ripple current, it also generates circulating capacitor current, which leads the line voltage by 90o, as shown in Figure 22. As observed, the circulating current through the capacitor is added to the load current and generates displacement between line voltage and line current. The displacement angle is given by: η ⋅ VLINE , MAX 2 ⋅ 2π f LINE ⋅ CEQ θ = tan −1 ( ) (36) POUT where CEQ is the equivalent capacitance that appears across the AC line (CEQ=CF1+CF2+CHF). [STEP-10] Soft-Start Capacitor Selection FAN9611/12 employs closed-loop soft-start, where the reference of the error amplifier is gradually increased to the final value corresponding to the nominal output voltage. The reference is also actively managed during the soft-start period to prevent the reference running away from the feedback voltage. The slope of the voltage reference is made a function of the error amplifier output voltage (VCOMP), i.e. the output power of the converter. The soft-start time is then adjusted according to load condition. The resultant displacement factor is: DF = cos( θ ) Since the displacement factor is related to power factor, the capacitors in the line filter stage should be selected carefully. With a given minimum displacement factor (DFMIN) at full load condition, the allowable effective input capacitance is obtained as: CEQ < It is typical to set he maximum rising speed of the soft-start capacitor such that it is 30%~60% of that of the output voltage, defined by the maximum power limit as: © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 (37) POUT η ⋅ VLINE , MAX 2 ⋅ 2π f LINE ⋅ tan(cos −1 ( DFMIN )) (38) www.fairchildsemi.com 12 AN-6086 (Design Example) Assuming the minimum displacement factor at full load is 0.99, the equivalent input capacitance is obtained as: CEQ < < POUT η ⋅ VLINE , MAX 2 ⋅ 2π f LINE ⋅ tan(cos −1 ( DFMIN )) 400 ⋅ tan(cos −1 (0.99)) = 2.7 μ F 0.95 ⋅ 2652 ⋅ 2π ⋅ 50 Thus, the sum of the capacitors in the input side should be smaller than 2.7µF. θ Figure 22. Line Current Displacement Figure 21. Equivalent Circuit of Line Filter Stage © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 13 AN-6086 PCB Layout Guidelines For high-power applications, two or more PCB layers are recommended to effectively use the ground pattern to minimize the switching noise interference from the two high-frequency outputs. The following guidelines are recommended for all layout designs, but especially strongly for the single-layer PCB designs. CS1 16 CS2 15 2 ZCD2 Figure 23 shows the single-layer PCB example, where the FAN9611/12 is on the bottom of PCB (SOIC package). 1 ZCD1 VDD 14 3 DRV1 13 5VB 4 DRV2 12 MOT 5 PGND 11 SS AGND 6 9 10 VIN FB 8 7 COMP OVP Power Ground and Analog Ground Power ground (PGND) and analog ground (AGND) should meet at one point only. All the control components should be connected to AGND without sharing the trace with PGND. The return path for the gate drive current and VDD capacitor should be connected to the PGND pin. The ground loops between the driver outputs (DRV1/2), MOSFETs, and PGND should be minimized. Adding the by-pass capacitor for noise on the VDD pin is recommended. It should be connected as close to the pin as possible. Gate Drive Pattern The gate drive pattern should be wide enough to handle 1A peak current. The gate drive pattern should be as short as possible to minimize interference. Current Sensing Current Sensing should be as short as possible. To minimize switching noise, current sensing should not make a loop. Input Voltage Sensing (VIN) Since the impedance of voltage divider is large and FAN9611/12 detects the peak of the line voltage, the VIN pin can be sensitive to the switching noise. Therefore, the trace connected to this pin should not cross traces with high di/dt to minimize the interference. The noise bypass capacitor for VIN should be connected as close to the pin as possible. Figure 23. Single-Layer PCB Layout Example © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 14 AN-6086 Design Summary Figure 24 shows the final schematic of the 400W interleaved BCM Boost PFC design example. PQ3230 cores are used for the boost inductors. L2 200uH D2 RURP860 N1 (N1:N2=10:1) N2 RURP860 200uH L1 LF D1 N1 (N1:N2=10:1) N2 LF Q1 FDPF18N50 Q2 1M RFB1 FDPF18N50 CF1 470nF CF3 470nF 470nF 220uF 2M ROV1 CHF2 47k 150nF CF2 150nF 220uF CO RZCD2 CHF1 47k RG RG RZCD1 15 15 0.022 GBJ1006 Rsense RIN1 2M CIN 0.022 Rsense RFB2 ROV2 7.56k 15k FAN9612 RIN2 1 ZCD1 CS1 16 2 ZCD2 CS2 15 3 5VB VDD 14 4 MOT DRV1 13 5 AGND DRV2 12 6 SS PGND 11 7 COMP VIN 10 8 FB OVP 9 18.9k 10nF CVDD2 CVDD1 RMOT C5V 220nF 78k 470nF CSS CV1 390nF CV2 22uF 2.2uF VDD from Aux power Supply 15nF RV1 82k Figure 24. Final Schematic of Design Example Figure 25. Boost Inductor Specification Table 1. Winding Specification N1 Pin Diameter / Thickness Turns 5Æ3 0.1mm × 100 (Litz wire) 0.05mm 0.2mm 0.05mm 30 3 3 3 Insulation Tape 2Æ4 N2 Insulation Tape Core: PQ3230 (Ae=161 mm2) Bobbin: PQ3230 Inductance: 200μH © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 15 AN-6086 6. Experimental Verification To show the validity of the design procedure presented in this application note, the converter of the design example was built and tested. All the circuit components are used as designed in the design example. Figure 26 and Figure 27 show the inductor current ripple cancellation for 115VAC and 230VAC condition, respectively. As can be observed, the sum of two inductor currents has very small ripple due to the interleaving operation. Figure 28 shows the brown-out protection. As designed, the protection trips when the line voltage drops below 70VAC. Figure 29 and Figure 30 show the soft-start waveforms at full load for 115VAC and 230VAC line voltage, respectively. As observed, there is no overshoot on the output voltage during startup. Figure 31 shows the measured efficiency for 115VAC and 230VAC line voltage. The full-load efficiency is 96.4% and 98.2% for 115VAC and 230VAC, respectively. The power factor is shown in Table 2. The power factor at full load is 0.993 and 0.988 for 115VAC and 230VAC, respectively. CH1: Gate drive signal VGS1 (20V/div) CH2: Line current (5A/div), CH4: (100VA/div) Line voltage Figure 28. Brownout Protection CH1: Gate drive signal VGS1 (20V/div) CH3: Output voltage (100V/div) CH4: Line current (5A/div) CH2: Inductor current IL1 (5A/div) CH4: Sum of two inductor current IL1+IL2 (5A/div) Figure 29. Soft-Start Waveforms at Full-Load and 115VAC Line Condition Figure 26. Inductor Current Waveforms at 115VAC CH2: Inductor current IL1 (5A/div) CH4: Sum of two inductor current IL1+IL2 (5A/div) CH1: Gate drive signal VGS1 (20V/div) CH3: Output voltage (100V/div) CH4: Line current (5A/div) Figure 30. Soft-Start Waveforms at Full-Load and 230VAC Line Condition Figure 27. Inductor Current Waveforms at 230VAC © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 16 AN-6086 Table 2. Measured Power Factor Line Voltage 100% Load 75% Load 50% Load 115VAC 0.993 0.990 0.984 230VAC 0.988 0.983 0.974 Figure 31. Measured Efficiency Definition of Terms η is the efficiency. ΔB is the maximum flux swing of the core at nominal output power in Tesla. Ae is the cross-sectional area of core. BMAX is the maximum flux density of boost inductor at maximum output power in Tesla. CDD is the total capacitance of capacitors connected to the VDD pin. fC is the crossover frequency. fCP is the high frequency compensation pole to attenuate the switching ripple. fCZ is the compensation zero. fLINE is the line frequency. fSW,MIN is the minimum switching frequency. ICS,LIM is the pulse-by-pulse current limit level determined by sensing resistor. IL,PK is the maximum peak inductor current at the nominal output power. IOUT is total nominal output current of two boost PFC stages. IOUT,MAX is the maximum output current, which corresponds to PMAX. KMAX is maximum power limiting factor (a ratio between the limited maximum output power and nominal output power). L is the boost inductance. NAUX is the number of turns of auxiliary winding in boost inductor. NBOOST is the number of turns of primary winding in boost inductor. PMAX is the limited maximum output power of two boost PFC stages (2PMAX,CH). PMAX,CH is the limited maximum output power per channel. POUT is total nominal output power of two boost PFC stages (2POUT,CH). POUT,CH is the nominal output power per channel. tHOLD is the required hold-up time. tON,MAX is the maximum on time determined by the MOT resistor. VCOMP is compensation pin voltage. VIN(t) is the rectified line voltage. VIN,PK is the amplitude of line voltage. VLINE is RMS line voltage. VLINE,HYS is the hysteresis RMS line voltage of brownout protection. VLINE,MAX is the maximum RMS line voltage. VLINE,MIN is the minimum RMS line voltage. VLINE,MINF is the RMS line voltage that results in minimum switching frequency. VLINE,OVP is the line OVP trip point in RMS. VON is UVLO start voltage for VDD. VOUT is the PFC output voltage. VOUT,LATCH is the output OVP trip point. VOUT,MIN is the allowable minimum output voltage during the hold-up time. VOUT,RIPPLE is the peak-to-peak output voltage ripple. VREF,SS is the reference voltage for soft-start and feedback compensation. © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 www.fairchildsemi.com 17 AN-6086 References [1] Fairchild Datasheet FAN9611 / FAN9612 Interleaved Dual BCM, PFC Controller [2] Fairchild Application Note AN-6027, Design of Power Factor Correction Circuit Using FAN7530 [3] Fairchild Power Seminar 2008-2009 Paper, Understanding Interleaved Boundary Conduction Mode PFC Converters [4] Fairchild Evaluation Board User Guide FEB279, 400W Evaluation Board using FAN9612 ((AN-8018) [5] Fairchild Application Note AN-8021, Building Variable Output Voltage Boost PFC Converters Using FAN9611/12 [6] Fairchild Evaluation Board User Guide FEB301, 400W Single-Layer Evaluation Board using FAN9612 (AN-8026) Related Datasheets FAN9611 / FAN9612 — Interleaved Dual BCM PFC Controllers FDPF18N50 — 500V N-Channel MOSFET, UniFET RURP860 — 8A, 600V UltraFast Diodes Author Hangseok Choi / Ph. D He received B.S., M.S., and Ph.D degrees in electrical engineering from Seoul National University in 1996, 1999, and 2002, respectively. From 2002 to 2007, he worked for Fairchild Semiconductor in Korea as a system and application engineer. He is currently working for Fairchild Semiconductor in NH, USA, as a principal system and application engineer. His research interests include soft-switching techniques, modeling, and control of converters. Important Notice DISCLAIMER FAIRCHILD SEMICONDUCTOR RESERVES THE RIGHT TO MAKE CHANGES WITHOUT FURTHER NOTICE TO ANY PRODUCTS HEREIN TO IMPROVE RELIABILITY, FUNCTION, OR DESIGN. FAIRCHILD DOES NOT ASSUME ANY LIABILITY ARISING OUT OF THE APPLICATION OR USE OF ANY PRODUCT OR CIRCUIT DESCRIBED HEREIN; NEITHER DOES IT CONVEY ANY LICENSE UNDER ITS PATENT RIGHTS, NOR THE RIGHTS OF OTHERS. LIFE SUPPORT POLICY FAIRCHILD’S PRODUCTS ARE NOT AUTHORIZED FOR USE AS CRITICAL COMPONENTS IN LIFE SUPPORT DEVICES OR SYSTEMS WITHOUT THE EXPRESS WRITTEN APPROVAL OF THE PRESIDENT OF FAIRCHILD SEMICONDUCTOR CORPORATION. As used herein: 1. Life support devices or systems are devices or systems which, (a) are intended for surgical implant into the body, or (b) support or sustain life, or (c) whose failure to perform when properly used in accordance with instructions for use provided in the labeling, can be reasonably expected to result in significant injury to the user. © 2009 Fairchild Semiconductor Corporation Rev. 1.0.4 • 4/22/10 2. A critical component is any component of a life support device or system whose failure to perform can be reasonably expected to cause the failure of the life support device or system, or to affect its safety or effectiveness. www.fairchildsemi.com 18