AN1452 Using the MCP19035 Synchronous Buck Converter Design Tool Author: This application note familiarizes the designer with Microchip's MCP19035 Synchronous Buck Converter Design Tool. Microchip Technology Inc. provides this design tool to minimize design effort and to help the designer estimate the static (i.e., the efficiency) and dynamic (load step response) performance, and the behavior of the step-down voltage regulator implemented with the MCP19035 controller. Sergiu Oprea Microchip Technology Inc. INTRODUCTION The MCP19035 is a high-performance, highly integrated, synchronous buck controller IC, packaged in a space-saving, 10-pin 3x3mm DFN package. Integrated features include high- and low-side MOSFET drivers, fixed-frequency voltage-mode control, internal oscillator, reference voltage generator, overcurrent protection circuit for both the high- and low-side switches, Power Good indicator and overtemperature protection. The development of a complete, high-performance synchronous buck converter requires a minimum number of external components. Some design effort is still necessary to calculate all the external component’s (inductor, MOSFETs, capacitors, compensation network) values and parameters. BACKGROUND The Synchronous Buck Converter The synchronous buck converter is an improved version of the classic, non-synchronous buck (stepdown) converter. This topology improves the low efficiency of the classic buck converter at high currents and low-output voltages. Figures 1 and 2 illustrate the power trains for the classic buck, and synchronous buck converter. L Q + - VIN FIGURE 1: COUT D RL Classic Buck Converter Power Train. L Q1 Q2 VIN FIGURE 2: + D - COUT RL Synchronous Buck Converter Power Train. 2012 Microchip Technology Inc. DS01452A-page 1 AN1452 The freewheeling diode of the classic buck converter is replaced with a MOS transistor in the synchronous buck converter. This greatly reduces the conduction losses when the converter operates at high-currents with low-output voltages. Since the synchronous buck converter is developed to deliver high output currents, it will mainly operate in the Continuous Current Mode (CCM). This application note assumes that the synchronous buck converter only operates in the CCM mode. The design process for a synchronous buck voltage regulator is split into two phases. In the first phase, the electrical parameters of the power train components (inductor, MOSFETs and capacitors) are calculated based on the target application needs provided by the power supply designer. Further, this design tool can estimate the power components’ losses based on the parameters provided by the designer. In the second phase, the design tool analyzes the AC (small signal) frequency response of the system and proposes a set of component values for the compensation network. The designer has the option to adjust the value of these components, if the frequency response of the compensated system does not meet the design targets. The MCP19035 synchronous buck controller implements the voltage-mode PWM control. For this kind of control strategy, a Type-III Compensation system is recommended. Based on these input parameters, the Design Tool calculates the system parameters and the power train component values (inductor, input and output capacitors values). C3 C2 R4 C1 R3 COMP EA VIN + R1 R2 VREF FIGURE 3: Network. Type-III Compensation Appendix A: “List of the Design Tool Formulas” lists the equations used by this design tool. “Fundamentals of Power Electronics” [1] provides all the theoretical background for the synchronous buck converter operation. THE MCP19035 SYNCHRONOUS BUCK CONVERTER DESIGN TOOL Design Tool Input In the first tab of the Design Tool, the designer provides the system input parameters, including the input and output voltages, maximum output current, switching frequency, input voltage ripple and the reference voltage. Also, the step load parameters must be provided here. An example of the input parameters are summarized in Figure 4. Input Parameters for Design Parameter Designator Input Voltage Output Voltage Output Current Switching Frequency Input Voltage Ripple Reference Voltage VIN VOUT IOUT Fs VRIN VREF 14 1.8 10 600000 0.2 0.6 V V A Hz V V Step Load Parameters IOH IOL Output Voltage Overshoot IOH IOL 7.5 2.5 0.1 A A V FIGURE 4: DS01452A-page 2 Units Notes 5V ≤ VIN ≤ 30V Fs = 300 kHz or 600 kHz Input Parameters Table. 2012 Microchip Technology Inc. AN1452 The second tab of the Design Tool summarizes the system parameters. The Power Train Components table contains two color-marked columns: completes these fields with the available standard component values To minimize error and ensure the best possible representation of the system's performance, all further calculations are done based on the user-input standard values of the power train components. • Suggested Values (green highlight) – shows the values calculated by the Design Tool • Standard Values (yellow highlight) – the designer Power Train Components Values (calculated) Component Suggested Values Standard Values (**) Units Inductor Value COUT(*) CIN CBOOT 0.87 135.1 10 0.276 1 200 20 0.33 μH μF μF μF * COUT is calculated based on standard value for inductor and not for suggested value ** Must be filled by the designer FIGURE 5: The Power Train Components Values Table. The Design Tool calculates the RMS currents for the inductor, high- and low-side MOSFETs, and both input and output capacitors. Using these RMS currents the designer determines the power train component’s parameters (MOSFETs, inductor and capacitors) following the recommendations from the MCP19035 data sheet. Components’ parameters are then manually entered into the Power Train Components Parameter table (Figure 6). Based on these parameters, the Design Tool estimates the losses and the expected efficiency of the converter (Figure 7). The total conduction time for the body diode will vary between 20 ns (set by the internal logic of the MCP19035) and a maximum value that depends on the MOSFET’s type for the MCP19035 version with adaptive Dead Time option. The total conduction time for the body diode cannot be accurately determined from the beginning of the design. The designer can initially use the 40 ns value. For the fixed Dead Time option of MCP19035, optimized to drive Microchip's MOSFETs, this value is fixed to 12 ns. The DC resistance of the inductor and the equivalent series resistance (ESR) of the capacitors are also available in each component data sheet. The RDSON, total gate charge and reverse recovery charge of the body diode parameters are available in the MOSFET’s data sheet. Refer to the MCP19035 Data Sheet for further details on MOSFETs’ selection. Power Train Components Parameters Component Parameter Designator Units High side MOSFET RDS(ON)HS QGATEHS 6 13.8 m RDS(ON) Total gate charge Total Conduction Time for the Body Diode Reverse Recovery Charge of the Body Diode RDS(ON)LS QGATELS tBD QRR 2.5 31 12 35 m Inductor DC Resistance CIN ESR COUT ESR LDCR 2 10 5 m m m RDS(ON) Total gate charge nC Low side MOSFET FIGURE 6: nC ns nC Power Train Components Parameters Table. 2012 Microchip Technology Inc. DS01452A-page 3 AN1452 The Design Tool estimates the losses and the final efficiency of the converter (see the table in Figure 7). The designer can modify several parameters of the power train components in an effort to optimize the efficiency of the converter. The estimated efficiency will depend on the accuracy of the parameters. Some difference between the predicted value and the measured value should be expected. Certain types of losses (for example, hysteresis losses of the inductor) are not calculated by the Design Tool. Refer to the inductor data sheet for details regarding these types of losses. Estimated System Losses High side MOSFET losses Conduction losses Switching losses Total losses Low Side MOSFET losses Conduction losses Body diode conduction losses Body diode reverse recovery losses Total losses Controller losses Inductor conduction losses COUT losses CIN losses Total losses Estimated Efficiency at Full Load FIGURE 7: W W W 0.2 0.0504 0.147 0.3974 W W W W 0.4 0.2 0.015 0.05 2.3016 88.7 W W W W W % Losses and Expected Efficiency Table. Loop Compensation The next step in the design is to stabilize the control loop. On the third tab, the Design Tool calculates the values of the compensation network components according with the design procedure described in the MCP19035 data sheet. The designer can also analyze the stability and the dynamic performance of the converter using the Frequency Domain Analysis tab in the Design Tool. Bode Plots The Bode plots method is an important engineering tool that can be used for frequency domain analysis of the closed loop systems. Stability and dynamic performance of closed-loop systems can also be estimated using these plots. A Bode plot is the graph representing the magnitude and/or phase of a transfer function, or other complex-domain quantity versus frequency. The magnitude, expressed in decibels, and the phase, expressed in degrees, are plotted on a logarithmic frequency scale. DS01452A-page 4 0.08 1.1592 1.2392 If H(s) is the transfer function of a linear, time-invariant system, the magnitude and phase are shown in the following equations: EQUATION 1: GAIN G dB = 20 log H s EQUATION 2: PHASE Im H s Phase H s = atan ----------------------Re H s The gain and phase can now be plotted on a logarithmic frequency scale. These are the Bode plots of the given transfer function. Similarly, if the converter closed-loop transfer function is known, the Bode plots can be used to analyze the stability and dynamic performance of the system. The Design Tool uses the Average Model of the buck converter developed in “Fundamentals of Power Electronics”[1]. The frequency response of the compensated system is obtained by multiplying the frequency response of the power train with the frequency response of the compensator (see Equation 3). 2012 Microchip Technology Inc. AN1452 + VIN - PWM Modulator HM(S) GAIN (dB) Power Train H P(S) Compensator HC(S) 90 70 50 30 10 -10 -30 -50 -70 -90 1 FIGURE 8: The Synchronous Buck Regulator System. EQUATION 3: The designer can now estimate the stability and dynamic performance of the system by inspecting the Bode plots. The Design Tool plots the Bode plots for power train, compensation circuit and compensated converter. 10 PHASE (Degrees) GAIN (dB) Bode Plots of the Power Train 20 0 -20 -40 -60 -80 -100 -120 -140 -160 -180 -200 1000 100000 FREQUENCY (Hz) FIGURE 9: Train. Bode Plots of the Power 1 100 10000 100 80 60 40 20 0 -20 -40 -60 -80 -100 1000000 PHASE (Degrees) GAIN (dB) Gain Phase The first parameter of interest is the system’s crossover frequency. The crossover frequency is the point where the gain of the system becomes 0 dB. A higher crossover frequency means a better dynamic performance of the system (better transient response). However, due to the stability criteria, this crossover frequency cannot be set infinitely high. Phase margin is the second parameter of interest, and directly related to the stability of the closed loop system. In a closed loop system that uses negative feedback, the phase margin is defined as the difference between the phase at the crossover frequency and 0°. The third parameter is the gain margin. This parameter is also related to the system stability and will indicate how far the system is from the instability point (0 dB). The gain margin is defined as the amount of gain that must be added to the system gain to reach the 0 dB point, calculated at the point where the phase reaches 0°. The Design Tool automates the calculation of these three parameters and plots the results. The designer can use these parameters to evaluate the stability of the closed loop system. Bode Plots of the Compensator 80 70 60 50 40 30 20 10 0 -10 -20 10000 FIGURE 11: Bode Plots of the Compensated System. HS s = HP s HM s HC s Gain Phase 100 FREQUENCY (Hz) FREQUENCY RESPONSE OF THE COMPENSATED SYSTEM 60 50 40 30 20 10 0 -10 -20 -30 -40 -50 -60 180 160 140 120 100 80 60 40 20 0 -20 -40 -60 -80 1000000 Gain Phase PHASE (Degrees) Bode Plots of the Compensated System VOUT y Fcrossover Phase Margin Gain Margin FIGURE 12: Parameters. 63000 62 1 62.1 22.9 Hz Degrees dB Closed Loop System FREQUENCY (Hz) FIGURE 10: Bode Plots of the Compensation Circuit. 2012 Microchip Technology Inc. DS01452A-page 5 AN1452 1 GAIN (dB) FIGURE 13: 90 75 60 45 30 15 0 -15 -30 -45 -60 -75 -90 Gain Phase 1 FIGURE 14: Noise, Compensation And Stability in Practical Systems PHASE (Degrees) Gain Phase 180 160 140 Phase 120 Margin 100 80 60 40 20 0 -20 -40 -60 -80 FCrossover 100 10000 1000000 FREQUENCY (Hz) Phase Margin. 180 160 140 120 Gain 100 Margin 80 60 40 20 0 -20 -40 -60 -80 FCrossover 100 10000 1000000 FREQUENCY (Hz) PHASE (Degrees) GAIN (dB) 90 75 60 45 30 15 0 -15 -30 -45 -60 -75 -90 Gain Margin. Stability Criterion The designer can estimate if the closed loop system is stable by verifying if the phase and gain margin fulfills the Nyquist stability criterion. The criterion states that a closed loop system is asymptotically stable if: • Phase margin is greater than 0° • Gain margin is greater than 0 dB However, for a real system where noise and high-order effects are present, these limits must be modified according to the following rules: • Phase margin must be greater than 45° • Gain margin must be greater than 6 dB The larger the values, the better stability. At the same time, the system becomes slower, with poor dynamic response to an external perturbation. A system with lower phase and gain margins offer a faster transient response, but is more sensitive to noise and can become unstable. DS01452A-page 6 The Design Tool uses an ideal, linearized model that is not able to include and analyze all phenomena present within a real-world, step-down PWM converter application. Some effects, such as the delays introduced by the PWM modulator, Error Amplifier bandwidth and switching elements (MOSFETs), can produce additional phase lag, decreasing the phase margin of the compensated system. A safe way to avoid these effects is to design the regulator with a phase margin greater than 50° using the Design Tool. The power train passive components (inductor, input and output filter capacitors) may have large tolerances. The values are also affected by the operating conditions: inductor’s inductance varies with the current, and the capacitance of the ceramic capacitors varies with the operating voltage. It is highly recommended to check the stability of the system for all limits of components tolerances. In general, the inductance of the inductor drops when the current increases. This variation also depends on the magnetic material that is used for the core. The capacitance of the ceramic capacitor decreases if the voltage across the terminals increases. All the variation curves are provided in the component’s data sheet and must be verified by the designer. As previously mentioned, setting the crossover frequency high results in faster transient response. If the crossover frequency is too high, the system control loop can become sensitive to noise even if it is still stable (i.e., the phase margin exceeds 45°). The noise that passes through the loop will adversely affect the PWM modulator, producing a jitter on the high and lowside driver's signals and impact the output voltage ripple. Figure 15 captures this noisy behavior. The low and high-side driver's signals have jitter, and the output voltage ripple is higher than in normal operation. This behavior can also occur at high input voltages because the gain of the PWM modulator increases with the input voltage. The designer must reduce the crossover frequency of this system to avoid this behavior at high input voltages. Notice that this noisy behavior may also occur when the system runs near the Critical Conduction Mode, where the current in the inductor reaches zero. In this case, the power train becomes a first-order system (versus a second-order system, typical for voltage-mode control PWM buck regulators) resulting in an overly-aggressive gain profile of the Type-III compensator, which introduces noisy behavior. In practice, however, this instability will not affect the performance of the system, and can be safely ignored. 2012 Microchip Technology Inc. AN1452 The designer must verify that the converter is stable over the entire input voltage range. Figure 16 shows an unstable system. A sinusoidal oscillation is superimposed over the output voltage. This sinusoidal oscillation has a frequency equal to the system crossover frequency. The amplitude of this sinusoidal oscillation will vary with the input voltage and output current. This kind of instability is always related to the compensation loop, and is mostly produced by low phase and gain margins. FIGURE 15: The Noisy System. FIGURE 16: The Unstable System. Design Summary with a typical application schematic. The frequency analyses results and the estimated, full-load efficiency are also plotted. The fourth tab of the Design Tool provides the design summary. This page lists all the values for the power train and compensation network components, together +VIN CIN ON MCP19035 OFF SHDN BOOT VIN HDRV CBOOT PWRGD C2 PHASE COMP LDRV FB +VCC Q1 Q2 +VOUT COUT CVCC C3 L CIN COUT CBOOT 1 20 200 0.33 µH µF µF µF R1 R2 R3 R4 C1 C2 C3 20 10 0.75 8.2 0.68 3.9 0.033 k: k: k: k: nF nF nF R4 FCROSSOVER Phase Margin Gain Margin R1 63000 62.1 22.9 Hz Degrees dB R3 R2 C1 Estimated Efficiency at Full Load FIGURE 17: 88.7 % The Design Summary. 2012 Microchip Technology Inc. DS01452A-page 7 AN1452 STEP-BY-STEP DESIGN EXAMPLE For the input voltage, enter the maximum value. This will ensure that the current ripple in the inductor will be maintained at 30% of the maximum output current at high-input voltages. This section presents a practical design example using the MCP19035 Synchronous Buck Converter Design Tool. Due to the space constraints of the final application, the converter must be compact, while maintaining high efficiency. The load that must be powered from this converter will produce a step load between 2.5A and 7.5A. The maximum output voltage overshoot during step load must be lower than 100 mV. The project implies the design of a step-down, synchronous buck converter using the MCP19035. The system has the following input parameters: TABLE 1: CONVERTER PARAMETERS Parameter Input Voltage Range Output Voltage Value Unit 8 – 14 V 1.8 V Maximum Output Current 10 A Input Voltage Ripple 0.2 V IOH (Step Load High Value) 7.5 A IOL (Step Load Low Value) 2.5 A Output Voltage Overshoot 0.1 V TABLE 2: For this application, the designer may choose the 600 kHz switching frequency version with optimized dead time. The higher switching frequency will help minimize the power train component’s size, while the optimized dead time option will increase the system’s efficiency. Step 1: Introducing the Parameters Start the MCP19035 Synchronous Buck Converter Design Tool. All the input parameters of the converter are introduced in the table on the first tab of the Design Tool. INPUT PARAMETERS FOR DESIGN Value(1) Unit VIN 14 V Output Voltage VOUT 1.8 V Output Current IOUT 10 A Parameter Input Voltage Designator Switching Frequency Fs 600000 Hz Input Voltage Ripple VRIN 0.2 V Reference Voltage VREF 0.6 V Step Load High IOH 7.5 A Step Load Low IOL 2.5 A 0.1 V Notes 5V = VIN = 30V Fs = 300 kHz or 600 kHz Step Load Parameters Output Voltage Overshoot Note 1: The values in this column must be filled in by the designer. DS01452A-page 8 2012 Microchip Technology Inc. AN1452 Step 2: Calculate the Values The second page of the Design Tool shows the calculated values for various system parameters, such as RMS currents for low- and high-side MOSFETs, the inductor and the input and output filtering capacitors (Table 3). Fill in the standard values of the power train according to the recommendations provided by MCP19035’s data sheet. For example, the Design Tool calculates an inductor value of 0.87 µH and, based on the recommendations, the next standard value is 1 µH. For the capacitor, it is generally advisable to choose a higher value, because ceramic capacitors have large tolerances and exhibit a negative capacitance variation with voltage across the terminals. TABLE 3: POWER TRAIN COMPONENTS VALUES (CALCULATED) Since this application requires high efficiency, Microchip's MCP87050 and MCP87022 MOSFETs will be used. The requested parameters are available in the components’ data sheet. These MOSFETs are suitable for use with the optimized dead time version of the MCP19035. In this case, the "Total Conduction Time for the Body Diode" parameter is fixed, and equals 12 ns. The DC resistance of the inductor and ESRs of the input and output capacitors are entered in the same table. All these parameters will affect the performance of the converter and the designer must carefully select them, in concordance with the MCP19035 data sheet’s recommendations. TABLE 4: POWER TRAIN COMPONENTS PARAMETERS Parameter High side MOSFET RDS(ON)HS 6 m QGATEHS 13.8 nC RDS(ON)LS 2.5 m QGATELS 31 nC tBD 12 ns Reverse Recovery Charge of the Body Diode QRR 35 nC Inductor DC Resistance LDCR 2 m CIN ESR 10 m COUT ESR 5 m Suggested Value Standard Value(2) Unit Inductor Value 0.87 1 µH Low side MOSFET COUT(1) 135.1 200 µF RDS(ON) 10 20 µF Total gate charge 0.276 0.33 µF Total Conduction Time for the Body Diode Component CIN CBOOT Note 1: 2: To calculate the value of the bootstrap capacitor (CBOOT), the high-side MOSFET’s parameters must be introduced in the Power Train Components Parameters table (Table 4). Choose the MOSFETs, inductor and filtering capacitor’s parameters, based on the RMS currents calculated by the Design Tool and following the recommendations from the MCP19035 data sheet. These parameters must be entered in Table 4 (Power Train Components Parameters table). 2012 Microchip Technology Inc. RDS(ON) Total gate charge COUT is calculated based on the standard value for inductor and not for suggested value. The values in this column must be filled in by the designer Designator Value(1) Unit Note 1: The values in this column must be filled in by the designer. Based on the parameters of the power train components, the Design Tool will estimate the system losses and the efficiency at full load. Note that the losses are affected by the input voltage; the worst case is at maximum input voltage, 14V in this case. DS01452A-page 9 AN1452 TABLE 5: ESTIMATED SYSTEM LOSSES Parameter Value Compensation Network Components (1) Conduction losses 0.08 W Switching losses 1.1592 W Total losses 1.2392 W Low-Side MOSFET losses Conduction losses 0.2 W Body diode conduction losses 0.0504 W Body diode reverse recovery losses 0.147 W Total losses 0.3974 W 0.4 W Controller losses Inductor conduction losses 0.2 W COUT losses 0.015 W CIN losses 0.05 W Total losses 2.3016 W 88.7 % Estimated Efficiency at Full Load Step 3: Frequency Domain Analysis The next step of the design is the frequency domain analysis. This analysis can be performed on the third tab of the Design Tool. The Design Tool calculates the values of the compensation network components according to the procedures described in the MCP19035 data sheet (Table 6). COMPENSATION NETWORK CALCULATED VALUES Calculated Values for the Compensation Network (1) Units 20 k R2 10 k R3 0.75 k R4 7.62 k C1 0.71 nF C2 3.71 nF C3 0.035 nF R1 Note 1: COMPENSATION NETWORK COMPONENTS Unit High-Side MOSFET losses TABLE 6: TABLE 7: Units R1 20 k R3 0.75 k R4 8.2 k C1 0.68 nF C2 3.9 nF C3 3.30E-02 nF Note 1: These values must be filled in by the designer. Based on these values, the Design Tool will plot the Bode plots and calculate the crossover frequency, phase and gain margin of the compensated system. Adjust the values of the compensation network components to modify the frequency response of the system. Note that the frequency response of the system is affected by the value of the input voltage. It is advisable to perform the frequency analyses for the entire range of the input voltage. The worst case occurs again at high input voltages because the PWM modulator gain increases with the input voltage. TABLE 8: SYSTEM PARAMETERS Parameter Value Unit 63000 Hz Phase Margin 62.1 Degrees Gain Margin 22.9 dB FCrossover Step 4: Design Summary The last tab of the Design Tool shows the summary of the design and the typical application schematic for the synchronous buck regulator, based on the MCP19035 device. The designer can generate the final schematic for the step down regulator with these component’s values. The values with yellow background must be filled in by the designer. The ones with green background are calculated by the tool. Enter the calculated values in the Compensation Network Components table (Table 7). DS01452A-page 10 2012 Microchip Technology Inc. AN1452 +VIN CIN ON MCP19035 OFF SHDN BOOT VIN HDRV CBOOT PWRGD PHASE COMP LDRV FB +VCC Q1 Q2 C2 +VOUT COUT CVCC C3 L CIN COUT CBOOT 1 20 200 0.33 µH µF µF µF R1 R2 R3 R4 C1 C2 C3 20 10 0.75 8.2 0.68 3.9 0.033 k: k: k: k: nF nF nF R4 FCROSSOVER Phase Margin Gain Margin R1 C1 63000 62.1 22.9 Hz Degrees dB R3 R2 Estimated Efficiency at Full Load FIGURE 18: 88.7 % The Design Summary. REFERENCES 1. Erikson, Robert W. and Maksimovic, Dragan – "Fundamentals of Power Electronics (Second Edition)", ©2001, Springer Science and Business Media, Inc. 2012 Microchip Technology Inc. DS01452A-page 11 AN1452 APPENDIX A: LIST OF THE DESIGN TOOL FORMULAS Parameter Name Equation Inductor Value (H)(for 30% current ripple) VOUT 1 1 L = VINMAX – V OUT ------------------- -------- -----------------------------------V INMAX f SW 0.3 I OUTMAX Inductor Peak Current (A) (for 30% current ripple) 0.3 I OUTMAX I LPEAK = I OUTMAX + -----------------------------------2 Inductor RMS Current (A) I LRMS = Minimum Capacitance for Input Capacitor (F) I OUT D 1 – D CINMIN = ---------------------------------------------------------------------------------------f SW V Ripple – D I OUT ESR RMS Current in the Input Capacitor (A) IRMS C Output Voltage Ripple (V) Output Capacitor Minimum Value (F) 2 2 I Ripple I OUT + ---------------3 IN I Ripple VOUT I OUT = I OUT + ---------------- D – ------------------------------- 12 VIN 1 VRipple = I Ripple ESR + -------------------------------------- 8 COUT f SW L I OH2– IOL2 C OUT = ----------------------------------2 2 V f – V OUT RMS Value for High-side Current (A) I RMS High-Side = I Ripple2 D I OUT2 + ---------------- 12 Conduction Losses for High-side MOSFET (W) PCOND High-Side = I RMS High-Side2 R DS on HS max Switching Losses for High-side MOSFET (W) V IN I OUT P SW High_Side = --------------------------- ts HL + ts LH fSW 2 Total Power Losses for High-side MOSFET (W) P Loss High-Side = PCOND High-Side + P SW High-Side RMS Current for Low-side MOSFET (W) I RMS Low-Side = Conduction Losses for Low-side MOSFET (W) Body Diode Conduction Losses (W) Body Diode Reverse Recovery Losses (W) DS01452A-page 12 I Ripple2 1 – D I OUT2 + ---------------- 12 P COND Low-Side = I RMS Low-Side 2 R DS on LS max PLoss BD = I OUT V F t BD f SW Q RR V IN f SW P RR = ---------------------------------------2 2012 Microchip Technology Inc. AN1452 APPENDIX A: LIST OF THE DESIGN TOOL FORMULAS (CONTINUED) Parameter Name Total Power Losses for Low-side MOSFET (W) Controller Losses (W) (considering that the internal circuitry losses are 0.005W) Inductor Losses (W) Output Capacitor Losses (W) (for 30% current ripple) Equation P Loss = P COND Low – Side + PLoss BD + P RR P Loss = VIN 0.005 + F S Q Gate,low + Q Gate,high 2 P Loss = DCRL I L RMS 0.3 IOUT PLoss = ESR COUT -------------------------3 Input Capacitor losses (W) V OUT I OUT 2 PLoss = ESR CIN I RMS High – -------------------------------- V IN Bootstrap Capacitor (F) Q G Total C BOOT = ------------------------ VDROOP Resonant Frequency of the LC Circuit (Hz) PWM Modulator Gain Quality Factor Angular Corner Frequency Transfer Function of the Power Train Transfer Function of the Type III Compensation Network Feedback resistor divider () 2012 Microchip Technology Inc. 1 f LC = ----------------------------------------2 L C OUT V IN A MOD = 20 log --------------------- = 20 log V IN V RAMP V OUT C OUT Q = ------------- -------------I OUT L 1 L COUT 0 = ---------------------------1 G VG s = G 0 ------------------------------------------2s s 1 + ----------- + ------ Q 0 0 1 1 s + ------------------ s + ------------------------------------- R 1 + R3 C 1 R 4 C 2 R1 + R 3 G s = – A 0 ------------------------------- -----------------------------------------------------------------------------------------------C2 + C3 R 1 R 3 C1 1 s s + ------------------------------- s + ------------------- R 4 C 2 C 3 R 3 C 1 V REF R 1 0.6 R 1 R 2 = --------------------------------- = --------------------------V OUT – VREF VOUT – 0.6 DS01452A-page 13 AN1452 APPENDIX A: LIST OF THE DESIGN TOOL FORMULAS (CONTINUED) Parameter Name Equation Capacitor C1 (F) L COUT C 1 = ---------------------------R1 Resistor R4 () fCO 1 R 4 = -------- -------- R1 f LC V IN Capacitor C2 (F) 2 L C OUT C 2 = ------------------------------------R4 Capacitor C3 (F) Resistor R3 () Input Power (W) 1 C 3 = --------------------------------2 R 4 fSW 1 R 3 = ----------------------------- C 1 f SW U OUT I OUTmax PIN = -----------------------------------------Eff Total converter losses (W) P Loss = P IN – P OUT Maximum RDS(on) () DS01452A-page 14 PLoss High – Side R DS on = --------------------------------------- 0.4 I RMS High – Side2 2012 Microchip Technology Inc. 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DS01452A-page 15 Worldwide Sales and Service AMERICAS ASIA/PACIFIC ASIA/PACIFIC EUROPE Corporate Office 2355 West Chandler Blvd. Chandler, AZ 85224-6199 Tel: 480-792-7200 Fax: 480-792-7277 Technical Support: http://www.microchip.com/ support Web Address: www.microchip.com Asia Pacific Office Suites 3707-14, 37th Floor Tower 6, The Gateway Harbour City, Kowloon Hong Kong Tel: 852-2401-1200 Fax: 852-2401-3431 India - Bangalore Tel: 91-80-3090-4444 Fax: 91-80-3090-4123 India - New Delhi Tel: 91-11-4160-8631 Fax: 91-11-4160-8632 Austria - Wels Tel: 43-7242-2244-39 Fax: 43-7242-2244-393 Denmark - Copenhagen Tel: 45-4450-2828 Fax: 45-4485-2829 India - Pune Tel: 91-20-2566-1512 Fax: 91-20-2566-1513 France - Paris Tel: 33-1-69-53-63-20 Fax: 33-1-69-30-90-79 Japan - Osaka Tel: 81-66-152-7160 Fax: 81-66-152-9310 Germany - Munich Tel: 49-89-627-144-0 Fax: 49-89-627-144-44 Atlanta Duluth, GA Tel: 678-957-9614 Fax: 678-957-1455 Boston Westborough, MA Tel: 774-760-0087 Fax: 774-760-0088 Chicago Itasca, IL Tel: 630-285-0071 Fax: 630-285-0075 Cleveland Independence, OH Tel: 216-447-0464 Fax: 216-447-0643 Dallas Addison, TX Tel: 972-818-7423 Fax: 972-818-2924 Detroit Farmington Hills, MI Tel: 248-538-2250 Fax: 248-538-2260 Indianapolis Noblesville, IN Tel: 317-773-8323 Fax: 317-773-5453 Los Angeles Mission Viejo, CA Tel: 949-462-9523 Fax: 949-462-9608 Santa Clara Santa Clara, CA Tel: 408-961-6444 Fax: 408-961-6445 Toronto Mississauga, Ontario, Canada Tel: 905-673-0699 Fax: 905-673-6509 Australia - Sydney Tel: 61-2-9868-6733 Fax: 61-2-9868-6755 China - Beijing Tel: 86-10-8569-7000 Fax: 86-10-8528-2104 China - Chengdu Tel: 86-28-8665-5511 Fax: 86-28-8665-7889 China - Chongqing Tel: 86-23-8980-9588 Fax: 86-23-8980-9500 Korea - Daegu Tel: 82-53-744-4301 Fax: 82-53-744-4302 China - Hangzhou Tel: 86-571-2819-3187 Fax: 86-571-2819-3189 Korea - Seoul Tel: 82-2-554-7200 Fax: 82-2-558-5932 or 82-2-558-5934 China - Hong Kong SAR Tel: 852-2401-1200 Fax: 852-2401-3431 Malaysia - Kuala Lumpur Tel: 60-3-6201-9857 Fax: 60-3-6201-9859 China - Nanjing Tel: 86-25-8473-2460 Fax: 86-25-8473-2470 Malaysia - Penang Tel: 60-4-227-8870 Fax: 60-4-227-4068 China - Qingdao Tel: 86-532-8502-7355 Fax: 86-532-8502-7205 Philippines - Manila Tel: 63-2-634-9065 Fax: 63-2-634-9069 China - Shanghai Tel: 86-21-5407-5533 Fax: 86-21-5407-5066 Singapore Tel: 65-6334-8870 Fax: 65-6334-8850 China - Shenyang Tel: 86-24-2334-2829 Fax: 86-24-2334-2393 Taiwan - Hsin Chu Tel: 886-3-5778-366 Fax: 886-3-5770-955 China - Shenzhen Tel: 86-755-8203-2660 Fax: 86-755-8203-1760 Taiwan - Kaohsiung Tel: 886-7-213-7828 Fax: 886-7-330-9305 China - Wuhan Tel: 86-27-5980-5300 Fax: 86-27-5980-5118 Taiwan - Taipei Tel: 886-2-2508-8600 Fax: 886-2-2508-0102 China - Xian Tel: 86-29-8833-7252 Fax: 86-29-8833-7256 Thailand - Bangkok Tel: 66-2-694-1351 Fax: 66-2-694-1350 Italy - Milan Tel: 39-0331-742611 Fax: 39-0331-466781 Netherlands - Drunen Tel: 31-416-690399 Fax: 31-416-690340 Spain - Madrid Tel: 34-91-708-08-90 Fax: 34-91-708-08-91 UK - Wokingham Tel: 44-118-921-5869 Fax: 44-118-921-5820 China - Xiamen Tel: 86-592-2388138 Fax: 86-592-2388130 China - Zhuhai Tel: 86-756-3210040 Fax: 86-756-3210049 DS01452A-page 16 Japan - Yokohama Tel: 81-45-471- 6166 Fax: 81-45-471-6122 10/26/12 2012 Microchip Technology Inc.

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