APPLICATION NOTE Output Voltage Ripple in Step-Down and Step-Up Switching Regulators Introduction Output voltage ripple is always an important performance parameter with DC-DC converters. For inductor-based switching regulators, several key factors can affect this important parameter, including switching frequency, duty cycle, and output capacitor value. Step-down and step-up switching regulators have different circuit topologies, so some factors that affect the output voltage ripple for step-down DC-DC converters will not affect output voltage ripple for step-up DC-DC converters. This application note analyzes factors affecting output voltage ripple based on the derived output voltage ripple equations for step-down and step-up DC-DC converter topologies in CCM. This document can help provide insight in understanding output voltage ripple. Step-Down Converter Output Ripple Step-Down IC IN SW Control Circuit + IL Q1 PMOS VS L Q2 NMOS C R VO FB - GND Figure 1: Step-Down DC-DC Converter. To derive the step-down DC-DC converter output voltage ripple equation, continuous conduction mode (CCM) operation is assumed. The output voltage VO includes the DC component VO and AC component ∆VO. VO is produced by the inductor current IL flowing through the load (R in Figure 1) and output capacitor (C in Figure 1). In a well designed converter, the output capacitor will provide a very low impedance to ground with respect to the load at the step-down DC-DC regulator switching frequency in order to filter the inductor AC ripple current (ΔIL). Hence almost all of the inductor AC ripple current will flow through the output capacitor, C in Figure 1. Inductor current:: i L = IL + ∆i L Output voltage: vO = VO + ∆vO Using the circuit in Figure 1, where the Q1 and Q2 transistors are alternatively turned on/off, the following inductor current components (DC and AC) can be derived: Inductor current DC component:IL = IO = VO R Inductor current AC component: ∆iL = VS - VO DT = VO (1 - DT) V Where D = duty cycle D = O VS L L and T = switching period. Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 202372A • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • September 21, 2012 1 APPLICATION NOTE Output Voltage Ripple in Step-Down and Step-Up Switching Regulators The output capacitor charging and discharging current is equal to the inductor AC ripple current. Figure 2 illustrates the typical output capacitor voltage ripple waveform resulting from the inductor AC ripple current flowing through the output capacitor. Using the “blue section”, or area under the waveform, of the output capacitor current (iC) waveform in Figure 2, the output voltage ripple equation can be derived: ∆vf = ∆iC VO = (1 - D) 8 · f · C 8 · f2 · L · C VSW VS Q1 close Q2 open 0 Q1 open Q2 close DT t T iL IO ∆i L 0 DT 2 t DT (1+D)T T 2 iC ∆iC=∆iL 0 DT 2 DT (1+D)T 2 t T vO VO ∆vO 0 DT 2 DT (1+D)T T t 2 Figure 2: Typical Waveforms of a Step-Down Converter. From the output voltage ripple equation, switching frequency (f), duty cycle (D), inductor value (L) and output capacitor value (C) can all affect output voltage ripple. The data curves in Figure 3 illustrate the effect of these parameters on output voltage ripple. 2 Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 202372A • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • September 21, 2012 APPLICATION NOTE Output Voltage Ripple in Step-Down and Step-Up Switching Regulators Step-Down Output Ripple vs. Frequency and C Step-Down Output Ripple vs. Frequency and L (C = 10µF; D = 0.50) 50 Output Voltage Ripple (mV) Output Voltage Ripple (mV) (L = 2.2µH; D = 0.50) C = 4.7µF C = 10µF C = 22µF 40 30 20 10 0 0.5 1 1.5 2 2.5 3 Frequency (MHz) 50 L = 1.4µH L = 2.2µH L = 4.7µH L = 6.8µH 40 30 20 10 0 0.5 1 1.5 2 2.5 Frequency (MHz) (a) 3 (b) Buck Output Ripple vs. Frequency and Duty Output Voltage Ripple (mV) (L = 2.2µH, C = 10µF) 50 D = 0.72 D = 0.50 D = 0.33 40 30 20 10 0 0.5 1 1.5 2 2.5 3 Frequency (MHz) (c) Figure 3: The Effect of Four Parameters [f, D, L, C] on Step-Down Converter Output Voltage Ripple. From Figure 3, the following is observed: • Switching frequencies between 1MHz ~ 2MHz result in 10mV or less output voltage ripple for output capacitor values of 4.7µF ~ 22µF and inductor values of 1.4μH ~ 6.8µH without high switching losses. • As the duty cycle is increased, output voltage ripple is decreased. In other words, duty cycle is inversely proportional to output voltage ripple. • As the inductor value is increased, output voltage ripple is decreased. In other words, inductor value is inversely proportional to output voltage ripple. • The output current has no effect on the output voltage ripple of a step-down DC-DC converter. Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 202372A • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • September 21, 2012 3 APPLICATION NOTE Output Voltage Ripple in Step-Down and Step-Up Switching Regulators Step-Up Converter Output Ripple L Step-Up IC IN SW IL D1 + ID1 Control Circuit VS Q1 NMOS C R VO FB - GND Figure 4: Step-Up DC-DC Converter. As with the step-down DC-DC converter, the step-up DC-DC converter output voltage ripple can be derived from the output capacitor charging and discharging current (iC) for CCM operation. Figure 5 illustrates the output voltage ripple waveform resulting from the capacitor current (iC). Time: Capacitor current: DT vo ic = R Using small ripple approximation Capacitor current: (1-D)T vo ic = iL R vo ≈ Vo iL ≈ IL, vo ≈ V o Vo ic = - R ic = IL - Integrate the capacitor current Output voltage ripple: Where D = duty cycle (D = 1 - 4 VS ) VO ∆vo = D • T • Vo R•C = Vo R IL • R - Vo • (1-D)T R•C and T = switching period. Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 202372A • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • September 21, 2012 APPLICATION NOTE Output Voltage Ripple in Step-Down and Step-Up Switching Regulators VSW VO - VD1 Q1 close Q1 open 0 DT t T iC IL - VO R 0 DT VO R t T vO ∆v O VO 0 DT 2 DT (1+D)T T t 2 Figure 5: Typical Waveforms of a Step-Up DC-DC Converter. Using the vO = 1 ∫ i dt equation, C c the step-up DC-DC converter output voltage ripple is derived: ∆vO = Where D = duty cycle (D = 1 - VS ) VO D · VO · T D · IO = R·C C·f and f = switching frequency = 1/T. The data curves in Figure 6 illustrate the effect of duty cycle (D), output current (IO), output capacitor value (C), and switching frequency (f) on step-up DC-DC converter output voltage ripple (∆vO). From those data curves, the following can be observed: • As the duty cycle is increased, output voltage ripple is increased. In other words, the duty cycle is proportional to output voltage ripple. • As the output capacitor value is decreased, output voltage ripple is increased. In other words, output capacitor value is inversely proportional to output voltage ripple. • As the output current is increased, output voltage ripple is increased. In other words, output current is proportional to output voltage ripple. • The inductor value has no effect on the output voltage ripple of a step-up DC-DC converter. Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 202372A • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • September 21, 2012 5 APPLICATION NOTE Output Voltage Ripple in Step-Down and Step-Up Switching Regulators Step-Up Output Ripple vs. Frequency and C Step-Up Output Ripple vs. Frequency and D (L = 2.2µH; D = 0.50) 200 D = 0.76 D = 0.52 D = 0.28 150 100 50 0 0.5 Output Voltage Ripple (mV) Output Voltage Ripple (mV) (C = 10µF; IO = 1A) 1 1.5 2 2.5 3 Frequency (MHz) 250 C = 4.7µF C = 10µF C = 22µF 200 150 100 50 0 0.5 1 1.5 2 2.5 Frequency (MHz) (a) Output Voltage Ripple (mV) (D = 0.50; C = 10µF) 200 IO = 0.1A IO = 0.5A IO = 1.0A 150 100 50 0 1 1.5 2 2.5 3 Frequency (MHz) (c) Figure 6: The Effect of Four Parameters [f, D, IO, C] on Step-Up Converter Output Voltage Ripple. 6 (b) Step-Up Output Ripple vs. Frequency and IO 0.5 3 Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 202372A • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • September 21, 2012 APPLICATION NOTE Output Voltage Ripple in Step-Down and Step-Up Switching Regulators Conclusion For step-up and step-down inductor based DC-DC converters, factors affecting output voltage ripple overlap for both converter topologies. The common factors for both DC-DC converter topologies are switching frequency, output capacitor value, and duty cycle. For the step-up DC-DC converter, inductor value is not a factor in influencing the output voltage ripple, while for the step-down DC-DC converter it is. This is also true for output current; Table 1 provides a brief comparison of the two different topologies regarding factors/parameters which influence output voltage ripple. Factors Affecting Output Voltage Ripple Type Output Voltage Ripple Formula D · IO C·f D=1- VO (1 - D) 8·f ·L·C D= ∆vO = Step-Up Step-Down ∆vO = Duty 2 VS VO VO VS Switch Frequency L √ √ √ C D IO √ √ √ √ √ Table 1: Factors and Parameters that Affect Output Voltage Ripple in Step-Down and Step-Up DC-DC Converter Topologies. Copyright © 2012 Skyworks Solutions, Inc. All Rights Reserved. Information in this document is provided in connection with Skyworks Solutions, Inc. (“Skyworks”) products or services. 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Skyworks Solutions, Inc. • Phone [781] 376-3000 • Fax [781] 376-3100 • [email protected] • www.skyworksinc.com 202372A • Skyworks Proprietary Information • Products and Product Information are Subject to Change Without Notice. • September 21, 2012 7