Application Report SLVA458B – August 2011 – Revised June 2018 Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator Sureena Gupta ................................................................................ PMP-Power Management Products ABSTRACT Some applications require a high current negative output voltage to be generated from a positive input voltage. Applications often requiring a negative output voltage are medical ultrasound scanners, semiconductor test equipment, RADAR, oscilloscopes (DSO) and massive MIMO (active antenna systems). This application report presents a solution for creating an inverting power supply using a synchronous buck converter. The purpose of this application report is to discuss how to create a negative power supply using a switching regulator (buck). The solution schematic is given along with component selection criteria and equations, so that designers can appropriately scale the solution to their own requirements. The document also includes a sample design implementation along with captured waveforms. 1 2 3 4 5 6 7 Contents Description of Application ................................................................................................... 3 Design Restrictions .......................................................................................................... 3 Solution and Part Used ..................................................................................................... 3 Design Restrictions .......................................................................................................... 5 Design Procedures .......................................................................................................... 5 5.1 Output Voltage ...................................................................................................... 5 5.2 Input Voltage Range................................................................................................ 6 5.3 Duty Cycle ........................................................................................................... 6 5.4 Output Current ...................................................................................................... 6 5.5 Operating Frequency ............................................................................................... 6 5.6 Inductor............................................................................................................... 6 5.7 Output Capacitor .................................................................................................... 7 5.8 Power Dissipation in Package .................................................................................... 7 5.9 Input Capacitors..................................................................................................... 7 5.10 Bypass Capacitor ................................................................................................... 8 5.11 Slow-Start Time ..................................................................................................... 8 5.12 Frequency Set Resistor ............................................................................................ 8 5.13 Frequency Response of the Inverting Regulator ............................................................... 8 5.14 Synchronizing to an External Clock .............................................................................. 9 Evaluation Results ......................................................................................................... 10 References .................................................................................................................. 13 List of Figures 1 Buck Topology ............................................................................................................... 3 2 Inverting Buck-Boost Topology 3 4 5 6 7 ............................................................................................ 4 Inverting Power Supply Schematic ........................................................................................ 5 Efficiency Curve ............................................................................................................ 10 Load Regulation ............................................................................................................ 10 Power Loss vs Load Current ............................................................................................. 11 Bode Plot (BW = 3.2 kHz, PM = 59.4°) (VIN = 5 V, VOUT = –5 V, IOUT = 2 A) ........................................ 11 SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator Copyright © 2011–2018, Texas Instruments Incorporated 1 www.ti.com 8 Bode Plot (BW = 4.9 kHz, PM = 72.5°) (VIN = 5 V, VOUT = –5 V, IOUT = 0 A) ........................................ 12 9 Switch Node (VIN = 5 V, VOUT = –5 V, IOUT = 0 A) 10 Switch Node Rising (VIN = 5 V, VOUT = –5 V, IOUT = 0 A) ...................................................................... .............................................................. 12 13 List of Tables .............................................................. 1 Electrical Characteristics for the Inverting Power Supply 2 Inverting Power Supply Requirements .................................................................................... 5 3 Electrical Characteristics for the Inverting Power Supply .............................................................. 3 5 Trademarks SWIFT is a trademark of Texas Instruments. 2 Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Copyright © 2011–2018, Texas Instruments Incorporated Description of Application www.ti.com 1 Description of Application This application report discusses creating an inverting power supply using a synchronous step-down regulator. The design generates a negative voltage from a positive input voltage. Applications that often require an inverted output voltage from a positive input voltage are those with amplifiers and data converters. Using a synchronous topology has certain advantages over a nonsynchronous topology like higher efficiency at low voltages. The synchronous topology stays in continuous conduction mode (CCM) even at very low currents as opposed to a nonsynchronous topology which runs into discontinuous conduction mode (DCM) when the current through the inductor is reduced to zero. The disadvantages of nonsynchronous topology in DCM are that it has a slow transient response, it needs slower compensation for the DCM shift, and it has additional component on the EVM board. These disadvantages can be eliminated by using a synchronous topology. 2 Design Restrictions The design restrictions for the application are listed in Table 1. To power up the board, the input voltage needs to be higher than the minimum required voltage for the device. The maximum allowable output voltage is limited by the maximum Vdev (voltage across the device, between the VIN pin and GND pin on the IC) minus the maximum input voltage. Because the MOSFETs are internal to the IC, the maximum load current cannot be more than the maximum current through the internal switches. Table 1. Electrical Characteristics for the Inverting Power Supply INVERTING POWER SUPPLY RESTRICTIONS 3 SYNCHRONOUS DEVICE USED TPS54620 Vin (min) > Vdev (min) (4.5 V) Vin (max) + Vout < Vdev (max) (17 V) Iout (max) < Iswitch (max) (7 A) Solution and Part Used To convert a synchronous buck regulator (as shown in Figure 1) into a buck boost topology (as shown in Figure 2), the inductor and output capacitor are connected just like in a buck converter, but the ground and output voltage test points are reversed in order to achieve a negative output voltage. Vin Internal to IC TPIC54620 Cin High Side Switch Lout Vout Low Side Switch REF Cout Feedback Network + PWM Control and Gate Drive Figure 1. Buck Topology SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator Copyright © 2011–2018, Texas Instruments Incorporated 3 Solution and Part Used www.ti.com Internal to IC Vin Cin High Side Switch Lout Low Side Switch REF Cout + PWM Control and Gate Drive Feedback Network -Vout Figure 2. Inverting Buck-Boost Topology The sample design to create a synchronous inverting power supply is presented in the next section using the TPS54620, which is a 4.5-V to 17-V input, 6-A synchronous step-down SWIFT™ converter. The sample device is used to illustrate the concept, but any buck regulator can be configured this way provided it matches the requirements previously listed. The electrical requirements of the sample design are listed in Table 2. 4 Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Copyright © 2011–2018, Texas Instruments Incorporated Design Restrictions www.ti.com Table 2. Inverting Power Supply Requirements VARIABLE DESCRIPTION RANGE / VALUE Input Voltage 5 V nominal 4.5 V to 5.5 V Vout Output Voltage –5 V Vout Output Voltage Ripple < 0.5% Iout Output Current 2A fsw Switching Frequency 300 kHz Vin 4 Design Restrictions The design restrictions for the application are listed in Table 3. To power up the board, the input voltage needs to be higher than the minimum required voltage for the device. The maximum allowable output voltage is limited by the maximum Vdev (voltage across the device, between the VIN pin and GND pin on the IC) minus the maximum input voltage. Because the MOSFETs are internal to the IC, the maximum load current cannot be more than the maximum current through the internal switches. Table 3. Electrical Characteristics for the Inverting Power Supply Inverting Power Supply Restrictions 5 Synchronous Device Used TPS54620 Vdev (min) (4.5 V) Vin (min) > Vin (max) + Vout < Vdev (max) (17 V) Iout (max) < Iswitch (max) (7 A) Design Procedures This section enlists the procedure to design an inverting power supply using the TPS54620 (synchronous step-down SWIFT™ converter). The schematic for the design is presented in Figure 3. Figure 3. Inverting Power Supply Schematic 5.1 Output Voltage The difference in the maximum input voltage, Vin (max), and the output voltage, VO, must not exceed the maximum operating device voltage of the regulator. For the TPS54620, the maximum operating device voltage, Vdev (max), is 17 V. spacer Vin (max) ≥ Vdev (max) + Vout (1) æ Vout ö R4 = R5 ´ ç - 1÷ è Vref ø (2) SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator Copyright © 2011–2018, Texas Instruments Incorporated 5 Design Procedures www.ti.com Because Vout for the sample design is –5 V and using Equation 1, the maximum input voltage for the power supply can be as high as 12 V, easily supporting the 5.5-V maximum input requirement in Table 2. Use Equation 2 to determine R4 for the desired output voltage, set R5 equal to 10 kΩ and Vref to 0.8 V for the TPS54620. R4 equals 52.5 kΩ (52.3-kΩ standard value). 5.2 Input Voltage Range The operating input voltage, Vin (min) of the power supply must be greater than the minimum device voltage, Vdev (min). For TPS54620, the Vdev (min) is 4.5 V. The minimum input voltage requirement for the power supply is 4.5 V, thus, satisfying Equation 3. spacer Vin (min) ≥ Vdev (min) 5.3 (3) Duty Cycle The ideal duty cycle for the inverting power supply is shown in Equation 4, neglecting the losses of the power switch and inductor. The output voltage, Vout, is negative and the input voltage, Vin, is positive, yielding a positive result for Equation 4. -Vout D= Vin - Vout (4) The maximum duty cycle, Dmax, is calculated by using the minimum input voltage, Vin (min), as substituted for input voltage, Vin in Equation 4. Assuming 4.5 V for Vin (min) and a Vout of –5 V, the maximum duty cycle, Dmax, is 0.53. Similarly, Dmin is evaluated by using maximum input voltage, Vin (max), and is calculated to be 0.48. 5.4 Output Current To estimate whether the selected switching regulator is capable of delivering the output current, use Equation 5. The user must know the device’s (TPS54620) minimum current limit, Icl (min) (7 A), maximum duty cycle, Dmax, and estimate the inductor ripple current value, ILripple. Using Equation 5, the maximum allowable output current for the design is 3.13 A, which is higher than the needed 2 A. ILripple ö æ Iout (max) £ ç Icl(min) ÷ ´ (1 - Dmax ) 2 è ø (5) 5.5 Operating Frequency The first step is to decide on a switching frequency for the regulator because of the tradeoff between higher and lower switching frequencies. Higher switching frequencies may produce a smaller solution size using lower valued inductors and smaller output capacitors, compared to a power supply than switches at a lower frequency. However, higher switching frequency causes extra switching losses, which hurt the converter’s efficiency and thermal performance. In this design, a moderate switching frequency of 300 kHz is selected to achieve both a small solution size and a high-efficiency operation. 5.6 Inductor To determine the inductor value, calculate the average inductor current, ILavg, at the maximum output current and minimum input voltage using Equation 6. Assuming maximum output current, Iout as 2 A and using maximum duty cycle Dmax, ILavg is 4.22 A. The inductor value is calculated, Equation 7, using a ripple current that is 25% of the average inductor current. Using the Dmin to calculate the minimum inductance value gives the largest inductance. Assuming Vin (max) of 5.5 V, Iout of 2 A, and a ƒsw of 300 kHz, the Lo is calculated as 8.22 µH. The nearest standard inductor of 10 µH is used for the inductor. The inductor saturation current must be greater than the 4.62 A of peak current calculated in Equation 8. The inductor rms current must be greater than 4.01 A calculated in Equation 9. 6 Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Copyright © 2011–2018, Texas Instruments Incorporated Design Procedures www.ti.com ILavg = Iout 1 - Dmax Vin(max) ´ Dmin Lo = ( f sw ´ ILavg ´ 0.25 ) ILpeak = Iout 1 - Dmax + (6) (7) Vin(min) ´ Dmax 2 ´ f sw ´ Lo 2 æ Vin ´ D ö 1 æ Iout ö ILrms = ç ´ ç ÷ ÷ + 1 D 12 è ø è f sw ´ Lo ø 5.7 (8) 2 (9) Output Capacitor The output capacitor must supply the current when the high-side switch is on. Use the minimum input voltage to calculate the output capacitance needed. This is when the duty cycle and the peak-to-peak current in the output capacitor are the maximum. Using the 0.5% voltage ripple specification, Vout, and Equation 10, Co (min) is 140 µF. Assuming the 0.5% voltage ripple and maximum duty cycle, the Rc, equivalent series resistance must be less than 5.41 mΩ, using Equation 11. The rms current for the output capacitor is 2.11 A using Equation 12. Three 47 μF, 10 V X7R in parallel are used for the output capacitor because of the low ESR and size. The output capacitor is derated by 15% because of the dc voltage. Iout(max) ´ Dmax) Co (min) ³ f sw ´ ΔVout (10) Rc £ ΔVout Iout Vin(min) ´ Dmax + 1 - Dmax 2 ´ f sw ´ Lo Icorms = Iout (max) ´ 5.8 (11) Dmax 1 - Dmax (12) Power Dissipation in Package The power dissipation in the package is dominated by the conduction losses and switching losses of the power switch and must not exceed the limitations of the package. The conduction and switching losses are calculated using Equation 13. The conduction losses are a function of the duty cycle, D, inductor rms current, ILrms, and on resistance, Rhs and Rls. The switching losses are a function of the turnon, tr, and turnoff, tf, times, switching frequency, output current, and input and output voltage. Pdevice is 0.6613 W assuming a tr and tf of 25 ns. 1 æ Iout ö Pdevice = D × ILrms2 ´ Rhs + (1 - D) ´ ILrms2 ´ Rls + ´ (Vin - Vout) ´ ç ÷ ´ (tr + tf) ´ f sw 2 è1 - D ø (13) 5.9 Input Capacitors The input capacitors between the PVIN pins and system ground are used to limit the voltage ripple of the input supply. Equation 14 to Equation 17 are used to estimate the capacitance, maximum ESR, and current rating for the input capacitor, Ci. Using Equation 14, the estimated average input current is 2.22 A. Using Equation 15 and Equation 16, the minimum required input capacitance is 165 µF and the maximum ESR is 20 mΩ. Using Equation 17, the input capacitor needs at least 2.32-A current rating. Three 68 μF, 10 V X7R in parallel are used for the output capacitor because of the low ESR and size. Iout ´ Dmax Iin (avg) = (1 - Dmax) (14) Ci = Iin(avg) f sw ´ 0.01 ´ Vin (min) SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback (15) Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator Copyright © 2011–2018, Texas Instruments Incorporated 7 Design Procedures www.ti.com ESRci £ Icirms = 0.01 ´ Vin (min) Iin (avg) (16) 2 æ æ Vin(min) ´ Dmax ö ö÷ ç ç ÷ Lo ´ f sw ç 2 è ø ÷ 2 ç (ILpeak - Iin(avg) ) + ÷ ´ Dmax + Iin(avg) ´ (1 - Dmax) 12 ç ÷ ç ÷ è ø (17) 5.10 Bypass Capacitor The TPS54620 needs a tightly coupled, ceramic bypass capacitor, connected to the VIN and GND pins of the device. Because the device GND is the power supply output voltage, the voltage rating of the capacitor must be greater than the difference in the maximum input and output voltage of the power supply. A minimum of 4.7 µF from the VIN pin to GND is recommended for the TPS54620, Cbp is chosen as 15 µF. Another 0.1-µF capacitor has been added as a bypass capacitor to clear high-frequency noise. This capacitor creates an AC path from the input voltage to the output voltage. As a result, transients on the input voltage rail can potentially also appear on the output voltage. For example, when the input voltage ramps up. To minimize this effect, Cbp should be kept relatively small, near the minimum recommended capacitance. 5.11 Slow-Start Time Placing a small ceramic capacitor on the SS/TR to the chip GND (that is, system Vout) adjusts the slowstart time on the TPS54620. The slow-start capacitor is calculated using Equation 18. The equation assumes a 2.3-μA pullup sourcing current and 10% to 90% measurement for time Tss. Using Equation 18, Css is evaluated as 10 pF. Css = tss ´ 2.3 ´ 10-6 0.8 (18) 5.12 Frequency Set Resistor The switching frequency is set with a resistor, RT, from the RT/CLK pin to the GND of the TPS54620 device. Using Equation 19, the frequency set resistor is 161 kΩ (162-kΩ standard value). 48000 RT(kW ) = - 2 0.997 f sw(kHz) (19) 5.13 Frequency Response of the Inverting Regulator Using a buck regulator as an inverting buck-boost regulator changes the feedback loop characteristic. So, a different design method is needed. The inverting power supply transfer function has two zeroes and a pole. Equation 20 is a simplified transfer function of an inverting power supply. The ESR zero, ƒz1, is the same as in a buck regulator, Equation 21, and is a function of the output capacitor and its ESR. The other zero is a right half plane zero, ƒz2. The frequency response of the ƒz2 results in an increasing gain and a decreasing phase. The ƒz2 frequency is a function of the duty cycle, output current, and the inductor. Equation 22 calculates the minimum frequency of the ƒz2 which is used to determine the crossover frequency. The dominant pole, ƒp1, is a function of the load current, output capacitor, and duty cycle, see Equation 23. Kbb is the dc gain and is used to calculate the frequency compensation components. The gmps variable is the transconductance of the power stage, which is 16 A/V for the TPS54620. The ƒz1 is estimated to be 265 kHz. The output capacitor is derated by 15% because of the dc voltage, and the ESR is assumed to be . The ƒz2 is estimated to be 16.93 kHz. Assuming resistance of the inductor, Rdc is 19 mΩ. The ƒp1 is estimated to be 796 Hz assuming a nominal duty cycle. Kbb is calculated as 13.33 V/V using Equation 24, assuming nominal input voltage and gmps as 16 A/V . 8 Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Copyright © 2011–2018, Texas Instruments Incorporated Design Procedures www.ti.com æ ö æ ö s s ç1 + 2 ´ p ´ f z1÷ ´ ç1 + 2 ´ p ´ f z2 ÷ è ø è ø T(s) = Kbb ´ æ ö s ç1 + 2 ´ p ´ f p1 ÷ è ø (20) 1 f z1 = (Rc ´ Co ´ 2 ´ p ) (21) -Vout ö (1 - Dmax ) ´ æç ÷ + Rdcx ((1 - Dmax ) - Dmax ) è Iout ø f z2 = Dmax ´ Lo ´ 2 ´ p 1+D f p1 = æ æ Vout ö ö çç÷ ´ Co ´ 2 ´ p ÷ è è Iout ø ø 2 æ Vout ö Vin ´ ç ÷ è Iout ø ´ gmps Kbb = (Vin + 2 ´ (-Vout )) (22) (23) (24) The crossover of the power supply should be set between the ƒp1 and 1/3 of ƒz2 frequencies. It is recommended to start with the crossover frequency, ƒco, given by Equation 25. The ƒco is estimated to be 3.67 kHz. f co = ( f p1 x f z2 )0.5 (25) The compensation resistor, Rcomp, needed to set the compensation gain at the fco frequency is calculated using Equation 26. The Vref is 0.8 V and gmea is 1300 μA/V for the TPS54620. æ ö æ ö f co -Vout Rcomp = ç ÷´ç ÷ è Kbb ´ f p1 ø è Vref ´ gmea ø (26) Rcomp is calculated using Equation 26 and is equal to 1.66 kΩ. Use the nearest standard value of 1.54 kΩ. The compensation zero is set to 1/2 of the dominant pole, ƒp1. To calculate the compensation zero capacitor, Czero, use Equation 27. Equation 27 gives 0.26 µF; use the next larger standard value which is 0.22 µF. The compensation pole is set to equal the RHP zero, ƒz2. Use Equation 28, to calculate the frequency compensation pole, Cpole, which gives 6.10 nF. The next standard value is 5.6 nF. 1 Czero = æ f p1ö ç 2 ÷ ´ 2p ´ Rcomp è ø (27) Cpole = 1 f z2 ´ 2p ´ Rcomp (28) 5.14 Synchronizing to an External Clock The TPS54620 has a CLK pin that can be used to synchronize the power supply switching frequency to an external system clock. A level shift circuit needs to be used to translate a system ground reference clock signal to the device’s ground. SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator Copyright © 2011–2018, Texas Instruments Incorporated 9 Evaluation Results 6 www.ti.com Evaluation Results Figure 4 to Figure 10 show the experimental test results of the Figure 1 design. h - Efficiency - % 100 90 VI = 4.5 V VI = 5 V VI = 5.5 V 80 70 0 -0.5 -1 -1.5 IL - Load Current - A -2 -2.5 Figure 4. Efficiency Curve -4.91 VO - Output Voltage - V -4.93 VI = 5 V -4.95 VI = 5.5 V VI = 4.5 V -4.97 -4.99 -5.01 -5.03 -5.05 0 -0.5 -1 -1.5 IL - Load Current - A -2 -2.5 Figure 5. Load Regulation 10 Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Copyright © 2011–2018, Texas Instruments Incorporated Evaluation Results www.ti.com 1.6 1.4 VI = 4.5 V 1.2 Power Loss - W VI = 5 V 1 VI = 5.5 V 0.8 0.6 0.4 0.2 0 0 -0.5 -1 -1.5 IL - Load Current - A -2 -2.5 Figure 6. Power Loss vs Load Current 100 225 80 180 60 135 Phase Gain - dB 40 90 45 20 Gain 0 0 -20 -45 -40 -90 -60 0.1 1 10 -135 100 f - Frequency - kHz Figure 7. Bode Plot (BW = 3.2 kHz, PM = 59.4°) (VIN = 5 V, VOUT = –5 V, IOUT = 2 A) SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator Copyright © 2011–2018, Texas Instruments Incorporated 11 Evaluation Results www.ti.com 100 225 80 180 60 135 Phase Gain - dB 40 90 45 20 0 0 Gain -20 -45 -40 -90 -60 0.1 -135 100 10 1 f - Frequency - kHz Figure 8. Bode Plot (BW = 4.9 kHz, PM = 72.5°) (VIN = 5 V, VOUT = –5 V, IOUT = 0 A) Figure 9. Switch Node (VIN = 5 V, VOUT = –5 V, IOUT = 0 A) 12 Creating an Inverting Power Supply Using a Synchronous Step-Down Regulator SLVA458B – August 2011 – Revised June 2018 Submit Documentation Feedback Copyright © 2011–2018, Texas Instruments Incorporated References www.ti.com Figure 10. Switch Node Rising (VIN = 5 V, VOUT = –5 V, IOUT = 0 A) 7 References 1. Using a Buck Converter in an Inverting Buck-Boost Topology, (SLYT286), 4Q 2007 Analog Applications Journal, Texas Instruments 2. Using the TPS5430 as an Inverting Buck-Boost Converter application report (SLVA257) 3. Create an Inverting Power Supply From a Step-Down Regulator application report (SLVA317) Revision History NOTE: Page numbers for previous revisions may differ from page numbers in the current version. Changes from A Revision (June 2012) to B Revision .................................................................................................... Page • • • • • • • Added second sentence to Abstract .................................................................................................... Changed third sentence of Section 1 ................................................................................................... Changed polarity of capacitor in Figure 2 .............................................................................................. Added content to last paragraph in Section 5.10 ..................................................................................... Changed first sentence of Section 5.13 ................................................................................................ Changed "ESR is assumed to be 5" to "ESR is assumed to be 5 mΩ" ............................................................ Changed "Rdc is 19 m" to "Rdc is 19 mΩ" ............................................................................................ 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