Application Report SLVAE22A – July 2018 – Revised March 2019 Power Stage Gain and Slope Compensation Measurement in PCM (Peak Current Mode) BUCK Converter Daniel Jing, Liang Zhang, Zhao Ma ABSTRACT This application report introduces a method to measure the power stage gain (GM-PS) and slope compensation (Se) in a PCM (Peak Current Mode) BUCK converter. It also introduces how to verify this method on the TPS65261. 1 2 3 4 5 6 7 Contents Introduction ................................................................................................................... Unified PCM BUCK Converter ............................................................................................. Power Stage Gain Measurement ......................................................................................... Slope Compensation Measurement ....................................................................................... Measurement Results Verification ......................................................................................... Summary ...................................................................................................................... References ................................................................................................................... 1 2 2 3 6 8 8 List of Figures 1 PCM BUCK Converter Block Diagram .................................................................................... 2 2 Simplified Small Signal Model for PCM BUCK Converter .............................................................. 3 3 PWM Comparator Input Signals ........................................................................................... 4 4 Vse for A Different Duty ...................................................................................................... 5 5 TPS65261 Typical Application Circuit ..................................................................................... 6 6 Measured Bode Plot vs. Calculated Bode Plot .......................................................................... 8 List of Tables 1 GM-PS Calculation Guidelines ................................................................................................ 3 2 Se Calculation Guidelines ................................................................................................... 5 3 GM-PS Calculation ............................................................................................................. 7 4 Se Calculation ................................................................................................................ 7 Trademarks All trademarks are the property of their respective owners. 1 Introduction PCM (Peak Current Mode) architecture is widely used in DC/DC converters. PCM architecture provides good performance and ease of compensation. Power stage gain and slope compensation play important roles in the PCM BUCK converter. They can suppress subharmonic oscillation and keep the control loop stable. With these parameters, you can deeply optimize power supply and ensure performance in mass production. Usually, the typical power stage gain value is provided in the datasheet, but the slope compensation is seldom provided since it is integrated. SLVAE22A – July 2018 – Revised March 2019 Submit Documentation Feedback Power Stage Gain and Slope Compensation Measurement in PCM (Peak Current Mode) BUCK Converter Copyright © 2018–2019, Texas Instruments Incorporated 1 Unified PCM BUCK Converter 2 www.ti.com Unified PCM BUCK Converter Figure 1 shows a PCM Buck converter, which is usually composed of several key blocks. It includes the following: • Error Amplifier (EA) • PWM Comparator (PWM) • Slope Compensation (SLP) • Current Sensing (CS) • Clock (CLK) • Power Stage • Output Stage The RC network after error amplifier compensates for the output pole and increases loop gain for stability. Typically, Figure 1 can explain PCM BUCK converters. VIN CS CLK iL VREF EA PWM COMP VOUT LX VFB Cff Rc R1 SLP Cb COUT GND Cc VFB iLoad R2 Figure 1. PCM BUCK Converter Block Diagram During normal operation, the voltage difference between the internal reference voltage (Vref) and the feedback voltage (VFB) is amplified and outputs at COMP node. The clock signal (CLK) turns on high-side FET. The sensed current (CS) compares with the COMP voltage minus slope compensation (SLP) and the output logic is set to turn off high-side FET. The low-side FET turns on for the rest of the period. Assuming the operating frequency is fixed, the slope compensation is linear, and the COMP is a pin that you can use to measure its voltage at this node. The whole application is explained based on this unified PCM model in CCM (Continuous Current Mode). 3 Power Stage Gain Measurement Power Stage Gain (GM-PS) is defined as the gain from COMP voltage (VCOMP) to inductor current (iL). Equation 1 calculates the Power Stage Gain, where Ri is the current sensing gain. GM-PS 3.1 1 Ri 'iL 'VCOMP (1) Simplified Small Signal Model for Power Stage Gain Ignoring the inductor current ripple, the load current (iLoad) is equal to the inductor current (iL) in CCM. Figure 2 shows a simplified whole system small signal model. 2 Power Stage Gain and Slope Compensation Measurement in PCM (Peak Current Mode) BUCK Converter Copyright © 2018–2019, Texas Instruments Incorporated SLVAE22A – July 2018 – Revised March 2019 Submit Documentation Feedback Power Stage Gain Measurement www.ti.com Power Stage Gain GM-PS iL = GM-PS * VCOMP VREF EA iL COMP VFB Cff GM-PS Rc VFB Cb Cc VOUT R1 R2 iLoad COUT Figure 2. Simplified Small Signal Model for PCM BUCK Converter Equation 2 calculates the AC small signal relationship between VCOMP and iLoad. iLoad iL GM PS * VCOMP (2) Equation 3 expresses the GM-PS. GM PS iLoad VCOMP (3) They are the small signal differential data where VCOMP and iLOAD are not the directly measured data. 3.2 Power Stage Gain Measurement Method GM-PS is the AC small signal parameter. It must be measured by differentiated method. Table 1 shows step-by-step GM-PS calculation guidelines. 1. Measure VCOMP at different loads in CCM from low current to high current. 2. Subtract VCOMP and load current with next data. 3. Equation 3 calculates GM-PS for each condition. Table 1. GM-PS Calculation Guidelines STEP 1 4 STEP 2 VCOMP iLoad VCOMP1 iLoad1 VCOMP2 VCOMP3 STEP 3 Delta VCOMP Delta iLoad GM-PS iLoad2 VCOMP2 - VCOMP1 iLoad2 - iLoad1 (iLoad2 - iLoad1) / (VCOMP2 - VCOMP1) iLoad3 VCOMP3 - VCOMP2 iLoad3 - iLoad2 (iLoad3 - iLoad2) / (VCOMP3 - VCOMP2) ... ... ... ... ... VCOMP(N) iLoad(N) VCOMP(N) - VCOMP(N-1) iLoad(N) - iLoad(N-1) (iLoad(N) - iLoad(N-1)) / (VCOMP(N) - VCOMP(N-1)) Slope Compensation Measurement Slope Compensation (Se) is an added artificial signal in the control loop. It dampens the inner current loop gain and eliminates subharmonic oscillation when duty is over 50%. A common rule is to keep the compensation slope above or equal to half of inductor current falling slope, Sf. 4.1 Relationship Between VCOMP and Se Since the PWM comparator is a high gain element, it is reasonable to consider the positive input equal to the negative input when the high-side FET is turned off. Figure 3 shows the steady-state. Equation 4 calculates the small signal relationship between VCOMP, iL, and Se. SLVAE22A – July 2018 – Revised March 2019 Submit Documentation Feedback Power Stage Gain and Slope Compensation Measurement in PCM (Peak Current Mode) BUCK Converter Copyright © 2018–2019, Texas Instruments Incorporated 3 Slope Compensation Measurement www.ti.com VCOMP Se Se Vse Vse iLoad * Ri i L * Ri iLpp * Ri iLpp * Ri Sn Sf TON TOFF Sf Sn TON TOFF Figure 3. PWM Comparator Input Signals VCOMP Vse VCOMP Se * TON (iLoad 1 * iLpp ) * Ri 2 where • iLpp is the inductor ripple current. Equation 5 calculates iLpp. VIN iLpp (4) VOUT VOUT 1 * * L VIN FSW where • • • Ri is the current sensing gain. Equation 1 and Equation 3 calculate Ri. TON is high-side FET ON time. Equation 6 calculates TON. You can also use an oscilloscope to measure the value. TOFF is high-side FET OFF time (5) VOUT 1 * VIN FSW TON where • • Sn is the inductor current rising slope Sf is inductor current falling slope (6) In addition, the other parameters including the VCOMP, switching frequency (FSW), input voltage (VIN), and output voltage (VOUT) can be measured in the lab. 4.2 Slope Compensation Measurement Method Slope compensation (Se) or Vse cannot be measured directly. It cannot be measured like GM-PS at a different loading since Vse does not change with the loading, but changes with duty. Equation 7 calculates Vse in a steady-state for a different duty under the same loading, but different VIN condition. Figure 4 illustrates Vse. Vse 4 Se * TON VCOMP (iLoad 1 * iLpp ) * Ri 2 Power Stage Gain and Slope Compensation Measurement in PCM (Peak Current Mode) BUCK Converter Copyright © 2018–2019, Texas Instruments Incorporated (7) SLVAE22A – July 2018 – Revised March 2019 Submit Documentation Feedback Slope Compensation Measurement www.ti.com VCOMP1 VCOMP2 Se Vse1 Se Vse2 iLoad * Ri i L * Ri iLpp1 * Ri i L * Ri Sn1 iLpp2 * Ri Sn2 Sf Sf TON1 TOFF1 TOFF2 TON2 High VIN Low VIN Figure 4. Vse for A Different Duty Since directly measured VCOMP contains DC bias voltage, which introduces error, the Se must be calculated by a differentiated method. Equation 8 and Equation 9 calculate the different Vse1 and Vse2. Vse1 Se * TON1 Vse2 Se * TON2 VCOMP1 (iLoad VCOMP2 (iLoad 1 * iLpp1) * Ri 2 (8) 1 * iLpp2 ) * Ri 2 (9) Equation 10 calculates Se. Subtract Equation 9 from Equation 8 and reform it. VCOMP2 Se VCOMP1 TON2 1 * (i i ) * Ri 2 Lpp2 Lpp1 TON1 where • FSW and Ri stay constant relative to VIN (10) Table 2 shows step-by-step Se calculation guidelines. 1. Measure VCOMP at different VIN values in the CCM from low VIN to high VIN. 2. Use Equation 5 to calculate TON for each condition. Use Equation 4 to calculate iLppfor each condition. 3. Subtract VCOMP, VIN, and iLpp with the next data. 4. Use Equation 10 to calculate Se for each condition. For some parts, the FSW and Ri are not constant. More accuracy Se values can be obtained by measuring FSW for each condition and measuring current sensing gain Ri. Section 3 describes this process. Table 2. Se Calculation Guidelines STEP 1 STEP 2 STEP 3 VCOMP VIN TON iLpp VCOMP1 VIN1 TON1 iLpp1 VCOMP2 VIN2 TON2 VCOMP3 VIN3 TON3 ... ... VCOMP(N) VIN(N) STEP 4 Delta VCOMP Delta VIN Delta iLpp Se iLpp2 VCOMP2 - VCOMP1 VIN2 - VIN1 iLpp2 - iLpp1 Equation 10 iLpp3 VCOMP3 - VCOMP2 VIN3 - VIN2 iLpp3 - iLpp2 Equation 10 ... ... ... ... ... ... TON(N) iLpp(N) VCOMP(N) - VCOMP(N-1) VIN(N) - VIN(N-1) iLpp(N) - iLpp(N-1) Equation 10 SLVAE22A – July 2018 – Revised March 2019 Submit Documentation Feedback Power Stage Gain and Slope Compensation Measurement in PCM (Peak Current Mode) BUCK Converter Copyright © 2018–2019, Texas Instruments Incorporated 5 Measurement Results Verification 5 www.ti.com Measurement Results Verification This section verifies the measurement method for GM-PS and Se on the TPS65261. 5.1 TPS65261 Measured GM-PS and Se TPS65261 is a triple synchronous BUCK converter that is widely used in the market. The BUCK1 is selected to perform this verification. Set the application condition to the following: • 12 V VIN • 3.3 V VOUT • 3 A loading • 609 KHz FSW • 4.7 µH inductor • 2 × 22 µF COUT Figure 5 shows the TPS65261 typical application circuit. R263 is changed to 10 kΩ and R262 is changed to 45.3 kΩ for the VOUT = 3.3 V setting. Due to the influence of parasitic parameters and measurement accuracy, the results shift slightly, so the average value is used for general purpose analysis. C26 22pF R263 20K C15 22pF R153 19.5K R152 39K C231 3.3nF L1 17 18 19 20 ROSC AGND 22 COMP1 R16 0 LX3 15 PGND3 14 LX1 PGND1 C28 10uF PVIN1 29 VIN 30 TPS65261 TPS65261-1 C16 47nF 13 C13 10uF C151 22uF C152 22uF C101 22uF C102 22uF Vin Vin 12 11 C12 10uF PGND2 VDIV L2 10 LX2 32 EN2 BST2 R9 C9 47nF 4.7uH Vout2 +3.3V Max. 2A SS2 0 C72 22pF C71 2.2nF 100K R3 9 8 7 FB2 6 5 2 1 V7V R7 30K C5 1uF R2 COMP2 EN1 MODE 31 PULL Vout3 +1.8V Max. 2A L3 PVIN3 PVIN2 4 C29 1uF 28 EN3 R30 20K 16 BST3 4.7uH 27 Vin R29 146K C182 22pF 4.7uH RESET Vin 26 BST1 3 C262 22uF 25 0 PGOOD C261 22uF C25 47nF FB1 23 24 SS1 R25 Vout1 +1.2V Max. 3A 21 R23 20K C17 10nF C181 2.2nF R18 30K R20 73.2K FB3 C232 22pF COMP3 C24 10nF SS3 R262 20K C8 10nF R102 39K RESET PGOOD 100K R103 8.67K C10 22pF Figure 5. TPS65261 Typical Application Circuit Table 3 shows a step-by-step power stage gain (GM-PS) calculation. The average GM-PS is 7.59 A/V and it is approximately equal to 7.4 A/V provided in the TPS6526x 4.5 V to 18 V Input Voltage, 3A/2A/2A Output Current Triple Synchronous Step-Down Converter Data Sheet . 6 Power Stage Gain and Slope Compensation Measurement in PCM (Peak Current Mode) BUCK Converter Copyright © 2018–2019, Texas Instruments Incorporated SLVAE22A – July 2018 – Revised March 2019 Submit Documentation Feedback Measurement Results Verification www.ti.com Table 3. GM-PS Calculation STEP 1 STEP 2 VCOMP(V) iLoad(A) 0.6075 0.50 0.6400 0.6719 STEP 3 Delta VCOMP(V) Delta iLoad(A) GM-PS(A/V) 0.75 0.0325 0.25 7.692 1.00 0.0319 0.25 7.837 0.7040 1.25 0.0321 0.25 7.788 0.7356 1.50 0.0316 0.25 7.911 0.7680 1.75 0.0324 0.25 7.716 0.8009 2.00 0.0329 0.25 7.599 0.8343 2.25 0.0334 0.25 7.485 0.8678 2.50 0.0335 0.25 7.463 0.9023 2.75 0.0345 0.25 7.246 0.9372 3.00 0.0349 0.25 7.163 Average Power Stage Gain GM-PS 7.590 Table 4 shows a step-by-step slope compensation (Se) calculation. The average Se is 1.86E+05 V/S. Table 4. Se Calculation STEP 1 STEP 2 STEP 3 VIN(V) VCOMP(V) Calculated TON(uS) Calculated iLpp(A) 4.5 0.9727 1.204 0.307 Delta VCOMP(V) Delta VIN(V) Delta iLpp(A) Calculated Se(V/S) 5 0.9409 1.084 0.392 -0.0318 0.5 0.042 2.18E+05 5.5 0.9165 0.985 0.461 -0.0244 0.5 0.035 2.01E+05 6 0.8972 0.903 0.519 -0.0193 0.5 0.029 1.89E+05 6.5 0.8812 0.834 0.568 -0.0160 0.5 0.024 1.84E+05 7 0.8668 0.774 0.609 -0.0144 0.5 0.021 1.96E+05 7.5 0.8541 0.722 0.646 -0.0127 0.5 0.018 2.00E+05 8 0.8432 0.677 0.677 -0.0109 0.5 0.016 1.95E+05 8.5 0.8340 0.637 0.705 -0.0092 0.5 0.014 1.85E+05 9 0.8259 0.602 0.730 -0.0081 0.5 0.012 1.82E+05 9.5 0.8187 0.570 0.752 -0.0072 0.5 0.011 1.81E+05 10 0.8119 0.542 0.772 -0.0068 0.5 0.010 1.92E+05 10.5 0.8061 0.516 0.791 -0.0058 0.5 0.009 1.79E+05 11 0.8009 0.493 0.807 -0.0052 0.5 0.008 1.75E+05 11.5 0.7961 0.471 0.822 -0.0048 0.5 0.008 1.78E+05 12 0.7918 0.452 0.836 -0.0043 0.5 0.007 1.73E+05 12.5 0.7878 0.433 0.849 -0.0040 0.5 0.006 1.75E+05 13 0.7842 0.417 0.860 -0.0036 0.5 0.006 1.70E+05 13.5 0.7807 0.401 0.871 -0.0035 0.5 0.005 1.80E+05 14 0.7774 0.387 0.881 -0.0033 0.5 0.005 1.84E+05 Average Slope Compensation Se 5.2 STEP 4 1.86E+05 Measured Bode Plot vs. Calculated Bode Plot Figure 6 shows the measured Bode Plot versus a simulated Bode Plot under a 2 A loading condition. This is performed by the TPS65261 SIMPLIS model with the above measured, calculated parameters GM-PS, and Se. The measured result is well-matched with a simulated result. The simulated GBW is 41 KHz and phase margin is 68 degrees. The lab-measured GBW is 42 KHz and phase margin is 66 degrees. SLVAE22A – July 2018 – Revised March 2019 Submit Documentation Feedback Power Stage Gain and Slope Compensation Measurement in PCM (Peak Current Mode) BUCK Converter Copyright © 2018–2019, Texas Instruments Incorporated 7 Summary www.ti.com 30 660 Gain_Meas Phase_Meas 600 Gain_Sim 540 Phase_Sim 20 480 10 420 0 360 -10 300 -20 240 -30 180 -40 120 -50 60 -60 0 Gain (dB) 40 -70 -80 1.00E+3 Phase (degree) Close Loop Frequency Response - Bode Plot 50 -60 1.00E+4 1.00E+5 Frequency (Hz) -120 4.00E+5 Fig6 Figure 6. Measured Bode Plot vs. Calculated Bode Plot 6 Summary This application report presents a method of measuring power stage gain (GM-PS) and slope compensation (Se) in a peak current mode (PCM) BUCK converter. This method is also validated in other PCM architecture converters, such as BOOST, BUCK-BOOST, and so forth. You can build the simulation model by using these internal parameters. Based on the model, the maximum optimization loop stability can be achieved. 7 References 1. Texas Instruments, TPS6526x 4.5 V to 18 V Input Voltage, 3A/2A/2A Output Current Triple Synchronous Step-Down Converter Data Sheet 2. Texas Instruments, TPS65261EVM-650 PMIC 3-A, 2-A, 2-A Output Current Evaluation Module User's Guide 8 Power Stage Gain and Slope Compensation Measurement in PCM (Peak Current Mode) BUCK Converter Copyright © 2018–2019, Texas Instruments Incorporated SLVAE22A – July 2018 – Revised March 2019 Submit Documentation Feedback Revision History www.ti.com Revision History NOTE: Page numbers for previous revisions may differ from page numbers in the current version. Changes from Original (July 2018) to A Revision ........................................................................................................... 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