Texas Instruments | Measure Power Stage Gain and Slope Compensation in PCM (Peak Current Mode) BUCK (Rev. A) | Application notes | Texas Instruments Measure Power Stage Gain and Slope Compensation in PCM (Peak Current Mode) BUCK (Rev. A) Application notes

Texas Instruments Measure Power Stage Gain and Slope Compensation in PCM (Peak Current Mode) BUCK (Rev. A) Application notes
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.
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1
Unified PCM BUCK Converter
2
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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
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Power Stage Gain Measurement
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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.
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Slope Compensation Measurement
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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)
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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
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5
Measurement Results Verification
5
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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
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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.
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Summary
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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
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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 ........................................................................................................... Page
•
Edited application report for clarity. ..................................................................................................... 1
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